
VeeDee: Haha, JT, you see how he handles your question? Same old trick.
cinci: What's your answer?
VeeDee: There's over 1000 posts in this thread telling you why it is wrong.
cinci: Yes, and they're all just like this one, a total waste of space. Next you'll probably mumble something about RoS which is also a waste of space.
There is nothing wrong with my analysis.
I already explained why the secant (chord) near the bottom of the wheel is longer in my right image than it is in my left image. Read your own explanation for why you think the pear model is correct, and you will see that you yourself said that there should be less length contraction near the bottom, and more near the top. That is the whole reasoning behind the pear shape, after all. If you are going to partake in this conversation, please do try to keep up. We don't need another mindless troll like cincirob, making ridiculous arguments just for the sake of arguing.
That is your claim, but it is easy to show that is wrong. Watch:
These are the coordinates of the events in the axle frame:
AXLE FRAME: Left Endpoint Aligns with Central Axis of Wheel
x'_L = 0.000
t'_L = 0.000
AXLE FRAME: Right Endpoint Aligns with Right Edge of Wheel
x'_R = 0.500
t'_R = 0.000
Notice that t'_L = t'_R = 0.000 which means those events are simultaneous in the axle frame.
Now YOU CLAIM these are the coordinates of the events in the road frame:
ROAD FRAME: Left Endpoint Aligns with Central Axis of Wheel
x_L = 0.000
t_L = 0.000
ROAD FRAME: Right Endpoint Aligns with Right Edge of Wheel
x_R = 0.152
t_R = 0.000
Notice that t_L = t_R = 0.000 which means those events are simultaneous in the road frame.
I guess you are not aware, having never studied relativity, that those events SHOULD NOT BE SIMULTANEOUS IN BOTH FRAMES. People who understand relativity know this intuitively. But for you, the idea will not penetrate your skull, no matter how many times it is explained. And you wonder why people are constantly telling you that you don't understand relativity.
I don't care if you don't want to believe the pole reaches the right edge of the wheel at t=0.866. But I have proven the pole cannot reach the right edge of the wheel at t=0.000, so you have no choice but to abandon that idea.
Yep. He can't answer. If he had said anything else but x=1.000 and t=0.866 he would be incorrect. But if he had said x=1.000 and t=0.866 then I would point out that the firecracker pops in the same place as the right edge of the wheel, and then he'd have to accept that happens at x=1.000 and t=0.866 just as we have been telling him all along. So he avoids the question like the plague. Sad.
You've missed the basic point, JT.I am not writing this merely "for the sake of arguing" but asking for your justification of the LONGER secant in the right image relative to the left image secant, when length contraction should reduce the right image secant's length compared with the left  NOT the comparison of the top & bottom of the right wheel. So I suggest some alternative 'explanations' open to you. You may have others.
The relevant right wheel secant is longer than the left wheel secant. Since the only difference between the two diagrams (in terms of "applied length contraction") is that there is additional linear length contraction applied to the right wheel (since it is seen by the road observer), the right image secant must be shorter than the left image secant due to said linear length contraction  which of course it is not!
Now I realize that you have to lengthen the secant due to the implication that the circumference at the bottom of the wheel has to stretch to make up for the "loss of circumference" at the top of the wheel (due to the combined spinning & linear length contraction of the right image)  but this creates further trouble of its own. So the lengthening of the secant in the right image relative to the left image secant remains unjustified by applying merely SR (as popularly conceived). Merely telling me to "keep up" as ******* used to do does not constitute an answer since the lengthening of the secant from the left to the right image is entirely unexplained except as a contrivance to 'explain' the "loss of circumference length" of the wheel due to its spinning.
However, I wouldn't pester you if I did not have an alternative answer ready.
Since 'circumferential length contraction' involving the spinning wheel causes an increase in the ratio of π (Relativity chapter 23) this has to be 'materialized' in some form. The only interpretation that can be represented pictorially is that the wheel's dimensions decrease in toto such that the right image wheel ought to be much smaller than it is, much smaller than you show it in the right image  in that way you can have the secant longer relative to the right wheel as a whole but SHORTER relative to the left wheel image secant.
It you can't accept that then you are reduced to claiming that your images are artificial contrivances since the "bits of wheel" you have imaged are from different places & times pasted together to try to create a physical image.
More importantly, cinci, I hope you are following this closely since I also wish your comments on a "contracted circumference" with spinning  & its implications!
TFOLZO
TFOLZO, what are you talking about? If the velocity of the perimeter of the wheel is 0.866c in the left image, then the velocity of the midpoint of the chord near the bottom is 0.750c in the left image. The negative sign refers to the bottom of the wheel rotating towards the left. In the right image, the velocity of the axle is +0.866c, where the positive sign refers to the wheel moving towards the right. The velocity of the midpoint of the chord near the bottom in the right image can then be calculated according to Einstein's velocity composition equation as (0.8660.750)/(1+(0.866*0.750))=0.331c. Note that the lesser magnitude velocity of 0.331c corresponds to less contraction (the curved line is longer), whereas the greater magnitude velocity of 0.750c corresponds to more contraction (the straight line is shorter).
If you did not know this, then how did you conclude the pear shape was correct? The pear is based on the idea that the longer curved line should be straight and horizontal, but still longer than it is in the left image. That is why the pear is fatter at the bottom. I guess you just agreed with cinci on this, without even understanding the principle behind it. What madness in this thread.
Last edited by JTyesthatJT; 08062014 at 06:32 PM.
JT: Yep. He can't answer. If he had said anything else but x=1.000 and t=0.866 he would be incorrect. But if he had said x=1.000 and t=0.866 then I would point out that the firecracker pops in the same place as the right edge of the wheel, and then he'd have to accept that happens at x=1.000 and t=0.866 just as we have been telling him all along. So he avoids the question like the plague. Sad.
cinci: Sad alright. I did say (x, t) = (1.000, .866) and you're claiming I didn't.
t = (t'  (v)x/c^2)/(1  V/c^2)^. = (0 + .866*.5)/.5 = .866
Surely you wouldn't have asked to the ycoordinate. It has nothing to do with the problem and shouldn't have been included in your original statement.
The firecracker in your problem is at rest in K'.
Now work the problem with the firecracker is moving at .75c relative to the K' frame. Do you know how?
I apologize, I didn't even notice that you wrote that. I saw your complaint that it was a different problem, and VeeDee implied that you didn't answer, so somehow I didn't even notice that. My error.
Good, so we agree on the coordinates of the firecracker event. Now, if the firecracker event is located at x'=0.500 and y'=0.866 at time t'=0.000, and the right end of the pole is also intersecting the right edge of the wheel at x'=0.500 and y'=0.866 at time t'=0.000, then those two events happen in the exact same place and time. Yet you claim one event transforms as x=0.152 and t=0.000 and the other transforms as x=1.000 and t=0.866 putting the events at different places, and different times.
Now, let's imagine that the only reason the firecracker pops is because the right end of the pole squeezes the firecracker against the right edge of the wheel, and that makes it pop. If the pole and the right edge of the wheel transform as x=0.152 at t=0.000 and the firecracker transforms as x=1.000 at t=0.866 then there is no cause for the firecracker to pop. Your model falls apart. My model says the right endpoint of the pole and the right edge of the wheel will be located at x=1.000 at t=0.866 which puts them in just the right place to squeeze the firecracker and make it pop. My model works where yours fails.
Regardless of its own speed, if the the firecracker is located at x'=0.500, y'=0.866 when it pops at time t'=0.000 according to frame K', that event transforms to frame K as x=1.000, y=0.866, t=0.866. Otherwise you end up with a model that falls apart, as explained above.
cinci: Nuts, I did a whole message and the site failed and lost it. Here we go again.
JT: Good, so we agree on the coordinates of the firecracker event. Now, if the firecracker event is located at x'=0.500 and y'=0.866 at time t'=0.000, and the right end of the pole is also intersecting the right edge of the wheel at x'=0.500 and y'=0.866 at time t'=0.000, then those two events happen in the exact same place and time. Yet you claim one event transforms as x=0.152 and t=0.000 and the other transforms as x=1.000 and t=0.866 putting the events at different places, and different times.
Now, let's imagine that the only reason the firecracker pops is because the right end of the pole squeezes the firecracker against the right edge of the wheel, and that makes it pop. If the pole and the right edge of the wheel transform as x=0.152 at t=0.000 and the firecracker transforms as x=1.000 at t=0.866 then there is no cause for the firecracker to pop. Your model falls apart. My model says the right endpoint of the pole and the right edge of the wheel will be located at x=1.000 at t=0.866 which puts them in just the right place to squeeze the firecracker and make it pop. My model works where yours fails.
cinci: Well, let's see What works and why.
First, you haven't shown how your wheel reaches the fire cracker at t = .866. Here's how your "model" really works.
The 60 degree point on the wheel (forget RoS, there is always some point at 60 degrees). It transforms into the road at
x = .25. at t = 0 (Look at your diagrams.)
For the wheel to hit the firecracker it has to move from .25 to 1.0, .75 units
According to your analysis, if it were a rod, it would be moving at .866c.
t(time at which the 60 degree point reaches x = 1) = dx/v = (1  .25)/.866 = .866 just as you say.
For the length contraction method,
x = .151559 at t = 0
Same logic as above,
t(time at which the 60 degree point reaches x = 1.000) = (1.000  .151559)/.979 = .866025.
So, this model works just like yours.
Now back to something rational. Here is the way I analyze the 60 degree chord with length contraction and the LTs. Find an error if you can and if you can't, then admit it.
Length of chord in axle frame = .5
Speed of chord relative to axle frame is Vch = .866*sin60 = .75
Rest length of chord is measured in (x", t").
Lch"(rest) = Lch'/(1  .75^2)^.5 = .755929
Or, Lch"(rest) = (Lch'  Vcht')/(1  Vch^2)^.5 = (.5  .75*0)/(1  .75^2)^.5 = .755929
Vch(relative to road) = (.75 + .866)/(1 + .75*.866) = .979695
Lch(road) = Lch"rest(1  Vch(relative to road)^2 )^.5 = .755929*(1  .979695)^2)^.5 = .151559
Or, Lch"(rest) = (L(road)  Vch(relative to road)*t)/(1  Vch(relative to road^2)^.5
.755929 = L(road)/( 1  .979659^2)^.5
L(road) = .755929(1  .979659^2)^.5 = .152559
Notice, the LT analysis (Italicized) gives the same answer as the length contraction formula method which shouldn't be a surprise to anyone.
You need to abandon your idea of looking at things in the road frame at t = .866. It has confused you.
And now some smart aleck comments from VeeDee who would follow anybody.
cinci: Just to dispel the rumors that I never did the Gron analysis here's a sample. Notice a couple of curved curved chords and the locations of spoke tips.
According to IMGUR where I retrieved it, it's 2 years old.
And here's one with a a curved spoke and some curved chords:
Last edited by cincirob; 08152014 at 12:19 PM.
JTyodatJT: TFOLZO, what are you talking about? If the velocity of the perimeter of the wheel is 0.866c in the left image, then the velocity of the midpoint of the chord near the bottom is 0.750c in the left image. The negative sign refers to the bottom of the wheel rotating towards the left. In the right image, the velocity of the axle is +0.866c, where the positive sign refers to the wheel moving towards the right.
Yes, JTydJT, I see what you are getting at, but the problem now is that with the right image axle velocity of +0.866c, & the velocity of the wheel perimeter being 0.866c, this means the velocity of the uppermost point of the circumference of said wheel (relative to the road observer) is now 0.866X2c = 1.732c  what madness in this thread!
The velocity of the midpoint of the chord near the bottom in the right image can then be calculated according to Einstein's velocity composition equation as (0.8660.750)/(1+(0.866*0.750))=0.331c. Note that the lesser magnitude velocity of 0.331c corresponds to less contraction (the curved line is longer), whereas the greater magnitude velocity of 0.750c corresponds to more contraction (the straight line is shorter).
Which argument necessarily implies that cinci's argument for the pearshaped wheel is correct since you are now arguing that the rightside image should 'bulge' more than the left side image (due to lesser length contraction)  except that you have 'curved up' the secant because of the reasons previously outlined.
If you did not know this, then how did you conclude the pear shape was correct?
Because the whole wheel on the right side is moving relative to the observer  more so on the top than on the bottom, as you quantify here, therefore the top of wheel, moving faster relative to the road observer, will be contracted more. In order to do so though, I had to "suspend disbelief" and pretend to ignore Einstein's "π in the sky" (i.e. π increases with rotation of a body, Relativity chapter 23) whereby the circumference of a wheel shortens from length contraction when the wheel is spun.
Your argument depends on the "instantaneous" claim that the tip of the wheel touching the road is at 0 velocity relative to the road observer (right image). However the whole wheel is "instantaneously" at 0 velocity for the axle observer (left image), especially as it is impossible to visualize a shortened circumference (& shortened secant in proportion) due to "circumferential length contraction"  apart from shrinking the whole wheel in size (which would certainly help reduce the 1.732c velocity at the top of the wheel)! .
The pear is based on the idea that the longer curved line should be straight and horizontal, but still longer than it is in the left image. That is why the pear is fatter at the bottom. I guess you just agreed with cinci on this, without even understanding the principle behind it. What madness in this thread.
Indeed  as seen by the top of your right wheel moving at 1.732c! In order to curve the secant however you seem to be relying upon Minkowski diagrams & logic to make that claim  logicchopping between "road times" & "axle times" to 'explain' the curvature of the secant. In theory at least this latter process can be circumvented by actual experimental evidence.
One would have thought  given the contradictory implications of the arguments  that the answer would have to be obtained from experimental evidence, actual photoshots of such relativistically moving wheels. In that way the Minkowski logic can be disposed of since you would then have 'real time' images of the wheel  to see whether it's pearshaped or elliptical.
TFOLZO
Last edited by TFOLZO; 08072014 at 08:25 AM.
As for what the left image & right image would look like after the appropriate modifications i.e. what we would expect from "photographic images" the following illustrations give some idea.
The left image with the wheel spinning but not moving would be circular:
O
The right image with wheel spinning & moving would be bulged at the base as you say (if the Minkowskiclaimed 'curved secant' is ignored).
∆
The wheel becomes almost 'delta shaped', though the edge at the bottom would 'bulge a bit downward' since the wheel has to touch the road at a point  but the wheel is now MUCH SMALLER due to the reduced length of the circumference  a situation that supports my friend John Callow's claim that length contraction implies a simultaneous "transverse length contraction" (though not in a 1:1 ratio). It also lets you diminish the velocity of the upper part of the circumference, perhaps even to below c relative to the road observer.
TFOLZO
In reply to AIP's this thread, re: Gron's Wheel.
I think my own marbles are in jeopardy here! Because I'm certain this is the SAME thread that's been "phyorg." for over a year now...barns...poles...etc,
.....
Strictly from an engineering perspective, I think "roller bearings" would be more appropriate than a "wheel w/ marbles" to extrapolate conditions with...it might even have some nice
practical considerations, such as the diffusion of load/weight in static conditions vs. "at speed".
(hey...some moderations of design might actually result in some patent money...who doesn't need a little more?! I wish my own mathematical skills were "up to snuff" for such
research...I would be "riding the short bus" compared w/ some of you here! Waaaay too fast for me)
(Thanks for reading!)
SYA: You just never understood what it meant.
cinci: You used to say I didn't know how to do it. Then you backed off to I just fumbled with equations to get it. Now you're saying I can do a detailed calculation but don't understand it.
I'm pretty sure those are the first calculated chords ever published. I must be a genius to be able to do that without understanding what I did.
SYA: And "killing the ellipse", lol.
cinci: A little strong perhaps because the ellipse is correct for a nonrotating structure. Why don't you go help JT fix his analysis instead of wasting time nipping at my heels.
Gerry Nightingale: Strictly from an engineering perspective, I think "roller bearings" would be more appropriate than a "wheel w/ marbles" to extrapolate conditions with...it might even have some nice
practical considerations, such as the diffusion of load/weight in static conditions vs. "at speed".
(hey...some moderations of design might actually result in some patent money...who doesn't need a little more?! I wish my own mathematical skills were "up to snuff" for such
research...I would be "riding the short bus" compared w/ some of you here! Waaaay too fast for me)
cinci: Bearings would be close except the outer race would be rotating. What is "phyorg"?
This is exactly what Cinci doesn't understand, doesn't want to understand, and probably can not understand because of his obsession with that xdirection rim point velocity.
If in the axle frame the firecracker at the end of the rod explodes when it touches the rim of the wheel at t'=0 x=.5 y.866, then that event (the full content of that event) MUSToccur in the road frame at t=.866 x=1 y=.866. Why? Because the rim atom is part of that exploding cracker, the pole (and its firecracker explosion at rim atom) transformation OBVIOUSLY suffices to get the correct time and position of that exploding rim atom in the road frame... . AND THUS CAN NOT OCCUR at t=0.
Cinci apparently sorry: definitelly still has not learned what an event is. He doesnt want to because then his xdirection rim point velocity falls apart!
The event's content is absolute. THIS MEANS, cinci, you CAN NOT split it in two events, WHATEVER your xdirection rim point velocity poem tells you. An event in the axle frame is exaclty that event in the road frame. Period. Shame you still don't get the basics of relativity! (Well, actually it's not a shame. There are more hotshots out there who hallucinate they know everything about relativity ...)
Cinci should spend his effort and time in finding out WHY his 'rim point xdirection velocity' scenario does not work. By doing that he might see the light how relativity works.
In reply to cincirob, re: your #1018 post.
It should be "physorg." Sorry.
(I also do not understand what you are arguing over w/regard to the "wheel" scenarios....sheesh!!! By "you" I mean the collective "you".)
....
The "wheel" is in rotation and then you wish to examine individual aspects of each segment in relation to each other vs. "contact" road points? Why? To prove what?
(or the axel's rotation vectors) Each component is subject to the same stressors w/regard to velocity, as per Relativity. End of story.
......
The last time I looked, bearings ARE "wheels" in terms of rotation...and examined at the surface contact points and disregarding the rest of the "wheel shape", you now have a "fulcrum & lever".
The "road" serves as a fulcrum, as well as the axle. Reduce the FoR's further still, and now there is only friction inplace, no "movement". Taken stepbystep, the entire concept of
"rolling wheel" becomes moot w/regard to velocity. (each FoR will that examines a specific point will reduce that points velocity to zero)
....
I do not understand all the equational quibbling over something so simple!
(Thanks for reading!)
Greetings, VeeDee  though I think I have known you under another name!
As Malcolm X might say, great to see that you've come along to...
...whip up crackers.
Luckily for me though, only cinci needs to make an eventful reply as to whether the explosion is one event or 'split' into two events! I observe the situation in great expectation!
TFOLZO
Lol.
You had the benefit of seeing the solns JT and I did first, then you fumbled to the same solns. You should explain how you did your process there, as normal folks just use the LTs, You never understood what your own method's solns meant either. If you did, you would have realized many years ago that the Gron analysis was in order.
If you haven't noticed, you're the only one who doesn't understand the Gron analysis, far as though who have studied the theory with the required tools. Then, one needs "an understanding of" the meaning of relativistic effects, amongst other things. TFOLZO doesn't count, because he never been at a point where he could understand relativity. The only difference between you and TFOLZO, is that he doesn't pretend to understand relativity theory while arguing it flawed. He just doesn't believe in it.
Thank You,
SinceYouAsked
Oh well, I have to expect this when I pretend for argument's sake to hold to the SR 'arguments'... ...and that means that I cannot respond to SYA's arguments in the proper way, lest I be banned for posting antiSR in the main forums.
TFOLZO
And to think that I thought that 'GRON' was an acronym for something like Group of Relativity's Operationalist Nerds or something similar.
SYA: You just never understood what it meant.
cinci: You used to say I didn't know how to do it. Then you backed off to I just fumbled with equations to get it. Now you're saying I can do a detailed calculation but don't understand it.
Lol.
cinci: I'm pretty sure those are the first calculated chords ever published. I must be a genius to be able to do that without understanding what I did.
SYA: You had the benefit of seeing the solns JT and I did first, then you fumbled to the same solns.
cinci: I did the chords first. I also did an independent analysis while you just copied Gron's equations. And you still don't understand the problems in the analysis.
SYA: You should explain how you did your process there, as normal folks just use the LTs, You never understood what your own method's solns meant either. If you did, you would have realized many years ago that the Gron analysis was in order.
cinci: Actually I published my tabular analysis. And you still don't understand the problems in the analysis.
SYA: And "killing the ellipse", lol.
cinci: A little strong perhaps because the ellipse is correct for a nonrotating structure. Why don't you go help JT fix his analysis instead of wasting time nipping at my heels.
SYA: If you haven't noticed, you're the only one who doesn't understand the Gron analysis, far as though who have studied the theory with the required tools. Then, one needs "an understanding of" the meaning of relativistic effects, amongst other things. TFOLZO doesn't count, because he never been at a point where he could understand relativity. The only difference between you and TFOLZO, is that he doesn't pretend to understand relativity theory while arguing it flawed. He just doesn't believe in it.
cinci: "Required tools", I used the same ones Gron did. It's taken you years to comprehend that he uses length contraction. Who knows how many more years until you understand the problems with his analysis?
Not if you use Einstein's velocity composition equation, which I just showed you in the very post to which you are responding. The velocity at the very top, according to the road frame, would be (0.866+0.866)/(1+(0.866*0.866))=0.9897c.
I did not curve the chord upwards, the Lorentz transformations did that. Unlike cincirob, I don't just apply my own notions to the geometry of the wheel. I let Minkowski diagrams do that for me. That way I don't run the risk of being completely wrong about what SR predicts, the way cincirob is.
Yes, you nailed it. I don't even feel like reading his response to me. I skimmed over it, and I can tell it does not say, "Gee, you're right, the pear is wrong after all!" which is the only appropriate response to my proving the pear incorrect. So, I am not even interested in reading what he wrote in detail. Maybe I'll look at it later, if I have nothing else to do. Probably not though.
Yes, of course the right end of the rod reaches x=1.000 at t=0.866.
But you say the edge of the wheel is not there at that time, you say it is located at x=0.152+(0.866*0.866)=0.902. But remember, the only reason the firework pops is because it was sandwiched between the rod and the edge of the wheel. Since you don't have the right edge of the wheel in the right place, the firecracker won't pop in the road frame, creating a contradiction. Thus the pear shape fails.
Unlike the pear, the ellipse allows the right edge of the wheel to be in the same location as the right end of the rod and the firecracker, x=1.000, t=0.866, just as you calculated. Thus the ellipse succeeds. If you can't understand this, there's not much anyone can do to help you.
cinci: For the length contraction method,
x = .151559 at t = 0
Same logic as above,
t(time at which the 60 degree point reaches x = 1.000) = (1.000  .151559)/.979 = .866025.
So, this model works just like yours.
JT: Yes, of course the right end of the rod reaches x=1.000 at t=0.866.
cinci: Of course? You've repeated over and over that the rest length method for the rod doesn't work. The method works for the rod, Agreed?
JT: But you say the edge of the wheel is not there at that time, you say it is located at x=0.152+(0.866*0.866)=0.902. But remember, the only reason the firework pops is because it was sandwiched between the rod and the edge of the wheel. Since you don't have the right edge of the wheel in the right place, the firecracker won't pop in the road frame, creating a contradiction. Thus the pear shape fails.
cinci: The pear acts like the pear acts. First I have to get you to admit that the length contraction method works for a rod as I asked above. So let's make sure you have the 4rod straight, do you?
JT: Unlike the pear, the ellipse allows the right edge of the wheel to be in the same location as the right end of the rod and the firecracker, x=1.000, t=0.866, just as you calculated. Thus the ellipse succeeds. If you can't understand this, there's not much anyone can do to help you.
cinci: Yes, the ellipse succeeds in that particular task, and for a very good reason. The analysis is for a static disk. Your analysis says that every point on the disk has the same velocity, v; ie, NO ROTATION. So those points, like the firecracker, are all in the same frame. And contact is made as I explained it to you.
The pear wheel is ROTATING. Rotation means relative velocities so the shape of the wheel is affected, but the shape is constant relative to the axle and, therefore, the shape moves at .866c. And if you draw your figure correctly, then the left end of the purple line is where you have the centerline of the ellipse and the right end becomes a point on the pear shape.
The point at the end of the chord is not permitted to continue in the xdirection and intercept the firecracker at t = .866 because it also has a ydirection velocity and an instant after you calculate what its xdirection length is, it rotates to a new position and no longer has a lower xdirection velocity. Of course there's always another rim point where the old one was to maintain the shape. The 90 degree point on the pear will ignite the firecracker at t = .866 because it is not affected by rotation.
Now argue all you want, but this is the second analysis that proves that you aren't accounting for rotation in the wheel shape. If I'm not correct, you should be able to prove how rotation affects the shape.
I'll deal with second part of your reply first JTyodatJT! I pointed out that length contraction should involve the top of the wheel preferentially since it is moving faster "relative to the road observer"(rrf).
I am mystified by how the Lorentz transformations allow you to curve the secant upward  but if you say that this is actually because of Minkowski diagram interpretations, I am happy to accept that since it is standard SR & GR reasoning. Cinci is different of course since he is ACTUALLY trying to make sense of the world.TFOLZO:Which argument necessarily implies that cinci's argument for the pearshaped wheel is correct since you are now arguing that the rightside image should 'bulge' more than the left side image (due to lesser length contraction)  except that you have 'curved up' the secant because of the reasons previously outlined.
JTyodatJT: I did not curve the chord upwards, the Lorentz transformations did that. Unlike cincirob, I don't just apply my own notions to the geometry of the wheel. I let Minkowski diagrams do that for me. That way I don't run the risk of being completely wrong about what SR predicts, the way cincirob is.
TFOLZO
Last edited by TFOLZO; 08082014 at 08:53 AM. Reason: quote marks wrong, grammar
I need some shorthand terminology, JTyodatJT thus I use the terms
rrf – “relative to the road frame” and
naf – “relative to the nonspinning axle frame.”
TFOLZO: ...the problem now is that with the right image axle velocity of +0.866c, & the velocity of the wheel perimeter being 0.866c, this means the velocity of the uppermost point of the circumference of said wheel (relative to the road observer) is now 0.866X2c = 1.732c  what madness in this thread!
Now that’s an interesting interpretation JTydJT. If I use the abbreviation crrf to mean “multiplied by c relative to the road frame” we have the bottom of the wheel traveling at 0, the wheel axle traveling at 0.866crrf, whereas the top of the wheel is 0.9897crrf. This evidently implies that there is “transverse length contraction” i.e. length contraction at right angles to the direction of motion i.e. the vertical axis in your left & right wheel images, transverse length contraction that you do not visualize.
Furthermore, if we translate these wheel values to the nonspinning axle frame (i.e. it is NOT spinning with the wheel) we have velocities in terms of cnaf (“multiplied by c relative to nonspinning axle frame”)*:
……………………..…………naf
Bottom of wheel:..0.866c
Wheel axle:…………..0
Top of wheel:….……0.866c
…………………………..rrf……….….naf
Bottom of wheel: 0…………...0.866c
Wheel axle:……….0.866c….…0
Top of wheel:..…0.9897c….…0.1237c (direct inference from rrf)
So not only does the wheel have to undergo transverse length contraction, but the top of the wheel has to undergo greater transverse length contraction in order to produce a velocity of only 0.9897crrf! This also leads to a direct prediction rrf that the top of the wheel would only be traveling at 0.1237c relative to the axle – not a surprise if the wheel is severely “transverse length contracted.”
However this means that the “length of circumference” passing backward under the bottom of the wheel is greater than the “length of circumference” passing forward over the top of the wheel. I.e. we have the absurd situation that most of the circumference of the wheel will “pile up” behind the wheel. Hence, JTydJT, you’ll be forced to agree that your clever claim for the top of the wheel traveling at 0.9897crrf is decidedly naff!
The real lesson here of course is for cinci: there is NO objective answer for the velocity of an atom at the very top of the spinning wheel.
Naf: 0.866c
Rrf: 0.9897c
Road frame observer’s SRdeduced inference re top of wheel velocity relative to axle: 0.1237c.
So which NAFF answer ******* would you like, cinci, or do you have yet another one?
I.e. the issue is objectively undecidable because there are no reliable or agreedupon ‘measuring sticks’ to provide a correct or satisfactory answer.
*Note that if we had a spinningaxle observer, spinning with the wheel, he would NOT find the wheel to be spinning but stationary hence the circumference of the wheel would be LARGER than that of the same wheel seen by a nonspinning observer – due to π having its normal value for the spinningaxle observer! This is why you, JTydJT, could credibly assert that the secant becomes longer at the bottom of the right wheel, because the original secant length is that seen by an observer spinning with the wheel, i.e. an observer to whom the wheel is relatively at rest. Hence we have three wheel sizes, not two, to consider. The wheel at rest (seen by the observer spinning with the wheel) is BIG & round; the wheel seen by the nonspinning axle observer is round but smaller (your left image); the wheel seen by the road observer is very tiny  I showed it as a triangle but it is properly pear shaped (due to Minkowski you claim it to be elliptical as in the right image)!
TFOLZO
TFOLZO, you are arguing against this geometry:
A better animation would show the elliptical wheel rolling to the right.
In reply to TFOLZO, re: your #1030 post.
I have a "wheel" in mind that's easier to work with, plus it comes a spoke! (kind of)
The Earth and the Moon. Although I must admit...the rotational vectors have been pretty much established. (still, there is a "pearshape" to work with of sorts, even w/o relativistic
speeds) Just consider the center of Earth as the hub, extend a "spoke parallel" to either pole (road surface) and you find a somewhat "flattened lightbulb" shape.
(sorry, I can't "cut & paste"...don't know how) I bet someone here could post a spiffy image of the "pearshape" effect.
Of course, the "wheel" would be considered "poletopole", rather than equatorial.
(Thanks for reading!)
TFOLZO: I am mystified by how the Lorentz transformations allow you to curve the secant upward  but if you say that this actually because of Minkowski diagram interpretations, ........
cinci: It has nothing to do with Minkowski diagrams. I get the curvature without using Minkowki and so does Gron.
In reply to JtyesthatJt, re: your #1033 post.
Thanks! But, you could also apply the "wheel" to the Earth's electromagnetic field as well...I think it is suitable for comparative analogy. Use Earth itself as a "hub" and 360deg. of arc
as "spokes"...I believe it will demonstrate a "frame dragging" effect w/respect to the "magnetic field spokes".
I guess then JT that you would concur that it is SOLELY the Minkowski diagrams that "permit" both spokes & secants to be curved  secants curved upwards. Yes, I can also admit that the secant can appear longer for the right wheel, because the left wheel itself, spinning, is smaller than the same wheel would be at rest. Presumably then the resting (nonspinning) wheel would have a longer secant than ever the curved secant in the right wheel  otherwise you would be stuck in having to explain why the secant was length extended rather than contracted with longitudinal motion (i.e. in the case of the right wheel)!
Your animation is OK as for me it already shows the elliptical wheel rolling to the right  but the animation has no more significance than that. It is not proof that secants "curve upward" i.e. bend transversely, when moving along a road relative to a stationary road observer.
If you want to prove that such changes actually occur to moving wheels then you need photographic evidence  which will of course not be as graphic as the photo, given the lower speeds. You need photographic evidence because your argumentation is ad hoc & selective.
You have NOT proven that such a wheel rolling along the road will NOT be pearshaped; rather you merely deduce it based on your 'deity' Minkowski's logic.
That, JTydJT, you can claim that the lower secant lengthens when the wheel moves along the road can only be permitted on the basis that you accept that a stationary spinning wheel must shrink in diameter in proportion to its angular velocity due to the reduction in length of its circumference due to "circumferential length contraction" (Relativity chapter 23) But then by the logic of the longitudinal or Fitzgerald length contraction, the faster motion of the top of the wheel relative to the road observer means that the top of the wheel will have lesser width i.e. the wheel will be pearshaped.
The point is  & cinci will nail you with this too  is that you cannot give an objective answer for the velocity of the top of the wheel: 1.732crrf which you deny; or 0.9897crrf which latter arithmetically gives the absurd result of 0.1237cnaf .
Once again you are stuck with mutual incompatibilities  one where the top of wheel is moving at 0.9897crrf (= 0.1237cnaf) which leads to the circumference 'band' being pushed behind the wheel since the top of the wheel is not moving fast enough to "send forward" the circumference band to the front then the bottom of the wheel which latter is moving at 0.866cnaf; the other where the top of the wheel travels at 1.732crrf, impossible according to SR!
IOW  you cannot answer the situation objectively for the wheel rolling along the road. While cinci is right to claim the wheel is pearshaped, this does NOT solve the circumferencespeed problem of ensuring that the amount of circumference moving forward equals the amount of circumference moving backward  without which a wheel will not work as a wheel (given that the wheel shrinks in its circumference when it spins but still functions as a wheel).
TFOLZO
Well now I am truly mystified, cinci!How can you possibly get curved secants (or curved spokes) just by using Lorentz transformation equations directly? Presumably it has something to do with the lengths of segments of the circumference  these segments being narrower towards the top of the wheel as JTydJT's illustration showed. Being wider at the bottom of the wheel you are presumably saying that the middle of the secant will stay put, but the edges be "pulled" circumferentially, presumably by the circumferential 'reduction' at the top of the wheel.
TFOLZO
Last edited by TFOLZO; 08082014 at 10:59 AM.
It would be even better if it showed the emission points on the rim and their progress towards the fixed camera on the road.
TFOLZO: How can you possibly get curved secants (or curved spokes) just by using Lorentz transformation equations directly?
cinci: Take a simple one, the 90 degree (horizontal spoke). Transform it to the road frame. Gron simply length contracts it. So if it's 1 unit long in the wheel, it's .5 units in the road.
If you have a clock t each end of it, they will not read the same because, taking a for axle and r for road,
t(a) = (t(r)  vx(r)/c^2)/(1  (v/c)^2)^.5
If you take the situation where t(r) = 0,
t(a) = vx(r)/c^2)/(1  (v/c)^2)^.5
This tells you that at x(r), you're seeing the point as it was dt = vx(r)/c^2)/(1  (v/c)^2)^.5 seconds ago. Since the wheel is rotating, the point you are transforming is the one that was there dt seconds ago which is the spoke at ~43 degrees. Go back and look at my diagram which draws a line between the spoke on the wheel in the axle frame (round) to the place where it appears on the ellipse.
No, if you're with me so far, you can look at the equation, t(a) = vx(r)/c^2)/(1  (v/c)^2)^.5, and see that the only thing that changes if you look at the midpoint of the horizontal spke will be x(r). The equation is linear in x. So the midpoint of the spoke will be rotated half as much as the tip. That gives you the curvature.
TFOLZO: Presumably it has something to do with the lengths of segments of the circumference  these segments being narrower towards the top of the wheel as JTydJT's illustration showed. Being wider at the bottom of the wheel you are presumably saying that the middle of the secant will stay put, but the edges be "pulled" circumferentially, presumably by the circumferential 'reduction' at the top of the wheel.
cinci: No, see above. Don't tell the boys I explained it without using a Minkowski diagram, they will start calling me a heretic and want to burn me at the stake. SYA will say I only stumbled on the answer while balancing my checkbook.
laurieag: It would be even better if it showed the emission points on the rim and their progress towards the fixed camera on the road.
cinci: You can find such animations at : Rolling Wheels
Yikes! I'd said that the rolling wheel lengths & velocity were objectively unresolvable, but you, cinci, have......underlined that fact with the greatest emphasis, demonstrating it beyond any doubt whatsoever.
I was thinking only of Fitzgerald contraction applications for LTEs (as is probably obvious to the readers ). You have added in the time dilation  which is of course what 'they' use with the Minkowski diagrams. Hence if one were actually to try to photograph a very fast spinning wheel (both from axle & road reference frames) the images would certainly be a bit blurred, but when you add in time dilation all bets are off. Why?
In a spinning wheel, the axle reference frame's time passes more slowly than the time at the circumference. When you consider a whole wheel moving along a road, the road reference frame clock is faster (road time passes quicker) than axle time; axle time is slower while circumference time, since circumference clocks move even faster then the axle relative to the road, will be slower still. No wonder GRON categorically excluded photographing such a wheel to see incipient effects  since in order to do such a thing the whole wheel has to be photographed at ONE time. (He though evaded the issue as he only invoked mechanical failure as the cause of the impossibility of objective testing).
Hence an objective answer to the elliptical versus pearshaped wheel question is infinitely less likely than Rolf Harris (age 84 now in prison) becoming headmaster of a girls' school. Thus all this thread can ever do is allow the participants to grandstand  like a conference of dictators of tinpot statelets impressing each other with grand gestures, costumes, equations and tales of future conquest, even though all of them bear mere variants of the same logo on their flags!
But some of the dictators had (have?) more potential & integrity than others  while others know it all to be just a game.
My interest, as you know, is serious science with practical results.
TFOLZO
For our readers understanding Lorentz Transformations I will show what the rolling wheel at t=0 road frame is made of (see sketches below).
Wheel rolling left to right in road frame.
We will follow 3 different rim atoms: a red atom, a blue atom, and a pink atom.
I show you where they are on the wheel per axle frame at
t'= 866
t'= .433
t'= .256
t'= 0
JT's firecracker is fixed to the red atom.
It explodes when that atom is at 60degrees, t'=0. (This is where the front of the rod is – not shown, but let's hope Cinci is smart enough to add this himself.)
Event B4 = end of rod hitting red rim point making firecracker explode.
Event B3, B2 and B1 are also events of that red rim atom (with the firecracker) but no explosion (because rod not at red atom yet).
I also show a few events of the other two rim atoms which will be usefull to see what the wheel in the road frame is made of.
The sketch shows how different sections through the wheel at different times per axle frame select specific events to compose the wheel in road frame at t=0. (A road frame cuts so to speak through different axle frames and picks up the events it finds at that section. That's why, cinci boy, the content of an event can never change from one frame to another. Because we deal here with 3D sections through 4D spacetime. Ever heard of 4D spacetime? No, because you don't need all that to make up your own 'relativity rim point velocity xcoordinate contraction theory', isn't it? Yes it is.)
In the road frame at t=0 THERE IS NO EVENT B4. It's the event B3 of the red atom that that pops up. It's at a higher level than y=.866 (obviously because the red rim atom is not yet at 60 degrees).
Take note that event B3 is NOT the event of the red atom and its firecracker exploding.
What atom is at level y=.866 in the road frame at t=0 ?
It is C2. That blue atom has nothing to do with the red atom. But it's the atom of the rim of the wheel at t=0 y=.866
I also added some events to show you how the curves of the spokes are formed. Please enjoy.
Not shown here but easy to understand:
At t=.866 in the road frame, event B4 will be at level y=.866. And what's the content of event B4? Indeed, it's the rod end hitting the red atom: firecracker explodes.
Taking all the above into account, it is obvious that Cinci's xdirection rim point coordinate scenario is complete nonsense. Especially his quote from post 1011: (forget RoS, there is always some point at 60 degrees), is the most ridiculous and the most absurd procedure only he can invent to find out what events of a rotating wheel per axle frame are simultaneous in the road frame.
Last edited by VeeDee; 10252017 at 09:06 AM. Reason: fixing img hosting problem
TFOLZO: Rolf Harris (age 84 now in prison)
Rolf TieMeKangarooDown Harris is in prison? How sad.
VeeDee: Ever heard of 4D spacetime? No, because you don't need all that to make up your own 'relativity rim point velocity xcoordinate contraction theory', isn't it? Yes it is.)
cinci: Gron didn't need it to make up his length contraction procedure either. Why do you need it?
VeeDee: Taking all the above into account, it is obvious that Cinci's xdirection rim point coordinate scenario is complete nonsense. Especially his quote from post 1011: (forget RoS, there is always some point at 60 degrees), .................................[/B]
cinci: You mean there isn't always a point at 60 degrees? Please explain.
VeeDee: .............. is the most ridiculous and the most absurd procedure only he can invent to find out what events of a rotating wheel per axle frame are simultaneous in the road frame.
cinci: Well at least you acknowledged that I invented something.
Dear cincirob,
You and I agree that this is what the wheel looks like in the axle frame:
We also agree that the firecracker pops at road coordinates x=1.000, y=0.866, t=0.866. Let's just focus on that for a minute.
Note that the firecracker is located on the edge of the wheel when it pops, and so it leaves a small burn mark on the wheel.
................
With the ellipse shape, the edge of the wheel is located in the same place as the firecracker popping, and so the firecracker popping leaves a small burn mark on the wheel.
................
With the pear shape, the edge of the wheel is NOT located in the same place as the firecracker popping, and so the firecracker popping DOES NOT leave a burn mark on the wheel.
This disproves the pear shape, and also proves that the shape MUST be an ellipse. Otherwise you are claiming there is a true paradox in relativity.
Laugh at cinci? Well, we're all guilty of that on this website... ...but why does VeeDee's alternative remind us so much of Monty Python's Last Supper with its 27 apostles & 3 Christs?  different times linked rigidly with different events rendering an overall 'photographic' rendition of the rolling wheel essentially impossible  especially with incompatible rim velocities at the top & bottom of the wheel. No wonder Pope Alexander VI (John Cleese) was more than obstreperous towards V. D. Michael 'Minkowski' AngeloPalin!
TFOLZO
Ya, that's what they all say when they do not understand the meaning of relativistic effects in collective. These kind of statements have been argued and put under since 1905, repeatedly. Folks will be repeating them for another 100 years. Of course, no one ever said that fused spacetime was an easy concept to grasp. The velocities of Gron's rolling wheel per ground, can be no other way.
It's funny that some folks don't seem to have trouble with a moving contracted inertial body with Born rigid atoms closer to one another than how they would exist at rest, yet soon as a body rotates with translation, they flap their hands in the air yelling "liar liar pants on fire". It's all the same, really. Think fused spacetime, and forget absolute space for a minute. That might help.
Thank You,
SinceYouAsked
Yes indeedy, you most preeminent of the dictators alluded to above  SinceYou'reAdolf  your first words below highlighted in red enscapsulate a difficult issue in relativity!It does indeed! Fortunately, your latter words, here highlighted red (& bold) illustrate the answer as to the fiery origin of the hot fusion of space'n'time.TFOLZO: Laugh at cinci? Well, we're all guilty of that on this website...
...but why does VeeDee's alternative remind us so much of Monty Python's Last Supper with its 27 apostles & 3 Christs?  different times linked rigidly with different events rendering an overall 'photographic' rendition of the rolling wheel essentially impossible  especially with incompatible rim velocities at the top & bottom of the wheel. No wonder Pope Alexander VI (John Cleese) was more than obstreperous towards V. D. Michael 'Minkowski' AngeloPalin!
Sure beats asking you which of the three or more answers for the velocity of the top of the rolling wheel seen by the road observer is the correct one  or its ReligioPythonesque equivalent as to who is the true JC (not John Cleese) in Monty Python's Last Supper  the fat Christ in the middle or the two skinny Ones on either side. Whatever answers you, SYA, give to either question is of equal physical significance!  Isn't that so cinci!?
TFOLZO
*Ja! Ja! Ja! Herr Major Hochstaedter!
Last edited by TFOLZO; 08092014 at 10:48 AM. Reason: Incomplete sentence & coloring
I don't need it. But it shows you what Lorentz Transformations do, and unfortunately for you that's not what you calculate.Yes, "there is always an atom at 60 degrees". So what? What has this to do with relativity, Lorentz Transformations, and RoS length contraction? Nothing! And you don't understand this because you don't know what Einstein relativity is about.
VeeDee: Taking all the above into account, it is obvious that Cinci's xdirection rim point coordinate scenario is complete nonsense. Especially his quote from post 1011: (forget RoS, there is always some point at 60 degrees), .................................[/B]
cinci: You mean there isn't always a point at 60 degrees? Please explain.
VeeDee: .............. is the most ridiculous and the most absurd procedure only he can invent to find out what events of a rotating wheel per axle frame are simultaneous in the road frame.
cinci: Well at least you acknowledged that I invented something.
Jcinci: JT, I'd like to continue to discuss this with you but let's agree on this: I have done Gron's analysis in detail and I understand exactly what he did and why he did it. And I have done the analyses of the rods and we agree on those, RoS and all. I won't continue any conversation here with anybody who claims otherwise.
Now, I recognize the disconnect with the pear that you described in your last message but here's the problem. I can and have shown that Gron's analysis doesn't change if you consider the disk at rest with points moving around it (the marble race); if you want to try to disprove that, be my guest. So it is not clear to me that the elliptical shape is correct because the rotating case cannot be distinguished from the nonrotating case. Unquestionably, a spinning or rotating disk must have internal velocities, contracted material and relativistic time effects. If Gron's analysis is correct, then you should be able to use all of those effects and calculate Gron's answer. If you can't do that, I say there is still a question. Everybody here claims his only goal is to understand relativity and teach others; this seems like a challenge and a great opportunity to do just that. So somebody needs to step up instead of repeating the same analysis over and over in divers ways.
Last edited by cincirob; 08092014 at 05:52 PM.
In reply to TFOLZO, re: your #1048 post.
(hahaha) Somebody remembers "Hogan's Heros".
TFOLZO...you know as well as anyone else that the "Gronwheel" examples are nothing more than "observational framedragging" effects...which is to say NOT a "true" observation.
(now, now...no ranting! I know that YOU know that "alles ist und ordnung" w/ regard to atom "positioning" in any given frame reference...(just think, you would actually be AGREEING
w/ Einstein in this!) I am thinking the entire "Gron wheel" example is an example of semantics of observation and nothing more.
(Thanks for reading!)
The velocity u for any atom of Gron's rolling disk per ground, is attained from the composition of velocities formula using all coordinate inputs from the axle's spacetime system, so the Composition of Velocities ...
u = √[(v² + w² + 2vwcosα)  (vwsinα/c)²] / (1+vwcosα/c²)
Plug in the instantaneous axle coordinates, you have the correct instantaneous ground result.
Thank You,
SinceYouAsked
When we consider the "length of circumference" passing forward over the wheel relative to that passing under the wheel we find unresolvable incompatibility  each incompatibility varying as to whether we are considering a rim observer, an axle observer (nonspinning) or the road observer. When one asks for an objective answer, there is none. Instead we get...
...an equation  presumably amenable to 'pearshaped' modification & refutation  yet another piece of grandstanding, mein F...
TFOLZO
I appreciate you acknowledging the 'disconnect' with the pear. It is actually more than just a disconnect, it is a blatant violation of causality. But I am glad that you understand there is a problem there.
I also appreciate that you have always acknowledged that Gron's analysis would be correct for a nonrotating circular disk with points moving around its circular perimeter at a constant speed of v, as measured by the axle frame. Now if we consider a rotating disk of the same dimensions, the axle frame would also measure the points as moving around its circular perimeter at a constant speed of v. So the points must transform identically.
The only difference is that the actual disk must be built a certain way. You already solved that problem when you invented the contracting/shrinking wheel. That wheel is larger when nonrotating, and smaller when rotating, but that is not a problem. That wheel's perimeter points transform exactly the same as the marble race, just as they must do. Anything else produces a violation of causality, as I have shown.
in reply to TFOLZO, re: your posts this thread.
What are "collective relativistic effects?" How are you establishing the parameters? Velocity v. time or what?
(Thanks for reading!)
JT: I appreciate you acknowledging the 'disconnect' with the pear. It is actually more than just a disconnect, it is a blatant violation of causality.
cinci: All you have shown is that it doesn't act as if it is nonrotating.
JT: But I am glad that you understand there is a problem there.
I also appreciate that you have always acknowledged that Gron's analysis would be correct for a nonrotating circular disk with points moving around its circular perimeter at a constant speed of v, as measured by the axle frame. Now if we consider a rotating disk of the same dimensions, the axle frame would also measure the points as moving around its circular perimeter at a constant speed of v. So the points must transform identically.
cinci: That's just your assumption. If it's correct, then you should be able to address the relativistic effects in the rotating disk and use the LTs to get a match with the Gron wheel. I think that's a tough sell because you apply the same Gron solution to a contracting wheel as you do to a Born rigid (noncontracting) wheel; and, we know there are some differences between the two outcomes. One works as a rack and pinion and one doesn't.
JT: The only difference is that the actual disk must be built a certain way. You already solved that problem when you invented the contracting/shrinking wheel. That wheel is larger when nonrotating, and smaller when rotating, but that is not a problem. That wheel's perimeter points transform exactly the same as the marble race, just as they must do. Anything else produces a violation of causality, as I have shown.
cinci: See above.
I don't know what the specific term "collective relativistic effects" means, GerryN... ...as these things are referred to in SinceYou'reAdolf's post #1047. To me all that stuff is just "implications of SR".
So click your heels, be appropriately grovel... er... subservient, und der Relativitätführer möge Sie unterrichten!
TFOLZO
Moderator Note:
TFLOZO, you will modify your attitude when addressing other members. No snide comments. No "oh so witty and ironic" modifications of their usernames.
The same goes for anyone else doing this, of course. STOP ACTING LIKE CHILDREN!
JT,
Congratulations, I read you and cinci got agreement on the firecracker popping at x=1.000, y=0.866, t=0.866.
But cinci still refutes the wheel rim to be at that point? In other words: he still doesn't understand one of the basic concepts of relativity: the content of an event does not change from frame to frame...
Why is he unable to understand this, so that we may help this poor guy... ?
Or does he simply not want to understand relativity? Let me guess....
Correct me if I'm wrong here, VeeDee......but shouldn't the highlighted portion read: the context of an event does not change from frame to frame...
I say this because an event is localized in time & space  a "point" in spacetime as it were  whereas what is really important is the external conditions of the event, that they should be the same in all frames in order to get an objective answer.
TFOLZO
In reply to TFOLZO, re: your #1061 post.
The "external conditions" should match ALL the other frames...excellent! (I am thinking the "wheel" seems to produce contrary observations via the mechanisms of "ars matematica", but
the facts of Relativity still hold true..."each FoR is true to itself". By this mandate, each "FoR" must also demonstrate conformity (no "frame" can demonstrate an inconsistency that
contradicts the other frames, such as an implied velocity "greater" than its neighbors) An event of observation seems to predicate an "event" in advance (chord structure) of an actual
occurrence, and by this "occurrence" one could say "both events can occur at the SAME TIME on the wheel, and therefore velocity can significantly the "reality" of wheel w/ respect to
the other frames "not moving as fast"....to me , this is completely illogical "logic" of observations, a "false" reality of truth.
(Thanks for reading!)
For a single constant rolling velocity, all of the different types of wheels will work as rack and pinion. Given the same rolling speed, and the same geometric dimensions, all of these wheels are indistinguishable from one another, at constant v. Therefore, your belief that they should be treated differently is unjustified.
In reply to TFOLZO, re: my #1056 reply.
Sorry...the "collective relativistic effects" reference is from "SYA" in #1047. (I'm still uncertain of the implications...is this a "real matter" or a "quantum entity" effect, or both?
Your reply here is very worrisome.
1. I showed that the firecracker leaves a burn mark on the rim of the ROTATING CIRCULAR wheel, according to the axle frame.
2. I showed that the firecracker leaves a burn mark on the rim of the ROLLING ELLIPTICAL wheel, according to the road frame.
3. I showed that the firecracker DOES NOT leave a burn mark on the rim of the ROLLING PEAR wheel, according to the road frame.
Do you understand that #3 contradicts #1, and that creates a real paradox? You cannot say that we should EXPECT the outcome to contradict #1, because the wheel is rotating. You cannot say that the lack of contradiction between #2 and #1 only proves the wheel is not rotating. Even rotating objects are not allowed to create paradoxical outcomes.
VeeDee: Congratulations, I read you and cinci got agreement on the firecracker popping at x=1.000, y=0.866, t=0.866.
But cinci still refutes the wheel rim to be at that point? In other words: he still doesn't understand one of the basic concepts of relativity: the content of an event does not change from frame to frame...
Why is he unable to understand this, so that we may help this poor guy... ?
Or does he simply not want to understand relativity? Let me guess....
cinci: Why don't you stop guessing and address my issue.
I have agreed and calculated that it all works just as Gron says if the wheel is not rotating, years ago.
If you the Big Cahuna of relativity you claim to be, then prove Gron's analysis includes the rotation of the disk structure and not just a point moving around of a nonrotating, round disk.
Stop telling me what you think I don't know and show us what you do know.
"A point moving around of a nonrotating, round disk". ???????? Wow! Are you dreaming?
Lorentz transformations keep track of events. Not "points moving around a non rotating structure".
You are COMPLETELY lost, boy. What next are you going to invent to blow smoke? Yes, you are an inventor. Congratulations. But you are definitely discussing your inventions on the wrong forum.
Stop telling me what you think I don't know and show us what you do know.
VeeDee: "A point moving around of a nonrotating, round disk". ???????? Wow! Are you dreaming?
Lorentz transformations keep track of events. Not "points moving around a non rotating structure".
You are COMPLETELY lost, boy. What next are you going to invent to blow smoke? Yes, you are an inventor. Congratulations. But you are definitely discussing your inventions on the wrong forum.
cinci: Just because you don't know how to do the analysis doesn't mean I don't. If you can't imagine a way to mechanically make this happen maybe you've never looked at a clock. I can recommend some books on creativity for you.
In other words you are totally incapable of reading where the rotation occurs in Gron's (101B) equation for x?
And I bet you don't even see where the rotation occurs in his (100) equation for x'?
And you are not playing games with us here?
Boring, really.
EDIT: Wait a second. Are you now going to tell me that the equation deals with a moving point but still on a nonrotating wheel? That kind of s**t?
Or because you see some gamma you automatically think it are only pure plain Fitzgerald contractions?
Tell me, I'm open for more jokes. Yes, I stick to this forum because I find you rather entertaining as far as your interpretation of Gron's equations are concerned. Very entertaining.
and not just a point moving around of a nonrotating, round disk.
Stop telling me what you think I don't know and show us what you do know.
The Gron analysis starts by relating moving points of the rotating bornrigid round disk to stationary points in the axle system. Now, the stationary points in the axle system are virtual points, occupied by moving atoms of the rotating disk. If one prefers, one can consider a stationary round disk of the same radius R, that's separated by (say) 1 millimeter on the zaxis from the rotating bornrigid disk of the same radius R (per axle). Two disks the same radius, parallel to one another, barely separated wrt z, one rotating and one not. The one that does not rotate, may have a grid upon it, denoting the cartesian or polar coordinates wrt the axisofrotation (axle).
Now as we all know, there are no relativistic distortions wrt axes orthogonal to the axis of motion, eg y and z. The relativistic distortions are wrt the axis of motion alone, in Gron's case x. In the axle system, one merely picks an atom of the rotating disk and chooses a moment in the axle system to consider it, t'. Thus, you capture the atom when at x',y',z' upon the instant t'. In relativity theory, this marks an EVENT called x',y',z',t'. Now then, it is this simple ... that event must occur in the ground system per the inverse LTs at ...
t = γ(t'+vx'/c²)
x = γ(x'+vt')
y = y'
z = z'
where γ = 1/√(1v²/c²)
This, the Gron analysis.
Now cincirob, what problem do you have with this?
When you talk about a point moving around a stationary round track, is this what you are talking about, or do you mean something different?
Thank You,
SinceYouAsked
SYA: When you talk about a point moving around a stationary round track, is this what you are talking about, or do you mean something different?
cinci: What part of your explanation would change if the disk were a static hoop sliding down the road and your selected point was a ball rolling around inside the hoop at v (centrifugal force would keep it there)?
If this isn't real enough for you then imagine a particle travelling around an accelerator and you're flying by at v.
VeeDee: Tell me, I'm open for more jokes. Yes, I stick to this forum because I find you rather entertaining as far as your interpretation of Gron's equations are concerned. Very entertaining.
cinci: I interpreted Gron's equations just fine. (See my plotted diagram.) My sole question is whether or not the ellipse is correct. What I find entertaining is that every time I ask that question somebody explains the curvature of the spokes which, if you understand Gron's analysis, has absolutely no bearing on the ellipse shape.
The ellips is correct.You hallucinate, man. There's pages here we explain you how events work in Lorentz transformations and you understand nothing of it. The only thing you can repeat is your own interpretation of relativity which doesn't make sense at all.What I find entertaining is that every time I ask that question somebody explains the curvature of the spokeswhich, if you understand Gron's analysis, has absolutely no bearing on the ellipse shape. ]
See sketches below.
Event B4 = pole end at rim and firecracker popping at t'=0 x'=.5 y'=.866
Event B4 is in the road frame at t=.866, at y=.866 x=1
Why?
Very easy: Lorentz Transformations, Gron equation 101A and 101B.
Cinci wants to know what's in the road frame at t=0 y=.866
Event B4 will not help us. That event does not meet the requirement of Gron equation 102 (in order to find out which events are in road frame at t=0).
Which event DOES occur in the road frame at t=0 y=.866 ?
It's the rim atom per the axle frame at angle 60° at t'=.433 (See event C2 sketches below). C2 passes the test of Gron equation 102.
Cinci, take note that this rim atom is NOT the rim atom that will hit the pole end at t'=0 (C2 is an event of the blue rim atom, not the red rim atom.)
That blue atom has at t'=0 arrived at 38,5 degrees (see event C4). This is important to know because theta is the angle at t'=0
We can now transform EVENT C2 from axle to road.
In Gron equation (101A) we plug EVENT C2 (Theta to be used is the angle for the blue atom at t'=0, not at t=.433)
This results in... t=0 ..... OBVIOUSLY!
For EVENT C2 Gron (101B) gives...
y=.866
x=.25
That's an ellips point.
Last edited by VeeDee; 10252017 at 09:08 AM. Reason: fixing img hosting problem
Cinci's marble race scenario ... we have a stationary (nonrotating) hollow hoop of radius R in the axle system. Next, we imagine marbles all bonded together as a bornrigidring endonend while rotating at steady relativistic rate within the hoop, never touching the inside walls of the hollow hoop. The rotation rate is ω with the requirement of no slippage during frictionless roll. The relative motion between any marble atom and ground atom at virtual contact is at "momentary relative rest wrt one another". Given such, ωR = v. Per the Gron analysis, the rotating circle of marbles per axle is a standard 1/γ contracted ellipse per ground. Add, both the rotating marblering and the ellipse have the same shape per any POV, including the ground, per Gron's analysis ...
OK, so if a stationary disk (with grid on it) were placed in parallel with Gron's rotating Bornrigid disk (both of the same R), and the rotation rate ω is such that the relative motion between any perimeter rotating diskatom and ground atom at virtual contact are at "momentary relative rest wrt one another" (so ωR = v). Now ... Q) Do you agree that the Gron analysis in this case adequately predicts the same outcome as your marble race?
If not, please explain why.
Thank You,
SinceYouAsked
cinci: What I find entertaining is that every time I ask that question somebody explains the curvature of the spokes
VeeDee: You hallucinate, man.
cinci: Hallucinating? :) Look at your message 1076. You did it again.
VeeDee: There's pages here we explain you how events work in Lorentz transformations and you understand nothing of it. The only thing you can repeat is your own interpretation of relativity which doesn't make sense at all.
cinci: Right, I just made this up:
Yeah, he thinks points moving around a nonrotating wheel are different than points comoving with a rotating wheel. So he wants proof we're using the latter, and not the former.
Yeah, that too. If the wheel comes out an elliptical shape, then he feels that is proof that the entire analysis is nothing more than pure Fitzgerald contraction. He thinks this because he does not remember that the pear shape was already proven wrong by the paradox it creates for the firecracker. The axle frame sees a burn mark on the rim, but the road frame does not see one. If the wheel stops rolling, everyone must agree whether there is a burn mark or not, but they can't agree, so the universe explodes. All because of cinici.
SYA: Cinci's marble race scenario ... we have a stationary (nonrotating) hollow hoop of radius R in the axle system. Next, we imagine marbles all bonded together as a bornrigidring endonend while rotating at steady relativistic rate within the hoop, never touching the inside walls of the hollow hoop.
cinci: If you bond them together at rest, then they will break apart. If you're going to add marbles and bond them together on the fly, I'm not interested in that particular problem because you're just turning it into the same problem
Why don't you just answer the question I asked? Too tough for you?
SYA: The rotation rate is ω with the requirement of no slippage during frictionless roll. The relative motion between any marble atom and ground atom at virtual contact is at "momentary relative rest wrt one another". Given such, ωR = v. Per the Gron analysis, the rotating circle of marbles per axle is a standard 1/γ contracted ellipse per ground. Add, both the rotating marblering and the ellipse have the same shape per any POV, including the ground, per Gron's analysis ...
OK, so if a stationary disk (with grid on it) were placed in parallel with Gron's rotating Bornrigid disk (both of the same R), and the rotation rate ω is such that the relative motion between any perimeter rotating diskatom and ground atom at virtual contact are at "momentary relative rest wrt one another" (so ωR = v). Now ... Q) Do you agree that the Gron analysis in this case adequately predicts the same outcome as your marble race?
cinci: You just worked the same problem as posed by Gron when you bond them all together. You know very well the point I'm making and you're trying to squirm out of dealing with it.
I agree that Gron's analysis is exact for the unconnected marbles and static structure as I defined it; I told you that years ago. The question is do you now believe it?
You answer my question, then we'll discuss rollup once you understand the answer to my question. Normal folks would be perfectly fine with that. It's really not that much to ask, given all the time that's been given you.
No, as I obviously stated above, the question was ... Q) Do you agree that the Gron analysis in this case adequately predicts the same outcome as your marble race?
Did your response above mean YES, or did it mean NO? How's about an answer. It's pretty easy ... YES or NO?
Your problem is that you change the subject every 2 seconds, to something entirely different, never giving any clear answers to anything. For example, I asked my question for a steadily rotating Bornrigid body, and instead of answering my question, you immediately began talking about what happens during the rollup process. Everyone knows it. If you stick to one point until you understand it, we can then proceed to the next, like what happens during the rollup.
My position is that the 2 scenarios are identical, and modeled by the Gron analysis properly.
Gron's analysis also handles unconnected marbles, that all travel a circle at steady rate per axle. You see, the only requirement that matters is this ... the marbles travel a circle at steady rotation rate ω = v/R (no slippage at ground contact). That requirement may be enforced "by definition" as I just did here for unconnected marbles, or by the requirement of Bornrigidity if all the marbles are bonded together endonend. Either way, the Gron analysis produces the same result.
No one here is arguing with you. They are correcting you, but you simply won't be told. You don't really want to be another Herbert Dingle, do you?
Thank You,
SinceYouAsked
You see cinci, this is the way the SYA regime operates! They demand you answer on the dotted line  a treaty based on 'yes' or 'no'. SYA is led to this because there is NO objective basis for his claims  he knows as well as you do that "circumferential length contraction" resulting in increased π is objectively unresolvable given the fixed length of the spokes of the wheel  the fixity of length of the spokes subject to both the circumferential & the linear length contraction (except perhaps vertically, normal to linear motion). Hence there is NO objective basis upon which you can say 'yes' or 'no' unequivocally, since his elliptical scenario & your pearshaped scenario do not qualify as objectively real situations.
Hence his demand for you to put your signature to his surrender document! "Ja oder nein!" eh, SYA!
*Dingle? Gee, SYA, I thought I was!!! What would cinci be then?  a DoofusDingle who affirms TD&LC yet rejects its implications?
TFOLZO
JT,
Cinci's issue is the apparent lack of addition of velocities in the LT calculations. But you did a very good job showing and teaching me how a moving pole per axle frame can be directly transformed from axle to road and give correct contraction per road results (I highlight this because Cinci loves bold type). Your posts on page 8 of this thread illustrate this very well. And what Gron does is exactly the same procedure, but for a rotating wheel. You checked it, SYA checked it, and I checked it. Ellips is the answer. End of story.
Cinci,
Your point is that Gron's LT do not incorporate the wheel rotation velocity?
In other words you are totally incapable of reading where the rotation occurs in Gron's (101B) equation for x?
And I bet you don't even see where the rotation occurs in his (100) equation for x'?
If you don't see
u't' +L'
you are totally lost? Is that it?
You WANT to see
u't' +L'
for the wheel rotation? Is that your problem?
You even demand the LT include
u't' +L'
for the rotating rim atoms?
And you refute the rotation velocity item in the LT (wheel rotating per axle frame)?
After 2000 posts it's about time we get informed what is the exact issue you want to discuss....
But if you see no rotation at all in the LT, then your case is hopeless...
SYA: Cinci's marble race scenario ... we have a stationary (nonrotating) hollow hoop of radius R in the axle system. Next, we imagine marbles all bonded together as a bornrigidring endonend while rotating at steady relativistic rate within the hoop, never touching the inside walls of the hollow hoop.
cinci: If you bond them together at rest, then they will break apart. If you're going to add marbles and bond them together on the fly, I'm not interested in that particular problem because you're just turning it into the same problem
Why don't you just answer the question I asked? Too tough for you?
SYA: You answer my question, then we'll discuss rollup once you understand the answer to my question. Normal folks would be perfectly fine with that. It's really not that much to ask, given all the time that's been given you.
SYA: The rotation rate is ω with the requirement of no slippage during frictionless roll. The relative motion between any marble atom and ground atom at virtual contact is at "momentary relative rest wrt one another". Given such, ωR = v. Per the Gron analysis, the rotating circle of marbles per axle is a standard 1/γ contracted ellipse per ground. Add, both the rotating marblering and the ellipse have the same shape per any POV, including the ground, per Gron's analysis ...
OK, so if a stationary disk (with grid on it) were placed in parallel with Gron's rotating Bornrigid disk (both of the same R), and the rotation rate ω is such that the relative motion between any perimeter rotating diskatom and ground atom at virtual contact are at "momentary relative rest wrt one another" (so ωR = v). Now ... Q) Do you agree that the Gron analysis in this case adequately predicts the same outcome as your marble race?
cinci: You just worked the same problem as posed by Gron when you bond them all together. You know very well the point I'm making and you're trying to squirm out of dealing with it.
I agree that Gron's analysis is exact for the unconnected marbles and static structure as I defined it; I told you that years ago. The question is do you now believe it?
SYA: No, as I obviously stated above, the question was ... Q) Do you agree that the Gron analysis in this case adequately predicts the same outcome as your marble race?
Did your response above mean YES, or did it mean NO? How's about an answer. It's pretty easy ... YES or NO?
Your problem is that you change the subject every 2 seconds, to something entirely different, never giving any clear answers to anything.
SYA: For example, I asked my question for a steadily rotating Bornrigid body, and instead of answering my question, you immediately began talking about what happens during the rollup process. Everyone knows it. If you stick to one point until you understand it, we can then proceed to the next, like what happens during the rollup.
SYA: My position is that the 2 scenarios are identical, and modeled by the Gron analysis properly.
Gron's analysis also handles unconnected marbles, that all travel a circle at steady rate per axle. You see, the only requirement that matters is this ... the marbles travel a circle at steady rotation rate ω = v/R (no slippage at ground contact). That requirement may be enforced "by definition" as I just did here for unconnected marbles, or by the requirement of Bornrigidity if all the marbles are bonded together endonend. Either way, the Gron analysis produces the same result.
No one here is arguing with you. They are correcting you, but you simply won't be told. You don't really want to be another Herbert Dingle, do you?
cinci: Allow me to correct you. What I say is the solution to the marble race, with unconnected marbles and static structure, is the Gron solution, exactly. To be sure Gron is correct for a rotating structure, somebody needs to take the velocities, contractions and time effects of a rotating structure into account and prove it is exactly like a nonrotating structure.
All the nonsense above where you changed the subject and introduced other models is you trying to avoid this issue. Your first statement above proves it: Next, we imagine marbles all bonded together as a bornrigidring endonend while rotating at steady relativistic rate within the hoop, never touching the inside walls of the hollow hoop. Not at all what I suggested.
If you respond to this with anything other that a refutation or confirmation of the underlined statement then it will be even more clear you are the one who is changing the subject and muddying the water. I'll ignore anything else.
Thank you, VeeDee, I am glad to have been of help. Not only does the pole transform with the correct contracted length, it also transforms with the correct composed velocity. That is because both the Length Contraction Formula (LCF) and the Velocity Composition Formula (VCF) are derived from the LT equations.
Who knows what cinci's issue is these days. Last I heard, he was saying that a point traveling a circular path at uniform speed does not model a purely rotating disk, or something like that. I mean, seriously?!?! This is as basic as it gets. We consider a point at rest on the purely rotating disk, and assume the point travels a circular path at uniform speed, with the axle as the center point. From that we can find the x' and y' coordinates of the point at any chosen time t'. That's the whole reason for starting in the axle frame, where the symmetry makes it easy to describe everything mathematically.
But this does not involve pears, so cinci doesn't like it. He must really like pears. He probably eats a pear with every meal.
All too easy, isn't it JTydJT?A point traveling in a circular path at uniform speed does NOT model a purely rotating disk since with the point you have no problem with length contraction stuff & perhaps even not with time dilation (and people wonder why I called you 'Pointdexter'!).
The point does NOT model a purely rotating disk because in the latter you have the counterfactual (i.e. objectively unresolvable) situation of constant length & size of the disc from the axle (i.e. constant spoke lengths if the wheel had spokes) despite the circumference growing ever SHORTER (& therefore increasing π  as in Relativity chapter 23).
Therefore you cockily claim you can leave the issue out, in this way simplemindedly merely 'squeezing' the disc (thus treated as nonrotating) into an elliptical shape thru oldfashioned linear length contraction. Cinci is annoyed  & rightly so I might add  about your (hyper)blinkered stance.
TFOLZO
Last edited by TFOLZO; 08142014 at 08:32 AM.
Apart from the adding of velocities I don't know what his issue is either.
If the rotating wheel is a circle per axle frame, then its an ellips per road frame. Lorentz Transformations prove it.
Gron's equations give an ellips, which is correct when starting with a rotating circular wheel per axle frame.
If Cinci still cannot grasp why Gron is correct, then Cinci has a huge problem.
Cinci thinks Gron's calculations forget addition of velocities but Cinci doesn't know even after being explained in detail how it works Gron doesn't need 'adding of velocities' if he keeps track of the events for t=0, as Gron does correctly. But Cinci doesn't understand how this works because he doesn't know what events are, what RoS means, etc. That's also why he can not read spacetime diagrams, be it Minkowski or Loedel. Cinci doesn't need all that to reinvent relativity his way.
Cinci simply doesn't understand anything of what Gron does. This is because Cinci thinks he knows everything about Einstein relativity, but to date he has not posted one message proving he does understand Einstein relativity. Every time the issue arises he jumps to other topics, preferably by asking questions himself.
What can we still do to help this poor guy after 1500 posts over two threads?
JT: We consider a point at rest on the purely rotating disk, and assume the point travels a circular path at uniform speed, with the axle as the center point. From that we can find the x' and y' coordinates of the point at any chosen time t'.
cinci: Let's see if you can answer a question. What happens if you consider a circular disk purely translating at v with a point moving around it with a tangential velocity of v?
As far as I can see, you would get......a line of 'scallops' i.e.
ᴖᴖᴖᴖᴖᴖ
...but, UNLIKE my illustration, the scallops would be touching each other as the contact point represents where the point moving around the disc reaches the road most closely.
Not half as much fun as a wheel with gearteeth around it however  and which would solve all your headaches in one go, cinci.
TFOLZO
The equations have an R' in them to represent the radius of the rotating wheel, as measured by the axle frame. If the wheel gets smaller for larger values of v, then one simply reduces the value of R' accordingly. You didn't really think a Pointdexter like me would have overlooked something so simple, now did you?
And the values of t' are all measurements of time taken from the axle frame. Axle frame clocks are not timedilated by motion of the wheel, because they are not on the wheel. They run at 1 second per second, in the axle frame.
I don't understand how you jump to the conclusion that the wheel is treated as nonrotating. That is the kind of nonsense that cinci likes to post.
JT: The nonrotating disk would drag along the road, heat up, and burst into flames. Better to use a rotating wheel.
cinci: Funny, but you know the answer. Nothing about Gron's analysis implies that there is a rotating structure.
This is a good point. The reason cinci resists learning so strenuously is because he is very comfortable doing relativity his own way. He thinks he can use length contraction for everything, and it is a simple calculation that he knows how to do. So, he is not concerned with anything else, even when it is proven that his resulting pear shape must be an incorrect answer, because it produces a paradox where the firecracker both 'does' and 'doesnot' make a burn mark on the wheel. He would rather be wrong, (and deny it), than to have to learn to do slightly more complicated calculations.
Yes it is quite remarkable that he holds himself as an expert, when his misunderstandings are written here for the whole world to see. The idea that one could use the contracted length of a translating pole to check Gron's wheel geometry is ludicrous. The time coordinates of the endpoints of the pole are t=0, but that is not the time when the right endpoint intersect the right edge of the wheel! What nonsense!
I don't see how we can help him if he refuses to learn. At least he agrees the marble race produces the same results as Gron's. Maybe he would finally get it if he would realise that there is a 1to1 correspondence between the marbles and points on the rotating wheel. This is easy to see from the axle frame, where both are merely going in circles, and not translating.
Very witty JTydJT! Well of course not, JTpdJT, but as a believer in an elliptical wheel you only apply the reduced R along the axis of motion. Unfortunately for you, this is NOT enough to counteract the reduction in length of the circumference due to Relativity chapter 23, hence if you really want to find a way to reduce the whole wheel in size while keeping the circumference intact & visualizable you are going to have to invoke transverse length contraction i.e. length contraction applied at right angles to the motion  as some like my friend John Callow does!
I can accept that your axle frame clocks are not time dilated by the wheel's spinning motion  but they become so (according to SR) when the wheel is moving relative to a road observer. And this is harder still when wheelrim clocks (not axleframe clocks) are compared to the roadobserver's clocks since the time dilation of the former would be variable on a regular basis depending on whether the wheelrim clock was at the top or at the bottom of the spinning wheel  since what 'creates' time dilation according to Big Al Einstein in relative motion between ANY two observers, even if one of the observers is undergoing an intermittent but regular motion.
Hence when you claim that the spinning wheel is elliptical relative to the road observer, this is tantamount also to denying that wheelrim clocks will undergo intermittent time dilation relative to the road observer (in defiance of SR), as they would then merely undergo the 'linear velocity' component of time dilation like the wheel axle, despite these wheelrim clocks flying about the rim of the elliptical wheel!
But even when the wheel is linearly stationary, applying time dilation to the circumference of the spinning wheel could be used to claim that the wheel is not rotating as fast as it seems to be (e.g. to a wheelrimbased observer telling the axle observer what he sees), over and above the 'unaccountable overshortening' of the circumference due to the increase in π.
The relative slowing of wheelrim clocks, particularly at the top of the wheel relative to the road, is the counterpart of cinci's point that the top half of the wheel, moving more quickly wrt the road observer will be lengthcontracted relative to the bottom half of the same wheel, hence the wheel's predicted pearshape.
Now I fully agree that the axle observer will NOT even find the wheel to have an elliptical shape, let alone a pearshaped one  and cinci will (I hope) agree wholeheartedly here  but the road observer has to be compared to hypothetical observers on every point of the rolling wheel. Hence if you apply SR to each point compared to the road observer you will, if you believe SR, assert that the wheel will become pearshaped due to the faster motion of the top of the wheel. You will probably here assert indignantly that the wheel is elliptical to the road observer, so my reply is:
My point is that the situation is objectively unresolvable, since by telling me that the wheel is spinning you cannot then explain the shortening of the circumference not corrected adequately by the 'elliptical wheel'. You also have a logical paradox between 1) & 2) where:
1) the axle observer finds the wheelrim observers' clocks time dilated relative to his own  but in a regular steady pattern.
2) the road observer however will find the time dilation of the wheelrim clocks to be irregular, varying with the position of the clocks on the wheel  not a surprise when the axleobserver sees the wheel as round while the road observer sees the wheel to be either pearshaped or elliptical!
All the Minkowski diagrams do here is subdivide the points on the wheel into different time measures (t', t'', t''', t'''' etc.), the wheel's shape being objectively unresolvable  and you well know (if cinci doesn't) what such logicchopping subjectivization of time leads to  Hugh Everett's ...!
TFOLZO
That's much ado about nothing, TFOLZO. There is no need to consider any clocks located on the wheel, but if we did they would be represented by t''. As it stands, if this were a bike wheel, we would be using bike clocks for t', not wheel clocks.
And the construction of the wheel determines whether its radius changes or not. A wheel made of only spokes (and no rim) does not change in radius for any speed. A wheel made of only a thin rim (and no spokes) does change radius for various speeds. We've been over these kinds of details ad nauseum over the years. Surely you can't imagine that you are the first to think of this now?
You are saying that a point traveling a circular path of R=1 with a speed of v does not describe the wheel, because it is just a point traveling a circle.
But if we start with a purely rotating wheel, according to the axle frame, and we consider a point comoving with the edge of the wheel, we find that it travels a circular path of R=1 with a speed of v.
Do you see the problem with your reasoning?
JT: You are saying that a point traveling a circular path of R=1 with a speed of v does not describe the wheel, because it is just a point traveling a circle.
cinci: What I said was that Gron's analysis does not deal with the structure of the wheel. You said it did. Do you see any problem with your statment?
JT: But if we start with a purely rotating wheel, according to the axle frame, and we consider a point comoving with the edge of the wheel, we find that it travels a circular path of R=1 with a speed of v.
Do you see the problem with your reasoning?
cinci: Saying that Gron's analysis doesn't deal with the structure of the wheel is irrefutable. If it weren't, either you or SYA would have refuted it. You haven't. SYA loped off track into analyses of different models and you tried to fob it off with a funny line. There is nothing in Gron's analysis about the rotating structure. I know you and SYA think it's cute to avoid answering questions, but it really just highlights the problem with the analysis, doesn't it?
If you can mathematically show that the rotating structure would act exactly like the static one, then I wouldn't have any problem with Gron's analysis and this would all be over. But you have to deal with the velocities and contractions that have to occur in Gron's model. Can you show the structure mechanics gives the same answer?
I've been trying to deal with the structure and, as you point out, it doesn't work. Now tell me how to make it work.
Did you try looking in the Gron paper for discussion of the structure of the wheel? There are pages and pages of it.
From page 6, Einstein's letter to Joseph Petzold dated August 19, 1919:
From page 26, "The theory of elastic media applied to the rotating disk" (Later followed up by Cavalleri in 1968)Originally Posted by Einstein
From page 27:Originally Posted by Clark
From page 30:Originally Posted by Grøn
From page 44, "Contracted rotating disk":Originally Posted by Grøn
And I thought you had invented the contracting wheel, but there it is right in the Gron paper.Originally Posted by Grøn
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