# Thread: Relativistic Rolling Wheel II

1. Originally Posted by cincirob
cinci: And what you say isn't even "the conventional wisdom". None of the major textbooks give this analysis.
But all relativity textbooks tell you how the coordinates of events transform from one frame to another, and they all agree it is done with the LT equations. There is nothing unconventional about that at all. And if you read your textbook carefully, you will see that it does not say that the events must be stationary in either of the frames. The reason is because it makes no sense to even talk about whether events are stationary or moving. Events only last for one instant of time, by definition!!!

Furthermore, if it is an appeal to authority that you would like, then consider this graphic and excerpt from the University of Colorado at Boulder:

This is what a cartwheel looks like moving at 87% of the speed of light. The cartwheel appears Lorentz contracted by a factor of 2 along the direction of motion.

The bottom of the cartwheel, where it touches the road, is not moving, and is not Lorentz contracted. You might think that the top of the cartwheel would have to move faster than the speed of light to overtake the axle moving at 87% of the speed of light; but of course it can't.

The cartwheel offers another example of the impossibility of completely rigid bodies in special relativity. In the frame of reference of someone riding on the axle (but not rotating), the rim is whizzing around and is Lorentz contracted, while the spokes are moving transversely, and are not contracted. Something must give: the rim must stretch, or the spokes compress.

Note that the above is exactly the same solution as Gron's.

Originally Posted by cincirob
cinci: And if you look through the literature, you will find people who disagree with Gron.
Some scholars might might disagree about exactly how to resolve the Ehrenfest paradox, but I bet none of them think the shape of the wheel in the road frame should be a pear shape. If you can find even one, I will be very impressed at your searching skills. However, I will also laugh at that particular scholar for being wrong.

2. Originally Posted by cincirob
You have no logic for accepting his ellipse. If the wheel weren't rotating, you would contract it per (1 - (v/c)^2)^.5. If it is rotating you say it's correct to contract it per (1 - (v/c)^2)^.5. Where's the logic?
The logic is in the Lorentz Transformations. Learn how to use Lorentz Tranformations properly. And more specifically moving objects in axle frame transforming to road frame. But after what we went through in all those previous posts I'm afraid you might be too stupid to ever understand it.
The Lorentz Transformations for a rotating wheel per axle give you an ellips shape with curved spokes in road frame. The tip of the spokes are on an ellips shape.
You gonna now tell me the spokes have nothing to do with the shape of the wheel, and blabla blabla. The more you repeat it, the more you confirm you know nothing about Lorentz transformations. Nada.
Spacetime diagrams would help you a lot but you are not interested in learning. You think because Gron doesn't need spacetime diagrams you don't need them either. The problem is that you are not that clever as Gron. Worse, you think you are more intelligent than Gron. Big joke.

3. Yes, as has been said many times already, the wheel is round in the axle POV "by definition". The scenario requires Born rigidity be maintained at relativistic rotation rate, something which Gron and every other great physicist knows to be an impossible situation. No matter, it's a thought experiment for the sake of exploring the relativistic effects at relativistic rotation rates, a kinematic scenario.

If the wheel occupies a round volume of space in the axle system, then it occupies a 1/gamma contracted elliptical volume of space per ground, per the LTs. It doesn't matter if the wheel rotates or not, nor does it matter how fast it rotates (if rolling w/o slippage is not a req't), so long as the translation rate between ground and axle is a inertial v of relativistic rate.

Thank You,

4. In post #1195 I was left wondering who was the other piano player in Who Framed Roger Rabbit?
Originally Posted by Jilan
Including the effects of time dilation I am thinking that the wheel will get rotated in the road frame, like this.
http://s18.postimg.org/3uyhs6o6h/image.jpg
I am sure you guys can come up with better graphs. Apologies again if it's upside down!
So I much appreciate, Jilan, that you've revealed yourself at last to step in on cinci's side here - since I consider 'tear drop' and 'pearshape' to be much the same thing, at least when "battling the Ellipsoids" like SYA, VD, JTydJT etc.

TFOLZO

5. Battling the Ellipsoids-I like it!

6. Originally Posted by VeeDee
The logic is in the Lorentz Transformations. Learn how to use Lorentz Tranformations properly. And more specifically moving objects in axle frame transforming to road frame. But after what we went through in all those previous posts I'm afraid you might be too stupid to ever understand it.
The Lorentz Transformations for a rotating wheel per axle give you an ellips shape with curved spokes in road frame. The tip of the spokes are on an ellips shape.
You gonna now tell me the spokes have nothing to do with the shape of the wheel, and blabla blabla. The more you repeat it, the more you confirm you know nothing about Lorentz transformations. Nada.
Spacetime diagrams would help you a lot but you are not interested in learning. You think because Gron doesn't need spacetime diagrams you don't need them either. The problem is that you are not that clever as Gron. Worse, you think you are more intelligent than Gron. Big joke.

Cinci,
You don't like Gron's ellips because you think it cannot be an ellips, because his gamma factor in the Lorentz Transformations 'only deal with the translation velocity', and therefore doesn't not take care of the rotation.
The reason his gamma factor does not have to deal with it is because we take the wheel per axle as it is per axle. And transform the shrunken and ROTATING circular wheel from there.
We are allowed to do that.
JT showed you how this procedure DOES give CORRECT results by showing how it works for a moving pole per axle. (see page 8 from post #735 onwards, and for any questions you might have, I bet JT will be glad to explain it once more). We take the contracted pole in the axle frame, MOVING per axle, and transform to road, obtaining correct result i.e. same result as contracting directly from rest frame to road by means of the gamma contraction with addition of velocities.

Are you now going to tell us -for JT's pole exercice- his calcs are wrong because he "only uses the velocity between axle and road" ? Do you? You should know you are wrong because by using "only the velocity between axle and road" he obtains the CORRECT final contraction.

The problem is that you are totally incapable of understanding one line of what is been written about the LorentzTransformation for transforming moving objects per axle.
All you did is dreaming up your own little scenario of 'transforming' the rolling wheel, but you never understood Einstein relativity, Gron, SYA, JT or my posts. Not a word of it.

7. I think it would help if cincirob looked at some all-inertial scenarios, instead of going round and round with the rotation scenario. He should prove to himself that all events transform from one frame to another according to the LT, regardless of whether the objects that created those events are moving or not.

For example, he agreed that the stationary firecracker popping at axle frame coordinates x'=0.500, y'=0.866, t'=0.000 transformed to road frame coordinates of x=1.000, y=0.866, t=0.866. He should test that with a moving firecracker. Say we add a firecracker to the right endpoint of the pole which was moving through the axle frame at 0.750c. If the moving firecracker pops at the same axle frame coordinates as the stationary firecracker, x'=0.500, y'=0.866, t'=0.000 does the moving firecracker popping event also transform to the road as x=1.000, y=0.866, t=0.866 or does it transform to a different place or time?

He should ask himself it if even makes sense that two firecrackers could pop in the same place in the axle frame, but pop in different places in the road frame. What would be the implications of that in terms of burn marks and contradictions? He should do the math as many different ways as he can think of, then think through the implications of the results. Which methods produce contradictions, and which do not? Does it make any sense to put 0.750c or 0.979c into the LT equations if the coordinates of x', y', z', and t' are all axle frame coordinates? Can the same answers be obtained using pole frame coordinates? Think it all through. Then he might be better equipped to consider the rolling wheel.

8. Originally Posted by JTyesthatJT
I think it would help if cincirob looked at some all-inertial scenarios, instead of going round and round with the rotation scenario. He should prove to himself that all events transform from one frame to another according to the LT, regardless of whether the objects that created those events are moving or not.

For example, he agreed that the stationary firecracker popping at axle frame coordinates x'=0.500, y'=0.866, t'=0.000 transformed to road frame coordinates of x=1.000, y=0.866, t=0.866. He should test that with a moving firecracker. Say we add a firecracker to the right endpoint of the pole which was moving through the axle frame at 0.750c. If the moving firecracker pops at the same axle frame coordinates as the stationary firecracker, x'=0.500, y'=0.866, t'=0.000 does the moving firecracker popping event also transform to the road as x=1.000, y=0.866, t=0.866 or does it transform to a different place or time?

He should ask himself it if even makes sense that two firecrackers could pop in the same place in the axle frame, but pop in different places in the road frame. What would be the implications of that in terms of burn marks and contradictions? He should do the math as many different ways as he can think of, then think through the implications of the results. Which methods produce contradictions, and which do not? Does it make any sense to put 0.750c or 0.979c into the LT equations if the coordinates of x', y', z', and t' are all axle frame coordinates? Can the same answers be obtained using pole frame coordinates? Think it all through. Then he might be better equipped to consider the rolling wheel.
You are 100% correct.
I thought he would have gone through that exercise, but it's obvious he is not interested in doing that at all. Cinci is only interested in what he thinks has to be correct: his own scenario. And he is so obsessed with it he cannot read the Lorentz Transformations the way he should. He is so obsesses he prefers seeing virual points moving on a non-rotating wheel, instead of considering real events of a rotating wheel. He doesn't want to understand it because Gron doesn't use the word "event" in his page. And thus Cinci thinks he doen't need to know what an event is. Same story for the spacetime diagrams. No wonder he ends up interpreting the Lorentz Transformations his own way.

9. Cincirob's marble race scenario, of radius R

For a steady rotation rate per axle, if the marbles are always abutted without relative movement as the circular ring of marbles rotates (welded together would be the same), then Gron's ground solns for particles at the disk perimeter (radius R per axle) are identical to Gron solns for cincirob's marble race. We might assume each wonder marble is the same size and shape as a perimeter particle.

I agree with the latest post of JT and VeeDee, and I too have said it many times before. Cincirob needs to learn more basic relativity, and must focus on the simplest all-inertial scenarios to have any chance ...

(1) first ... he needs to understand the difference between locations in 3-space, versus locations in spacetime (ie events), and one great way to do that is to explain the center of an expanding lightsphere wrt it's emission event (POE) per those who move relatively (both at the POE event, one carrying the emitter).

(2) secondly ... he needs to learn how simultaneous events defining a stationary (say) spheroid in its own proper frame, maps into a system that moves relatively as an asynchronous elongated ellipsoid. In doing so, he'll come to learn the meaning of time-dilation in conjunction with length-contraction, and he'll come to better understand the relativistic effect of time desynchronization. The spheroid is the very best analysis for this, because considerations of light traveling along axes orthogonal to the direction of the motion is also important to consider.

(3) thirdly ... he needs to run the calculation (using in part the LTs) to explain how a body exists in either of 2 systems when said body moves through both systems.

If Cincirob does these things, and learns them, he'll have no further questions or complains regarding the Gron analysis.

Thank You,

10. Those are excellent suggestions, SYA. Awhile back, I remember thinking that if cincirob had to transform some light ray events, he would see the usefulness of doing things with the full LT equations. After all, there is no rest frame for light, so cincirob's "rest frame method" fails immediately for light.

But as VeeDee said, cincirob is probably not interested in doing any of the things we suggested.

11. I know. If cincirob was going to study these things, he'd have done so many years ago when we first encouraged him to do so. But then, we've always hung out for the entertainment value anyways, so. I wonder what Thomas is up to these days? Same old same old, you figure? He was a great example of Ignorance is Bliss.

Thank You,

12. VeeDee: But all relativity textbooks tell you how the coordinates of events transform from one frame to another, and they all agree it is done with the LT equations. There is nothing unconventional about that at all. And if you read your textbook carefully, you will see that it does not say that the events must be stationary in either of the frames. The reason is because it makes no sense to even talk about whether events are stationary or moving.

cinci: True for events, but when you deal with objects, you have to be careful about when events occur. Measuring the length of an object requires locating the ends of it at the same instant. That's why the barn width transforms to a different length than the pole when measured in a third frame.

VeeDee: Furthermore, if it is an appeal to authority that you would like, then consider this graphic and excerpt from the University of Colorado at Boulder:

cinci: I'd prefer somebody like John Wheeler of Rindler. I don't know who did the Boulder thing.

Calling me stupid doesn't answer this question: If the wheel weren't rotating, you would contract it per (1 - (v/c)^2)^.5. If it is rotating you say it's correct to contract it per (1 - (v/c)^2)^.5. Where's the logic?

The Lorentz transformations deal with relative motions. These two situations don't have the same relative motions. If you can take the rotational motions and get the same answer as the non-rotating, then you have an answer.

13. Originally Posted by cincirob
Calling me stupid doesn't answer this question: If the wheel weren't rotating, you would contract it per (1 - (v/c)^2)^.5. If it is rotating you say it's correct to contract it per (1 - (v/c)^2)^.5. Where's the logic?

The Lorentz transformations deal with relative motions. These two situations don't have the same relative motions. If you can take the rotational motions and get the same answer as the non-rotating, then you have an answer.
In other words you didn't -and don't- understand one word of my post #1206
Relativistic Rolling Wheel II

As expected.

14. Originally Posted by cincirob
JT: But all relativity textbooks tell you how the coordinates of events transform from one frame to another, and they all agree it is done with the LT equations. There is nothing unconventional about that at all. And if you read your textbook carefully, you will see that it does not say that the events must be stationary in either of the frames. The reason is because it makes no sense to even talk about whether events are stationary or moving.

cinci: True for events, but when you deal with objects, you have to be careful about when events occur. Measuring the length of an object requires locating the ends of it at the same instant. That's why the barn width transforms to a different length than the pole when measured in a third frame.
Of course we always have to be careful about where and when events occur. But whenever a known point on the wheel is co-located with a known point in the axle frame, that is an event. For the case of a uniformly rotating circular wheel, we can easily know where and when every point on the wheel will be co-located with known points in the axle frame. So we have an infinite number of events to choose from. All we have to do is find which ones transform to a single time in the road frame, for example t=0.000, and we have the wheel's shape in the road frame. There is nothing unconventional about this, it is simply transforming events. And the end result tells you the geometry of the wheel, so you don't have to worry about any lengths.

15. Cinci, Do you appreciate that a uniform rate of rotation in the axis FOR does not lead to a uniform rate of rotation in the road frame because of time dilation?

16. JT: Of course we always have to be careful about where and when events occur. But whenever a known point on the wheel is co-located with a known point in the axle frame, that is an event. For the case of a uniformly rotating circular wheel, we can easily know where and when every point on the wheel will be co-located with known points in the axle frame. So we have an infinite number of events to choose from. All we have to do is find which ones transform to a single time in the road frame, for example t=0.000, and we have the wheel's shape in the road frame. There is nothing unconventional about this, it is simply transforming events. And the end result tells you the geometry of the wheel, so you don't have to worry about any lengths.

cinci: What you do with a rim point is not consistent with what you do for a coincident pole. If you take a point in the axle frame, let's make it more concrete, if the axle is attached to a car, and you take the coincident point on the car, then there's no question what you do in either case to find that point in the road frame. You can do the pole as I have shown and you can do the point on the car by simple length contraction. It works in the pole case because I find a frame where I know the location of both ends of the pole at time = zero (t" = 0) in that frame. In the case of the car, I know the locations of both coincident points on the car at t = 0. Now you have two coincident points on the wheel. They aren't in either frame and their locations are not know at an identical time at both ends.

Let's look at three cases.

1. A pole moving relative to the axle frame and coincident with a chord. One way to transform it to the road is to find its rest frame (x",y",t") where you measure the location of its end points where both end points are at t" = 0. Then you transform it to the road using its combined velocity.

2. Let's put the axle on a car so that its a concrete object. There is a length on the car that is coincident with the same chord as above. You know where its end locations are at t' = 0 [axle frame (x',y',t')]. You find the road position by length contraction where the relative velocity is v.

3. Now deal with the chord. You say it's identical to case 2. Maybe you're right. I say prove it by starting with the velocities and contractions of the wheel and show you get the same answer. At the moment, it's nothing but an assumption.

Don't bother telling me anybody answered this. Don't bother telling me I don't understand relativity.

And don't bother telling me it's RoS. Here's what RoS tells you: the tip of the 60 degree chord shows up in the road frame as it was a short time earlier when it was at 72.7 degrees.

So skip repeating a calculation I can now do in my sleep. Just assume the chord I'm talking about in 1,2 and 3 is the 72.7 degree chord.

17. cincirob,

We don't have to prove that the LT's transform events correctly, using nothing but the relative frame velocity v=0.866 in the LT. That is very well known to everyone who understands SR properly. If you don't think events transform this way, then you need to study your relativity text book. Read the section on the LT's and what they do.

Attach a firecracker to the rim of the wheel, and when that firecracker is located at any particular axle frame coordinates, (x',y',z',t') let the firecracker pop. That is a real event, and it leaves a burn mark on the rim of the wheel. Apply the LT to those coordinates, using nothing but v=0.866, and you will know where that same event happens in road frame coordinates. From this we know that all rim events transform via the LT to points on the ellipse. The center of the wheel is always located at x=vt, so we know where the center of the wheel is at all times in the road frame. You can transform any rim event, compare it to the location of the center of the wheel, and verify that the rim event is on the ellipse.

18. And, if you are worried that the firecracker attached to the wheel is moving through the axle frame, then let it be a stationary firecracker in the axle frame. It makes no difference.

19. Cincirob,

No matter how many more times you re-ask the very same old questions, it will never change the answers already provided you repeated for so very long.

Again, if you wish to have help running this analysis from the proper frame of Gron's non-inertial rotating born rigid disk, you will have to first prove you have mastered the fundamentals of relativity we have already pointed out as your deficiencies. There's no harm in that. I mean, you have spent over a decade confused about the meaning of Gron's solns, so what's a couple of months of learning basic SR going to hurt? You've been thru higher education before, so you should realize the importance of that. I'm just saying,

Thank You,

20. Someone should start a new thread for the rotating frame of the wheel. I've got lot's of ideas...

21. VeeDee: In other words you didn't -and don't- understand one word of my post #1206
Relativistic Rolling Wheel II

As expected.

cinci: No, it means you don't understand that the question has nothing to do with post #1206. As usual.

22. JT: We don't have to prove that the LT's transform events correctly, using nothing but the relative frame velocity v=0.866 in the LT. That is very well known to everyone who understands SR properly. If you don't think events transform this way, then you need to study your relativity text book. Read the section on the LT's and what they do.

cinci: All you've proved lately is that you can ignore questions. Here's another you can ignore: Have you proved that the firecracker isn't just moving around a non-rotating disk?

Since I know you won't answer it, allow me. No.

23. Originally Posted by cincirob
cinci: All you've proved lately is that you can ignore questions. Here's another you can ignore: Have you proved that the firecracker isn't just moving around a non-rotating disk?

Since I know you won't answer it, allow me. No.
All I can do is show you that the location and velocity of each firecracker is always identical to a corresponding atom of the rotating disk.

If you think that the firecrackers are flying around in circles on their own, then why don't you prove that they are doing just that?

If you think you can ask me for such absurd proofs, then I can ask them of you also.

So, prove there is no rotating disk. LOL!!!!!

24. JT: All I can do is show you that the location and velocity of each firecracker is always identical to a corresponding atom of the rotating disk.

If you think that the firecrackers are flying around in circles on their own, then why don't you prove that they are doing just that?

cinci: I already did it a couple of years ago.

If you want to show the disk is doing it you need forces. If you think your model is doing that...........................

JT: If you think you can ask me for such absurd proofs, then I can ask them of you also.

So, prove there is no rotating disk. LOL!!!!!

cinci: You have to prove there is one.

25. cinci: I think I've gotten all I'm going to get here so I won't post on this thread again. Amuse yourselves now. Smoke 'em if you've got 'em.

26. And so it was written !

Thank You,

27. Originally Posted by cincirob
And don't bother telling me it's RoS. Here's what RoS tells you: the tip of the 60 degree chord shows up in the road frame as it was a short time earlier when it was at 72.7 degrees.

So skip repeating a calculation I can now do in my sleep. Just assume the chord I'm talking about in 1,2 and 3 is the 72.7 degree chord.[/B]
1/
What you probably mean is (see sketches): the tip of the red 60 degree spoke at axle time t'=0 (my B4 event) is not in the road frame t=0, but the spoke tip of that red spoke when it was was at 72,7 degrees in the axle frame t'= -0.256 (my B3 event) is in the road frame t=0.

We all know that.
But what YOU probably don't know is the 72.7 spoke tip (y'=0.955) in axle frame is in the road frame at .... t=0 y=0.955, x=0.148 !
By the way: Lorentz Tranformations give y=y'.

By the way: Somebody understanding relativity would never say something like:<<the tip of the 60 degree chord shows up in the road frame as it was a short time earlier when it was at 72.7 degrees. >>,
because the 60 degree chord of spoke tip does NOT show up in the road t=0.
It took us weeks to sort out what you meant by "the tip of the 60 degree chord shows up", even when I told you you have to be more specific when you deal with your 'points'. Unfortunately you are the kind of guy that doesn't give a shit about communicating properly.

2/
The spoke tip in ROAD frame t=0 at y=.866 is the axle frame 60 degrees spoke tip (see C2 on sketch below). That blue C2 spoke tip in axle frame is in road frame t=0, at y=.866 x=.25
Why? Lorentz transformations.

Unfortunately there is no hope left you will ever understand anything of all this.

If you don't agree with this, and we know you don't, show us your Lorentz Transformation of chord/spoke tip 72.7 degrees in axle frame t'=-0.256 to road frame. That cannot be any problem for somebody that -quote- "can do the calcs in his sleep".

t=?
x=?
y=?

28. Nice explanation, VeeDee. But cincirob will just complain that no one ever answered his question(s), so he does not have to deal with any of this anymore... lol...

29. Originally Posted by JTyesthatJT
Nice explanation, VeeDee. But cincirob will just complain that no one ever answered his question(s), so he does not have to deal with any of this anymore... lol...
Sigh, it's his way.

Thank You,

30. Originally Posted by JTyesthatJT
Nice explanation, VeeDee. But cincirob will just complain that no one ever answered his question(s), so he does not have to deal with any of this anymore... lol...
The problem he doesn't deal with anything.
Hopeless

31. You guys seem a bit lost lost now.....end of an era?

32. Originally Posted by Jilan
You guys seem a bit lost lost now.....end of an era?
It's a long story, with eerie similarities to that of Herbert Dingle. Both cincirob and Dingle considered themselves experts on Special Relativity (SR), even though they both had some serious misunderstandings about how the theory actually works in practice. Another thing they both had in common was that they rarely (if ever) accepted corrections from others who pointed out their mistakes. One main difference between them is that cincirob always believed SR was a good theory, whereas Dingle campaigned against it for nearly two decades. Amazingly, cincirob kept the faith in SR even though his mistaken version of it predicted physically impossible contradictions.

In Dingle's time, there were no internet forums, so his rants were in the form of letters published in science magazines. Knowledgeable scientists would then publish letters explaining Dingle’s errors to him in excruciating detail. Just as with cincirob, Dingle was not affected in the least by these corrections. I don't know if it was their ego, or their stubbornness, or what prevented them from realising and correcting their errors. At times it was almost as if these guys believed they were incapable of making mistakes, and that it would be a waste of time for them to carefully consider the corrections given to them.

If cincirob wants to retire from this thread, and keep his misunderstandings uncorrected, that is fine with me. I can't speak for the others here, but to me they seem fine with it as well. As the saying goes, "You can lead a horse to water, but you cannot make it drink."

33. Originally Posted by Jilan
You guys seem a bit lost lost now.....end of an era?
It's not the end, it's not the beginning of the end, it's the end of the beginning

Thank You,

34. Originally Posted by JTyesthatJT
It's a long story, with eerie similarities to that of Herbert Dingle. Both cincirob and Dingle considered themselves experts on Special Relativity (SR), even though they both had some serious misunderstandings about how the theory actually works in practice. Another thing they both had in common was that they rarely (if ever) accepted corrections from others who pointed out their mistakes. One main difference between them is that cincirob always believed SR was a good theory, whereas Dingle campaigned against it for nearly two decades. Amazingly, cincirob kept the faith in SR even though his mistaken version of it predicted physically impossible contradictions.
And then there was Thomas, lest we forget he

Trivia ... you know where the term "dingbat" came from?

Thank You,

And then there was Thomas, lest we forget he
OMG, Thomas... He and I were talking about SR and he refused to get past square one with the Lorentz transforms. Considering he was an anti-relativist I changed the subject to the Galilean transforms, and to my surprise, he refused to get past square one with those as well!! There's just no pleasing some folks. Sheesh...

Trivia ... you know where the term "dingbat" came from?
First time I heard it was when Archie called Edith that in the sitcom, "All in the Family." Where is it really from?

36. Originally Posted by JTyesthatJT
First time I heard it was when Archie called Edith that in the sitcom, "All in the Family." Where is it really from?
That may be it's origin? I'm not sure. Wiki only defines it as a typesetting character or spacer for printing.

Thank You,

That may be it's origin? I'm not sure. Wiki only defines it as a typesetting character or spacer for printing.
Oh, I thought you were going to tell me the real origin. Maybe it was named after Dingle, lol.

38.

Cincirob argued ...

1) The LT solns are correct in Gron's analysis, yet cinci has long argued Gron's elliptical shape is wrong because he misapplied the LTs.
2) Gron's rotating disk has a radius of R'=1 per the axle frame observer (A), rolling on a ground moving at v=-0.866c.
3) Cinci introduced an inertial rod, to prove his point ...
4) A records a moving inertial length-contracted rod at height y'= 0.866 (above the disk's axle) to be unit length a LA=1.
5) Per A, when a linear cord of (at y'=+0.866) Gron's rolling disk is momentarily superposed with the moving rod, both then are the length LA=1.
6) The ground observer G moves at -0.866c wrt axle observer A, because the rolling disk's axle translates at 0.866c per the ground observer G.
7) G holds the moving rod at length LG = (LA*1/√(1-v²/c²))*√(1-u²/c²), where u = 2v/(1+v²/c²), so for v=0.866c then LG = (1*2)/7 = 0.28571

OK, so we know that Gron's rolling wheel is only LG = 0.5 long (wrt x at y=y'=0.866) per ground observer G, yet the inertial rod must be LG = 0.28571 per G ... even though they are the same x' length per the axle observer A. Is this a problem, relativistically? No. Yet, cincirob has long argued it an error on Gron's behalf. So while cincirob says the LTs are correct, he also argues that Gron does not apply them correctly under the case of rotation, and thus Gron's theory is all wrong. Hmmm.

Cincirob then points out that the inertial rod must have a proper length of LP*1/√(1-v²/c²) = 1*2 = 2. Given such, he presumes that the length of the disk-cord (of atoms) associated with y=y'=0.866 per A, should have the same proper length (2 units) per the rest length of those atoms per the noon-inertial disk POV itself. Yet, he never concedes that the linear string of disk atoms defined by the axle observer A (in his instant t') must be non-linear in either the non-inertial non-euclidean disk POV and/or the ground POV. Hmmm.

Then, cincirob says Gron never took the various differing motions of the disk atoms into account in his analysis, nor did Gron consider the composed velocity of each individual atom, as though that's a problem of sort. Did Gron ever need to do this in his analysis? Of course not. Did Gron ever care about the proper length of disk cords in the non-inertial disk POV? Of course not, as it was never required. Cincirob says the Gron analysis is wrong, and cannot be validated until all those calculations are done. Hmmm.

Thank You,
You have a few numerical errors there, which are all related to each other. The velocity of the rod at y'=0.866 as measured by the axle frame is u'=0.750c because cincirob wanted it to have the same velocity as the wheel-point located at x'=0.000 y'=0.866. Therefore the proper length of the rod LP=LA*(1/√(1-u'²/c²)) = 1.000*1.512 = 1.512 and the velocity of the rod according to the road frame is u = (u' + v) / (1 + (u'v/c²)) = 0.979c and thus the ground holds the moving rod at length LG = LP*√(1-u²/c²)=0.303.

40. Here's a repost, in the correct thread, and with the corrections JT pointed out (thanx) ...

Cincirob argued ...

1) The LT solns are correct in Gron's analysis, yet cinci has long argued Gron's elliptical shape is wrong because he misapplied the LTs.
2) Gron's rotating disk has a radius of R'=1 per the axle frame observer (A), rolling on a ground moving at v = -0.866c.
3) The ground observer G moves at -0.866c wrt axle observer A, because the rolling disk's axle translates at 0.866c per the ground observer G.
4) Cinci introduced an inertial rod, to prove his point ...

5) A records an inertial length-contracted rod at height y'= 0.866 (above the disk's axle) moving at w=0.75c toward +x' to be unit length a LA=1.
6) The gamma factor for w = 0.75c is then ... γw = 1/√(1-w²/c²) = 1.5118
7) Per A, when a linear cord of (at y'=+0.866) Gron's rolling disk is momentarily superposed with the moving rod, both then are the length LA=1.
8) The proper length of the inertial rod is then LP = LAw = (LA*(1/√(1-w²/c²)) = 1.5118 units if length.
9) G holds the moving rod at length LG = LPu = (LAw)/γu = (LA*(1/√(1-w²/c²))*√(1-u²/c²), where u = (w+v)/(1+wv/c²) which for v=0.866c and w=0.75c is then u = 0.9797c. The gamma factor for a velocity of u = 0.9797c is γu = 1/√(1-u²/c²) = 4.9877 ....... and so LG = (LAw)/γu = (1*1.5118)/4.988 = 0.3030

OK, so we know that Gron's rolling wheel is only LG = 0.5 long (wrt x at y=y'=0.866) per ground observer G, yet the inertial rod must be LG = 0.3030 per G ... even though they are the same x' length (unit length) per the axle observer A. Is this a problem, relativistically? No. Yet, cincirob has long argued it an error on Gron's behalf. So while cincirob says the LTs are correct, he also argues that Gron does not apply them correctly under the case of rotation, and thus Gron's theory is all wrong. Hmmm.

Cincirob then points out that the inertial rod must have a proper length of LP*1/√(1-w²/c²) = 1*1.5118 = 1.5118. Given such, he presumes that the disk-cord (of atoms) associated with y=y'=0.866 per A (which is linear per A) "should have the same proper length as the inertial rod (1.5118 units). Yet, he never concedes that the linear string of disk atoms defined by the axle observer A (in his instant t') must (generally) be curved due to their rotation, in either the non-inertial non-euclidean disk POV and/or the ground POV. Hmmm.

Then, cincirob says Gron never took the various differing motions of the disk atoms into account in his analysis, nor did Gron consider the composed velocity of each individual atom, as though that's a problem of sort. Did Gron ever need to do this in his analysis? Of course not. Did Gron ever care about the proper length of disk cords in the non-inertial disk POV? Of course not, as it was never required. Cincirob says the Gron analysis is wrong, and cannot be validated until all those calculations are done. Hmmm.

Thank You,

41. Edit: unfolded loedel diagram deleted

42. If the firecracker pops at y'=0.866 in the axle frame, then it also pops at y=0.866 in the road frame. At road time t=0.000 the spoke tip is higher, at y=0.955. But then later, at road time t=0.866, the spoke tip is in the same place as the popping event, at y=0.866.

Don't let cincirob get you confused, lol...

43. Thanks, JT, I knew I messed up the chord and spokes somewhere...
This looks better:
Edit: But still wrong:

44. Originally Posted by VeeDee
Thanks, JT, I knew I messed up the chord and spokes somewhere...
This looks better:
Looks pretty cool!! I'm not sure why you're showing t'=-0.866, which does not really pertain to anything in particular. But it still looks nice!

45. Originally Posted by JTyesthatJT
Looks pretty cool!! I'm not sure why you're showing t'=-0.866
I added the t'=-0.866 wheel, with spoke and chord, to show the wheel rotates in the axle frame: different positions for spoke and chord relative to the t'=0 wheel...
, which does not really pertain to anything in particular.
It shows where the position of the spoke (and chord) is for the wheel that gives its y'=0.866 rim atom to the t=0 ellips. (I should have been more specific in the sketch.)
I thought that might help Cinci because he is completely lost in the chord / rim / points / atoms ...

But it still looks nice!

46. Originally Posted by VeeDee
I added the t'=-0.866 wheel, with spoke and chord, to show the wheel rotates in the axle frame: different positions for spoke and chord relative to the t'=0 wheel...
Yes, it does show that the wheel rotates in the axle frame.

Originally Posted by VeeDee
It shows where the position of the spoke (and chord) is for the wheel that gives its y'=0.866 rim atom to the t=0 ellips. (I should have been more specific in the sketch.)
Oh I see. You must be transforming x=0.500 t=0.000 to get t'=-0.866. That is actually an ellipse point located at y=0.000 at the right edge of the wheel. If you intended to transform the point at y=0.866, that would be x=0.250. That would transform as t'=-0.433 but it still has nothing to do with the chord or the spoke. Only the wheel atoms which happen to be located at x=0.250 at t=0.000 transform to t'=-0.433.

At t=0.000 the actual spoke tip is located at x=0.148297, y=0.954999 which transforms to t'=-0.256874. Other points along the spoke transform progressively to later times, with t'=0.000 being the coordinate at the axle.

47. Originally Posted by JTyesthatJT
Oh I see. You must be transforming x=0.500 t=0.000 to get t'=-0.866. That is actually an ellipse point located at y=0.000 at the right edge of the wheel. If you intended to transform the point at y=0.866, that would be x=0.250. That would transform as t'=-0.433
Correct. I took the wrong red line to measure t' from. My intention was and is to draw the t'=-0.433 wheel. I corrected the sketch, see below.
but it still has nothing to do with the chord or the spoke.
Indeed. It was not meant to be a spoke or chord atom. My intention was to show the wheel with spoke and chord position for -quote/ post #1245- for the wheel that gives its y'=0.866 rim atom to the t=0 ellips.
I showed this because I think there is some confusion about what Cinci means by 'chord' and what we use it for. We consider a chord of atoms rotating, part of the wheel, but cinci only considers an abstract 'coincident' chord, always at height y'=y=0.866
Only the wheel atoms which happen to be located at x=0.250 at t=0.000 transform to t'=-0.433.
Correct.
x=0.250 at t=0.000 is a rim coordinate but has nothing to do with the spoke end or chord end hit by the firecracker.
At t=0.000 the actual spoke tip is located at x=0.148297, y=0.954999 which transforms to t'=-0.256874. Other points along the spoke transform progressively to later times, with t'=0.000 being the coordinate at the axle.
Correct. But not shown on the my diagram because in concentrates on what happens at level y=y'=0.866 throughout. (Showing how the curves are formed was done in sketch post #1227)

48. Originally Posted by VeeDee
...my diagram ... concentrates on what happens at level y=y'=0.866 throughout.
Yes, now it makes perfect sense to me. Very nice!

49. Only problem, cinci doesn't want to learn how to read spacetime diagrams

After having answered his questions again and again, I'm hoping that cincirob is manufacturing a new argument of sort.

Thank You,

50. What happened to the remaining posts of this thread? There's at least about 10 pages or more missing !!!???

51. Originally Posted by VeeDee
What happened to the remaining posts of this thread? There's at least about 10 pages or more missing !!!???
The forum died. When it came back several years worth of posts were missing.

52. Yes, the forum died. Whenever you let people harboring personal vendettas (some with multiple identities) take over a forum it ides when their target leaves. I left...it died.

53.

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