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Thread: Relativistic Rolling Wheel II

  1. #1 Relativistic Rolling Wheel II 
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    To the administrators:

    I am unable to use the thread, "Relativistically Rolling Wheel" I started. Each time I use it, it acts normally for a short time but then locks up. It gives me a message that is is running a long script but if I click the stop script button it either remainds locked up or closes. I was able to post a short message earlier today but then it locked up again.

    Other threads do not seem to have the problem so I have opened this one to see it it has the problem.

    cincirob
    Last edited by KJW; 02-25-2014 at 06:07 AM. Reason: Added link to original thread
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    JT, I have been unable to study what you have done because of the problem noted above.

    Here is a your last message, I believe:

    If I had used the length contraction formula in figures 3a and 3b, I would been double-dipping, and I would get the wrong answer. As you well know, one cannot simply apply length contraction to something that is already length contracted. This is a limitation of the length contraction formula. What I show above is that the full LT's do not have that limitation.

    Therefore, we can start in the axle frame, where symmetry is assumed, and use the LT's and one value of v to transform everything to the road frame. We are NOT double dipping, because the LT's do not have that limitation. Once you understand that, you will understand that Gron treats the velocities properly using the LT's.

    cinci: I'm guessing a little bit here. If you are using the times shown on your diagrams you can transform between two frames as you have done. The problem with Gron is that he doesn't use the times.
    ******************
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    Quote Originally Posted by cincirob View Post
    cinci: I'm guessing a little bit here. If you are using the times shown on your diagrams you can transform between two frames as you have done. The problem with Gron is that he doesn't use the times.
    ******************
    I'm glad we agree that my transformation is okay. Which clocks do you think the times should come from, clocks fixed to the wheel, or clocks fixed to the fender?
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    Quote Originally Posted by cincirob View Post
    JT, I have been unable to study what you have done because of the problem noted above.

    Here is a your last message, I believe:

    Quote Originally Posted by JTyesthatJT View Post
    If I had used the length contraction formula in figures 3a and 3b, I would been double-dipping, and I would get the wrong answer. As you well know, one cannot simply apply length contraction to something that is already length contracted. This is a limitation of the length contraction formula. What I show above is that the full LT's do not have that limitation.

    Therefore, we can start in the axle frame, where symmetry is assumed, and use the LT's and one value of v to transform everything to the road frame. We are NOT double dipping, because the LT's do not have that limitation. Once you understand that, you will understand that Gron treats the velocities properly using the LT's.

    Quote Originally Posted by cincirob View Post
    I'm guessing a little bit here. If you are using the times shown on your diagrams you can transform between two frames as you have done. The problem with Gron is that he doesn't use the times.
    Cincirob,

    Just curious, what makes you think that Gron did not use times in his analysis?

    Thank You,
    SinceYouAsked

    PS ... if you have a 2nd web browser on your computer, try that one and see if it works any better. My AOL browser has had trouble, but Google Chrome always works good. Google Chrome is free for download too.
    Last edited by SinceYouAsked; 02-25-2014 at 05:38 AM.
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  5. #5  
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    The following is a copy of my last post in the original thread:


    Quote Originally Posted by cincirob View Post
    Because you can't find the length of the pole in a third frame by transforming it from the barn frame. In that problem you must find its length in the rest frame of the pole and transform that to the third frame.
    That's a deficiency of the length contraction formula, not Lorentz transformations. With a Lorentz transformation, I can transform the moving pole in the barn frame to the third observer's frame. I don't need to know the rest length of the pole, just the length in the barn frame, and it will produce the correct length in the third observer's frame. How does it achieve this when the length contraction formula can't? Because unlike the length contraction formula, the Lorentz transformation includes the velocity of the pole in the barn frame.


    Quote Originally Posted by cincirob View Post
    KJW: Since you still haven't commented on the conveyor belt, I'll ask you directly: Do you think that the observer on the conveyor belt is equivalent to the observer on the road? If not, then you have misunderstood the principle of relativity.

    cinci: Yes, it's equivalent.
    Oh good. Then tell me how the observer on the conveyor belt affects the stresses and strains of the rollers so that this observer's point of view becomes an important consideration.


    Quote Originally Posted by cincirob View Post
    If you ask that observer to tell you what the x-direction velocities are of chords that happen to be horizontal at a particular instant, will he tell you that they are all the same velocity v?
    Of course not.


    Quote Originally Posted by cincirob View Post
    The chords of the wheel are all moving at different velocities and they are contracting them all with one velocity.
    This does not follow from the use of one velocity in the Lorentz transformation because there are multiple velocities in the object being transformed.


    Quote Originally Posted by cincirob View Post
    You can Lorentz transform a moving object, but you must transform it from its rest frame to whatever frame you're interested in.
    That's a contradiction. An object isn't moving in its rest frame.


    Quote Originally Posted by cincirob View Post
    The principle of relativity is this: ........to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good.

    How does this tell you that once you understand how velocities affect an object in one frame that you can ignore them in another? Consider this a direct question.
    That may have been how the principle of relativity was expressed in Einstein's time, but we've moved on since then. The principle of special relativity can be expressed simply as: The laws of physics are the same in all inertial frames of reference. It implies that I can solve a physical problem in any one inertial frame of reference and Lorentz transform that solution to any other inertial frame of reference.


    Quote Originally Posted by cincirob View Post
    We're not discussing my approach, we're discussing Gron's approach.
    I'm not. I'm discussing your understanding of the problem. You criticised Gron's approach and I'm discussing the validity of your criticism. However, I'm not actually trying to prove that Gron's approach is correct, but rather I'm considering your criticism on its own merit.


    Quote Originally Posted by cincirob View Post
    I haven't questioned the fact that there are notions that everyone agrees on nor have I said anything contrary to those notions. I have said that length contraction is real. Whatever else you think I don't understand doesn't change the fact that you think it isn't.
    But do you know what is actually invariant? Unless you do, then you can't really apply relativistic principles to problems. This includes length contraction. Simply saying that length contraction is real or not real isn't particularly meaningful. One needs to have a precise understanding of what length contraction is. Quoting Rindler doesn't demonstrate your understanding of length contraction. Because of the way you are trying to apply length contraction, I am led to the conclusion that you don't really understand its true nature.

    Consider the following: Observer A is moving relative to observer B at relativistic velocity. Both observers are carrying identical rulers. Observer A determines that observer B's ruler is shorter than his own ruler, and observer B determines that observer A's ruler is shorter than his own ruler. Both rulers can't be shorter than each other. So how do you resolve this apparent contradiction?


    Quote Originally Posted by cincirob View Post
    The Gron analysis doesn't deal with them at all when it transforms the wheel to the road frame.
    Except in the description of the object being transformed, you don't need the stresses and strains when transforming from the axle frame to the road frame.


    Quote Originally Posted by cincirob View Post
    According to your comments here Gron could not have a proper solution because he didn't use anything beyond the scope of relativity. Do you agree with me then that Gron has a flawed solution. This is another direct question.
    As I said much earlier, I haven't looked at Gron's analysis, so I can't answer questions specifically about his approach. But from what you and others have said, it seems to me that Gron has not dealt with the full problem that you have stated. Whether it's flawed or not depends on the intended scope of his solution. Simply being limited in scope doesn't make it flawed because any approach is going to be limited in some way. The validity of Gron's approach isn't important to me (which I why I haven't looked at it). I'm more interested in the problem itself (though not enough to perform a full solution).
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by cincirob View Post
    To the administrators:

    I am unable to use the thread, "Relativistically Rolling Wheel" I started. Each time I use it, it acts normally for a short time but then locks up. It gives me a message that is is running a long script but if I click the stop script button it either remainds locked up or closes. I was able to post a short message earlier today but then it locked up again.

    Other threads do not seem to have the problem so I have opened this one to see it it has the problem.

    cincirob
    I can't replicate that issue ( I am using Safari on an iMac ), but I'll see what can be done.
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  7. #7  
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    Quote Originally Posted by Markus Hanke View Post
    I can't replicate that issue ( I am using Safari on an iMac ), but I'll see what can be done.
    I'm using Internet Explorer 11 under Windows 7 and I find the forum software to be quite frustrating to use. I frequently have to close the browser and start again. For example, if I post, I generally have to close the browser to post again or edit a post.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    KJW: The following is a copy of my last post in the original thread:

    cinci: Thanks.

    I could give my answers to the points below but I believe we'll just go around in circles. Let me approach it another way and if you want me to answer the points below after that, I will. I ask JT and SYA to comment also.

    1. Imagine a hula hoop with marbles running with no friction around the inside of it.

    2. Space the marbles as the tips of the spokes in a wheel would be.

    3. Observe this contraption from a relatively moving frame, the equivalent of a road observer.

    4. I believe the road observer will "see" an ellipse whose minor dimension is the major dimension contracted by (1 - (v/c)^2)^.5. This is because he is observing a static circular structure.

    5. I believe the Lorentz transformation will give the same shape.

    6. If you figure out where the marbles are located in the road observer's frame, I believe you will get locations identical to the Gron solution.

    Everybody please say whether you agree or disagree with this.

    My point is that this solution cannot be the same as the solution for a rolling wheel that has any consideration of the material in the wheel be it Ehrenfest, added-material-on-the-fly, or plastic deformation. If you agree with the solution above, and still think Gron's solution is correct for these material considerations, please explain why.
    **********************
    Last edited by KJW; 02-26-2014 at 09:34 AM. Reason: Removed extraneous text that may cause confusion
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    Quote Originally Posted by cincirob View Post
    I could give my answers to the points below but I believe we'll just go around in circles. Let me approach it another way and if you want me to answer the points below after that, I will. I ask JT and SYA to comment also.

    1. Imagine a hula hoop with marbles running with no friction around the inside of it.

    2. Space the marbles as the tips of the spokes in a wheel would be.

    3. Observe this contraption from a relatively moving frame, the equivalent of a road observer.

    4. I believe the road observer will "see" an ellipse whose minor dimension is the major dimension contracted by (1 - (v/c)^2)^.5. This is because he is observing a static circular structure.

    5. I believe the Lorentz transformation will give the same shape.

    6. If you figure out where the marbles are located in the road observer's frame, I believe you will get locations identical to the Gron solution.

    Everybody please say whether you agree or disagree with this.
    Can you clarify these first ...

    wrt 1 ... You speak of "marbles running", and that means they move in the hoop. As such there would be a rotation of those marbles about the axle, and you do not say what the rate of the rotation is, whether or not it is even steady, and whether all marbles move at the same angular rate or not (per axle).

    wrt 2 ... you do not say whether the spoke tips that the marbles represent are rotating or not.

    Also, is your fundamental question in regards to whether the Lorentz-Fitzgerald contraction formula (LCF) works as well as the Lorentz transformations in so far as their ability to determine the length of a moving body?

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    SinceYouAsked
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    Duplicate post, please ignore. See next post.

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    Quote Originally Posted by cincirob View Post
    My point is that this solution cannot be the same as the solution for a rolling wheel that has any consideration of the material in the wheel be it Ehrenfest, added-material-on-the-fly, or plastic deformation. If you agree with the solution above, and still think Gron's solution is correct for these material considerations, please explain why.
    Well first, just to keep the recent exchanges on track, your assumption that the Lorentz-Fitzgerald Contraction Formula (LCF) should work for your momentarily-horizontal-chord of a rotating-wheel is flat wrong. You need to rethink that until you get it right. OK then ...

    The Gron analysis considered only a steady rotation rate. As all relativistically rolling wheel scenarios, Gron's considered an impossible requirement, Gron's being ... the wheel magically attained a steady relativistic rotation rate "with Born rigidity maintained". Now, there are (of course) "gamma times more atoms" along any circumference than for a non-rotating wheel, assuming uniform density throughout the wheel is also assumed, but the Gron analysis simply does not care how that happened. It merely assumes Born rigidity exists at said steady rotation rate.

    Your above statement is in regards to the "roll-up process", which Ehrenfest considered but Gron ignored. The real material of the rolling wheel must deform as it's rotation increases enough. At a point long before any relativistic rotation rate is attained, the wheel is destroyed by the classical effects of centrifugal force. If those forces are whimsically wished away, then the contraction of atoms along circumferences (per axle) require the wheel to deform, assuming Born rigidity is to be maintained throughout. More atoms (by the factor of γ) have to shift into a circumference to allow Born rigidity to be maintained uniformly. That's not a realistic activity either, but what the heck, this whole analysis is about impossible rolling wonder wheels. I could state in my scenario definition that "the wheel deforms to recipe", ie that atoms shift from locations elsewhere upon the z-axis to fill any circumference as it rolls up to relativistic rate (Born rigidity always existing). We don't care about the shape of the wheel wrt Z because no motion exists in that dimension. But who cares? It's not like Gron disagreed with Ehrefest's analysis. Bottom line, you need to free yourself from the idea that you, I, Gron, Einstein, Ehrenfest (or anyone else) believes a wheel could exist at a relativistic-rotation-rate simply because we we all choose to consider the impossible WHAT IF scenario. IOW, nobody cares that the GRON analysis ignored the roll-up process Erhenfest discussed, because that's very old news. Nobody cares, because everyone knows these analyses deal with WONDER WHEELS for the sake of exploring the implications of the LTs for rotation at relativistic rate. It's a KINEMATIC ANALYSIS, and in no way suggests a wheel should be able to exist as such.

    Bottom line, Gron's soln is correct for the modeling of the atomic locations of a "wonder wheel". No one on the earth, can or has, modeled a real wheel rotating at relativistic rate, because no such wheel has ever existed. All that Gron modeled, as all others have, is a kinematic representation of a wonder wheel, or equivalently stated as ... a real wheel under impossible conditions. The wheel should be considered as a wire-frame wheel built in Autocad, abiding by whatever apriori scenario requirements stated, with the locations of point-coordinates in the various spacetime systems related via the LTs. It's truely the relation of point-coordinates of spacetime systems, and one may "imagine" the coordinates to represent "atomic locations" if they so desire given the apriori requirements of the scenario are maintained (eg Born rigidity), impossible or not.

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    SinceYouAsked
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    Quote Originally Posted by cincirob View Post
    cinci:

    1. Imagine a hula hoop with marbles running with no friction around the inside of it.

    2. Space the marbles as the tips of the spokes in a wheel would be.

    3. Observe this contraption from a relatively moving frame, the equivalent of a road observer.

    4. I believe the road observer will "see" an ellipse whose minor dimension is the major dimension contracted by (1 - (v/c)^2)^.5. This is because he is observing a static circular structure.

    5. I believe the Lorentz transformation will give the same shape.

    6. If you figure out where the marbles are located in the road observer's frame, I believe you will get locations identical to the Gron solution.

    Everybody please say whether you agree or disagree with this.
    **********************
    Since you did not specifically say so, I would like to add these
    #1 should say that all the marbles are traveling at the same speed as measured by the hula hoop frame
    #2 should say that all the marbles are evenly spaced as measured by the hula hoop frame
    #4 should not use the word "see" but since you put the word in "scare quotes" I think I know what you mean
    #6 should say that the marbles would be spaced in such a way that they are closer together at the top and father apart at the bottom, as measured by the road frame

    Given those changes, I think I would agree to that.


    Quote Originally Posted by cincirob View Post
    cinci: My point is that this solution cannot be the same as the solution for a rolling wheel that has any consideration of the material in the wheel be it Ehrenfest, added-material-on-the-fly, or plastic deformation. If you agree with the solution above, and still think Gron's solution is correct for these material considerations, please explain why.
    **********************
    If I superimpose a rotating wheel on top of the hula-hoop contraption, I find that the spoke tips and the marbles line up exactly. This never changes. Thus the x,t coordinates of each spoke tip is always the same as the adjacent marble. How on earth can you imagine that they would not transform the same way to the road frame?
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    SYA: Can you clarify these first ...

    cinci: Really? You're having trouble understanding this?
    ******************


    SYA: wrt 1 ... You speak of "marbles running", and that means they move in the hoop. As such there would be a rotation of those marbles about the axle, and you do not say what the rate of the rotation is, whether or not it is even steady, and whether all marbles move at the same angular rate or not (per axle).

    cinci: I said the marbles are as the tips of the spokes in a wheel. If you're having trouble with this, don't bother responding.
    ***********************


    cinci: I said they represent the tips of the spokes of a wheel. Are the tips of a wheel at steady? Do they all move at the same rate?
    ****************************


    SYA: wrt 2 ... you do not say whether the spoke tips that the marbles represent are rotating or not.



    Also, is your fundamental question in regards to whether the Lorentz-Fitzgerald contraction formula (LCF) works as well as the Lorentz transformations in so far as their ability to determine the length of a moving body?
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    cinci: My point is that this solution cannot be the same as the solution for a rolling wheel that has any consideration of the material in the wheel be it Ehrenfest, added-material-on-the-fly, or plastic deformation. If you agree with the solution above, and still think Gron's solution is correct for these material considerations, please explain why.

    SYA: Well first, just to keep the recent exchanges on track, your assumption that the Lorentz-Fitzgerald Contraction Formula (LCF) should work for your momentarily-horizontal-chord of a rotating-wheel is flat wrong. You need to rethink that until you get it right. OK then ...

    cinci: You seem to be confused. I don't think the LCF works on the chords, you, JT, and Gron do.
    *******************


    The Gron analysis considered only a steady rotation rate. As all relativistically rolling wheel scenarios, Gron's considered an impossible requirement, Gron's being ... the wheel magically attained a steady relativistic rotation rate "with Born rigidity maintained". Now, there are (of course) "gamma times more atoms" along any circumference than for a non-rotating wheel, assuming uniform density throughout the wheel is also assumed, but the Gron analysis simply does not care how that happened. It merely assumes Born rigidity exists at said steady rotation rate.

    Your above statement is in regards to the "roll-up process", which Ehrenfest considered but Gron ignored. The real material of the rolling wheel must deform as it's rotation increases enough. At a point long before any relativistic rotation rate is attained, the wheel is destroyed by the classical effects of centrifugal force. If those forces are whimsically wished away, then the contraction of atoms along circumferences (per axle) require the wheel to deform, assuming Born rigidity is to be maintained throughout. More atoms (by the factor of γ) have to shift into a circumference to allow Born rigidity to be maintained uniformly. That's not a realistic activity either, but what the heck, this whole analysis is about impossible rolling wonder wheels. I could state in my scenario definition that "the wheel deforms to recipe", ie that atoms shift from locations elsewhere upon the z-axis to fill any circumference as it rolls up to relativistic rate (Born rigidity always existing). We don't care about the shape of the wheel wrt Z because no motion exists in that dimension. But who cares? It's not like Gron disagreed with Ehrefest's analysis. Bottom line, you need to free yourself from the idea that you, I, Gron, Einstein, Ehrenfest (or anyone else) believes a wheel could exist at a relativistic-rotation-rate simply because we we all choose to consider the impossible WHAT IF scenario. IOW, nobody cares that the GRON analysis ignored the roll-up process Erhenfest discussed, because that's very old news. Nobody cares, because everyone knows these analyses deal with WONDER WHEELS for the sake of exploring the implications of the LTs for rotation at relativistic rate. It's a KINEMATIC ANALYSIS, and in no way suggests a wheel should be able to exist as such.

    Bottom line, Gron's soln is correct for the modeling of the atomic locations of a "wonder wheel". No one on the earth, can or has, modeled a real wheel rotating at relativistic rate, because no such wheel has ever existed. All that Gron modeled, as all others have, is a kinematic representation of a wonder wheel, or equivalently stated as ... a real wheel under impossible conditions. The wheel should be considered as a wire-frame wheel built in Autocad, abiding by whatever apriori scenario requirements stated, with the locations of point-coordinates in the various spacetime systems related via the LTs. It's truely the relation of point-coordinates of spacetime systems, and one may "imagine" the coordinates to represent "atomic locations" if they so desire given the apriori requirements of the scenario are maintained (eg Born rigidity), impossible or not.

    cinci: From this I infer that you agree that Gron's analysis would be exact for the marble and hula hoop; therefore, it could not possibly be correct for any sort of rolling structure with all the complications you note above. Is that right?
    **********************
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    JT: Since you did not specifically say so, I would like to add these
    #1 should say that all the marbles are traveling at the same speed as measured by the hula hoop frame

    cinci: Yes, just like the spoke tips of a wheel.
    ********************


    JT: #2 should say that all the marbles are evenly spaced as measured by the hula hoop frame

    cinci: Yes, just like the spoke tips of a wheel.
    ********************


    JT: #4 should not use the word "see" but since you put the word in "scare quotes" I think I know what you mean

    cinci: That was to keep the nitpickers from pointing that SR doesn't give you what the observer actually sees. If that scares you, you must be very nervous about this.
    **********************


    JT: #6 should say that the marbles would be spaced in such a way that they are closer together at the top and father apart at the bottom, as measured by the road frame

    cinci: Are you saying that I have to describe the Gron solution that you've been vehemently defending and that we both worked out in detail some time age? Give me a break.
    **********************


    JT: Given those changes, I think I would agree to that.

    cinci: Great!
    ************


    cinci: My point is that this solution cannot be the same as the solution for a rolling wheel that has any consideration of the material in the wheel be it Ehrenfest, added-material-on-the-fly, or plastic deformation. If you agree with the solution above, and still think Gron's solution is correct for these material considerations, please explain why.

    JT: If I superimpose a rotating wheel on top of the hula-hoop contraption, I find that the spoke tips and the marbles line up exactly. This never changes. Thus the x,t coordinates of each spoke tip is always the same as the adjacent marble. How on earth can you imagine that they would not transform the same way to the road frame?

    cinci: Oh, I don't know. Maybe I'd worry about the fact that if I didn't let the wheel distort the wheel to offset relativistic effects in the wheel frame, the points wouldn't line up at all. For instance, if I connect just two adjacent marbles with a straight length, they wouldn't maintain their spacing as the wheel marbles are brought up to speed.

    If I connect each one with a link to the next one I get what amounts to chords of the wheel and I can take away the hula hoop. Now I have rolling wheel, assuming I shape the links so that they fill out the circle. One way to construct this is to start with the hula hoop and add the links at speed which means they are contracted in the wheel frame. In spite of what you or SYA say, these links don't transform the same way that points on the fixed hula hoop transform.

    Now you've been arguing that you can transform between two relatively moving frames. And I believe you can if you include the relativistic time effects of the space-time points you're transforming. And while the time on the hula hoop at all points is t, the axle frame time, the time at the ends of the links is not because they are moving relative to the axle frame.
    ****************************
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    Quote Originally Posted by SYA View Post
    Can you clarify these first ...

    Quote Originally Posted by cincirob View Post
    Really? You're having trouble understanding this?
    It's generally difficult to understand your questions, because they are generally inconsistent with mainstream relativity.

    Quote Originally Posted by SYA View Post
    wrt 1 ... You speak of "marbles running", and that means they move in the hoop. As such there would be a rotation of those marbles about the axle, and you do not say what the rate of the rotation is, whether or not it is even steady, and whether all marbles move at the same angular rate or not (per axle).

    Quote Originally Posted by cincirob View Post
    I said the marbles are as the tips of the spokes in a wheel. If you're having trouble with this, don't bother responding.
    The trouble I'm having, is in knowing whether your marbles move wrt the hoop. See below ...

    Quote Originally Posted by SYA View Post
    wrt 2 ... you do not say whether the spoke tips that the marbles represent are rotating or not.

    Quote Originally Posted by cincirob View Post
    I said they represent the tips of the spokes of a wheel. Are the tips of a wheel at steady? Do they all move at the same rate?
    You've been trying to use the length contraction formula (LCF) to determine the shape of your rotating chord in the ground system. Everyone's been telling you for quite some time now, that the LCF requires inertial motion, and thus cannot work for your chord since its rotating. The wheel cannot rotate if your chord is to be defined by the LCF in the ground system. If the wheel does not rotate, the spokes do not rotate, and as such your co-located marbles would not rotate either. So the question is, do your marbles move wrt hoop? If they do (at relativistic rate), then your chord contraction hypothesis is mistaken, but the marbles will always transform as the colocated spoke-tips do, no matter if rotating at steady rate or not rotating at all.

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    Quote Originally Posted by cincirob View Post
    JT: Given those changes, I think I would agree to that.

    cinci: Great!
    ************
    Yes, your marble contraption is fine with me.


    Quote Originally Posted by cincirob View Post
    cinci: If I connect just two adjacent marbles with a straight length, they wouldn't maintain their spacing as the wheel marbles are brought up to speed.
    ************
    That's true, but connecting only one pair of marbles would not be analogous to a homogeneous wheel. You'd need to connect all the marbles in the same way.


    Quote Originally Posted by cincirob View Post
    cinci: If I connect each one with a link to the next one I get what amounts to chords of the wheel and I can take away the hula hoop. Now I have rolling wheel, assuming I shape the links so that they fill out the circle. One way to construct this is to start with the hula hoop and add the links at speed which means they are contracted in the wheel frame.
    ************
    Adding the chords the way you describe is fine with me. But it does not cause any of the marbles to get closer together or farther apart in the hula hoop frame. So, when you remove the hula hoop, the marbles in your wheel are arranged in an identical fashion to your original marble contraption. Thus, if I superimpose your rotating wheel on top of the marble contraption, I find that the marbles in both contraptions always line up exactly.


    Quote Originally Posted by cincirob View Post
    cinci: In spite of what you or SYA say, these links don't transform the same way that points on the fixed hula hoop transform.
    ************
    One would transform the marbles using the exact same values for x,t and v in both cases. So they would transform to the road frame identically.


    Quote Originally Posted by cincirob View Post
    cinci: Now you've been arguing that you can transform between two relatively moving frames. And I believe you can if you include the relativistic time effects of the space-time points you're transforming. And while the time on the hula hoop at all points is t, the axle frame time, the time at the ends of the links is not because they are moving relative to the axle frame.
    ****************************
    In your original marble contraption, clocks attached to the marbles will not match clocks attached to the hula hoop. After you connect the marbles and take away the hula hoop, the clocks on the marbles will still not match clocks attached to (say) a fender that is placed around your wheel. The time coordinates of both contraptions remain identical in every way.
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    Quote Originally Posted by cincirob View Post
    My point is that this solution cannot be the same as the solution for a rolling wheel that has any consideration of the material in the wheel be it Ehrenfest, added-material-on-the-fly, or plastic deformation. If you agree with the solution above, and still think Gron's solution is correct for these material considerations, please explain why.
    Quote Originally Posted by SYA View Post
    Well first, just to keep the recent exchanges on track, your assumption that the Lorentz-Fitzgerald Contraction Formula (LCF) should work for your momentarily-horizontal-chord of a rotating-wheel is flat wrong. You need to rethink that until you get it right. OK then ...
    Quote Originally Posted by cincirob View Post
    You seem to be confused. I don't think the LCF works on the chords, you, JT, and Gron do.
    Nope. You think that Gron's analysis is wrong, because the perimeter shape of the rolling wheel is the same no matter if rotating or not. You mistakenly assume that the Length Contraction Formula (LCF) must apply to the rotating chord simply because (1) the perimeter shape is the same either way, and (2) the atoms of the rotating chord (per axle) have the same momentary horizontal velocity as a purely translating chord (per axle). Yet, all atoms of the rotating wheel "rotate over any duration", and as such, cannot possibly remain on any linear path of uniform translation per the ground ... "something the LCF requires". Your shortcoming, is that you do not understand how the spacetime systems exist wrt each other in the continuum. If you did, you would know why the perimeter shape is the same either way, and why the radial elements must dynamically curve per ground. You would also then see why the wheel atoms do not exist identically the same in both cases, rolling vs translating, per ground.

    Quote Originally Posted by SYA View Post
    Bottom line, Gron's soln is correct for the modeling of the atomic locations of a "wonder wheel". No one on the earth, can or has, modeled a real wheel rotating at relativistic rate, because no such wheel has ever existed. All that Gron modeled, as all others have, is a kinematic representation of a wonder wheel, or equivalently stated as ... a real wheel under impossible conditions. The wheel should be considered as a wire-frame wheel built in Autocad, abiding by whatever apriori scenario requirements stated, with the locations of point-coordinates in the various spacetime systems related via the LTs. It's truely the relation of point-coordinates of spacetime systems, and one may "imagine" the coordinates to represent "atomic locations" if they so desire given the apriori requirements of the scenario are maintained (eg Born rigidity), impossible or not.

    Quote Originally Posted by cincirob View Post
    From this I infer that you agree that Gron's analysis would be exact for the marble and hula hoop; therefore, it could not possibly be correct for any sort of rolling structure with all the complications you note above. Is that right?
    I agree that Gron's analysis produces the same solns for your marbles versus co-located spoketips, rotating or not. The LTs do not care WHY an atom exists where it does, it only cares about its position and inertial rate. It is correct for a Born-rigid rolling-structure too, for all the same reasons.

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    Quote Originally Posted by JTyesthatJT View Post
    Adding the chords the way you describe is fine with me. But it does not cause any of the marbles to get closer together or farther apart in the hula hoop frame.
    If we completely ignore the centrifugal force and consider only the relativistic length contraction, then because the natural (unstressed) length of the material links is length contracted in the hoop frame, the marbles will radially contract in order to maintain the unstressed length of the material links. This differs from the wheel because the spokes of the wheel maintain the radius of the outer rim. However, by symmetry, the contracted arrangement of material links will still be circular with the marbles equally spaced in the hoop frame, and will transform to an ellipse in the frame corresponding to the road frame for the wheel, with the faster marbles closer together than the slower marbles, just like the spokes of the wheel.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by KJW View Post
    Quote Originally Posted by JT
    Adding the chords the way you describe is fine with me. But it does not cause any of the marbles to get closer together or farther apart in the hula hoop frame.
    If we completely ignore the centrifugal force and consider only the relativistic length contraction, then because the natural (unstressed) length of the material links is length contracted in the hoop frame, the marbles will radially contract in order to maintain the unstressed length of the material links. This differs from the wheel because the spokes of the wheel maintain the radius of the outer rim. However, by symmetry, the contracted arrangement of material links will still be circular with the marbles equally spaced in the hoop frame, and will transform to an ellipse in the frame corresponding to the road frame for the wheel, with the faster marbles closer together than the slower marbles, just like the spokes of the wheel.
    As you say, the natural (unstressed) length of each material link would be length-contracted in the hoop frame. However, the same can be said of the marbles traveling around the hoop. At least as far as I can understand cincirob's marble-contraption-wheel, the material links are added while rotating, and their length-contracted lengths just happen to match the distance between the marbles. As such, the marbles would be unaffected. So even without spokes, the radius of the outer rim would be maintained. I'm not sure why you and I disagree here, as we seem to agree on everything else.

    EDIT: cinci's own description of adding the links is of no help here. He said,

    "If I connect each one with a link to the next one I get what amounts to chords of the wheel and I can take away the hula hoop. Now I have rolling wheel, assuming I shape the links so that they fill out the circle. One way to construct this is to start with the hula hoop and add the links at speed which means they are contracted in the wheel frame."

    It would have been helpful if he had specified whether or not the links were long enough to span the distance between the marbles in the hoop frame. If not, he should have said that the links would not fit unless marbles moved closer together, making it impossible to connect the last pair of marbles unless the hula hoop was allowed to deform inward. His invocation of the "wheel frame" is beyond unhelpful and actually worrisome. Hopefully that was just a careless error.
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    Quote Originally Posted by JTyesthatJT View Post
    At least as far as I can understand cincirob's marble-contraption-wheel, the material links are added while rotating, and their length-contracted lengths just happen to match the distance between the marbles. As such, the marbles would be unaffected.
    Ah, I wasn't considering that. I took the links to be added at rest.


    Quote Originally Posted by JTyesthatJT View Post
    I'm not sure why you and I disagree here, as we seem to agree on everything else.
    I think it's because we interpreted the problem differently.


    EDIT: It's clear that I misread what cincirob said. Sorry. I was more focussed on the absence of the spokes than the way the links were added.
    Last edited by KJW; 02-26-2014 at 11:42 AM.
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    SYA: You've been trying to use the length contraction formula (LCF) to determine the shape of your rotating chord in the ground system. Everyone's been telling you for quite some time now, that the LCF requires inertial motion, and thus cannot work for your chord since its rotating.

    cinci: No, I don't really care how it transforms since I think there is another way to work the problem. My only point is that it will not transform exactly like a static chord; that is, if I built the same chord across the hula hoop. To assume they will look the same to the road observer seems highly unlikely, don't you think?
    ***********************


    SYA: The wheel cannot rotate if your chord is to be defined by the LCF in the ground system. If the wheel does not rotate, the spokes do not rotate, and as such your co-located marbles would not rotate either.

    cinci: Ridiculous! Remember, what the road observer sees cannot change the dynamics of the wheel.
    ***************


    SYA: So the question is, do your marbles move wrt hoop? If they do (at relativistic rate), then your chord contraction hypothesis is mistaken, but the marbles will always transform as the colocated spoke-tips do, no matter if rotating at steady rate or not rotating at all.

    cinci: Everybody else understands that the marbles are rotating relative to the hoop because that is exactly what I said. But if you're going to say they act just like spoke tips on a solid wheel, you have to be able to check that answer. You can't just assume it. Looking at chords as I have suggested is a way to check that. You haven't proposed any better check and I don't think you can.

    You haven't even answered the question of whether Gron's analysis is accurate for the marbles. How about a yes or no there instead of pretending you don't understand the question.
    ****************
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    JT: At least as far as I can understand cincirob's marble-contraption-wheel, the material links are added while rotating, and their length-contracted lengths just happen to match the distance between the marbles. As such, the marbles would be unaffected.

    KJW: Ah, I wasn't considering that. I took the links to be added at rest.

    cinci: If you start out with the links and marbles at rest, accelerating the marbles will cause the links to have a tendency to contract. So if you add material or let them stretch (in fact you can build them so that the mechanically "telescope") then at speed they have a larger rest length.

    My point is that the road observer must deal with this new length. I simply can't believe he will get the same answer as he does for marbles constrained to the hula hoop.

    Therefore, if Gron's analysis is accurate for the unconnected marbles, I can't believe the same solution applies when they are connects as the would be in a wheel.
    ***************************
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    JT: As you say, the natural (unstressed) length of each material link would be length-contracted in the hoop frame. However, the same can be said of the marbles traveling around the hoop.

    cinci: You should just consider the marbles to be points.
    **************


    JT: At least as far as I can understand cincirob's marble-contraption-wheel, the material links are added while rotating, and their length-contracted lengths just happen to match the distance between the marbles. As such, the marbles would be unaffected. So even without spokes, the radius of the outer rim would be maintained. I'm not sure why you and I disagree here, as we seem to agree on everything else.

    cinci: "Just happen to be" is the issue here. They have to be length contracted from lengths that would be longer at rest.
    ********************


    JT: EDIT: cinci's own description of adding the links is of no help here. He said,

    "If I connect each one with a link to the next one I get what amounts to chords of the wheel and I can take away the hula hoop. Now I have rolling wheel, assuming I shape the links so that they fill out the circle. One way to construct this is to start with the hula hoop and add the links at speed which means they are contracted in the wheel frame."


    JT: It would have been helpful if he had specified whether or not the links were long enough to span the distance between the marbles in the hoop frame. If not, he should have said that the links would not fit unless marbles moved closer together, making it impossible to connect the last pair of marbles unless the hula hoop was allowed to deform inward. His invocation of the "wheel frame" is beyond unhelpful and actually worrisome. Hopefully that was just a careless error.

    cinci: It wasn't an error at all. If you link them all up, the links all want to contract at speed. When you say the wheel has its rest dimensions in the axle frame at speed, the links all have to be contracted but from lengths that are longer than the rest length of the links. Think Ehrenfest. What do you think happens to chords there.
    **************************
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    Quote Originally Posted by cincirob View Post
    JT: At least as far as I can understand cincirob's marble-contraption-wheel, the material links are added while rotating, and their length-contracted lengths just happen to match the distance between the marbles. As such, the marbles would be unaffected.

    KJW: Ah, I wasn't considering that. I took the links to be added at rest.

    cinci: If you start out with the links and marbles at rest, accelerating the marbles will cause the links to have a tendency to contract. So if you add material or let them stretch (in fact you can build them so that the mechanically "telescope") then at speed they have a larger rest length.

    My point is that the road observer must deal with this new length. I simply can't believe he will get the same answer as he does for marbles constrained to the hula hoop.

    Therefore, if Gron's analysis is accurate for the unconnected marbles, I can't believe the same solution applies when they are connects as the would be in a wheel.
    ***************************
    MARBLES IN A HULA HOOP:
    1. The circular path of the marbles has a length of 2piR in the hula hoop frame
    2. For N number of equally-spaced marbles, the center-to-center arc distance between each pair of adjacent marbles will be 2piR/N in the hula hoop frame
    3. All of the marbles travel around the path at constant speed, v, in the hula hoop frame

    MARBLES CONNECTED BY TELESCOPING LINKS:
    1. The circular path of the marbles still has a length of 2piR in the hula hoop frame (even after the hula hoop is removed)
    2. For N number of equally-spaced marbles, the center-to-center arc distance between each pair of adjacent marbles will still be 2piR/N in the hula hoop frame (even after the hula hoop is removed)
    3. All of the marbles still travel around the path at the same constant speed, v, in the hula hoop frame (even after the hula hoop is removed)

    The input variables in the LT's are x, y, z, t and v. Superimposing the two scenarios means they would share the same value of z. Because of #1 and #2 both scenarios have the same x, and y values. Because of #3, the two scenarios both have the same v and t values. Since the input variables are all the same in both scenarios, the LT transformation of marble coordinates is going to give the same answer for both scenarios. It's as simple as that.
    Last edited by JTyesthatJT; 02-27-2014 at 02:02 AM.
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    Cinci: OK, let’s do it simply:
    1. If I add the links to the marbles (and remove the hula hoop), then the points are on the links and moving relative to the axle frame.
    2. The points on the hula hoop (not the marbles) are fixed in the axle frame, not moving relative to it.
    3. Objects at rest in a frame transform to another frame differently than moving objects in a frame transform to a different frame.
    4. If you choose to prove me wrong with your calculations, don’t use the 3 – 9:00 chord as SYA suggests. He knows that chord is also fixed in the x-direction and will not show the problem.
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    Quote Originally Posted by cincirob View Post
    Cinci: OK, letís do it simply:
    1. If I add the links to the marbles (and remove the hula hoop), then the points are on the links and moving relative to the axle frame.
    2. The points on the hula hoop (not the marbles) are fixed in the axle frame, not moving relative to it.
    3. Objects at rest in a frame transform to another frame differently than moving objects in a frame transform to a different frame.
    We have already agreed that the marbles in the original marble contraption transform the way Gron says they do. And the marbles in the original contraption were already moving relative to what would be the axle frame. They don't just start to move after you connect them with the links. So how can you suddenly decide that the movement of the marbles through the axle frame causes them to transform differently than Gron's solution?
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    Quote Originally Posted by SYA View Post
    You've been trying to use the length contraction formula (LCF) to determine the shape of your rotating chord in the ground system. Everyone's been telling you for quite some time now, that the LCF requires inertial motion, and thus cannot work for your chord since its rotating.

    Quote Originally Posted by cincirob View Post
    No, I don't really care how it transforms since I think there is another way to work the problem. My only point is that it will not transform exactly like a static chord; that is, if I built the same chord across the hula hoop. To assume they will look the same to the road observer seems highly unlikely, don't you think?
    Interesting. How the body exists in the ground system depends upon the LTs, and you say you don't care about that. Yet, you've been arguing for almost ever that the LTs cannot support the GRON prediction, even though he used the LTs to make his prediction. Go figure. There can be no difference between your marbles and the colocated wheel atoms, given they are always colocated

    Quote Originally Posted by SYA View Post
    So the question is, do your marbles move wrt hoop? If they do (at relativistic rate), then your chord contraction hypothesis is mistaken, but the marbles will always transform as the colocated spoke-tips do, no matter if rotating at steady rate or not rotating at all.

    Quote Originally Posted by cincirob View Post
    Everybody else understands that the marbles are rotating relative to the hoop because that is exactly what I said. But if you're going to say they act just like spoke tips on a solid wheel, you have to be able to check that answer. You can't just assume it. Looking at chords as I have suggested is a way to check that. You haven't proposed any better check and I don't think you can.
    I see you have recently switched from horizontal linear chords to circular-arc chords. Very sorry, but that doesn't change anything whatever. You are just as mistaken about that, as the horizontal chord. Your circular-arc-chord of marbles (connected or not) transforms exactly as always-colocated spoketips do. Yet, a non-rotating circular-arc-chord does not transform exactly as a rotating circular-arc-chord, not because the shape differs, but rather because the atomic configuration differs across the chord. The LTs require that.

    Quote Originally Posted by cincirob View Post
    You haven't even answered the question of whether Gron's analysis is accurate for the marbles. How about a yes or no there instead of pretending you don't understand the question.
    See above ^

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    SYA: You've been trying to use the length contraction formula (LCF) to determine the shape of your rotating chord in the ground system. Everyone's been telling you for quite some time now, that the LCF requires inertial motion, and thus cannot work for your chord since its rotating.

    cinci: No, I don't really care how it transforms since I think there is another way to work the problem. My only point is that it will not transform exactly like a static chord; that is, if I built the same chord across the hula hoop. To assume they will look the same to the road observer seems highly unlikely, don't you think?


    SYA: Interesting. How the body exists in the ground system depends upon the LTs, and you say you don't care about that. Yet, you've been arguing for almost ever that the LTs cannot support the GRON prediction, even though he used the LTs to make his prediction. Go figure. There can be no difference between your marbles and the colocated wheel atoms, given they are always collocated

    cinci: If you believe that you must believe that a static chord in the wheel frame transforms exactly like on that is rotating relative to that frame. The reason I said I don't care how you do it is that you tell me that rotation doesn't allow me to transform the rod as if it isn't rotating. OK, there may be some truth to that, but then you have to transform it some other way, you can't just ignore its velocities, lateral or rotating.
    *************************


    SYA: So the question is, do your marbles move wrt hoop? If they do (at relativistic rate), then your chord contraction hypothesis is mistaken, but the marbles will always transform as the colocated spoke-tips do, no matter if rotating at steady rate or not rotating at all.

    cinci: No, the marbles always transform according to the shape of the hula hoop which is static in the axle frame. You have to prove that a rotating structure transforms and identically and you haven't.
    *****************


    cinci: Everybody else understands that the marbles are rotating relative to the hoop because that is exactly what I said. But if you're going to say they act just like spoke tips on a solid wheel, you have to be able to check that answer. You can't just assume it. Looking at chords as I have suggested is a way to check that. You haven't proposed any better check and I don't think you can.

    SYA: I see you have recently switched from horizontal linear chords to circular-arc chords. Very sorry, but that doesn't change anything whatever. You are just as mistaken about that, as the horizontal chord.

    cinci: And I see that you're not very good at understanding description of physical objects. I suggested that, after the links were added to the marble contraption, removing the hula hoop left a solid wheel. Of course some nitpicker would say that structure isn't round, you know, like you. So I simply said add some material to the chord to fill out the circle. There's still a straight chord that is horizontal. Maybe you poor visualization skills contribute to your misunderstanding of relativity here.
    *************************


    SYA: Your circular-arc-chord of marbles (connected or not) transforms exactly as always-colocated spoketips do.

    cinci: OK, then you should be able to produce a Lorentz transformation analysis which includes the velocity of the chords that verifies this claim. I don't think you can.
    **********************


    SYA: Yet, a non-rotating circular-arc-chord does not transform exactly as a rotating circular-arc-chord, not because the shape differs, but rather because the atomic configuration differs across the chord. The LTs require that.

    cinci: Interesting. There's no such thing as a circular arc chord. What I describes was the segment of a circle. Now you're saying that rotating things transform differently than static things. When did this occur to you?
    ********************


    cinci: You haven't even answered the question of whether Gron's analysis is accurate for the marbles. How about a yes or no there instead of pretending you don't understand the question.

    SYA: See above.

    cinci: How about a yes or no? Afraid to commit in case KJW changes is mind about this. He already said he has a question in his mind about the Gron analysis. Are you getting panicky?
    *********************************************
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    Cinci: OK, let’s do it simply:
    1. If I add the links to the marbles (and remove the hula hoop), then the points are on the links and moving relative to the axle frame.
    2. The points on the hula hoop (not the marbles) are fixed in the axle frame, not moving relative to it.
    3. Objects at rest in a frame transform to another frame differently than moving objects in a frame transform to a different frame.


    JT: We have already agreed that the marbles in the original marble contraption transform the way Gron says they do.
    cinci: Well you agreed, SYA is afraid to, and KJW hasn't answered unless I missed it with all the trouble with the site.
    *********************


    JT: And the marbles in the original contraption were already moving relative to what would be the axle frame. They don't just start to move after you connect them with the links. So how can you suddenly decide that the movement of the marbles through the axle frame causes them to transform differently than Gron's solution?

    cinci: I didn't say anything about the marbles changing. In the case of the marbles, you aren't transforming anything about the marbles to get the elliptical shape; you are transforming the shape of the hula hoop which is not moving relative to the axle frame. After you add the links, you have to transform the links; I don't think the links transform like the hula hoop because they move relative to the axle frame while the hoop does not.

    The marbles play no role in forming the shape of the wheel in the road frame in either case.
    *******************************

    *****************************
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    Quote Originally Posted by cincirob View Post
    JT: And the marbles in the original contraption were already moving relative to what would be the axle frame. They don't just start to move after you connect them with the links. So how can you suddenly decide that the movement of the marbles through the axle frame causes them to transform differently than Gron's solution?

    cinci: I didn't say anything about the marbles changing. In the case of the marbles, you aren't transforming anything about the marbles to get the elliptical shape; you are transforming the shape of the hula hoop which is not moving relative to the axle frame. After you add the links, you have to transform the links; I don't think the links transform like the hula hoop because they move relative to the axle frame while the hoop does not.

    The marbles play no role in forming the shape of the wheel in the road frame in either case.
    *******************************
    With your original marble contraption, you had marbles moving through the hula hoop. You said that the marbles were arranged like spoke tips on a wheel. You also said that when everything is transformed to the road frame, the marbles transform in the same way as the spoke tips in Gron's analysis. Those marbles were moving relative to what would be the axle frame.

    Now you are saying that only the hula hoop transforms to the road frame as an ellipse, and the marbles have nothing to do with it. You are changing your story.


    Quote Originally Posted by cincirob View Post
    JT: We have already agreed that the marbles in the original marble contraption transform the way Gron says they do.
    cinci: Well you agreed, SYA is afraid to, and KJW hasn't answered unless I missed it with all the trouble with the site.
    *******************************
    What we agreed to was that the marbles moving through the hula hoop transform to the road in the same way as Gron's spoke tips. We were not ignoring the marbles and only transforming the hula hoop itself.
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    OK,

    Given the style of clip-it responding, and the general confusion regarding LT application to rotation, the points that have been made by cinci are becoming further confused and diluted over time. To keep the focus, I decided to make a concise response here, versus responding to the many clip-it responses individually.

    So in regards to cincirob's new (actually old) marble scenario, rotating marbles transform differently than non-rotating marbles, even though the overall perimeter shape of the marbles (in collective) is the same either way in any inertial system. So while the perimeter shape is the same either way per ground, the density distribution of the marbles along that perimeter (per ground) differs between the 2 cases. So while the perimeter shape is the same, the internal configuration of the marbles wrt that shape differs. None of this changes the fact that the GRON analysis properly applies the LTs to the rotating case, and that GRON's analysis did in fact encompass the motion of disk atoms per axle ... attained by sets of LT input coordinates in collective. This, of course, means said motion of rotation is transformed to the ground system even though the LTs use only the translation rate between axle and ground.

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    Quote Originally Posted by cincirob to JT View Post
    The marbles play no role in forming the shape of the wheel in the road frame in either case.
    The marbles themselves, in any instant, collectively constitute a perimeter shape in the non-rotating inertial frame that's always co-located with the hoop's rotation axis (call it the axle system, for short). In our case, that is always a circle, given their defined motion in the axle system. As such, the marbles define a perimeter shape in all POVs, although to predict that perimeter shape requires the LTs and the motion plot of the marbles in the axle system. That's what Gron did.

    To say that the marbles play no role in defining their own collective shape, is to say that shapes are not defined by material entity. No one's ever gonna believe that no matter how many times or ways it is restated.

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    Quote Originally Posted by SinceYouAsked View Post
    Given the style of clip-it responding, and the general confusion regarding LT application to rotation, the points that have been made by cinci are becoming further confused and diluted over time.
    I agree that cinci is only becoming more confused over time. It is wonderful that he is finally considering the axle frame, (i.e. the hula hoop frame), but I don't think he is being objective about it. He seems to have already made up his mind that when the marbles are all connected with arc-shaped links, the contraption should not transform as an ellipse in the road frame. Since he has already agreed that the unconnected marbles in the hula hoop do transform as an ellipse, he knows he needs to explain the difference.

    I think he was hoping the connective links would lead all of us to consider his favorite tool in relativity, the Length Contraction Formula (LCF). But his least favorite tool in relativity, the Lorentz Transformations (LT's) tell us that if the connective links do not change the coordinates of the marbles in the hula hoop frame, then they still transform as an ellipse, and therefore we don't need to consider the LCF. Frustrated that his preconceived conclusion is not materialising, he is now engaging in back-pedaling, (i.e. "the marbles have nothing to do with the shape," and, "the LT's must be applied using the composed velocity").
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    JT: With your original marble contraption, you had marbles moving through the hula hoop. You said that the marbles were arranged like spoke tips on a wheel. You also said that when everything is transformed to the road frame, the marbles transform in the same way as the spoke tips in Gron's analysis. Those marbles were moving relative to what would be the axle frame.

    Now you are saying that only the hula hoop transforms to the road frame as an ellipse, and the marbles have nothing to do with it. You are changing your story.
    Cinci: You have to know that you’re transforming the hoop and not the marbles. You are transforming points on the hoop that are adjacent to points on the hoop. How do you know this? You use the relative velocity of the hoop to the road. You make no attempt to even determine the velocities of the marbles in the x-direction and you are using an x-direction LT.

    OK, let’s put a chord on the hula hoop. And let’s agree that I can put a link between two points at the ends of this chord. I’m going to describe, with numbers the difference between a moving link joining two marbles and a chord of the hoop.

    Let’s pick the half chord of which is at the tip of a spoke that is 60 degrees from horizontal with a wheel radius of R = 1. V is the relative velocity of the road to the axle. Wheel velocity is .866.

    The x-direction length of the chord is L(hoop chord in axle frame) = Rcos60 = 1*.5 = .5

    The length of the superimposed link in the axle frame is the same: L(link in axle frame) = .5

    The velocity of L(hoop chord) relative to the axle frame is zero.

    The velocity of the link relative to the axle frame is:

    V(link rel to axle) = rw = Rsin60*v/R = 1*.866*.866/1 = .75

    The rest length of the link must be:

    L(link at rest) = L(link in axle frame)/(1 – (V(link rel to axle)^2)^.5 = .5/(1 - .75^2)^.5 = .756

    The relative velocity of the link to the road is:

    V(link rel to road) = (v + V(link to axle)/(1 + vV(link to axle) = (.866+.75)/(1 +.866*.75) = .976

    The length of the link in the road frame is:

    L(link in road) = L(link at rest)(1 - V(link rel to road)^2)^.5 = .756(1 - .976^2)^.5 = .174

    Back to the hoop chord. The length of the hoop chord in the road is

    L(chord in road) = L(hoop chord in axle frame)(1 – v^2)^.5 = .5(1 - .866^2)^.5 = .25

    So, the hoop will form an ellipse, the links will not.

    SYA is mumbling that I haven’t been consistent about this but he knows better. I’ve been saying the same thing for a long, long time and nobody has pointed out anything wrong with it. I can back up everything in it in any relativity text book.
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    SYA: I think he was hoping the connective links would lead all of us to consider his favorite tool in relativity, the Length Contraction Formula (LCF). But his least favorite tool in relativity, the Lorentz Transformations (LT's) tell us that if the connective links do not change the coordinates of the marbles in the hula hoop frame, then they still transform as an ellipse, and therefore we don't need to consider the LCF. Frustrated that his preconceived conclusion is not materialising, he is now engaging in back-pedaling, (i.e. "the marbles have nothing to do with the shape," and, "the LT's must be applied using the composed velocity").

    cinci: Oh it materialized. It's just that you don't understand it and couldn't make it materialize.

    It's all there with numbers. Take your shot. Show us how using the LTs makes it different. I'm tired of all the innuendo and no substance from you. You comments are little more than spam; it's time to show us something or go away.
    **********************
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    Quote Originally Posted by cincirob View Post
    Cinci: You have to know that youíre transforming the hoop and not the marbles.
    **********************
    Earlier you agreed we were transforming the marbles:


    Quote Originally Posted by cincirob View Post
    JT: #6 should say that the marbles would be spaced in such a way that they are closer together at the top and father apart at the bottom, as measured by the road frame

    cinci: Are you saying that I have to describe the Gron solution that you've been vehemently defending and that we both worked out in detail some time age? Give me a break.
    **********************


    JT: Given those changes, I think I would agree to that.

    cinci: Great!
    ************

    If you thought Gron was only transforming the hoop, you would not have agreed with #6, that the marbles would transform in such a way that they are closer together at the top, and farther apart at the bottom. There is nothing on the hoop that does that. This shows that you are now changing your story. Your earlier position was that the MARBLES in the hula hoop transform to Gron's solution.
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    Perhaps I'm losing my marbles trying to understand what you're saying!

    So am I to presume here that each marble is NOT attached to a particular spoke but can roll around anywhere in a 'hoop' formed by the circumference of the wheel?

    TFOLZO
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    Quote Originally Posted by TFOLZO View Post
    Perhaps I'm losing my marbles trying to understand what you're saying!

    So am I to presume here that each marble is NOT attached to a particular spoke but can roll around anywhere in a 'hoop' formed by the circumference of the wheel?
    It is my pleasure to refer you to post #8 where cinci proposes the contraption in which marbles are inside a hula hoop:

    Quote Originally Posted by cincirob View Post
    cinci:

    1. Imagine a hula hoop with marbles running with no friction around the inside of it.

    2. Space the marbles as the tips of the spokes in a wheel would be.

    3. Observe this contraption from a relatively moving frame, the equivalent of a road observer.

    4. I believe the road observer will "see" an ellipse whose minor dimension is the major dimension contracted by (1 - (v/c)^2)^.5. This is because he is observing a static circular structure.

    5. I believe the Lorentz transformation will give the same shape.

    6. If you figure out where the marbles are located in the road observer's frame, I believe you will get locations identical to the Gron solution.
    The marbles are equally spaced inside the hula hoop (like spoke tips). All the marbles move in unison around the circumference of the hula hoop, like a wheel inside a fender.

    It is interesting to note that in item 6, cincirob says that he believes the marbles' locations in the road frame would be identical to the Gron solution. He seems to have changed his mind on that. He seems to be saying now that the Gron solution does not give the locations of the marbles after all. He's all over the place. I'm losing my marbles trying to figure out what his current position is.
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    JT: Earlier you agreed we were transforming the marbles:

    cinci: Read #4: 4. I believe the road observer will "see" an ellipse whose minor dimension is the major dimension contracted by (1 - (v/c)^2)^.5. This is because he is observing a static circular structure. Does that say he transformed the marbles?
    **********************


    JT: The marbles are equally spaced inside the hula hoop (like spoke tips). All the marbles move in unison around the circumference of the hula hoop, like a wheel inside a fender.

    It is interesting to note that in item 6, cincirob says that he believes the marbles' locations in the road frame would be identical to the Gron solution. He seems to have changed his mind on that. He seems to be saying now that the Gron solution does not give the locations of the marbles after all. He's all over the place. I'm losing my marbles trying to figure out what his current position is.

    cinci: Wow! I don't know how to make it any simpler. The Gron solution gives the location of the marbles guided by a static structure. What I've proved by showing this to be the case is that Gron's solution has nothing at all to do with rolling wheels.

    If his solution is correct for the marble contraption, then it cannot be correct for a rolling wheel.
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    Since we cannot agree on losing our marbles...
    Quote Originally Posted by cincirob View Post
    JT: Earlier you agreed we were transforming the marbles:

    cinci: Read #4: 4. I believe the road observer will "see" an ellipse whose minor dimension is the major dimension contracted by (1 - (v/c)^2)^.5. This is because he is observing a static circular structure. Does that say he transformed the marbles? **********************

    JT: The marbles are equally spaced inside the hula hoop (like spoke tips). All the marbles move in unison around the circumference of the hula hoop, like a wheel inside a fender.

    It is interesting to note that in item 6, cincirob says that he believes the marbles' locations in the road frame would be identical to the Gron solution. He seems to have changed his mind on that. He seems to be saying now that the Gron solution does not give the locations of the marbles after all. He's all over the place. I'm losing my marbles trying to figure out what his current position is.

    cinci: Wow! I don't know how to make it any simpler. The Gron solution gives the location of the marbles guided by a static structure. What I've proved by showing this to be the case is that Gron's solution has nothing at all to do with rolling wheels.

    If his solution is correct for the marble contraption, then it cannot be correct for a rolling wheel. ***********************
    ...perhaps you could try the thread "a Toothed Wheel rolling along a surface" on the SR&GR forum since the gear-wheel teeth substitute for the 'rolly' quality of the marbles. It provides a different way to visualize the problem so that we don't get stuck to the edge (of the wheel) as the marbles seem to be.

    TFOLZO
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    Quote Originally Posted by cincirob View Post
    cinci: Wow! I don't know how to make it any simpler. The Gron solution gives the location of the marbles guided by a static structure.
    ***********************
    Okay, so you and I agree that "marbles guided by a static structure" result in the Gron solution. Do we also agree that Gron solution is not just an elliptical hula hoop, but on that ellipse are located marbles which are closer together at the top, and farther apart at the bottom? If so, you can't say that only the hula hoop itself is being transformed. Agreed?


    Quote Originally Posted by cincirob View Post
    cinci: What I've proved by showing this to be the case is that Gron's solution has nothing at all to do with rolling wheels.

    If his solution is correct for the marble contraption, then it cannot be correct for a rolling wheel.
    ***********************
    It's hilarious that you think you've "proved" that. You have not even "claimed" that adding the links changes the marbles' coordinates in any way. If the marbles' coordinates are the same in both cases, then the LT's say they transform the same way with or without the links. Don't forget that "marbles guided by a static structure" are not at rest in what would be the axle frame, so you cannot start complaining about that when you add the links.
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    Quote Originally Posted by cincirob to JT View Post
    You have to know that you’re transforming the hoop and not the marbles. You are transforming points on the hoop that are adjacent to points on the hoop. How do you know this? You use the relative velocity of the hoop to the road. You make no attempt to even determine the velocities of the marbles in the x-direction and you are using an x-direction LT.
    There is no need to consider the x-velocity of the marble, given one cares only to relate the atomic locations between the 2 inertial systems "over duration". The rotational rate (ω) of any marble, and its distance from the axis of rotation (R'), is all that's required to determine the marble's location in the inertial frame co-located with the center-of-rotation. Call that the axle frame, for short. So at any axle time t', one can determine the location of a moving marble in the axle system. That atom is co-located with a point in axle spacetime, call that "an event" (devoid of motion). If co-located in one system, then co-located in all systems. Using the translation velocity (v) between axle and ground, any specific coordinate in axle spacetime relates to a single corresponding coordinate in ground spacetime, via the LTs. No other velocity is required! We can therefore map the location of any and all marbles at any time t' of the axle system (and over duration), to its corresponding spacetime coordinate in the ground system. From the LT transformation solutions-set, one can easily determine the velocity of any marble at any time t in the ground system, however that is required "only if" one in fact does request it. It is not required to determine the shape of the wheel or it's spokes, in any ground instant of time, which was the scope of the Gron analysis as I understand it. The Gron analysis only cared about mapping the location of moving disk atoms (or coordinates) in both systems. From that mapping, the shape of the wheel and spokes are of course determinable. Nor does one need to determine the rest length of any contiguous string of wheel atoms (or hoop contraption atoms) to determine their individual atomic locations in either axle or the ground system.

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    Quote Originally Posted by TFOLZO View Post
    Since we cannot agree on losing our marbles ...

    ... perhaps you could try the thread "a Toothed Wheel rolling along a surface" on the SR&GR forum since the gear-wheel teeth substitute for the 'rolly' quality of the marbles. [B]It provides a different way to visualize the problem so that we don't get stuck to the edge (of the wheel) as the marbles seem to be.
    Thanx, but no thanx TFOLZO. A toothed wheel changes nothing. It does not make the scenario simpler, nor can it provide any deeper insight. In fact, it can only complicate it further. This discussion is about the misunderstandings cincirob has regarding the meaning of relativistic effects, not how to make an impossible wonder wheel (track, or contraption) a possible reality for relativistic rates.

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    cinci: Wow! I don't know how to make it any simpler. The Gron solution gives the location of the marbles guided by a static structure.

    JT: Okay, so you and I agree that "marbles guided by a static structure" result in the Gron solution. Do we also agree that Gron solution is not just an elliptical hula hoop, but on that ellipse are located marbles which are closer together at the top, and farther apart at the bottom? If so, you can't say that only the hula hoop itself is being transformed. Agreed?

    cinci: That is a separate operation from getting the shape. Getting these locations is simply figuring out how much time displacement there is between the axle and each spoke tip. To get the new location, you find out where the marble was in the hula hoop at the correct time and transform that point of the hula hoop. So no, you are not transforming the marbles, you’re transforming the hula hoop.
    **************************


    cinci: What I've proved by showing this to be the case is that Gron's solution has nothing at all to do with rolling wheels.

    If his solution is correct for the marble contraption, then it cannot be correct for a rolling wheel.


    JT: It's hilarious that you think you've "proved" that.

    Cinci: I proved his analysis is for a static structure. If you think a hula hoop sliding down the road accurately represents a rolling wheel, I can’t help you. It should be obvious that it doesn’t.
    *********************


    JT: You have not even "claimed" that adding the links changes the marbles' coordinates in any way.

    Cinci: Of course I did. The shape of the wheel will not be an ellipse if the links determine it. Gron’s analysis says the half-chord at 60 degrees will be .25 and the links analysis say it will be .174.

    But after you know Gron’s analysis is for a static structure, what else do you need to know it’s not a wheel analysis?
    ****************************


    JT: If the marbles' coordinates are the same in both cases, then the LT's say they transform the same way with or without the links.

    Cinci: My analysis says otherwise. Tell me which part of it is wrong and why.
    ***********************


    JT: Don't forget that "marbles guided by a static structure" are not at rest in what would be the axle frame, so you cannot start complaining about that when you add the links.

    Cinci: No, the marbles aren’t at rest, but their velocities don’t determine how they transform to the road frame; the static structure does that. In a rolling wheel there isn’t a static structure so Gron’s analysis doesn’t account for the rolling to determine the shape of the wheel.
    The links don’t change the position of the marbles in the axle frame, but they do change it in the road frame. The links replace the hula hoop and act like a rolling wheel.
    **********************
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    SYA: Thanx, but no thanx TFOLZO. A toothed wheel changes nothing. It does not make the scenario simpler, nor can it provide any deeper insight. In fact, it can only complicate it further. This discussion is about the misunderstandings cincirob has regarding the meaning of relativistic effects, not how to make an impossible wonder wheel (track, or contraption) a possible reality for relativistic rates.

    cinci: I am not the originator of the analysis of "an impossible wonder wheel", Dr Gron is. And I don't support it, you do. Or at least you used to. Based on this message, I'd say you have completely backed away from Dr. Gron's analysis.

    Welcome back from the Dark Side. I'm happy to have shown you the light.
    **************************
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    cincirob to JT: You have to know that you’re transforming the hoop and not the marbles. You are transforming points on the hoop that are adjacent to points on the hoop. How do you know this? You use the relative velocity of the hoop to the road. You make no attempt to even determine the velocities of the marbles in the x-direction and you are using an x-direction LT.

    SYA: There is no need to consider the x-velocity of the marble, given one cares only to relate the atomic locations between the 2 inertial systems "over duration". The rotational rate (ω) of any marble, and its distance from the axis of rotation (R'), is all that's required to determine the marble's location in the inertial frame co-located with the center-of-rotation. Call that the axle frame, for short. So at any axle time t', one can determine the location of a moving marble in the axle system. That atom is co-located with a point in axle spacetime, call that "an event" (devoid of motion). If co-located in one system, then co-located in all systems. Using the translation velocity (v) between axle and ground, any specific coordinate in axle spacetime relates to a single corresponding coordinate in ground spacetime, via the LTs. No other velocity is required! We can therefore map the location of any and all marbles at any time t' of the axle system (and over duration), to its corresponding spacetime coordinate in the ground system. From the LT transformation solutions-set, one can easily determine the velocity of any marble at any time t in the ground system, however that is required "only if" one in fact does request it.

    cinci: Everything up to here is exactly what I've been telling you for some time now.
    *********************


    SYA: It is not required to determine the shape of the wheel or it's spokes, in any ground instant of time, which was the scope of the Gron analysis as I understand it.

    cinci: This is simply wrong.
    *****************


    SYA: The Gron analysis only cared about mapping the location of moving disk atoms (or coordinates) in both systems.

    cinci: Then he should have described a model like the hula hoop and marbles instead of calling it a rolling wheel. This is more evidence that you no longer believe Gron's analysis describes a rolling wheel.
    ************************************************


    SYA: From that mapping, the shape of the wheel and spokes are of course determinable. Nor does not need to determine the rest length of any contiguous string of wheel atoms (or hoop contraption atoms) to determine their individual atomic locations in either axle or the ground system.

    cinci: Give it up. At least JT is sticking to his guns. You won't even deal with the issues.
    ***********************
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    TFOLZO: Since we cannot agree on losing our marbles ...

    ... perhaps you could try the thread "a Toothed Wheel rolling along a surface" on the SR&GR forum since the gear-wheel teeth substitute for the 'rolly' quality of the marbles. [B]It provides a different way to visualize the problem so that we don't get stuck to the edge (of the wheel) as the marbles seem to be.

    SYA: Thanx, but no thanx TFOLZO. A toothed wheel changes nothing. It does not make the scenario simpler, nor can it provide any deeper insight. In fact, it can only complicate it further. This discussion is about the misunderstandings cincirob has regarding the meaning of relativistic effects, not how to make an impossible wonder wheel (track, or contraption) a possible reality for relativistic rates.

    cinci: SYA won't go here TFOLZO because it is a place where Gron's solution fails completely. In SYA's solution, the teeth on the wheel become 1/(1 - (v/c)^2)^.5 times as long and so will not fit the straight gear of the road. Remember it rolls out 4piR. But if you look at the contact area of the wheel and the road they have no relative velocity and should always fit. SYA can't handle this so he blows it off.

    It is also interesting that his only two claims now is that the wheel is impossible (yet he believes Gron's solution) and that I don't understand relativity (yet he never explains what it is I don't understand).
    ********************
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    Quote Originally Posted by cincirob to JT View Post
    You have to know that you’re transforming the hoop and not the marbles. You are transforming points on the hoop that are adjacent to points on the hoop. How do you know this? You use the relative velocity of the hoop to the road. You make no attempt to even determine the velocities of the marbles in the x-direction and you are using an x-direction LT.[/I]

    Quote Originally Posted by SYA View Post
    There is no need to consider the x-velocity of the marble, given one cares only to relate the atomic locations between the 2 inertial systems "over duration". The rotational rate (ω) of any marble, and its distance from the axis of rotation (R'), is all that's required to determine the marble's location in the inertial frame co-located with the center-of-rotation. Call that the axle frame, for short. So at any axle time t', one can determine the location of a moving marble in the axle system. That atom is co-located with a point in axle spacetime, call that "an event" (devoid of motion). If co-located in one system, then co-located in all systems. Using the translation velocity (v) between axle and ground, any specific coordinate in axle spacetime relates to a single corresponding coordinate in ground spacetime, via the LTs. No other velocity is required! We can therefore map the location of any and all marbles at any time t' of the axle system (and over duration), to its corresponding spacetime coordinate in the ground system. From the LT transformation solutions-set, one can easily determine the velocity of any marble at any time t in the ground system, however that is required "only if" one in fact does request it.

    Quote Originally Posted by cincirob View Post
    Everything up to here is exactly what I've been telling you for some time now.
    Well, first, everyone knows that that is a lie. Second, if that were true, everyone here who has been correcting you repeatedly knows you would never have been asking your many questions that continually need correction. You are not fooling anyone. Remember, the thread here speaks for itself.

    Quote Originally Posted by SYA View Post
    It is not required to determine the shape of the wheel or it's spokes, in any ground instant of time, which was the scope of the Gron analysis as I understand it.

    Quote Originally Posted by SYA View Post
    This is simply wrong.
    Not wrong, however I would admit my choice of words was not the best in that particular sentence. First, one must map the points of the rotating disk in the axle system, then transformed them to the ground system. That's a goal. The reason that was the goal, is because that needs done to ever map the rolling disk in the ground system. Once mapped by the LTs, no guessing is required. From the transformed solns, one then may determine anything else desired wrt the ground POV, which may include the shape and size of the disk, the shape and size of its radial elements per ground, the shape and size of chords of the disk, and the velocity of any atom of the disk. The shape, size, location, speed, and direction of any disk atom is determinable in the ground system at any instant t, if so desired.

    Quote Originally Posted by SYA View Post
    The Gron analysis only cared about mapping the location of moving disk atoms (or coordinates) in both systems.

    Quote Originally Posted by cincirob View Post
    Then he should have described a model like the hula hoop and marbles instead of calling it a rolling wheel. This is more evidence that you no longer believe Gron's analysis describes a rolling wheel.
    Don't be silly. You loose even more credibility with statements such as these. And, anyone who actually does understand the Gron analysis, knows it applies to any steadily rotating body whatever, which of course would include your hula hoop.

    Quote Originally Posted by SYA View Post
    From that mapping, the shape of the wheel and spokes are of course determinable. Nor does not need to determine the rest length of any contiguous string of wheel atoms (or hoop contraption atoms) to determine their individual atomic locations in either axle or the ground system.
    Quote Originally Posted by cincirob View Post
    Give it up. At least JT is sticking to his guns. You won't even deal with the issues.
    Every question you have ever posed in these threads, is answered by a glance at the 3-space Minkowski figure I posted here, just for you ...

    see post ... Relativistically Rolling Wheel

    which is supported by these figure as well ... Relativistically Rolling Wheel

    I posted those geometric figures to help you, because you never understood the math.

    If you would do what had been requested so many times before, and learn spacetime figures, no one would be wasting all their time here trying to help you understand relativity theory. Think about it.

    Thank You,
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    Last edited by SinceYouAsked; 02-28-2014 at 10:04 PM.
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    Quote Originally Posted by cincirob to TFOLZO View Post
    It is also interesting that his (SYA's) only two claims now is that the (real) wheel (of relativistic rate) is impossible (yet he believes Gron's solution) and that I don't understand relativity.
    I suppose my many claims regarding you, could indeed be "summarized" by those 2 there. One of your better posts here.

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    OK, so let's summarize cincirob then ...

    For relativistic rates of rotation ...

    (1) believes the Gron analysis is incorrect, an incorrect application of the LTs to the rotating case.
    (2) believes the Gron analysis cannot support real material bodies, and as such assumes Gron's analysis in error.
    (3) believes the Gron analysis ignores the atomic (composed) velocities in the ground system, and thus cannot be correct.
    (4) believes the Gron analysis solns do not encompass the motion of rotation, since the LTs use only the translation velocity between ground and axle.
    (5) believes the rest length of rotating wheel chords needs determined in its non-inertial rotating frame to accurately predict its existence in the inertial ground system.
    (6) believes the Gron analysis and solns violate the Fitzgerald Length Contraction formula (LCF).

    None of these are correct, and each have been adequately addressed too many times to count. Relativity theory is not easy, and not everyone can understand it.

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    Quote Originally Posted by cincirob View Post
    JT: Okay, so you and I agree that "marbles guided by a static structure" result in the Gron solution. Do we also agree that Gron solution is not just an elliptical hula hoop, but on that ellipse are located marbles which are closer together at the top, and farther apart at the bottom? If so, you can't say that only the hula hoop itself is being transformed. Agreed?


    cinci: That is a separate operation from getting the shape. Getting these locations is simply figuring out how much time displacement there is between the axle and each spoke tip. To get the new location, you find out where the marble was in the hula hoop at the correct time and transform that point of the hula hoop. So no, you are not transforming the marbles, you’re transforming the hula hoop.
    **********************
    So when you said this...

    Quote Originally Posted by cincirob View Post
    cinci: 6. If you figure out where the MARBLES are located in the road observer's frame, I believe you will get locations identical to the Gron solution.
    **********************
    ...you were not talking about the MARBLES?

    Fine. Show us all how you would determine the location of the MARBLES in the road frame. Then we can all see for ourselves if your solution matches Gron's solution or not.


    Quote Originally Posted by cincirob View Post
    Cinci: The links don’t change the position of the marbles in the axle frame, but they do change it in the road frame. The links replace the hula hoop and act like a rolling wheel.
    **********************
    The LT's say that two sets of identical x,y,z,t,-v axle coordinates transform to two sets of identical x',y',z',t',v road coordinates. So what you say above is in contradiction to the LT's and therefore wrong in relativity theory. You are making up your own theory instead of using relativity.

    In other words, if the links don’t change the positions of the marbles in the axle frame, they do not change the positions of the marbles in the road frame either.
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    Cinci: You have to know that you’re transforming the hoop and not the marbles. You are transforming points on the hoop that are adjacent to points on the hoop. How do you know this? You use the relative velocity of the hoop to the road. You make no attempt to even determine the velocities of the marbles in the x-direction and you are using an x-direction LT.

    SYA: There is no need to consider the x-velocity of the marble, given one cares only to relate the atomic locations between the 2 inertial systems "over duration". The rotational rate (ω) of any marble, and its distance from the axis of rotation (R'), is all that's required to determine the marble's location in the inertial frame co-located with the center-of-rotation. Call that the axle frame, for short. So at any axle time t', one can determine the location of a moving marble in the axle system. That atom is co-located with a point in axle spacetime, call that "an event" (devoid of motion). If co-located in one system, then co-located in all systems. Using the translation velocity (v) between axle and ground, any specific coordinate in axle spacetime relates to a single corresponding coordinate in ground spacetime, via the LTs. No other velocity is required! We can therefore map the location of any and all marbles at any time t' of the axle system (and over duration), to its corresponding spacetime coordinate in the ground system. From the LT transformation solutions-set, one can easily determine the velocity of any marble at any time t in the ground system, however that is required "only if" one in fact does request it.

    Everything up to here is exactly what I've been telling you for some time now.


    SYA: Well, first, everyone knows that that is a lie. Second, if that were true, everyone here who has been correcting you repeatedly knows you would never have been asking your many questions that continually need correction. You are not fooling anyone. Remember, the thread here speaks for itself.

    Cinci: All of the above refers to the angular relocation of the spoke tips and curved spoke calculations and I have agreed with them.

    Nothing above refers to how you get the ellipse. And nothing I’ve ever read in relativity textbooks says I can just ignore relative velocities. In all your so-called answers to my questions, you have never once provided a reference that supports what you say. I’m not trying to fool anyone and you should stop trying.
    *************************


    SYA: It is not required to determine the shape of the wheel or it's spokes, in any ground instant of time, which was the scope of the Gron analysis as I understand it.

    Cinci: This is simply wrong.
    *****************


    SYA: Not wrong, however I would admit my choice of words was not the best in that particular sentence. First, one must map the points of the rotating disk in the axle system, then transformed them to the ground system. That's a goal. The reason that was the goal, is because that needs done before anything else may be deduced. From the transformed solns, one then may determine anything else desired wrt the ground POV, which may include the shape and size of the disk, the shape and size of its radial elements per ground, the velocity of any atom of the disk. The shape, size, speed, and direction of any disk atom is determinable in the ground system at any instant t, if so desired.

    Cinci: No reference, no dice. This doesn’t get the job done and it isn’t what Gron did.

    Here you refer only to single atoms but a wheel is not constructed of single unconnected atoms. He referred to the rim and he length contracted it using a single velocity. It’s long past time you should be purposely misrepresenting what Gron did.
    ******************************


    SYA: The Gron analysis only cared about mapping the location of moving disk atoms (or coordinates) in both systems.

    Cincirob: Then he should have described a model like the hula hoop and marbles instead of calling it a rolling wheel. This is more evidence that you no longer believe Gron's analysis describes a rolling wheel.


    SYA: Don't be silly.

    Cinci: I’m not. I let you take care of the silliness.
    ***************


    SYA: You loose even more credibility with statements such as these. And, anyone who actually does understand the Gron analysis, knows it applies to any steadily rotating body whatever, which of course would include your hula hoop.

    Cinci: Another proof that you just rant when you respond to me. The hula hoop isn’t rotating. Everybody does know that.
    *****************


    SYA: From that mapping, the shape of the wheel and spokes are of course determinable. Nor does not need to determine the rest length of any contiguous string of wheel atoms (or hoop contraption atoms) to determine their individual atomic locations in either axle or the ground system.

    [B]Cinci: Again, your ignorance of what I have been saying is boldly displayed; your only passion is to criticize.

    In regard rest length comments, please provide any reference independent of Gron that supports this claim.
    ******************{/B]

    [I]Cinci: Give it up. At least JT is sticking to his guns. You won't even deal with the issues.{/I]

    SYA: Every question you have ever posed in these threads, is answered by a glance at the 3-space Minkowski figure I posted here, just for you ...

    Cinci: Gron didn’t use a Minkowski diagram. It’s his analysis that I’m interested in. Stick to the problem.
    ***************


    SYA: see post ... Relativistically Rolling Wheel

    which is supported by these figure as well ... Relativistically Rolling Wheel

    I posted those geometric figures to help you, because you never understood the math.

    Cinci: Well here’s another critique instead of a scientific explanation. Sorry, can’t use non-unspecific critques and I can probably buy and sell you when it comes to math.
    ****************
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    Yada yada yada.

    As I've said cinci, some folks are simply not equipped to understand the relativity. I, KJW, Markus, and JTyesthatJT all agree that the Gron analysis is consistent with proper application of relativity theory to the rotating body as it exists in inertial systems. At some point, you need to consider that you are the one who falls short of understanding, and restudy the relativity to determine why you stand alone, lost in deep left field. Take some time, rethink what everyone has already told you. Remember, you're the fellow who thinks "a pivoting wheel pinned to the ground" better predicts the rolling wheel's shape (something no one else agrees with). That, in and of itself, shows that you do not yet understand relativity. No need to list all your other problems (which I did in the prior post). Take some time off, and study. It cannot hurt any.

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    Quote Originally Posted by SinceYouAsked View Post
    cinci ... determine why you stand alone, lost in deep left field.
    This^
    SinceYouAsked likes this.
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    SYA: Yada yada yada.

    Cinci: I agree. This like most of your posts are just ďyada yada yadaĒ.
    **********************


    SYA: As I've said cinci, some folks are simply not equipped to understand the relativity. I, KJW, Markus, and JTyesthatJT all agree that the Gron analysis is consistent with proper application of relativity theory to the rotating body as it exists in inertial systems.

    Cinci: And so do I, if the model he is analyzing is a static round structure with points moving around the structure. I have even done that analysis.

    The problem with it is a static structure is a poor model for a rolling wheel. Anybody with knowledge of relativity should see that.

    But we donít know what you really believe since you have lately been taking the position that the wheel is impossible.

    And you canít include KJW on your team just yet. He hasnít attempted the analysis and he has commented that based on my comments and other he doubts it.
    ********************


    SYA: At some point, you need to consider that you are the one who falls short of understanding, and restudy the relativity to determine why you stand alone, lost in deep left field.

    Cinci: Maybe left field is a good place. It was I who pointed out to you that Gronís analysis is exact for a non-rotating structure.

    Iíve also showed why I think the Gron analysis would not produce an ellipse if he did it according to the velocities of the elements of the wheel. If that is so obviously wrong and if you are so relativity savvy, why havenít you pointed out a single error in it?
    ****************************


    SYA: Take some time, rethink what everyone has already told you. Remember, you're the fellow who thinks "a pivoting wheel pinned to the ground" better predicts the rolling wheel's shape (something no one else agrees with). That, in and of itself, shows that you do not yet understand relativity. No need to list all your other problems (which I did in the prior post). Take some time off, and study. It cannot hurt any.

    Cinci: You never sound more phony than when you pontificate instead of commenting on science. It doesnít work on me so stop wasting your time. If you think it looks good to some audience who you think is hanging on your every word well then you have a problem that relativity canít solve.

    Your list of my ďproblemsĒ raises questions that you cannot answer. So they are your problems. I can find reference for everything I claimÖ.you have none.

    I havenít been discussing the pivoting wheel solution here but since you brought it up, it solves a problem with the Gron analysis that you never address. Because the contact point between a rack and pinion have no relative velocity, they should work at all speeds. The pivoting wheel analysis says they will.

    Your problem is that you claim one has to start in the axle frame and make physical changes to the wheel based on that frame only. The problem with this is that you are giving the axle frame a privileged status. Not a good idea in relativity.
    ****************************
    Last edited by cincirob; 03-02-2014 at 07:18 AM.
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    Alrighty then.

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    Below I provide a derivation of cincirob's favorite equation, the Length Contraction Formula (LCF). Please note that it assumes there is an inertial frame in which the object is stationary at all times. For the case of a chord on a rolling wheel, this condition is not met, because the chord does not remain stationary over time. In cases where this important condition is not met, the LCF only provides an approximation of the lengths involved. Sometimes the approximation might be sufficient, but other times it might be wildly inaccurate. Therein lies the problem with applying the LCF blindly to chords on a rolling wheel.

    ................

    In inertial reference frame K, let the coordinates x₁ and x₂ represent the locations of the endpoints of a projectile moving along the x axis. If the locations are measured simultaneously (t₁=t₂) then the length-contracted length of the projectile as measured in frame K would be:
    L = x₂ - x₁

    In another inertial reference frame K', where the projectile is stationary, the coordinates x₁' and x₂' represent the locations of the endpoints of the projectile at all times. This is important because transforming x₁ and x₂ to this frame can yield coordinates which represent different times in this frame. Only if the projectile is truly stationary in frame K' can we say that simultaneous measurements are not required to determine the proper length of the projectile, which in that case would be:
    Lₒ = x₂' - x₁'

    The Lorentz transform equations relate the spacial coordinates like this:
    x₁' = γ(x₁ - vt₁)
    x₂' = γ(x₂ - vt₂)

    Substituting the above Lorentz transform equations into (Lₒ = x₂' - x₁') yields:
    Lₒ = γ(x₂ - vt₂) - γ(x₁ - vt₁)

    Factoring out gamma yields:
    Lₒ = γ((x₂ - vt₂) - (x₁ - vt₁))

    Distributing yields:
    Lₒ = γ(x₂ - vt₂ - x₁ + vt₁)

    Substituting (t₁ = t₂) which represents simultaneous measurements in frame K yields:
    Lₒ = γ(x₂ - vt₁ - x₁ + vt₁)

    Combining terms yields:
    Lₒ = γ(x₂ - x₁)

    Substituting (L = x₂ - x₁) yields:
    Lₒ = γL

    Rearranging yields:
    L = Lₒ / γ

    Which is cinci's beloved Length Contraction Formula, the LCF, upon which he relies so heavily in his arguments. Food for thought, I'd say.
    Last edited by JTyesthatJT; 03-02-2014 at 08:29 AM.
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    Indeed, and another point worth mentioning which cincirob has clearly never understood to date, is ...

    Any point moving thru some inertial system is always momentarily co-located with some specific point of that system. Call that a co-location event. The LTs tell us where that co-location event exists in any other inertial system, no matter if the velocity between the 2 inertial systems is v=0, or not.

    What do you think the odds are that any of this will help? I don't see the need to make a career out of teaching cincirob relativity, although there is the entertainment factor. If cincirob comes to grips with it all, it'll be fascinating to see how he handles breaking the news to us.

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    Quote Originally Posted by SinceYouAsked View Post
    Indeed, and another point worth mentioning which cincirob has clearly never understood to date, is ...

    Any point moving thru some inertial system is always momentarily co-located with some specific point of that system. Call that a co-location event. The LTs tell us where that co-location event exists in any other inertial system, no matter if the velocity between the 2 inertial systems is v=0, or not.
    Yes, I believe cinci needs to forget about lengths, and start over with the concept of events. The reason he uses the LCF instead of the LT's is because he understand lengths, (in the classical sense at least), but he does not seem to understand events at all.


    Quote Originally Posted by SinceYouAsked View Post
    What do you think the odds are that any of this will help?
    At this point, I don't even have hope that anything I say will help cinci. Maybe what I post will be of interest to someone else, though.
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    Quote Originally Posted by JTyesthatJT View Post
    Yes, I believe cinci needs to forget about lengths, and start over with the concept of events. The reason he uses the LCF instead of the LT's is because he understand lengths, (in the classical sense at least), but he does not seem to understand events at all.
    Indeed. One other problem, is that cinci thinks 30 yr experience in mechanical engineering validates his opinions of the relativity.

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  62. #62  
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    Quote Originally Posted by SinceYouAsked View Post
    Indeed. One other problem, is that cinci thinks 30 yr experience in mechanical engineering validates his opinions of the relativity.
    Now, now.
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    JT: Below I provide a derivation of cincirob's favorite equation, the Length Contraction Formula (LCF). Please note that it assumes there is an inertial frame in which the object is at rest at all times.

    Cinci: Make up your own analysis, I don’t assume this at all. Never did.
    ******************************


    JT: For the case of a chord on a rotating wheel, this condition is not met. One can always find an inertial frame in which the endpoints of chord on a rotating wheel are instantaneously at rest, but that is never so over any duration of time.

    Cinci: Yes, and it’s that instant that I use. Just like your analysis.

    When you do your analysis, don’t you assume exactly the same instantaneous duration? Don’t you also select the tips of the spokes at one point in time? If not, then tell me what duration of time that one of the curved spokes is in the location that you plot for it.
    ************************************


    JT: In cases where that condition is not met, the LCF only provides an approximation of the lengths involved. Sometimes the approximation might be sufficient, but other times it might be wildly inaccurate.

    Cinci: What part of the analysis below tells you that it will sometimes be wildly inaccurate? And What part of it tells you that when you assume an instantaneous position you are accurate and I am not?
    ****************************


    JT: Therein lies the problem with applying the LCF blindly to chords on a rotating wheel.

    Cinci: This has been my point all along. You are blindly applying the length contraction formula to the chords of the wheel with no regard for its rest length, the distortions or reconstructions of it you assume, or its velocity. I would think leaving out those three pieces of information would lead to wildly inaccurate results.

    You just proved that applying the Lorentz transformation is identical to the length contraction formula. Of course you didn’t have to prove that, it’s in every textbook on relativity ever written. But now that you have proved it, how can you say you are doing something else in your analysis?
    ********************************
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    SYA: Indeed, and another point worth mentioning which cincirob has clearly never understood to date, is ...

    Any point moving thru some inertial system is always momentarily co-located with some specific point of that system. Call that a co-location event. The LTs tell us where that co-location event exists in any other inertial system, no matter if the velocity between the 2 inertial systems is v=0, or not.

    cinci: The key words here is "momentarily" and point. It's an object and just like ends of the pole in the pole-and-barn, you know they aren't collocated with the ends of the barn in any relatively moving frame.
    *****************


    SYA: What do you think the odds are that any of this will help? I don't see the need to make a career out of teaching cincirob relativity, although there is the entertainment factor. If cincirob comes to grips with it all, it'll be fascinating to see how he handles breaking the news to us.

    cinci: Apparently it hasn't helped you or JT. After proving that the LTs and length contraction formula are consistent with each other, you still don't get it.
    ************************


    SYA: Indeed. One other problem, is that cinci thinks 30 yr experience in mechanical engineering validates his opinions of the relativity.

    cinci: Not at all. But they do validate my descriptions of the mechanics of a rotating object where you seem to be clueless.

    I laid out what I've been saying in very simple terms recently and it is shown below. You have not rasied a single technical challenge to it. If it's all wrong, then teach me. Show me which steps are wrong an explain why. YOu need to stop talking about me ans start talking about the problem. If you can't, then you're just blowing smoke.

    OK, let’s put a chord on the hula hoop. And let’s agree that I can put a link between two points at the ends of this chord. I’m going to describe, with numbers the difference between a moving link joining two marbles and a chord of the hoop.

    Let’s pick the half chord of which is at the tip of a spoke that is 60 degrees from horizontal with a wheel radius of R = 1. V is the relative velocity of the road to the axle. Wheel velocity is .866.

    The x-direction length of the chord is L(hoop chord in axle frame) = Rcos60 = 1*.5 = .5

    The length of the superimposed link in the axle frame is the same: L(link in axle frame) = .5

    The velocity of L(hoop chord) relative to the axle frame is zero.

    The velocity of the link relative to the axle frame is:

    V(link rel to axle) = rw = Rsin60*v/R = 1*.866*.866/1 = .75

    The rest length of the link must be:

    L(link at rest) = L(link in axle frame)/(1 – (V(link rel to axle)^2)^.5 = .5/(1 - .75^2)^.5 = .756

    The relative velocity of the link to the road is:

    V(link rel to road) = (v + V(link to axle)/(1 + vV(link to axle) = (.866+.75)/(1 +.866*.75) = .976

    The length of the link in the road frame is:

    L(link in road) = L(link at rest)(1 - V(link rel to road)^2)^.5 = .756(1 - .976^2)^.5 = .174

    Back to the hoop chord. The length of the hoop chord in the road is

    L(chord in road) = L(hoop chord in axle frame)(1 – v^2)^.5 = .5(1 - .866^2)^.5 = .25

    So, the hoop will form an ellipse, the links will not.

    *********************
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    Quote Originally Posted by SYA View Post
    Indeed. One other problem, is that cinci thinks 30 yr experience in mechanical engineering validates his opinions of the relativity.

    Quote Originally Posted by cincirob View Post
    Not at all. But they do validate my descriptions of the mechanics of a rotating object where you seem to be clueless.
    One day, you are going to beg me for forgiveness, if you are lucky. OK then ...

    Quote Originally Posted by cincirob View Post
    I laid out what I've been saying in very simple terms recently and it is shown below. You have not rasied a single technical challenge to it. If it's all wrong, then teach me. Show me which steps are wrong an explain why. You need to stop talking about me ans start talking about the problem. If you can't, then you're just blowing smoke.

    OK, let’s put a chord on the hula hoop. And let’s agree that I can put a link between two points at the ends of this chord. I’m going to describe, with numbers the difference between a moving link joining two marbles and a chord of the hoop.

    Let’s pick the half chord of which is at the tip of a spoke that is 60 degrees from horizontal with a wheel radius of R = 1. V is the relative velocity of the road to the axle. Wheel velocity is .866.

    The x-direction length of the chord is L(hoop chord in axle frame) = Rcos60 = 1*.5 = .5

    The length of the superimposed link in the axle frame is the same: L(link in axle frame) = .5

    The velocity of L(hoop chord) relative to the axle frame is zero.

    The velocity of the link relative to the axle frame is:

    V(link rel to axle) = rw = Rsin60*v/R = 1*.866*.866/1 = .75

    The rest length of the link must be:

    L(link at rest) = L(link in axle frame)/(1 – (V(link rel to axle)^2)^.5 = .5/(1 - .75^2)^.5 = .756

    The relative velocity of the link to the road is:

    V(link rel to road) = (v + V(link to axle)/(1 + vV(link to axle) = (.866+.75)/(1 +.866*.75) = .976

    The length of the link in the road frame is:

    L(link in road) = L(link at rest)(1 - V(link rel to road)^2)^.5 = .756(1 - .976^2)^.5 = .174

    Back to the hoop chord. The length of the hoop chord in the road is

    L(chord in road) = L(hoop chord in axle frame)(1 – v^2)^.5 = .5(1 - .866^2)^.5 = .25

    So, the hoop will form an ellipse, the links will not.
    OK, so first, your L(link in road) = .174 should be 0.164, using your numbers. But it doesn't matter, because your V(link rel to road) = .976 was also wrong. It should be V(link rel to road) = .979 ... which results in L(link in road) = .151.

    Your hoop is stationary and non-rotating, so the x-component-length of that hoop-section is also always stationary per axle, so always inertial. As such, it indeed contracts from x' = 0.5 (axle) to x = 0.25 (ground) given v_trans = 0.866c.

    Here's your problem -> You mis-assume the length contraction formula (LCF) should work on the link even though your link rotates in the axle system. Sorry, but the LCF does not then apply in the way you hope it does.

    Your analysis here is fine for a link that does not rotate, because then the LCF could effectively apply. Only problem is, you defined your own scenario for a rotating link considered at an instant of axle time. It's ends connect 2 marbles that steadily rotate in the hoop, and as such your link always rotates with the marbles. That changes everything, although you have not yet understood that. As such, your L(link at rest) = .756 is flat wrong since your link does in fact rotate with the marbles, which in turn damages the rest of your analysis that uses that result.

    Before I ever consider the non-inertial rest length of a rotating link, you will first have to prove you understand relativity theory. I say that, because you have already proven you do not understand it. To do that, you must tell me that you are convinced that an entity may be transformed by the LTs from one inertial system in which it moves, to another inertial system in which it also moves. This is the easy part of relativity theory. Trying to determine the rest length of a non-inertial rotating link (or chord) is not half as easy. Before one learns calculus, they must first learn algebra I. You're gonna need to prove to me that you understand how to transform moving entity between inertial systems, before I'll consider determination of non-inertial rest lengths of rotating chords (which I can BTW).

    Given your style of dialog, and your history, I am convinced that you cannot be taught what you need to know, if your usual style of dialog ensues. I would have to figure out some other method of conveying it to you, whereby you do not have the opportunity to dilute and derail the dialog continually in your usual manner. Otherwise, this could go on for years here without success (already has, as some of us know). I'll think about it, decide if I wish to bother or not, and let you know when I'm good and ready. You will also have to learn Minkowski figures, and prove you understand them, for me to bother.

    Cheers,
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    SYA: OK, so first, you have a type-O. Your L(link in road) = .174 should be *0.164*.

    Cinci: Yes, thanks for finding the typo.
    **************


    SYA: Your hoop is stationary and non-rotating, so the x-component-length of that hoop-section is also always stationary per axle, so always inertial.

    As such, it indeed contracts from x' = 0.5 (axle) to x = 0.25 (ground) given v_trans = 0.866c.

    *Here's your problem ->* You mis-assume the length contraction formula (LCF) should work on the link even though your link rotates in the axle system. Sorry, but the LCF does not then apply in the way you hope it does.

    Your analysis here is fine for a link that does not rotate, because then the LCF could effectively apply. Only problem is, you defined your own scenario for a rotating link considered at an instant of axle time. It's ends connect 2 marbles that steadily rotate in the hoop, and as such your link always rotates with the marbles. That changes everything, although you have not yet understood that. As such, your L(link at rest) = .756 _is flat wrong_ since your link does in fact rotate with the marbles, which in turn damages the rest of your analysis that uses that result.

    Cinci: I’m surprised you think it’s a problem. In the Gron analysis a link exists between the tips of the two spokes defined in the problem and it is rotating. So if I can’t apply length contraction in this fashion, neither can he. The material in a wheel is not inertial and yet he applies the same transformation to it as you describe above for inertial link chord in the hoop.

    I breathlessly await your response.
    *********************


    SYA: Before I ever consider the non-inertial rest length of a rotating link, you will first have to prove you understand relativity theory. I say that, because you have already proven you do not understand it. To do that, you must tell me that you are convinced that a moving entity may be transformed by the LTs to another inertial system in which it also moves. This is the easy part of relativity theory. Trying to determine the rest length of a non-inertial rotating link (or chord) is not half as easy. Before one learns calculus, they must first learn algebra I. You're gonna need to prove to me that you understand how to transform moving entity between inertial systems, before I'll consider determination of non-inertial rest lengths of rotating chords (which I can BTW).

    Cinci: Well since you just proved you don’t understand that the wheel in Gron’s analysis is rotating, let’s wait until you figure that out.
    ***********************


    SYA: Given your style of dialog, and your history, I am convinced that you cannot be taught what you need to know, if your usual style of dialog ensues. I would have to figure out some other method of conveying it to you, whereby you do not have the opportunity to dilute and derail the dialog continually in your usual manner. Otherwise, this could go on for years here without success (already has, as some of us know). I'll think about it, decide if I wish to bother or not, and let you know when I'm good and ready. You will also have to learn Minkowski figures, and prove you understand them, for me to bother.

    Cinci: Why do you bother with this trash talk? Surely you know by now that I don’t pay any attention to it.

    And you couldn’t teach anybody anything with your approach. Good teaching requires listening to your student and ANSWERING QUESTIONS. Look how long it’s taken for you to even address what I’ve been saying. And, by the way, simply saying I can’t do it this way doesn’t mean anything. You have no reference for what you say. And now you have your foot firmly in your mouth.

    My whole point has been that you can’t transform a rotating wheel as Gron does it; and further, even if you could you need to consider more than he did.
    ***********************************
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    Quote Originally Posted by cincirob View Post
    Iím surprised you think itís a problem. In the Gron analysis a link exists between the tips of the two spokes defined in the problem and it is rotating. So if I canít apply length contraction in this fashion, neither can he. The material in a wheel is not inertial and yet he applies the same transformation to it as you describe above for inertial link chord in the hoop. I breathlessly await your response.
    Gron transformed spacetime coordinates of rotating radial elements per the axle frame.

    Quote Originally Posted by cincirob View Post
    And you couldnít teach anybody anything with your approach. Good teaching requires listening to your student and ANSWERING QUESTIONS.
    Good students listen to what is being taught, and reflect on it, until they get it. Each student requires their own time.

    Quote Originally Posted by cincirob View Post
    My whole point has been that you canít transform a rotating wheel as Gron does it; and further, even if you could you need to consider more than he did.
    Well, I transformed a rotating wheel like Gron did; and further, I considered no more than he did. If anything, I considered less than he did. Nonetheless, my ground solns matched his ground solns. I had the benefit of seeing JTyesthatJT's analysis first. KJW and Markus have done it, their way, and they seem to have attained the same solns as Gron. The only one here who doesn't get the same soln, is the guy who thinks a pivoting wheel pinned to the ground produces a better prediction for the rolling wheel's shape than Gron's analysis did. Gron considered a rolling wheel. If you do not realize why your idea is preposterous, then you should be studying instead of trying to determine a rotating chord's length in its own non-inertial POV. Have you boned up on Minkowski's model yet?

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    Quote Originally Posted by cincirob View Post
    JT: Below I provide a derivation of cincirob's favorite equation, the Length Contraction Formula (LCF). Please note that it assumes there is an inertial frame in which the object is at rest at all times.

    Cinci: Make up your own analysis, I don’t assume this at all. Never did.
    ******************************
    You seem to have missed the whole point of my derivation above in post #58. Anyone who uses this equation...
    L = Lₒ / γ
    ...is implicitly assuming that the object in question remains stationary in some inertial frame FOR ALL TIME. The equation relies on that condition being met.

    Here, let's try an example with your pear-shaped wheel. In the road frame, imagine there is a straight horizontal line drawn across your wheel somewhere up at the neck of the pear-shape. The endpoints of that length-contracted line are represented in the road frame by two x coordinates...
    x₁ and x₂
    ...measured at the same times in the road frame...
    t₁ = t₂
    ...and the length-contracted length of the line is represented like this:
    L = x₂ - x₁

    Since you believe you can use the length contraction equation, you believe the rest length of the line must be...
    Lₒ = γL

    But the two x coordinates transform to two different times in the inertial frame that you think is the "rest frame" of that line, as follows:
    t₁' = γ(t₁ - (vx₁ / c≤))
    t₂' = γ(t₂ - (vx₂ / c≤))
    There is nothing wrong with measuring the endpoints of a stationary line at two different times, but if the line is moving, you must measure them at the same time. Unfortunately for your model, the line is moving through the inertial frame that you have chosen to call its "rest frame". Objects are not supposed to move through their own rest frames.


    Quote Originally Posted by cincirob View Post
    JT: For the case of a chord on a rotating wheel, this condition is not met. One can always find an inertial frame in which the endpoints of chord on a rotating wheel are instantaneously at rest, but that is never so over any duration of time.

    Cinci: Yes, and it’s that instant that I use. Just like your analysis.
    ******************************
    The equation you use relies on the object being at rest in some inertial frame FOR ALL TIME. It is not sufficient to treat the object as if it is at rest, or to pretend that only one instant of time matters. There is a known time interval between the two measurements of its endpoints, and the object is known to move during that known time interval.


    Quote Originally Posted by cincirob View Post
    Cinci: When you do your analysis, don’t you assume exactly the same instantaneous duration? Don’t you also select the tips of the spokes at one point in time? If not, then tell me what duration of time that one of the curved spokes is in the location that you plot for it.
    ******************************
    I plot the points on the wheel as they exist in one instant of road-time, and those points transform back to the axle frame as a variety of DIFFERENT AXLE TIMES. Since they represent different axle times, I would not try to use those spacial coordinates to even approximate any physical lengths of lines drawn on the wheel, as measured in the axle frame. The wheel would be in different states of rotation at different axle times. Pure and simple.


    Quote Originally Posted by cincirob View Post
    JT: In cases where that condition is not met, the LCF only provides an approximation of the lengths involved. Sometimes the approximation might be sufficient, but other times it might be wildly inaccurate.

    Cinci: What part of the analysis below tells you that it will sometimes be wildly inaccurate? And What part of it tells you that when you assume an instantaneous position you are accurate and I am not?
    ******************************
    It is all explained above, and in my derivation post. In summary, the length contraction formula is derived from the LT's by stipulating that there is an inertial frame in which the object remains stationary AT ALL TIMES. This allows the rest length of the object to be determined by measuring its endpoints at two different times in its own frame. If the object moves between those two measurements which are taken at at two different times, then one gets an incorrect (or inaccurate) length. Since the chords and spokes are never at rest in any inertial frame for any duration of time, there is no hope at all that your method will produce accurate results.


    Quote Originally Posted by cincirob View Post
    JT: Therein lies the problem with applying the LCF blindly to chords on a rotating wheel.

    Cinci: This has been my point all along. You are blindly applying the length contraction formula to the chords of the wheel with no regard for its rest length, the distortions or reconstructions of it you assume, or its velocity. I would think leaving out those three pieces of information would lead to wildly inaccurate results.
    ********************************
    I do not use the Length Contraction Formula at all, and it is most certainly not the same thing as the LT's.


    Quote Originally Posted by cincirob View Post
    Cinci: You just proved that applying the Lorentz transformation is identical to the length contraction formula. Of course you didn’t have to prove that, it’s in every textbook on relativity ever written. But now that you have proved it, how can you say you are doing something else in your analysis?
    ********************************
    What I showed was that one can derive the LCF from the LT's by stipulating that there is an inertial frame in which the object remains stationary AT ALL TIMES. I showed there is a huge difference between the LCF and the LT's but somehow you conveniently missed the point.
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    Quote Originally Posted by JTyesthatJT to cinci View Post
    There is nothing wrong with measuring the endpoints of a stationary line at two different times, but if the line is moving, you must measure them at the same time. Unfortunately for your model, the line is moving through the inertial frame that you have chosen to call its "rest frame". Objects are not supposed to move through their own rest frames.
    ... that^

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    Dear members, cinci is having trouble trying to post a reply on this forum. He asked me to post it for him, which I have done here below. Everything in the quote is his own words.
    Quote Originally Posted by cincirob
    cinci: To SYA,

    Here is the bottom line to all your critiques: A barn could be imagined in the frame of the wheel and positioned so that it just overlays the chord in my analysis. A pole (as in the pole-and-barn problem) could moving so that it is super-imposed on the chord.

    The analysis I showed would be correct for the pole as viewed by the road observer. You confirmed such an analysis yourself earlier in the thread.

    Now you would have me believe that the rotation of the chord means that I no longer have to deal with the rest length of the chord or the velocity of the chord relative to the road; rotation magically makes all that go away. All I have to do is take the axle frame measurement and contract it by the velocity of the axle relative to the road.

    As for me, I donít believe the rotation has no effect and the analysis I did would only be an approximation. In fact I can point out why you canít really get the proper shape in the road frame this way.

    On the other side of the coin, I can explain exactly what your analysis is correct for and it doesnít include any account of rotating structure. So in the axle frame you believe that relativity considerations have all sorts of structural effects on the wheel; but, in the road these effects donít exist. Really?

    If you want to go with that, thatís your problem. But if you want me to believe it, you need a better explanation than simply repeating that I donít understand relativity like a mantra.
    *****************************
    So when you reply with praise/exultation/despair/frustration etc. to the quotation, please direct this to the author of the quote and not the 'umble messenger.

    TFOLZO
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    You reject a toothed wheel...
    Quote Originally Posted by SinceYouAsked View Post
    Thanx, but no thanx TFOLZO. A toothed wheel changes nothing. It does not make the scenario simpler, nor can it provide any deeper insight. In fact, it can only complicate it further. This discussion is about the misunderstandings cincirob has regarding the meaning of relativistic effects, not how to make an impossible wonder wheel (track, or contraption) a possible reality for relativistic rates.

    Thank You,
    SinceYouAsked
    ...but join in the even-more difficult & comic discussion of marbles distributed along the wheel 'hoop'. If a marble moves relative to the wheel frame it has its own reference frame, yet another complicating factor. I thought you would have preferred something you could get your teeth into - rather than a wonder wheel replete with rolling marbles. A toothed wheel provides a practical means of comparison on the wheel rim itself - as I suspect even cincirob would concur with!

    So do I detect instead the opportunistic spirit of the irrepressible buccaneer, SinceYeAsked?

    TFOLZO
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    Quote Originally Posted by TFOLZO View Post
    You reject a toothed wheel...
    ...but join in the even-more difficult & comic discussion of marbles distributed along the wheel 'hoop'. If a marble moves relative to the wheel frame it has its own reference frame, yet another complicating factor. I thought you would have preferred something you could get your teeth into - rather than a wonder wheel replete with rolling marbles. A toothed wheel provides a practical means of comparison on the wheel rim itself - as I suspect even cincirob would concur with!

    So do I detect instead the opportunistic spirit of the irrepressible buccaneer, SinceYeAsked?

    TFOLZO
    Hi TFOLZO,

    Theoretically, if all classical forces are wished away, a rack and pinion could work kinematically speaking, if the round wheel upholds Born rigidity while rotating at steady relativistic rotation rate and the teeth-and-slots are the same length at rest at contact. What I said, was that it would fail the roll up process.

    There's no need to consider rack and pinion, because the wheel analysis is simplest and all the very same things apply. The rim-atom and road atom must be uncontracted per each other at ground contact, for otherwise they are moving wrt each other and so the wheel effectively hydroplanes. No sense changing the scenario, if one does not yet understand the round wheel scenario.

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    SYA: There's no need to consider rack and pinion, because the wheel analysis is simplest and all the very same things apply. The rim-atom and road atom must be uncontracted per each other at ground contact, for otherwise they are moving wrt each other and so the wheel effectively hydroplanes. No sense changing the scenario, if one does not yet understand the round wheel scenario.

    cinci: It’s the same scenario. And there’s very good reason to look at it both ways: if you can’t look at it from the road frame and get a solution similar to the wheel frame approach, then your solution is in doubt. Interestingly, my proposed approximate solutions from the two frames look about the same. Do yours?
    *******************************
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    Quote Originally Posted by SYA View Post
    There's no need to consider rack and pinion, because the wheel analysis is simplest and all the very same things apply. The rim-atom and road atom must be uncontracted per each other at ground contact, for otherwise they are moving wrt each other and so the wheel effectively hydroplanes. No sense changing the scenario, if one does not yet understand the round wheel scenario.

    Quote Originally Posted by cincirob View Post
    It’s the same scenario. And there’s very good reason to look at it both ways: if you can’t look at it from the road frame and get a solution similar to the wheel frame approach, then your solution is in doubt. Interestingly, my proposed approximate solutions from the two frames look about the same. Do yours?
    If it's the same scenario, then there's no need to consider rack and pinion, because you do not understand the round wheel scenario yet. That's like the guy who cannot learn addition (2+2=4) "switching to subtraction to try and learn the addition" ( -(-2-2 ) = 4 ). Then, the guy advertises he discovered some new form of general mathematics, and that addition is wrong. Except, you are doing something more akin to this ... -(-2-2 ) = 5 .

    One can look at it from the road frame first. Here's the thing cincirob ... no relativistically rotating wheel can ever exist, and so we will never have a direct observation of it to know how the atoms of the wheel are distributed and move. As such, one must deduce how the wonder wheel exists, while whimsically assuming born rigidity is maintained, thereby wishing away classical forces that would deform the symmetrical wheel of steady relativistic rotation rate. Per the axle frame, there exists only rotation. Applying sound assumptions based upon classical mechanics and relativity, one can logically determine the location and velocity of any rotating wheel atom per the axle system. Then, one simply transforms to the ground, as Gron did. The wheel is found to possess dynamically curving radial elements, and varying atomic density distributions across it, per ground.

    You wish to start from the ground system, before ever understanding how Gron's analysis works. Your apriori assumption is that the relativistically rolling wheel exists in its original proper shape and size, so just as it did before roll-up. Yet, the ground POV doesn't see this, and instead sees a wheel contracted into a pear shape, because the wheel is considered "at any instant" as a pivioting wheel pinned to the ground. Now then, why do you make the assumption that a pivoting wheel models the rolling wheel, if considered in the instant? Simple, because at non relativistic (ie everyday classical) rates, the pivot-arc formula does produce the same atomic velocities as the rolling wheel atoms upon their cycloid paths, if considered in only the ground instant. IOWs, YOU GUESS that a relativistic roll rate should not change anything in that respect. Here's the thing ... Gron's analysis makes no guesses. It used rock solid classical and relativistic assumptions to determine the atomic locations and velocities in the axle system. Again ... no guessing was required.

    The Gron soln proves that YOUR GUESS is unsound. Add, you argue that GRON cannot transform wheel atoms from axle system to ground system, because they move in both systems. That's an ERROR on your behalf, which means you do not understand relativity theory. The LTs transform events of one system to events as they exist in another system that moves relatively. Events have no length or duration, as they are 0-dimensional points in spacetime. They DO NOT CARE whether the EVENT inputted represents a stationary body versus a moving body. One is as good as the other. If spacetime input-coordinates represent a moving body, then the multiple sets of coordinates plot it to travel across space over duration. If the spacetime input-coordinates represent a stationary body, then multiple sets of coordinates plot it to travel thru time alone. The LTs could care less, as they transform whatever 0-dimensional coordinates that are inputted. An event HERE in the axle system, IS the same event THERE in the ground system, plain and simple as per the LTs.

    My opinion is, you need to understand how the Gron analysis works first, then discuss hypotheses of your own that differ.

    Thank You,
    SinceYouAsked
    Last edited by SinceYouAsked; 03-05-2014 at 11:49 PM.
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    cinci: It’s the same scenario. And there’s very good reason to look at it both ways: if you can’t look at it from the road frame and get a solution similar to the wheel frame approach, then your solution is in doubt. Interestingly, my proposed approximate solutions from the two frames look about the same. Do yours?

    SYA: If it's the same scenario, then there's no need to consider rack and pinion, because you do not understand the round wheel scenario yet. That's like the guy who cannot learn addition (2+2=4) "switching to subtraction to try and learn the addition" ( -(-2-2 ) = 4 ). Then, the guy advertises he discovered some new form of general mathematics.

    cinci: The question here isn’t about what I know, it’s about what you know. Apparently you’re still struggling with basic arithmetic.
    *********************************


    SYA: One can look at it from the road frame first. Only problem is, that is much more difficult than starting from the axle frame. You would have us believe that the relativistically rolling wheel may be considered in the classical sense (per ground), or maybe even considered as a pivoting wheel pinned to the ground.

    cinci: I look at it the same way you look at the rim of the wheel which you assume is pivoting around the axle. When is a pivot not a pivot? When you’re stuck for an answer?
    ***************************


    SYA: That's a complete and utter guess on your part. The Gron analysis starts from the axle frame for obvious reasons, ie the symmetry allows for clear deduction as to where and when any wheel atom is at any one axle time t'. Transforming to the ground frame produces the result Gron obtained, with dynamically curving radial elements, and a wheel that has varying atomic density distributions across it. Your approach, requires that you GUESS how the radial elements and atomic distributions exist across the wheel per ground, and there's no solid foundation upon which your premises are rooted.

    cinci: I suppose you could describe what I do this way. But I also suppose that it’s better than ignoring all the atomic density distributions and varying velocities as you do. Please don’t embarrass yourself by claiming you do consider them.
    *****************************


    SYA: You must either assume the rolling wheel exists as it does classically at non-relativistic rates, or that a pivoting wheel better defined the rolling wheel's shape per ground than a rolling wheel does ...

    cinci: I don’t assume it exists classically, you do; you assume it’s a non-rotating shape.
    ******************


    SYA: …….the former is unsubstantiated and actually proven unacceptable by the Gron analysis, the latter being preposterous per the accepted theory of relativity.

    cicni: Nobody has been able to prove the pivoting wheel doesn’t represent the rolling wheel. Ceratainly Gron didn’t prove it by ignoring the detailed velocities of the wheel.
    ****************************


    SYA: It does not surprise me that your proposed approximate solutions from the two frames look about the same, given you think a pivoting wheel better predicts the shape of a rolling wheel than a rolling wheel does, for relativistic roll rate.

    cinci: It shouldn’t be a surprise because it makes sense that the relativistic effects in the road would be greater above the axle than below it. Why don’t you tell us why they look the same in your analysis? Or just tell us in a general way what a road based analysis would look like and why.
    ******************************


    SYA: Gron starts from the axle frame, because the symmetry allows for reasonable and sound deductions of the relativistically rotating wheel.

    cinci: But there’s nothing symmetrical about it in the road frame based on velocities relative to the road, is there?
    *****************************


    SYA: The same deductions cannot be made from the ground POV with any assuredness. Since no relativistically rolling wheel can exist to make direct observations as to how it exists per ground, we must make sound assumptions based on known classical mechanics and relativity. Gron did that. You do not.

    cinci: They why are you summarily unable to answer any of the questions above? Why do all your answers end up being ad hominem attacks instead of science?
    **********************
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    Alrighty then,

    Thank You,
    SinceYouAsked
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    You sly sneaky sea-dog SinceYeAsked!
    Quote Originally Posted by SinceYouAsked View Post
    Hi TFOLZO,

    Theoretically, if all classical forces are wished away, a rack and pinion could work kinematically speaking, if the round wheel upholds Born rigidity while rotating at steady relativistic rotation rate and the teeth-and-slots are the same length at rest at contact. What I said, was that it would fail the roll up process.

    There's no need to consider rack and pinion, because the wheel analysis is simplest and all the very same things apply. The rim-atom and road atom must be uncontracted per each other at ground contact, for otherwise they are moving wrt each other and so the wheel effectively hydroplanes. No sense changing the scenario, if one does not yet understand the round wheel scenario.

    Thank You,
    SinceYouAsked
    You leave the readers all at sea when considering an alternative!

    I did not consider a rack and pinion scenario. I considered ONLY gear teeth on the wheel. You are the one who slyly inserts racks and rack-teeth!

    There are no rack-teeth on the ground, no teeth for the gear teeth to grip onto on the ground. In this way the gear teeth thickness becomes a surrogate measure of length contraction!

    Then again, as a sea-dog I guess you have little experience of landlubbery things like wheels - and I have never heard of a rack carried aboard a sailing ship to torment the miscreant sailors. Usually Schrodinger's cat-o'-nine-tails and Lorentzian keelhauling are enough to keep all of 'em in line!

    So SYA, ye better keep the Crow's Nest posted on the lookout for a sub - a substandard torpedo from the cincirobian U-boat!

    TFOLZO
    Last edited by TFOLZO; 03-06-2014 at 06:59 AM. Reason: Explanatory sentences added
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    Maybe this will all make sense for you guys, if we consider teeth and slots with 64 sides each, like octagons upon octagons?

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    Quote Originally Posted by SinceYouAsked View Post
    Maybe this will all make sense for you guys, if we consider teeth and slots with 64 sides each, like octagons upon octagons?
    LOL, I'm sure that will help clear up all the confusion.
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    Hey cincirob, I'm glad to see you are able to post again. I'd like to go back to your marble contraption, if that's okay with you. While the marbles are moving through the hula hoop, you add the links at speed, so that they are length-contracted to the correct size to span each pair of adjacent marbles. After you remove the hula hoop, you can imagine each link touching the road and being instantaneously at rest with it. Therefore, in the road frame, as each link comes in contact with the road, each link would be its own rest length.

    If you wanted to calculate the roll-out distance in the road frame, you could add up all of the rest lengths of all of the links which come in contact with the road. Thus, by your own model, for the case of an axle speed of v=0.866c, gamma=2, your wheel should roll out approximately 2*2piR per rotation, as measured in the road frame. I can't imagine why you would not agree with that, considering that I am being careful to use your own methodology. But if you do disagree, I'd like to discuss why. Thanks.
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    Quote Originally Posted by cincirob View Post
    Itís the same scenario. And thereís very good reason to look at it both ways: if you canít look at it from the road frame and get a solution similar to the wheel frame approach, then your solution is in doubt. Interestingly, my proposed approximate solutions from the two frames look about the same. Do yours?[/I]

    Quote Originally Posted by SYA View Post
    If it's the same scenario, then there's no need to consider rack and pinion, because you do not understand the round wheel scenario yet. That's like the guy who cannot learn addition (2+2=4) "switching to subtraction to try and learn the addition" ( -(-2-2 ) = 4 ). Then, the guy advertises he discovered some new form of general mathematics. Except, you are doing something more akin to this ... -(-2-2 ) = 5 .

    Quote Originally Posted by cincirob View Post
    The question here isnít about what I know, itís about what you know. Apparently youíre still struggling with basic arithmetic.
    You were a mechanical engineer for 30 years, did you say?

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    cinci: I never said I disagreed with it in the Gron analysis. But look at what you’re doing. You use the composed velocity of zero at the contact point and the rest length of the chord. 180 degrees away you use the contracted length of the chord and the velocity of the wheel. Why don’t you use the composed velocity and the rest length in both places?

    In fact, if you do what Gron does, you would take the contracted length, contract it again, and get piR for the roll out. In the wheel frame it makes perfect sense to get 2*2piR because the road is contracted and the circumference isn't. But if you transform the shape the way he does you get contradictions.

    The trouble with the site comes and goes.
    *****************************
    Last edited by cincirob; 03-07-2014 at 03:06 AM. Reason: Added second paragraph
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    To SYA,

    You haven't answered any of the questions from my last post to you. It doesn't take 30 years of experience to know you're lost. I direct my comments to the issues and you play with nonsense arithmetic to avoid answering questions.

    I don't know what you do for a living, but engineers are expected to give answers. This thread is filled with my answers and your obvious dodges.
    **************************
    Last edited by cincirob; 03-07-2014 at 03:11 AM.
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    Quote Originally Posted by cincirob View Post
    cinci: I never said I disagreed with it in the Gron analysis. But look at what you’re doing. You use the composed velocity of zero at the contact point and the rest length of the chord. 180 degrees away you use the contracted length of the chord and the velocity of the wheel. Why don’t you use the composed velocity and the rest length in both places?
    *****************************
    I don't normally use any composed velocities or rest lengths -- not at the contact point or any other point. I just did that to show you that your own methodology is telling you that the wheel should roll out 2*2piR in the road frame. Normally I just use the LT's and the relative velocity between the axle and the road. I can apply the LT's and v to ANY point on the wheel and still demonstrate that the wheel should roll out 2*2piR in the road frame. I've already shown you examples using the highest point on the wheel, and also the right-most point on the wheel. If you'd like, I can show you again using any wheel point you choose.

    So the real question should be, "Why did cincirob claim for years that the wheel would roll out 2piR in the road frame?" The answer is because you were modeling the wheel as pivoting at the contact point. The rim on that type of "wheel" would not have to be built at speed. That model deceived you into thinking the rest lengths of the chords would be the same as if they were built when the wheel was at rest, rather than built when the wheel was rotating at speed. Now you have two different approaches to choose from. Do you choose the built-at-speed model, or the built-at-rest model?
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    SYA: Theoretically, if all classical forces are wished away, a rack and pinion could work kinematically speaking, if the round wheel upholds Born rigidity while rotating at steady relativistic rotation rate and the teeth-and-slots are the same length at rest at contact. What I said, was that it would fail the roll up process.

    cinci: Dead wrong. You hold the rest dimensions for the rotating wheel in the wheel frame and the rack is contracted in that frame. They will not mesh correctly.

    And now you're making my argument about no relative velocity at the contact point? :-)

    Next you're going to tell me I should solve the problem in the road frame assuming a pivot.
    ****************************
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    Quote Originally Posted by SYA View Post
    Theoretically, if all classical forces are wished away, a rack and pinion could work kinematically speaking, if the round wheel upholds Born rigidity while rotating at steady relativistic rotation rate and the teeth-and-slots are the same length at rest at contact. What I said, was that it would fail the roll up process.

    Quote Originally Posted by cincirob View Post
    Dead wrong. You hold the rest dimensions for the rotating wheel in the wheel frame and the rack is contracted in that frame. They will not mesh correctly. And now you're making my argument about no relative velocity at the contact point? :-)
    Sorry, but what you say makes no sense. Again, the rack and pinion cannot work unless the slots and the teeth are of the same length (say L) when at relative rest with one another, when at contact. If the ground holds the teeth and slots at some length L upon contact, then the axle holds them both at length L/gamma upon contact. This is really not that complicated. Why you have so much difficulty with it, is hard to figure.

    Quote Originally Posted by cincirob View Post
    Next you're going to tell me I should solve the problem in the road frame assuming a pivot.
    Nah, that would be silly. The wheel rolls down the road, by definition.

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    Quote Originally Posted by cincirob View Post
    To SYA,

    You haven't answered any of the questions from my last post to you. It doesn't take 30 years of experience to know you're lost. I direct my comments to the issues and you play with nonsense arithmetic to avoid answering questions.

    I don't know what you do for a living, but engineers are expected to give answers. This thread is filled with my answers and your obvious dodges.
    I've worked with many engineers, some really bad, some excellent. If you ever learn spacetime diagrams, your revelations will come from a glance at the 3 figures posted in this post ...

    Relativistically Rolling Wheel

    I recommend you study spacetime diagrams, while you studying SR. Alas, you are not likely to be wise enough take on that desperately needed challenge.

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    Sorry, but what you say makes no sense. Again, the rack and pinion cannot work unless the slots and the teeth are of the same length (say L) when at relative rest with one another, when at contact. If the ground holds the teeth and slots at some length L upon contact, then the axle holds them both at length L/gamma upon contact. This is really not that complicated. Why you have so much difficulty with it, is hard to figure.

    cinci: It probably doesn’t make any sense to you since it now becomes obvious that you don’t understand Gron’s analysis. If the teeth still fit, then the wheel would roll out 2piR instaed of 2*2piR at v = .866. Tell him JT.
    ******************************
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    JT: I don't normally use the composed velocity or the rest length at all. I just did that to show you that your own methodology is telling you that the wheel should roll out 2*2piR in the road frame.

    Cinci: I already knew that. But you only knew it because in the wheel frame the road contracts. Now you know my method gets the same answer by analyzing it in the road frame. If you use Gron’s method of contracting the wheel frame chord using v you will get the wrong answer. What I’ve been telling you for some time now is that Gron’s analysis is inconsistent between frames. You just proved that my method isn’t. My method shows the ellipse is wrong.
    ********************************


    JT: Normally I just use the LT's and the relative velocity between the axle and the road. I can apply that methodology to any point on the wheel and still demonstrate that the wheel should roll out 2*2piR in the road frame. I've already shown you examples using the highest point on the wheel, and also the right-most point on the wheel. If you'd like, I can show you again using any wheel point you choose.

    cinci: What I’d like you to do is show what a chord looks like at some other point of the wheel using the method that you now agree works for the roll out.
    *************************


    JT: So the real question should be, "Why did cincirob claim for years that the wheel would roll out 2piR in the road frame?" The answer is because you were modeling the wheel as pivoting at the contact point, and the rim on that type of "wheel" would not have to be built at speed.

    inci: I never claimed that the Gron analysis didn’t roll out 2*2piR. I do claim that a realistic model wouldn’t roll out 2*2piR because there is no relative velocity at the contact point.
    ****************************


    JT: That model deceived you into thinking the rest lengths of the chords would be the same as if they were built when the wheel was at rest, rather than built when the wheel was rotating at speed. Now you have two different approaches to choose from. Do you choose the built-at-speed model, or the built-at-rest model?

    cinci: The question now isn’t about some other model, it’s about Gron’s. His model should tell you the same roll out in both frames, but it doesn’t. This is one of the conflicts in his analysis.

    I don’t have to make any choice here, you do. You have to decide whether you’re going to stick with the ellipse model that gives the wrong roll out if you analyze it in the road frame.
    **************************
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    Quote Originally Posted by SYA View Post
    Sorry, but what you say makes no sense. Again, the rack and pinion cannot work unless the slots and the teeth are of the same length (say L) when at relative rest with one another, when at contact. If the ground holds the teeth and slots at some length L upon contact, then the axle holds them both at length L/gamma upon contact. This is really not that complicated. Why you have so much difficulty with it, is hard to figure.

    Quote Originally Posted by cincirob View Post
    It probably doesnít make any sense to you since it now becomes obvious that you donít understand Gronís analysis.
    I've never seen anyone so willing to embarass himself repeatedly in public, as you do!

    Quote Originally Posted by cincirob View Post
    If the teeth still fit, then the wheel would roll out 2piR instead of 2*2piR at v = .866. Tell him JT.
    Just curious, are you asking me or telling me here?

    Don't be silly. Gron's disk "already exists at speed". If his wonder disk was instead a wonder rack and pinion, he could easily assume the teeth fit the rack's slots flushly upon contact. No matter what type of wheel it is, including rack and pinion, it must roll out gamma*2piR over a full rotation, if no hydroplaning or slippage. In Gron's analysis, there is no wonderous roll-up period of his wonder disk.

    Anything else?

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    SYA: Sorry, but what you say makes no sense. Again, the rack and pinion cannot work unless the slots and the teeth are of the same length (say L) when at relative rest with one another, when at contact. If the ground holds the teeth and slots at some length L upon contact, then the axle holds them both at length L/gamma upon contact. This is really not that complicated. Why you have so much difficulty with it, is hard to figure.

    cinci: It probably doesn’t make any sense to you since it now becomes obvious that you don’t understand Gron’s analysis.

    SYA: I've never seen anyone so willing to embarass himself repeatedly in public, as you do!

    [i]cinci: If the teeth still fit, then the wheel would roll out 2piR instead of 2*2piR at v = .866. Tell him JT.

    SYA: Just curious, are you asking me or telling me here?

    cinci: Why would I ask you? You obviously don’t know.
    ***************************


    SYA: Don't be silly.

    cinci: I’m watching you do that.
    ************************


    SYA: Gron's disk "already exists at speed". If his wonder disk was instead a wonder rack and pinion, he could easily assume the teeth fit the rack's slots flushly upon contact.

    cinci: You still don’t get it. It’s not a matter of “fitting” them, you need more teeth.
    *****************************


    SYA: No matter what type of wheel it is, including rack and pinion, it must roll out gamma*2piR over a full rotation, if no hydroplaning or slippage. In Gron's analysis, there is no wonderous roll-up period of his wonder disk.

    cinci: Yes, we all agree to gamma*2piR. But Gron does talk about roll-up and points out that the spokes don’t contract. This is why physicists say the wheel must be built at speed. But nobody except you thinks they are building more teeth.
    *******************************


    SYA: Anything else?

    cinci: No, you have your foot far enough in your mouth to suit me.
    *********************************
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    If the axle observer records the rotating pinion's circumference at 2piR, then the ground observer must record it to roll out a linear length of gamma*2piR. Whether the wonder-pinion teeth fit flush into the wonder-rack slots upon contact, depends only on the relativistic wonder-scenario definition. Gron's wonder-scenario assumed a wonder-disk that simply existed at speed in the Born rigid state. There's no law of nature that says a wonder-rack cannot have enough slots to accommodate a wonder-pinion, for repeated consecutive circumferential roll-outs. There's no law of nature that says a wonder-scenario cannot define a pinion with a desired number of teeth, let alone wonder-rack slots of identical length when at contact. A wonder is a wonder is a wonder. It's a wonder that cincirob has so much difficulty with relativistic effects.

    Now, you need to first learn to understand the round wheel (or disk), before tackling other things you do not understand.

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    SYA: If the axle observer records the rotating pinion's circumference at 2piR, then the ground observer must record it to roll out a linear length of gamma*2piR.

    cinci: Yes, we’ve all known that for long time now. I’m happy that you’ve caught up.
    *******************


    SYA: Whether the wonder-pinion teeth fit flush into the wonder-rack slots upon contact, depends only on the relativistic wonder-scenario definition. Gron's wonder-scenario assumed a wonder-disk that simply existed at speed in the Born rigid state. There's no law of nature that says a wonder-rack cannot have enough slots to accommodate a wonder-pinion. A wonder is a wonder is a wonder. It's a wonder that cincirob has so much difficulty with relativistic effects.

    cinci: Obviously the problem the rest of us see is that a working rack and pinion accelerated up to relativistic speeds would not work in the Gron analysis because the teeth would not fit at speed. Now you can pretend that we were discussing something else but that’s just you covering your tracks.

    And, you still haven’t answered my questions so why don’t you stop wasting space on this thread?
    ****************************
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    Cincirob,

    All your questions have been answered too may times to count now. You just don't understand it, so that's that as they say. You really should try a little harder, and argue much less. No reputable relativist here agrees with anything you say. Your pear wheel should really be in an alternatives thread. I once asked you to bring your complaints of Gron, and your pear hypothesis, to a reputable forum ... and we find here that neither Markus or KJW agree with you either. You might try PhysicsForums and ScienceChatForum next, but I can guarantee that you'll find the same results there. No one agrees with your assertions. At some point, you need to realize you need more time studying and less time arguing, just to be polite about it here.

    So next, I fully expect you to come back and state "more strenuously" that none of your questions have been answered. Keep saying it, and eventually TFOLZO might come to agree with you.

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    SinceYouAsked
    Last edited by SinceYouAsked; 03-08-2014 at 09:52 AM.
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    SYA: All your questions have been answered too many times to count now. You just don't understand it, so that's that as they say. You really should try a little harder, and argue much less. No reputable relativist here agrees with anything you say. Your pear wheel should really be in an alternatives thread. I once asked you to bring your complaints of Gron, and your pear theory, to a reputable forum ... and we find here that neither Markus or KJW agree with you either. You might try PhysicsForums and ScienceChatForum next, but I can guarantee you'll find the same result. No one agrees with your assertions. At some point, you need to realize you need more time studying and less time arguing, just to be polite about it here.

    cinci: You mentioned my 30 (actually 40+) year career as an engineer. In that time I dealt with many design ideas from other people and in many cases had to dissuade them for various reasons. I know how that is done; one has to give valid reasons for ones arguments. And I know you haven’t come close to that. Simply saying my ideas are bad or claiming I don’t understand relativity doesn’t cut it. Those are only your opinions. Claiming rotation makes Gron’s analysis correct with no real explanation of how doesn’t cut it either. You wouldn’t last 2 weeks in the jobs I’ve held with your attitude and approach. You are a phony.

    Right now JT has proved that my suggested approach to Gron’s analysis is consistent with the Gamma*2piR result for roll out by calculating it in the road frame and getting the same answer in the wheel frame. Gron’s doesn’t. You didn’t even understand the rack and pinion problem and won’t admit it. Copping out by claiming you were describing some other problem is a bad joke.

    Your message above is like 95% of your messages to me, a waste of space, containing not a single technical idea. As far as being polite is concerned, you have called me a liar on this thread. You’re the last person who should bring up politeness.
    ***********************************
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    Quote Originally Posted by cincirob View Post
    You mentioned my 30 (actually 40+) year career as an engineer. In that time I dealt with many design ideas from other people and in many cases had to dissuade them for various reasons. I know how that is done; one has to give valid reasons for ones arguments. And I know you haven’t come close to that. Simply saying my ideas are bad or claiming I don’t understand relativity doesn’t cut it. Those are only your opinions. Claiming rotation makes Gron’s analysis correct with no real explanation of how doesn’t cut it either. You wouldn’t last 2 weeks in the jobs I’ve held with your attitude and approach. You are a phony.
    OK, so on the one hand we have cincirob claiming he walked on water as an ME. On the other hand, we have cincirob unable to understand how relativity applies to numerous things, the Gron analysis being just one. Makes one wonder whether you ever saw water, let alone walked on it.

    You are wrong that a POV induces stresses unto a rotating body.
    You are wrong that Gron's analysis does not require a gamma*2piR rollout for a single rotation, per ground.
    You are wrong that a body cannot be transformed by the LTs to a target inertial frame, unless it is at rest in the reference frame.
    You are wrong that Gron guesses a rolling disk should attain the shape of a purely translating disk.
    You are wrong that a pivoting wheel pinned to the ground can better predict the shape of a wheel rolling down the road.
    You are wrong that your inertial rod and your rotating wheel-chord are equivalent, even if considered in the instant per axle.
    Yet, you assert you walked on water as a great ME.

    Quote Originally Posted by cincirob View Post
    Right now JT has proved that my suggested approach to Gron’s analysis is consistent with the Gamma*2piR result for roll out by calculating it in the road frame and getting the same answer in the wheel frame. Gron’s doesn’t.
    Tell you what. Let's see what JTyesthatJT has to say about your assertion here. Then, we'll know. Gron's analysis is consistent with relativity contrary to your belief, so I serious doubt JT will agree that Gron fails, being JT understands relativity.

    Quote Originally Posted by cincirob View Post
    Your message above is like 95% of your messages to me, a waste of space, containing not a single technical idea. As far as being polite is concerned, you have called me a liar on this thread. You’re the last person who should bring up politeness.
    100% of everyone's posts "to help you", have been a waste of time, thus far. And, folks have given much of their time. My primary goal, was to ensure you did not corrupt innocent passers-by with ill-equipped understanding.

    I'm just wondering how long it will be before you ever come to realize how embarrassed you should really be right now? No offense.

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    Quote Originally Posted by cincirob to JT View Post
    The question now isnít about some other model, itís about Gronís. His model should tell you the same roll out in both frames, but it doesnít. This is one of the conflicts in his analysis.
    How many weeks do you plan to argue this particular misunderstanding of yours?

    Quote Originally Posted by cincirob to JT View Post
    I donít have to make any choice here, you do. You have to decide whether youíre going to stick with the ellipse model that gives the wrong roll out if you analyze it in the road frame.
    Well, I was just wondering how long we are all going to have to endure this? I choose Gron's analysis which gives the roll-out distance per relativity theory, thank you.

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    SYA: OK, so on the one hand we have cincirob claiming he walked on water as an ME. On the other hand, we have cincirob unable to understand how relativity applies to numerous things, the Gron analysis being just one. Makes one wonder wonder whether you ever saw water, let alone walked on it.

    You are wrong that a POV induces stresses unto a rotating body.
    You are wrong that Gron's analysis does not require a gamma*2piR rollout for a single rotation, per ground.

    cinci: Wrong. I have always agreed that this is the case for Gron and reiterated a couple of days ago to JT when he showed that my proposal for transformation agrees with it.
    *********************************


    SYA: You are wrong that a body cannot be transformed by the LTs to a target inertial frame, unless it is at rest in the reference frame.

    cinci: I’m willing to learn. Do the pole and barn pole in a third frame and show me.
    ********************************


    SYA: You are wrong that Gron guesses a rolling disk should attain the shape of a purely translating disk.

    cinci: Never said this. He gets it with length contraction.
    *************************


    SYA: You are wrong that a pivoting wheel pinned to the ground can better predict the shape of a wheel rolling down the road.

    cinci: Maybe, but you can’t explain why.
    *****************************


    SYA: You are wrong that your inertial rod and your rotating wheel-chord are equivalent, even if considered in the instant per axle.

    cinci: Maybe, but again, you haven’t explained why.
    **********************


    SYA: You are wrong on just about everything imaginable.

    cinci: Well you do say I’m wrong about things you only imagined I said; for instance, Gron’s roll out. Are you still angry because I called you out on your mistake on the rack and pinion?
    **************************************


    Yet, you assert you walked on water as a great ME.

    cinci: Thanks for proving that all you have done is [I]say[I] I’m wrong. I didn’t say I walked on water as an ME. I said I knew how to give rational explanations to people with different ideas. You just proved….again….that you don’t.
    *******************************


    [I]cinci: Right now JT has proved that my suggested approach to Gron’s analysis is consistent with the Gamma*2piR result for roll out by calculating it in the road frame and getting the same answer in the wheel frame. Gron’s doesn’t.[I]

    SYA: Tell you what. Let's see what JTyesthatJT has to say about your assertion here. Then, we'll know. Gron's analysis is consistent with relativity, contrary to your belief.

    cinci: Maybe, but if he does disagree, he will have an explanation.
    ***********************************
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    Quote Originally Posted by cincirob View Post
    Cinci: If you use Gron’s method of contracting the wheel frame chord using v you will get the wrong answer.
    ********************************
    Gron's method is NOT to length-contract the axle-frame chord using v and then say that is how far the wheel will roll in the road frame. His method is to apply the LT's to points anywhere on the wheel using v. That is how the LT's work, you should try them some time. Gron gets the correct answer for the gamma*2piR roll out using the LT's and v.


    Quote Originally Posted by cincirob View Post
    Cinci: What I’d like you to do is show what a chord looks like at some other point of the wheel using the method that you now agree works for the roll out.
    *************************
    I do agree that using your methodology gives us the correct roll-out. However, I do not agree that your method gives you the right shape of the chord. Your method says that if the chord is a straight horizontal line in the axle frames, then it is also a straight horizontal line in the road frame. Your method also says that the chord fits inside the circular fender in the axle frame, but that same chord is too long to fit inside the elliptical fender in the road frame. That is just plain wrong. Your methodology does not tell you that the chord curves in the road frame so that it does fit inside the elliptical fender. You can find the missing curvature by applying ROS at the end of your process, (a step you have done in the past, but often forget to apply). Or you can find the curvature by simply using the LT's and v in the first place.

    I only used your method to get you to see that your own model is telling you that the wheel rolls out gamma*2piR in the road frame. That is something you were missing all this time because you thought you could build the rim of the wheel at rest, and then pivot it around a point on the road. Once you began starting with the marble contraption, you were effectively starting in the axle frame, and that is where you saw for yourself that the the rim should be built at speed, not at rest.


    Quote Originally Posted by cincirob View Post
    JT: So the real question should be, "Why did cincirob claim for years that the wheel would roll out 2piR in the road frame?" The answer is because you were modeling the wheel as pivoting at the contact point, and the rim on that type of "wheel" would not have to be built at speed.

    cinci: I never claimed that the Gron analysis didn’t roll out 2*2piR. I do claim that a realistic model wouldn’t roll out 2*2piR because there is no relative velocity at the contact point.
    ****************************
    We are talking about your marble contraption, not Gron's model. You said your marble contraption was a realistic model for the wheel, because after you connected the marbles with links, and removed the hula hoop, it correctly modeled a rolling wheel. That is the wheel that you now agree rolls out gamma*2piR in the road frame, because each link can be imagined to be instantaneously at rest with the road, one after another. So, I suggest you discard your edge-pinned-disk model now, since it contradicts your newer marble-contraption model.
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    Quote Originally Posted by SYA View Post
    OK, so on the one hand we have cincirob claiming he walked on water as an ME. On the other hand, we have cincirob unable to understand how relativity applies to numerous things, the Gron analysis being just one. Makes one wonder wonder whether you ever saw water, let alone walked on it.

    You are wrong that Gron's analysis does not require a gamma*2piR rollout for a single rotation, per ground.

    Quote Originally Posted by cincirob View Post
    Wrong. I have always agreed that this is the case for Gron and reiterated a couple of days ago to JT when he showed that my proposal for transformation agrees with it.
    Well, you said this ...

    cinci: Right now JT has proved that my suggested approach to Gronís analysis is consistent with the Gamma*2piR result for roll out by calculating it in the road frame and getting the same answer in the wheel frame. Gronís doesnít.

    So the big mystery is as to what cincirob really means in the highlight above?

    Starting from the axle frame, Gron's analysis predicts the ground observer must record the roll-out as gamma*2piR, even though a stationary tape measure at rest with the axle records the rotating rim at 2piR. So when you say "Gron's doesn't", what on earth do you mean?

    Quote Originally Posted by SYA View Post
    You are wrong that a body cannot be transformed by the LTs to a target inertial frame, unless it is at rest in the reference frame.

    Quote Originally Posted by cincirob View Post
    Iím willing to learn. Do the pole and barn pole in a third frame and show me.
    At this venture, one could run every analysis under the sun, and derive OEMB step by step for you. Draw pictures, and connect all the dots. You will continue to disagree and argue, for years to come. Your ink is already on the paper. The question is, how many more scenarios will you demand after you disagree with the barn and pole scenario?

    Quote Originally Posted by SYA View Post
    You are wrong that Gron guesses a rolling disk should attain the shape of a purely translating disk.

    Quote Originally Posted by cincirob View Post
    Never said this. He gets it with length contraction.
    I'll restate, just for you then ...

    You are wrong that Gron guesses a rolling disk should attain the shape of a purely translating disk, "per the length contraction formula".

    Quote Originally Posted by SYA View Post
    You are wrong that a pivoting wheel pinned to the ground can better predict the shape of a wheel rolling down the road.

    Quote Originally Posted by cincirob View Post
    Maybe, but you canít explain why.
    This figure explained why ... http://i.imgur.com/qA7zrPk.png which was posted long long ago.

    The rolling wheel rotates "in the same volume of space", as it travels thru time upward. BTW, a non-rotating wheel would do the same, which should clue you in on a few things. At any rate, your pivoting wheel, would circle about a pin pinned fixed to the ground, and thus would travel (per axle) in a full circle about the pin as it travels up the time axis. It does not take genius to determine the shape of the wheel (per ground) differs in those 2 cases, because the shape of the wheel is defined by the intersection of the slanted x,y plane at t=0 upon the world-tube of the wheel in axle spacetime. You are going to have to take a little initiative on your own to grasp that concept.

    Quote Originally Posted by SYA View Post
    You are wrong that your inertial rod and your rotating wheel-chord are equivalent, even if considered in the instant per axle.

    Quote Originally Posted by cincirob View Post
    Maybe, but again, you havenít explained why.
    The atoms of your horizontal chord differ in the size per axle, because the atoms of each of the 2 cases move at different velocities. They have to, because in one case they are rotating, and they other case they are not and only translating. That "rotation", makes a difference contrary to your long lasting belief.

    Quote Originally Posted by SYA View Post
    You are wrong on just about everything imaginable.

    Quote Originally Posted by cincirob View Post
    Well you do say Iím wrong about things you only imagined I said; for instance, Gronís roll out. Are you still angry because I called you out on your mistake on the rack and pinion?
    You have not understood anything anyone has told you to date, so why should you understand what I said about rack and pinion. That would be nothing short of a miracle. The relativists here understand me, but you do not. Do the math.

    Quote Originally Posted by SYA View Post
    Yet, you assert you walked on water as a great ME.

    Quote Originally Posted by cincirob View Post
    Thanks for proving that all you have done is [I]say[I] Iím wrong. I didnít say I walked on water as an ME. I said I knew how to give rational explanations to people with different ideas. You just provedÖ.againÖ.that you donít.
    Nothing you have said to date here is rational, because it's all been incorrect, far as relativity theory goes. Everyone has explained it all to you repeatedly again and again. Then, you say no one answers your questions. An infinite circle. Remember, you're the only one here who is in disagreement, and if you think that's because you are special (in a good way), you are mistaken.

    Quote Originally Posted by cincirob View Post
    Right now JT has proved that my suggested approach to Gronís analysis is consistent with the Gamma*2piR result for roll out by calculating it in the road frame and getting the same answer in the wheel frame. Gronís doesnít.

    Quote Originally Posted by SYA View Post
    Tell you what. Let's see what JTyesthatJT has to say about your assertion here. Then, we'll know. Gron's analysis is consistent with relativity, contrary to your belief.

    Quote Originally Posted by cincirob View Post
    Maybe, but if he does disagree, he will have an explanation.
    JT has already explained this to you 50 times, and already made his statement on the matter in this forum to boot. He is not going to explain it any differently than he already had the last 50 times. Why should you "all of a sudden understand"? Unlike to ever happen. Afterwards, you'll repeat that no one answers your questions.

    Thank You,
    SinceYouAsked
    Reply With Quote  
     

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