# Thread: Length Contraction of Space Between Objects

1. cinci: As for the pole, the time at its right edge is t = -Vx/(1 - V^2)^.5

JT: Actually the road time at the right edge of the pole is this:
t = γ(t' + (vx' / cē)) = 0.866
Where:
γ = 2.000
v = 0.866
t' = 0.000
x' = 0.500

Is there some reason you don't use the LT's for this?

cinci: That is the LT. Is there some reason you don't recognize it?

cinci: ...and you can get x from LCF.

JT: Or you can get x from this equation for x:
x = γ(x' + vt') = 1.000
Where:
γ = 2.000
v = 0.866
t' = 0.000
x' = 0.500

Again, is there some reason you don't use the LT's for this?

cinci: Is there some reason you're not discussing the fact that I showed you how to do the spaceship problem using the LCF?

Considering a pole that is coincident with the chord of a spoke 60 degrees above horizontal in the wheel frame of a wheel rolling at v = .866c, the length of the pole in the axle frame = 1*sin(60) = .5; its velocity relative to the axle frame = .866*cos(60) = .75; in its rest frame
L = .5/(1 - .75^2)^.5 = .7559; in the road frame L = .7559*(1 - .979^2)^.5 = .1516; at the end of the pole t = .7559*.979 = -.74 or t = .1516*.979/(1 - .979^2)^.5 = -.74.

Is there some reason you're asking these question beyond trying to prove I don't understand relativity? If there isn't, then tell me what it is or stop asking them.

2. The wheel keeps rolling!

3. Originally Posted by cincirob
cinci: As for the pole, the time at its right edge is t = -Vx/(1 - V^2)^.5

JT: Actually the road time at the right edge of the pole is this:
t = γ(t' + (vx' / cē)) = 0.866
Where:
γ = 2.000
v = 0.866
t' = 0.000
x' = 0.500

Is there some reason you don't use the LT's for this?

cinci: That is the LT. Is there some reason you don't recognize it?
I didn't recognize it because you wrote it wrong. You didn't write the t' at all, (presumably because it is zero in this case) and you have a negative sign where it should be positive, because we need the inverse to transform from the axle frame to the road frame.

Originally Posted by cincirob
cinci: ...and you can get x from LCF.

JT: Or you can get x from this equation for x:
x = γ(x' + vt') = 1.000
Where:
γ = 2.000
v = 0.866
t' = 0.000
x' = 0.500

Again, is there some reason you don't use the LT's for this?

cinci: Is there some reason you're not discussing the fact that I showed you how to do the spaceship problem using the LCF?
I had already said that you should be able to do it, because S2 is just as valid of a frame as O, and you made the LCF work for O and S1.

Originally Posted by cincirob
cinci: Considering a pole that is coincident with the chord of a spoke 60 degrees above horizontal in the wheel frame of a wheel rolling at v = .866c, the length of the pole in the axle frame = 1*sin(60) = .5; its velocity relative to the axle frame = .866*cos(60) = .75; in its rest frame
L = .5/(1 - .75^2)^.5 = .7559; in the road frame L = .7559*(1 - .979^2)^.5 = .1516; at the end of the pole t = .7559*.979 = -.74 or t = .1516*.979/(1 - .979^2)^.5 = -.74.

Is there some reason you're asking these question beyond trying to prove I don't understand relativity? If there isn't, then tell me what it is or stop asking them.
Your calculation of t''=-0.740 is the time in the pole's own frame when the right edge of the pole is located at x=0.152 in road coordinates. That is not the time when the right edge of the pole is coincident with the right edge of the wheel, because that happens at x=1.000 and t=0.866 in road frame coordinates. Can you replicate those road coordinates doing things 'your way' or do you disagree with those coordinates?

4. cinci: As for the pole, the time at its right edge is t = -Vx/(1 - V^2)^.5

JT: Actually the road time at the right edge of the pole is this:
t = γ(t' + (vx' / cē)) = 0.866
Where:
γ = 2.000
v = 0.866
t' = 0.000
x' = 0.500

Is there some reason you don't use the LT's for this?

cinci: That is the LT. Is there some reason you don't recognize it?

JT: I didn't recognize it because you wrote it wrong. You didn't write the t' at all, (presumably because it is zero in this case) and you have a negative sign where it should be positive, because we need the inverse to transform from the axle frame to the road frame.

cinci: Really? You didn't recognize it because I didn't use your particular terminology? Weak. And the negative sign is correct for positive values of x like the leading side of the wheel. As Gron says, the spokes are "retarded in time" so that the 60 degree spoke appears at 72.7 degrees, 12.7 degree opposite to the direction of rotation.

But I shouldn't be surprised since you still don't think Gron's X = (1 - (v/c)^2)^.5cos(wt' + Q) is length contraction.

cinci: ...and you can get x from LCF.

JT: Or you can get x from this equation for x:
x = γ(x' + vt') = 1.000
Where:
γ = 2.000
v = 0.866
t' = 0.000
x' = 0.500

Again, is there some reason you don't use the LT's for this?

cinci: Is there some reason you're not discussing the fact that I showed you how to do the spaceship problem using the LCF?

JT: I had already said that you should be able to do it, because S2 is just as valid of a frame as O, and you made the LCF work for O and S1.

cinci: What you said was: "But that method does not work for more complex scenarios, such as when S1 is to measure his distance to S2, or when we want to know the location of where and when the right edge of a pole is coincident with the right edge of a wheel." I made it work for the "complex scenario". Get over it.

cinci: Considering a pole that is coincident with the chord of a spoke 60 degrees above horizontal in the wheel frame of a wheel rolling at v = .866c, the length of the pole in the axle frame = 1*sin(60) = .5; its velocity relative to the axle frame = .866*cos(60) = .75; in its rest frame
L = .5/(1 - .75^2)^.5 = .7559; in the road frame L = .7559*(1 - .979^2)^.5 = .1516; at the end of the pole t = .7559*.979 = -.74 or t = .1516*.979/(1 - .979^2)^.5 = -.74.

Is there some reason you're asking these question beyond trying to prove I don't understand relativity? If there isn't, then tell me what it is or stop asking them.

JT: Your calculation of t''=-0.740 is the time in the pole's own frame when the right edge of the pole is located at x=0.152 in road coordinates. That is not the time when the right edge of the pole is coincident with the right edge of the wheel, because that happens at x=1.000 and t=0.866 in road frame coordinates. Can you replicate those road coordinates doing things 'your way' or do you disagree with those coordinates?

cinci: No, as I showed in the past, the pole doesn't wind up at x = 1 and t = .866. Since you asked me another question, I assume these questions are only to prove I don't understand relativity. I'm not going to answer questions for that reason. You've stumbled all over yourself trying to prove that length contraction can't be used to solve problems and now you're trying to keep your ridiculous quest to prove I don't understand relativity going. Go play with SYA; I'm out of this game.

5. Originally Posted by cincirob
JT: Your calculation of t''=-0.740 is the time in the pole's own frame when the right edge of the pole is located at x=0.152 in road coordinates. That is not the time when the right edge of the pole is coincident with the right edge of the wheel, because that happens at x=1.000 and t=0.866 in road frame coordinates. Can you replicate those road coordinates doing things 'your way' or do you disagree with those coordinates?

cinci: No, as I showed in the past, the pole doesn't wind up at x = 1 and t = .866.
Oh really? Let's see. The right end of the pole is located at x=0.152 at t=0.000, (in road frame coordinates). The pole's velocity through the road frame is 0.979c. So, at t=0.866 it should have moved a distance of 0.979*0.866=0.848. And the x coordinate which is 0.848 to the right of x=0.152 would be x=0.848+0.152=1.000. That puts the right end of the pole at x=1.000 at t=0.866, (in road frame coordinates).

6. JT: Oh really? Let's see. The right end of the pole is located at x=0.152 at t=0.000, (in road frame coordinates). The pole's velocity through the road frame is 0.979c. So, at t=0.866 it should have moved a distance of 0.979*0.866=0.848. And the x coordinate which is 0.848 to the right of x=0.152 would be x=0.848+0.152=1.000. That puts the right end of the pole at x=1.000 at t=0.866, (in road frame coordinates).

cinci: Congratulations! You have successfully copied a calculation I did for you months ago.

Now if you just could just copy what I've told you about length contraction.............

7. Originally Posted by cincirob
cinci: The pole doesn't wind up at x = 1 and t = .866.

Think of a firecracker popping at axle frame coordinates x'=0.500 and axle time t'=0.000. The firecracker leaves a burn mark on the right edge of the pole, and the right edge of the wheel.

That event happens at x=1.000 t=0.866 because of this simple calculation:

x = γ(x' + vt') = 1.000
t = γ(t' + (vx' / cē)) = 0.866

Where:
γ = 2.000
v = 0.866
t' = 0.000
x' = 0.500

If your version of relativity were correct, there would be a PARADOX because the firecracker would not be co-located with the right edge of the pole, or the right edge of the wheel.

8. Originally Posted by JTyesthatJT
Think of a firecracker popping at axle frame coordinates x'=0.500 and axle time t'=0.000. The firecracker leaves a burn mark on the right edge of the pole, and the right edge of the wheel.

That event happens at x=1.000 t=0.866 because of this simple calculation:

x = γ(x' + vt') = 1.000
t = γ(t' + (vx' / cē)) = 0.866

Where:
γ = 2.000
v = 0.866
t' = 0.000
x' = 0.500

If your version of relativity were correct, there would be a PARADOX because the firecracker would not be co-located with the right edge of the pole, or the right edge of the wheel.

The fact Cinci doesn't get this proves he knows nothing about relativity yet. Cincirob has not learned yet that the physical content of an event is absolute: it doesn't change through/after Lorentz Transformation. Only the coordinates change. Not the physical content the coordinates refer to. If in the axle frame the event = pole end atom at wheel rim atom and popping, then THAT event will be in the road frame (and all frames) exactly that: pole end atom at wheel rim atom and popping.
And as long as Cinci doesn't get this we are wasting our time with LT, LCF, RoS, etc.

9. JT: If your version of relativity were correct, there would be a PARADOX because the firecracker would not be co-located with the right edge of the pole, or the right edge of the wheel.

VeeDee: The fact Cinci doesn't get this proves he knows nothing about relativity yet. Cincirob has not learned yet that the physical content of an event is absolute: it doesn't change through/after Lorentz Transformation. Only the coordinates change. Not the physical content the coordinates refer to. If in the axle frame the event = pole end atom at wheel rim atom and popping, then THAT event will be in the road frame (and all frames) exactly that: pole end atom at wheel rim atom and popping.
And as long as Cinci doesn't get this we are wasting our time with LT, LCF, RoS, etc.

cinci: All you've done so far is waste your time trying to prove I don't understand Gron's analysis. JT put his finger on it; it looks like a paradox.

The firecracker example makes the Gron solution look correct and now (finally) everybody agrees on what the pole coincident with a chord does. The pole is a test of the Gron solution and it looks like a paradox. The question I've been asking and that you, SYA, and JT claim to have answered is how you resolve the paradox but you haven't answered it. If you're as smart as you think you are, explain that it isn't really a paradox.

By the way, here are three things that won't resolve it:

1) explaining the Gron solution over and over and over ad infinitum (everybody here already knows how to do it)

2) ignoring the pole analysis

3) claiming that I don't understand relativity.

If any of you invoke any of these in your next post, we'll all know you don't have an answer and are just blowing smoke.

I have suggested one way to resolve it. Gron's solution may not be correct for a rotating wheel because it can be shown that it IS correct if you're just looking at what happens to imaginary points moving around a stationary disk; and that would agree with both the firecracker and the finger test.

As SYA says, "I eagerly await." Actually I'm not eager at all because, dollars-to-donuts, all I will get is one of the three answers above which, by the way, I will summarily ignore.

10. JY #191
But the volume of an object is mostly empty space between its atoms. So, if we measure an object as length contracted by a factor of 1/gamma, we aren't just measuring the atoms themselves as length-contracted, but also the space between the atoms must be contracted by that same factor.

Also, earlier we were talking about the distance between two point-like spaceships. There was nothing but empty space between them, yet we calculated the distance between them to be contracted.
The position of an object is measured relative to another object.
The em fields which determine the form of objects, also extend beyond the objects, as for chemical bonds, or are used separately for controls in experiments. There is no known method to measure a sample of (empty) space. Objects move through space, but space does not move.

The calculations for dimensionless ships is bogus. If you ping the "ship" with light, what reflects it back to the observer? I.e. how do you make a measurement?

Here's a simple example:
U is your rest frame. Using 4 identical cubes of length 1s, form two independent pairs with the blocks in tandem, separated by 1s. Pairs A and B move relative to you at .6 and .8 respectively. Considering there is only one space before the blocks were introduced, what is the lc factor for the space between each pair?

11. Jilian #192
Phyti, you are thinking about this is the wrong way in my opinion. "Length contraction is a motion induced phenomena ( I think you meant phenomenon) resulting in deformed em fields" is not really getting what relativity is about. There is no deformation of the fields, or even of spacetime for that matter. All there is a a rotation of the spacetime axes. Deformation is really the wrong word in my opinion. Only when one frame is considered from the other are the axes between space and time different to what is measured in a rest frame.
Length contraction is one of two phenomena, the other being time dilation.
You are speaking in theoretical terms. Spacetime, rotations, and coordinate transformations are manipulations in an abstract model. I'm speaking in terms of physical phenomena, perception and reality.

12. Originally Posted by VeeDee
Originally Posted by JTyesthatJT
Think of a firecracker popping at axle frame coordinates x'=0.500 and axle time t'=0.000. The firecracker leaves a burn mark on the right edge of the pole, and the right edge of the wheel.

That event happens at x=1.000 t=0.866 because of this simple calculation:

x = γ(x' + vt') = 1.000
t = γ(t' + (vx' / cē)) = 0.866

Where:
γ = 2.000
v = 0.866
t' = 0.000
x' = 0.500

If your version of relativity were correct, there would be a PARADOX because the firecracker would not be co-located with the right edge of the pole, or the right edge of the wheel.

The fact Cinci doesn't get this proves he knows nothing about relativity yet. Cincirob has not learned yet that the physical content of an event is absolute: it doesn't change through/after Lorentz Transformation. Only the coordinates change. Not the physical content the coordinates refer to. If in the axle frame the event = pole end atom at wheel rim atom and popping, then THAT event will be in the road frame (and all frames) exactly that: pole end atom at wheel rim atom and popping.
And as long as Cinci doesn't get this we are wasting our time with LT, LCF, RoS, etc.

That is true, and things are even worse than that. Look at his post #209, where cincirob now thinks the burn-mark paradox which he caused can be blamed on Gron!!! LOL!!!

13. Originally Posted by cincirob
cinci: All you've done so far is waste your time trying to prove I don't understand Gron's analysis. JT put his finger on it; it looks like a paradox.

The firecracker example makes the Gron solution look correct and now (finally) everybody agrees on what the pole coincident with a chord does. The pole is a test of the Gron solution and it looks like a paradox. The question I've been asking and that you, SYA, and JT claim to have answered is how you resolve the paradox but you haven't answered it. If you're as smart as you think you are, explain that it isn't really a paradox.
It isn't really a paradox because the firecracker pops at x=1.000 and t=0.866 in road frame coordinates, and the right edge of the pole and the right edge of the wheel are both located at x=1.000 at road time t=0.866. Therefore the burn marks are created all at once in the road frame, just as they are created all at once in the axle frame.

The only reason it looks like a paradox is because you think the right edge of the pole and the right edge of the wheel are somehow NOT located in the same place as the firecracker popping.

14. Originally Posted by cincirob
Cinci:
...
I have suggested one way to resolve it.
There is nothing to be resolved. Gron's calcs (Lorentz Transformations) show you what the wheel looks like in the road frame: an ellips. And the spokes are curved. And the way Gron does it is correct. Too bad if you think it's wrong.
Gron's solution may not be correct for a rotating wheel because it can be shown that it IS correct if you're just looking at what happens to imaginary points moving around a stationary disk;
Forget it. Nothing imaginarey points moving around a stationary disk. Gron does it the correct way: Lorentz Tranforming coordinates of events. Too bad if you are unable to understand it.
and that would agree with both the firecracker and the finger test.
Nobody needs you impagery points blabla and your coincident chord/pole blabla. Lorentz transformations is about coordinates of events. Events with physical content. Unfortumately you showed us over and over again you don't know what that means. But Gron does. SYA does. JT does. And thousands of people dealing with Einstein relativity do. And you should learn it to be able to understand what relativity is about, instead of trying to sell your baloney relativity scenario.
If in the axle frame the event = pole end atom at wheel rim atom and popping, then THAT event will be in the road frame (and all frames) exactly that: pole end atom at wheel rim atom and popping. Anything else is nonsense. Or do you want to rewrite relativity, Cinci? Wake up, boy!

15. Cinci: I have suggested one way to resolve it.

VeeDee: There is nothing to be resolved. Gron's calcs (Lorentz Transformations) show you what the wheel looks like in the road frame: an ellips. And the spokes are curved. And the way Gron does it is correct. Too bad if you think it's wrong.

cinci: So you chose #3. Why am I not surprised?

16. Originally Posted by cincirob
cinci: Just as I suspected, you have no imagination.
I have plenty of imagination but I don't need it in Einstein relativity. Relativity works perfectly well with no-nonsense Lorentz Transformations, and definitely doesn't need your kind of 'imagination'.

17. JT: The only reason it looks like a paradox is because you think the right edge of the pole and the right edge of the wheel are somehow NOT located in the same place as the firecracker popping.

cinci: Why I question it isn't mysterious or unknown to you. Using the exact equations of relativity I have tried to look at the structural effects of relativity by looking at the velocities and relativistic effects of a chord in the wheel. When I do that, it doesn't come out the same as Gron's. I'm used to doing stresses in structures and there are usually many ways to figure them out and all the different ways give the same answer. So I'm not just "somehow" questioning it, there is a reason. So you have selected #2, just ignore the things you can't explain.

Now if we can just get SYA to repeat Gron's analysis one more time, we will have the hat trick.

18. Originally Posted by cincirob
JT: The only reason it looks like a paradox is because you think the right edge of the pole and the right edge of the wheel are somehow NOT located in the same place as the firecracker popping.

cinci: Why I question it isn't mysterious or unknown to you. Using the exact equations of relativity I have tried to look at the structural effects of relativity by looking at the velocities and relativistic effects of a chord in the wheel. When I do that, it doesn't come out the same as Gron's. I'm used to doing stresses in structures and there are usually many ways to figure them out and all the different ways give the same answer. So I'm not just "somehow" questioning it, there is a reason.

The pole is just an approximation to what a real chord is doing. The pole does not rotate around the axle, it just translates past it. Therefore, the pole does not end up curved in the road frame, the way Gron's chords do. You should not even expect to get the same results from the pole as you would get from a real chord.

19. Originally Posted by JTyesthatJT
The pole is just an approximation to what a real chord is doing. The pole does not rotate around the axle, it just translates past it. Therefore, the pole does not end up curved in the road frame, the way Gron's chords do. You should not even expect to get the same results from the pole as you would get from a real chord.
Cinci thinks because there are always atoms -but not the same- at the 11 - 1 o'clock chord he can use simple LCF calculation to determine length contraction of the real wheel chord. This is absurd, but quite normal for people like cinci not being aware relativity and LT are about coordinates of events, not just abstract points. Cinci first has to learn what an event is. Until then he is wasting his and our time.

20. Originally Posted by cincirob
JT: The only reason it looks like a paradox is because you think the right edge of the pole and the right edge of the wheel are somehow NOT located in the same place as the firecracker popping.

cinci: Why I question it isn't mysterious or unknown to you. Using the exact equations of relativity I have tried to look at the structural effects of relativity by looking at the velocities and relativistic effects of a chord in the wheel. When I do that, it doesn't come out the same as Gron's.
Your inertial cord analyses fails to account for "rotation". Of course you are not going to understand Gron's solns, if you think a horizontal inertial cord transforms to the ground the same as a momentarily horizontal superposed rotating cord (of the wheel). Alas, you simply won't be told, and so again, that's that as they say. To understand it, you need to learn some basics of relativity. Spacetime events would be a good start.

Originally Posted by cincirob
I'm used to doing stresses in structures and there are usually many ways to figure them out and all the different ways give the same answer. So I'm not just "somehow" questioning it, there is a reason. So you have selected #2, just ignore the things you can't explain.
No one cares. No matter how many stress analyses you may have done in your engineering career, you never analyzed the situation of relativistic rates. Your analyses were all classical analyses of everyday situations (even if cutting edge). There was nothing moving at appreciable rates of light speed. So, apples and oranges. Your problems are not everyday stresses, but rather understanding the meaning of the LTs.

Originally Posted by cincirob
Now if we can just get SYA to repeat Gron's analysis one more time, we will have the hat trick.
The funny thing is, you don't yet realize how silly a thing that is to say, especially in public. Astounding

Thank You,

21. JT: The pole is just an approximation to what a real chord is doing. The pole does not rotate around the axle, it just translates past it. Therefore, the pole does not end up curved in the road frame, the way Gron's chords do. You should not even expect to get the same results from the pole as you would get from a real chord.

VeeDee: Cinci thinks because there are always atoms -but not the same- at the 11 - 1 o'clock chord he can use simple LCF calculation to determine length contraction of the real wheel chord. This is absurd, but quite normal for people like cinci not being aware relativity and LT are about coordinates of events, not just abstract points. Cinci first has to learn what an event is. Until then he is wasting his and our time.

cinci: Actually, I only think about the pole one point at a time, just like Gron. VeeDee says it's absurd to use a simple calculation to make this transformation but that is exactly my point. Gron transforms them as if they have a simple velocity using length contraction. Of course he recognized RoS and for the tip of the 60 degree tip he transforms the 72.7 degree point at t = 0.

22. The "simplest" and "most incorrect" approach is the pole flying by the wheel in the axle frame. Just because that pole fits the wheel in the axle frame, is no reason to assume that pole will also fit the wheel in the road frame. It doesn't. In the road frame, the pole we've been discussing is shorter than the width of the wheel.

It is much more sophisticated to analyse the actual points on the rotating & rolling wheel, as Gron does. The person who prefers the above method has no business complaining that Gron's method is too simple.

23. Originally Posted by cincirob
JT: The pole is just an approximation to what a real chord is doing. The pole does not rotate around the axle, it just translates past it. Therefore, the pole does not end up curved in the road frame, the way Gron's chords do. You should not even expect to get the same results from the pole as you would get from a real chord.

VeeDee: Cinci thinks because there are always atoms -but not the same- at the 11 - 1 o'clock chord he can use simple LCF calculation to determine length contraction of the real wheel chord. This is absurd, but quite normal for people like cinci not being aware relativity and LT are about coordinates of events, not just abstract points. Cinci first has to learn what an event is. Until then he is wasting his and our time.

cinci: Actually, I only think about the pole one point at a time, just like Gron. VeeDee says it's absurd to use a simple calculation to make this transformation but that is exactly my point. Gron transforms them as if they have a simple velocity using length contraction. Of course he recognized RoS and for the tip of the 60 degree tip he transforms the 72.7 degree point at t = 0.
Actually, you think of the pole "all 3-space points at a time", not one 4d spacetime event at a time. If you did the latter, you would recognize why the Fitgerald Length Contraction Formula alone does not work for rotating bodies.

And yes, here you point out again that you do not understand why Gron uses the translation velocity v between axle and ground in his LT transformations. Something else you need work on. If you ever take the time to learn spacetime events, all your confusions vanish. Alas, but how to get cinci to do what he has refused to do for so so many years straight now? This is the question.

Thank You,

24. The day Cinci knows what events are in Einstein relativity he will buy us cake and a bottle of champagne. He should.

25. I think cincirob should just tell us how the firecracker pop can possibly leave a burn mark on the right edge of the wheel, considering that he thinks the right edge of the wheel at y=0.866 does not have road coordinates x=1.000 t=0.866 whilst the firecracker pop DOES have road coordinates x=1.000 t=0.866. If they are not in the same place, at the same time, then how does the burn mark form?

26. Originally Posted by JTyesthatJT
I think cincirob should just tell us how the firecracker pop can possibly leave a burn mark on the right edge of the wheel, considering that he thinks the right edge of the wheel at y=0.866 does not have road coordinates x=1.000 t=0.866 whilst the firecracker pop DOES have road coordinates x=1.000 t=0.866. If they are not in the same place, at the same time, then how does the burn mark form?
It is theoretically conceivable that magic wheels can support such, but that assumes of course that no river fairies lose their touch. OK, so a little humor aside ...

Most would say ... If in the same place at the same time per the one, then in the same place at the same time per all. This is not a relativity requirement, it's a requirement of both reality and any logical theory, given the scale is above the (confused) quantum level Aristotle, Galileo, and Newton each supported that as well. I don't recall Hawking having debated it either. Now Dingle, he may be an exception there?

Thank You,

27. Originally Posted by JTyesthatJT
I think cincirob should just tell us how the firecracker pop can possibly leave a burn mark on the right edge of the wheel, considering that he thinks the right edge of the wheel at y=0.866 does not have road coordinates x=1.000 t=0.866 whilst the firecracker pop DOES have road coordinates x=1.000 t=0.866. If they are not in the same place, at the same time, then how does the burn mark form?
Watch this: to save his *ss Cinci might answer that the front end of the pole DOES hit the wheel rim, and firecracker popping, BUT that this still doesn't mean the upper part of the wheel is not smaller than the bottom part ...
Wrong of course.
A pole flying by at level 7 o'clock - 5 o'clock with firecracker popping will show up in the road frame at exact same x-coordinate(s) as the other pole. Same x-coordinate for the event "front atom of rod at wheel atom and poppin and leaving burn mark." I.o.w. no pear shaped wheel.

28. JT: The "simplest" and "most incorrect" approach is the pole flying by the wheel in the axle frame. Just because that pole fits the wheel in the axle frame, is no reason to assume that pole will also fit the wheel in the road frame. It doesn't. In the road frame, the pole we've been discussing is shorter than the width of the wheel.

cinci: You're missing the point. You can construct a wheel as follows: Start with a simple ring. Pick points at 60 degree intervals around it. Connect those points with rods. Now look at the motion and relativistic effects on those rods.

JT: It is much more sophisticated to analyse the actual points on the rotating & rolling wheel, as Gron does. The person who prefers the above method has no business complaining that Gron's method is too simple.

cinci: It's length contraction. It isn't any more sophisticated than that.

SYA: Actually, you think of the pole "all 3-space points at a time", not one 4d spacetime event at a time. If you did the latter, you would recognize why the Fitgerald Length Contraction Formula alone does not work for rotating bodies.

And yes, here you point out again that you do not understand why Gron uses the translation velocity v between axle and ground in his LT transformations. Something else you need work on. If you ever take the time to learn spacetime events, all your confusions vanish. Alas, but how to get cinci to do what he has refused to do for so so many years straight now? This is the question.

cinci: I understand spacetime points well enough to have understood Gron's analysis years ago including the curved chords and, before anyone else in the world as far as I can tell, the curved chords. I also understand that Gron's analysis works for a static, round structure with points moving around it; the three of you don't seem to comprehend that. If you're as smart as you think you are, then you should be able to prove that a static round structure with points moving around it acts just like a rotating round structure. That's been my question for all those years and to date none of you haven't even attempted an answer. All these claims that I don't understand relativity are just the three of you dodging that question....for all these years.

The next, and only, post on this subject that I will respond to is an answer to that question. So when I don't respond to your next diatribe it will be because you don't have the answer. I eagerly await the right response, but I'm not going to live forever so put a move on and stop wasting everyone's time.

I suggest you start another thread with that answer as you have successfully diverted this one from its intended subject. Failing that, I suggest you go back to the old wheel thread and continue convincing yourselves of whatever it is you're trying to convince yourself of there. I'll check there when I need a good laugh.

29. So cincirob is going to refuse to explain his burn mark paradox, because he knows there is no good explanation. At best, it looks like we are back to where we were at this point in time.

Oh, and it has already been explained that points moving uniformly along a circular path are identical to points at rest on the edge of a rotating circular disk. If one cannot understand that, then one has little hope of understanding anything else about the wheel. Might as well ask if the pole is really just points moving uniformly in a straight line. Sheesh.

Check this out.

And this.

30. JT:So cincirob is going to refuse to explain his burn mark paradox, because he knows there is no good explanation. At best, it looks like we are back to where we were at this point in time.

cinci: The burn mark and the finger test both work for the non-rotating model; therefore, you can't prove you have the correct rotating model.

31. Originally Posted by cincirob
JT:So cincirob is going to refuse to explain his burn mark paradox, because he knows there is no good explanation. At best, it looks like we are back to where we were at this point in time.

cinci: The burn mark and the finger test both work for the non-rotating model; therefore, you can't prove you have the correct rotating model.
But we have proven the pear model is incorrect, because it fails both tests.

32. Originally Posted by cincirob
SYA: Actually, you think of the pole "all 3-space points at a time", not one 4d spacetime event at a time. If you did the latter, you would recognize why the Fitgerald Length Contraction Formula alone does not work for rotating bodies.

And yes, here you point out again that you do not understand why Gron uses the translation velocity v between axle and ground in his LT transformations. Something else you need work on. If you ever take the time to learn spacetime events, all your confusions vanish. Alas, but how to get cinci to do what he has refused to do for so so many years straight now? This is the question.

[B]cinci: I understand spacetime points well enough to have understood Gron's analysis years ago including the curved chords and, before anyone else in the world as far as I can tell, the curved chords.
Lol. Alrighty then.

Originally Posted by cincirob
I also understand that Gron's analysis works for a static, round structure with points moving around it
Gron's analysis handles anything, unless one redefines the scenario into la la land. Gron's analysis works for any rotating body with an inertial axis-of-rotation, for any rotation rate ω (that does not attain or exceed a speed c motion). A static (non rotating) disk with a rotating ring of atoms about its outer perimeter "are two separate bodies, doing each their own thing", but Gron's analysis can handle that fine given the axes of rotation are inertial. One would be analyzing 2 bodies at once using Gron's analysis, that's all.

Originally Posted by cincirob
the three of you don't seem to comprehend that. If you're as smart as you think you are, then you should be able to prove that a static round structure with points moving around it acts just like a rotating round structure. That's been my question for all those years and to date none of you haven't even attempted an answer.
Has already been done, many times in your own threads here. You should think about what everyone posts for you, instead of electing the argumentative strategy. Gron's analysis is the very same for a rotating Born rigid rotating ring of atoms of r,ω as for the outer perimeter atoms of a Born rigid rotating disk of same r,ω. It has to be, because the atoms of both those rings are by definition always "in the same place at the same time" during their rotation.

Far as your static disk goes ... the perimeter ring of atoms about a static (non rotating) disk do not have the same LT solns as your superposed rotating ring of atoms. They cannot, because the disk's perimeter atoms are inertial, while the rotating ring of atoms are moving non-inertially. Corresponding atoms between those 2 entities change in their relative position over time, since one rotates and the other not. All POVs agree on this. You seriously cannot see that?

Originally Posted by cincirob
All these claims that I don't understand relativity are just the three of you dodging that question....for all these years.
Well, let's see. For years, and no matter how many have explained to you otherwise, you claim that Gron's soln is correct for a static disk with a rotating ring around it, but that Gron's analysis is wrong given his own round Born rigid rotating disk. You base this on your having worked on structures and stresses as a mechanical engineer your entire career. Why not go through the few basic scenarios of relativity, that JT has forever been hoping you would try, and see what comes of it? I mean, you've already restated your arguments for decades, why not take a couple weeks on some basics just for the heck of it? What can it harm?

Thank You,

33. JT: But we have proven the pear model is incorrect, because it fails both tests.

cinci: You could prove the wheel doesn't transform to a question mark too, but that doesn't prove anything about the ellipse. Do you ever use logic?

34. cinci: I understand spacetime points well enough to have understood Gron's analysis years ago including the curved chords and, before anyone else in the world as far as I can tell, the curved chords.

SYA: Lol. Alrighty then.

cinci: "Lol" is just your way of dodging the facts.

cinci: I also understand that Gron's analysis works for a static, round structure with points moving around it.

SYA: Gron's analysis handles anything, unless one redefines the scenario into la la land. Gron's analysis works for any rotating body with an inertial axis-of-rotation, for any rotation rate ω (that does not attain or exceed a speed c motion). A static (non rotating) disk with a rotating ring of atoms about its outer perimeter "are two separate bodies, doing each their own thing", but Gron's analysis can handle that fine given the axes of rotation are inertial.

cinci: In other words, my statement is correct. Why didn't you just say that?

SYA: One would be analyzing 2 bodies at once using Gron's analysis, that's all.

cinci: No, that isn't all. And by making this statement you admit you haven't answered my question.

If there is a nonrotating component guiding the points, the non-rotating component structure can be analyzed for contractions and time effects without question. The rotating points are constrained by the solution of the static disk.

There is nothing in Gron's analysis that deals with the rotation of the structure itself. Most authors claim one can build the Gron rotating wheel on the fly; in fact, they say it must be done that way. My question deals with the possibility of building Gron's wheel in such a manner. I can't figure out how to do it. Why don't you geniuses tell me how?

cinci: the three of you don't seem to comprehend that. If you're as smart as you think you are, then you should be able to prove that a static round structure with points moving around it acts just like a rotating round structure. That's been my question for all those years and to date none of you haven't even attempted an answer.

SYA: Has already been done, many times in your own threads here. You should think about what everyone posts for you, instead of electing the argumentative strategy. Gron's analysis is the very same for a rotating Born rigid rotating ring of atoms of r,ω as for the outer perimeter atoms of a Born rigid rotating disk of same r,ω. It has to be, because the atoms of both those rings are by definition always "in the same place at the same time" during their rotation.

[B]cinci: Born rigidity seems to say that you can spin a disk up to some speed with out it suffering relativistic effects. The Gron solution says that's OK but when I transform it to another frame relativity starts working again. Einstein used the Born rigid disk in his 1920 book to say that he couldn't use special relativity with its Cartesian coordinate system on the disk. I guess you're smarter than Albert now:

For this reason it is not possible to obtain a reasonable definition of time with the aid of clocks which are arranged at rest with respect to the body of reference. A similar difficulty presents itself when we attempt to apply our earlier definition of simultaneously in such a case, but I do not wish to go any farther into this question. 4
Moreover, at this stage the definition of the space co-ordinates also presents unsurmountable difficulties. If the observer applies his standard measuring-rod (a rod which is short as compared with the radius of the disc) tangentially to the edge of the disc, then, as judged from the Galileian system, the length of this rod will be less than 1, since, according to Section XII, moving bodies suffer a shortening in the direction of the motion. On the other hand, the measuring-rod will not experience a shortening in length, as judged from K, if it is applied to the disc in the direction of the radius. If, then, the observer first measures the circumference of the disc with his measuring-rod and then the diameter of the disc, on dividing the one by the other, he will not obtain as quotient the familiar number = 3.14 , but a larger number, 2 whereas of course, for a disc which is at rest with respect to K, this operation would yield exactly. This proves that the propositions of Euclidean geometry cannot hold exactly on the rotating disc,

SYA: Far as your static disk goes ... the perimeter ring of atoms about a static (non rotating) disk do not have the same LT solns as your superposed rotating ring of atoms.

cinci: Of course they don't. I never said they did. What I said was that if the points (rolling balls in a hula hoop, if you need a physical situation) follow the circle in the "axle" frame and they must follow the ellipse in the "road" frame.

This proves you never answered my question. You don't understand it.

SYA: They cannot, because the disk's perimeter atoms are inertial, while the rotating ring of atoms are moving non-inertially. Corresponding atoms between those 2 entities change in their relative position over time, since one rotates and the other not. All POVs agree on this. You seriously cannot see that?

cinci: Are you saying Gron's solution won't tell you where the points are in the "road" frame? Again, you just proved you don't understand the question.

cinci: All these claims that I don't understand relativity are just the three of you dodging that question....for all these years.

SYA: Well, let's see. For years, and no matter how many have explained to you otherwise, you claim that Gron's soln is correct for a static disk with a rotating ring around it, but that Gron's analysis is wrong given his own round Born rigid rotating disk. You base this on your having worked on structures and stresses as a mechanical engineer your entire career. Why not go through the few basic scenarios of relativity, that JT has forever been hoping you would try, and see what comes of it? I mean, you've already restated your arguments for decades, why not take a couple weeks on some basics just for the heck of it? What can it harm?

cinci: There isn't any indication that I don't understand JTs work. But there isn't any indication that it's other than a static disk with points moving around it. Born rigidity is an assumption; basically it says that the disk acts as if it isn't rotating. So if that's where you're going, then it's just a static disk with points moving around it.......as I have told you oh so many times.

You do know Born rigidity doesn't really exist, right? There are plenty of physicists that say Gron's wheel has to be built on the fly. They say that because Born rigidity doesn't exist because it denies relativity. I'm saying that building it on the fly doesn't seem to work either. Why don't you prove to me that it does?

35. Originally Posted by cincirob
JT: But we have proven the pear model is incorrect, because it fails both tests.

cinci: You could prove the wheel doesn't transform to a question mark too, but that doesn't prove anything about the ellipse. Do you ever use logic?
After all this time and discussion, you still can't think of a way to determine the shape of the wheel in the road frame? How many years have you been working on this problem? Is it over five now? I think so.

Try putting fingers, at rest in the axle frame, all around the edge of the rotating circular wheel. Let the finger tips touch the edge of the wheel in all places. Measure the horizontal distance between each pair of finger tips, and then apply your beloved length contraction formula to calculate those distances in the road frame. What shape do you get? Hint: It starts with an e.

36. JT: After all this time and discussion, you still can't think of a way to determine the shape of the wheel in the road frame? How many years have you been working on this problem? Is it over five now? I think so.

cinci: Well you already weren't using logic and now you have departed reality. I worked this poblenm out a long time ago as you well know.

JT: Try putting fingers, at rest in the axle frame, all around the edge of the rotating circular wheel. Let the finger tips touch the edge of the wheel in all places. Measure the horizontal distance between each pair of finger tips, and then apply your beloved length contraction formula to calculate those distances in the road frame. What shape do you get? Hint: It starts with an e.

cinci: Now do it with a non-rotating disk; what do you get? Hint: It begins with e.

I can't believe you still don't understand length contraction or that you use it in Gron's solution?

37. Originally Posted by cincirob
JT: Try putting fingers, at rest in the axle frame, all around the edge of the rotating circular wheel. Let the finger tips touch the edge of the wheel in all places. Measure the horizontal distance between each pair of finger tips, and then apply your beloved length contraction formula to calculate those distances in the road frame. What shape do you get? Hint: It starts with an e.

cinci: Now do it with a non-rotating disk; what do you get? Hint: It begins with e.
Yes, a non-rotating circular disk also contracts to an ellipse. What does that have to do with the price of tea in China?

Originally Posted by cincirob
cinci: I can't believe you still don't understand length contraction or that you use it in Gron's solution?
I understand that you love to use the length contraction formula. That is why I gave you a way to solve for the shape which relies on nothing else but the length contraction formula.

38. Originally Posted by cincirob
cinci: I understand spacetime points well enough to have understood Gron's analysis years ago including the curved chords and, before anyone else in the world as far as I can tell, the curved chords.

SYA: Lol. Alrighty then.

cinci: "Lol" is just your way of dodging the facts. I also understand that Gron's analysis works for a static, round structure with points moving around it.

SYA: Gron's analysis handles anything, unless one redefines the scenario into la la land. Gron's analysis works for any rotating body with an inertial axis-of-rotation, for any rotation rate ω (that does not attain or exceed a speed c motion). A static (non rotating) disk with a rotating ring of atoms about its outer perimeter "are two separate bodies, doing each their own thing", but Gron's analysis can handle that fine given the axes of rotation are inertial.

cinci: In other words, my statement is correct. Why didn't you just say that?

SYA: One would be analyzing 2 bodies at once using Gron's analysis, that's all.

cinci: No, that isn't all. And by making this statement you admit you haven't answered my question.

If there is a non-rotating component guiding the points, the non-rotating component structure can be analyzed for contractions and time effects without question. The rotating points are constrained by the solution of the static disk.

There is nothing in Gron's analysis that deals with the rotation of the structure itself.
You say " There is nothing in Gron's analysis that deals with the rotation of the structure itself ". Let's see if you have a leg to stand on ...

(1) Gron's analysis begins with LT inputs definitions ...

t(r,θ,t)
x(r,θ,t) = rcos(ωt+θ)
y(r,θ,t) = rsin(ωt+θ)

Note the ω term there has units such as ... radians per sec.
Now, do you still hold to your belief system that Gron's analysis did not deal with rotation of the structure?

(2) Gron's LT solns are ...

T(r,θ,t) = γ[t-( rēω/cē)cos(ωt+θ)]
X(r,θ,t) = γ[rcos(ωt+θ)-rωt]
Y(r,θ,t) = y(r,θ,t) = rsin(ωt+θ)

where ... γ = √(1- rēωē/cē)

Note the ω term there has units such as ... radians per sec.
Now, do you still hold to your belief system that Gron's analysis did not deal with rotation of the structure?

***********************************************

As has been very clear for a long time, Cincirob does not understand how the LTs can transform a moving point in the axle system to the ground system in which it also moves. The reason ... he compares simultaneous space between axle and ground, instead of comparing a collection of 4 dimension LT coordinates inputs per axle to their respective 4 dimensional LT coordinate solns per ground. Put simply, he thinks that given the modeling of a material entity, the LT coordinate inputs can only model a stationary one, ie one that does not move over duration per axle. IOWs, he does not understand events.

Now instead of learning how relativity handles 4 dimensional events in fused spacetime, Cincirob avoids the issue by re-injecting and re-arguing very old arguments, eg wonderous wheel building procedures for wonder wheels, or the need to add real material on the fly, etc, as though that's going to save him some how. This has gone on for years and years. Thus far, cincirob does not want to be helped, because he has reraised the same questions.

So here, Cinci was addressing a post in regards to ...

"Does Gron's model handle the rotation of the body and its structure?"

But midstream changed the subject to this ...

"Some physicists suggest wonder wheels must be built on the fly".

Yet, Gron's model did not address building a wonder wheel, or the roll up period. It is Born rigid at speed, by definition. So the post response was specifically addressing how (and if) Gron's model handles the rotation of the structure, and cinci now immediately forced us into ... wonderous building procedures for magic wheels.

Cincirob ... No real wheel can exist at relativistic rotation rates, and any reputable physicist knows it. Classical forces would destroy the wheel long before, as they all know. That's why Gron DEFINED his wheel at speed, to avoid all the rediculous complaints of how the wheel could be made to exist as such. It's a kinematic thought experiment for the sake of exploring the implications of relativistic effects with rotation.

Thank You,

39. It should be noted that Gron's wheel is defined as rolling from right to left in the road frame. For the rest of us, who let the wheel roll from left to right in the road frame, the equations would be like this:

T(r,θ,t) = γ[t + (rēωē/cē)rcos(ωt+θ)]
X(r,θ,t) = γ[rcos(ωt+θ)+rωt]
Y(r,θ,t) = rsin(ωt+θ)

where
γ = 1 / √(1- rēωē/cē)

........

Also, since v=rω, x'=rcos(ωt+θ), and y'=rsin(ωt+θ), we can write those as the standard inverse LT equations:

T = γ(t' + (vx' / cē))
X = γ(x' + vt')
Y = y'

where:
γ = 1 / √(1 - vē/cē)

40. SYA: Cincirob ... No real wheel can exist at relativistic rotation rates, and any reputable physicist knows it. Classical forces would destroy the wheel long before, as they all know.

cinci: I used to design the rotating disks that keep you in the air when you fly on an airplane. Do you really think this is news to me?

SYA: That's why Gron DEFINED his wheel at speed, to avoid all the rediculous complaints of how the wheel could be made to exist as such.

cinci: You already lost this argument. I told you Gron's analysis works for a non-rotating disk. Your argument is that he uses the mythical Born rigid wheel. And what is the principle characteristic of that mythical wheel? It acts like it isn't rotating. A rose by any other name....................?

And now you fall back on the "defined at speed" which means "built on the fly" that you have denied more times than I can count. What I have done is try to flesh out that idea by seeing what it takes to build it on the fly...................and it doesn't appear to work by your own arguments. Give it up. You're out of ideas.

SYA: It's a kinematic thought experiment for the sake of exploring the implications of relativistic effects with rotation.

cinci: Translation: you believe it doesn't quite measure up to reality. You have joined my club.

41. Originally Posted by cincirob
SYA: Cincirob ... No real wheel can exist at relativistic rotation rates, and any reputable physicist knows it. Classical forces would destroy the wheel long before, as they all know.

cinci: I used to design the rotating disks that keep you in the air when you fly on an airplane. Do you really think this is news to me?
I would not be surprised, actually.

Originally Posted by cincirob
SYA: That's why Gron DEFINED his wheel at speed, to avoid all the rediculous complaints of how the wheel could be made to exist as such.

[B]cinci: You already lost this argument. I told you Gron's analysis works for a non-rotating disk. Your argument is that he uses the mythical Born rigid wheel. And what is the principle characteristic of that mythical wheel? It acts like it isn't rotating. A rose by any other name....................?
A mythical disk it is. Gron never said it could exist in any reality, at relativistic rotation rate. Maybe you can point out in Gron's paper where "he said" he built a disk on the fly, versus assuming it simply existed as round and Born rigid at steady rotation rate. Please show the reference.

You're right, Gron's model works for a non rotating disk, but then this was known in 1905. If Gron's rotating wheel acted like it wasn't rotating, then for starters the radial elements would not dynamically curve per ground, geesh.

Originally Posted by cincirob
cinci: And now you fall back on the "defined at speed" which means "built on the fly" that you have denied more times than I can count. What I have done is try to flesh out that idea by seeing what it takes to build it on the fly...................and it doesn't appear to work by your own arguments. Give it up. You're out of ideas.
Very sorry, but no matter how many times you say it, "assumed to exist at speed" does not mean "built on the fly". It's a thought experiment, and Gron has his own scenario definitions and apriori requirements.

Also, no one will ever care about helping you wonderously build magic wheels on the fly, until you first learn about spacetime events and come to grips with Gron's analysis.

Originally Posted by cincirob
SYA: It's a kinematic thought experiment for the sake of exploring the implications of relativistic effects with rotation.

cinci: Translation: you believe it doesn't quite measure up to reality. You have joined my club.
Old news. For years and years now, every time you claim "Gron built a wheel on the fly", we tell you that the wheel is fictitious and assumed to exist "at speed". Yet, you keep saying it again and again. How many more years must this be endured? All you need to do, is go thru a few basic all inertial relativity scenarios that JT has repeatedly encouraged.

42. As long as Cinci pretends Gron's analysis deals with a non-rotating wheel instead of a rotating wheel it's obvious Cinci doesn't understand one letter of Gron's analysis. The reason is that Cinci doesn't understand one letter of Einstein relativity. It's as simple as that.

43. SYA: A mythical disk it is. Gron never said it could exist in any reality, at relativistic rotation rate. Maybe you can point out in Gron's paper where "he said" he built a disk on the fly, versus assuming it simply existed as round and Born rigid at steady rotation rate. Please show the reference.

cinci: Please show the where I said Gron said it. I said other physicists say it. Grow up and stick to the facts.

SYA: You're right, Gron's model works for a non rotating disk, but then this was known in 1905.

cinci: Really? I figured it out for myself. Why have you been denying it when I say it?

SYA: If Gron's rotating wheel acted like it wasn't rotating, then for starters the radial elements would not dynamically curve per ground, geesh.

cinci: I think the problem with you is that you don't understand modeling. Otherwise you wouldn't make obviously ridiculous statements like this one. Is your imagination so limited that you can't envision a hula hoop with a marble rolling around inside at the rim of a stationary disk representing the tip of a spoke and another one half that size with marbles located so that the in the disk frame the two marbles always make a straight line so that the inner one represents the midpoint of that spoke? Really?

44. Originally Posted by cincirob
SYA: If Gron's rotating wheel acted like it wasn't rotating, then for starters the radial elements would not dynamically curve per ground, geesh.

cinci: I think the problem with you is that you don't understand modeling. Otherwise you wouldn't make obviously ridiculous statements like this one.
The problem cinci, is that you need to learn about 4d events, as the LTs use them and Gron used the LTs. You are "on record" as having stated that LTs cannot be used in the determination of the length of a body given it moves in both systems. <- Therein lies one of your main problems. Correct that, and your confusion on all these matters may readily vanish. Every relativist here knows exactly why you are stuck, but alas, you simply won't be told.

Thank You,

45. SYA: If Gron's rotating wheel acted like it wasn't rotating, then for starters the radial elements would not dynamically curve per ground, geesh.

cinci: I think the problem with you is that you don't understand modeling. Otherwise you wouldn't make obviously ridiculous statements like this one.

SYA: The problem cinci, is that you need to learn about 4d events, as the LTs use them and Gron used the LTs.

cinci: And how will that help you understand a simple model? I notice that you left out the part of my post that makes you look silly. Why did you do that?

SYA: You are "on record" as having stated that LTs cannot be used in the determination of the length of a body given it moves in both systems.

cinci: Actually I'm on the record for saying length you can't use length contraction as Gron does and the pole and barn problem proves it. It took me three years to get you to understand that and now you have apparently forgotten again.

SYA: Therein lies one of your main problems. Correct that, and your confusion on all these matters may readily vanish. Every relativist here knows exactly why you are stuck, but alas, you simply won't be told.

cinci: The one of the relativists here should figure out why a rotating wheel and a non-rotating wheel give identical answers and show an analysis that proves it. So far, no luck.

46. I have a question, if I may ask. How does the rotating axle frame differ from the axle frame that is not rotating in the road frame? There seems to be a disagreement on whether there is a difference or not.

47. Originally Posted by Jilan
I have a question, if I may ask. How does the rotating axle frame differ from the axle frame that is not rotating in the road frame? There seems to be a disagreement on whether there is a difference or not.
When SYA, VeeDee, and I refer to the axle frame, we are talking about the non-rotating frame in which the axle is considered stationary. If this wheel were part of a train, then we could also call this the train frame. If this wheel were part of a bicycle, then we could also call this the bike frame.

We usually don't talk about the rotating frame in which the wheel is considered stationary, because rotating frames are not inertial frames. The road frame, and the (non-rotating) axle frame are both inertial frames, so we tend to only refer to those frames.

Unfortunately there is a tendency for some folks to refer to the axle frame as the "wheel frame," which sounds more like the rotating frame.

48. Originally Posted by cincirob

The one of the relativists here should figure out why a rotating wheel and a non-rotating wheel give identical answers and show an analysis that proves it. So far, no luck.
The shape of the wheel rim in the road frame is in both cases an ellips.
But in both cases the events the ellips is made of at a t road time are different.
Unfortunately you won't be able to understand this because you don't know what events are.

49. Ok, good, I am clear on that that then. How is the translation made from a rotating axle to a non-rotating one?

50. Originally Posted by Jilan
How is the translation made from a rotating axle to a non-rotating one?
I'm not sure what you are asking.

Imagine a rotating circular disk with a hole in the center. Insert an axle through the hole, and hold the axle stationary. The axle is non-rotating, but the wheel is rotating around it. Thus, the axle frame is an inertial frame in which the center point of the wheel does not move.

51. Originally Posted by VeeDee
The shape of the wheel rim in the road frame is in both cases an ellips.
But in both cases the events the ellips is made of at a t road time are different.
Unfortunately you won't be able to understand this because you don't know what events are.
Indeed, cinci simply won't be told

Thank You,

52. I am sorry if I am being obtuse, but unless we are talking about a wagon wheel here isn't the wheel attached to the axle?

53. Originally Posted by Jilan
Ok, good, I am clear on that that then. How is the translation made from a rotating axle to a non-rotating one?
I think you mean ...

How is the transformation made from a rotating axle POV to a non-rotating ground POV?

If so, then ... Not easily. The LTs alone cannot achieve this. There are non-inertial formulae developed from Rindler's analyses and figures, that might help do the job. It's rather complex though, and beyond the scope of the LTs alone. I have not seen a transformation online for rotating disk POV to inertial ground POV. If one exists, I'd like to see it. It may have been done, not sure. The scope of Gron's analysis did not require such a complex transformation, because Gron never defined a POV attached to the rotating disk. Gron's analysis simply says that ... if the wheel exists as such and sunch per axle, then it must exist as such and such per ground, per the LTs.

Thank You,

54. Originally Posted by Jilan
I am sorry if I am being obtuse, but unless we are talking about a wagon wheel here isn't the wheel attached to the axle?
The wheel should be considered to be rotating about ball bearings mounted about the fixed stationary non-rotating axle.

just to add to that ...

If the wheel had no axle and just rolled along with one particular wheel-atom always at the wheel's axis-of-rotation, then one could consider the POV of that rotating atom (call it POVrot), but that's a non inertial POV that must use a non-euclidean spacetime system to map its surroundings, and so the LTs would not directly apply since they were designed exclusively for inertial POVs which use euclidean spacetime systems. However, to use the LTs, one could consider the POV of a non-rotating atom (POVnon-rot) that is (say) 1 micron in separation wrt the z-axis from the rotating POV (POVrot) ... and run the LTs from that non-rotating inertial POV to the ground POV.

Thank You,

55. Originally Posted by Jilan
I am sorry if I am being obtuse, but unless we are talking about a wagon wheel here isn't the wheel attached to the axle?
If the axle were co-rotating with the wheel, then the so-called 'axle frame' would be a rotating frame. Then we would not want to use that frame, for the same reason we do not want to use the 'wheel frame'. We need a non-rotating reference frame in which the wheel rotates, and the spacial location of the wheel's center point does not change. That is what we have been calling the 'axle frame', but it could just as well have been called the 'wagon frame' if the wheel were part of a wagon.

Edit: Oh, I see SYA already explained it quite nicely.

56. Originally Posted by cincirob
Every relativist here knows exactly why you are stuck, but alas, you simply won't be told.

cinci: The one of the relativists here should figure out why a rotating wheel and a non-rotating wheel give identical answers and show an analysis that proves it. So far, no luck.
EDIT: I should add, the figures below depict a single spoke of the wheel. 5 equal distant points (atoms) of that spoke as mapped in both the axle and ground spacetime systems. Those 5 points exist simultaneously at t=0 per ground, but they exist per axle with equally spaced temporal separations of t'=0.216.

Note that points affixed to the disk (no matter if disk rotates or not) always occupies the very same volume of AXLE space in any axle instant of time t'. This is why the disk must have the same perimeter shape and size per any POV, including the GROUND, no matter what its rotation rate ... given the same axle translation rate, and assuming the shape that never changes in the AXLE system. Gron's disk and shape are defined as "Born rigid and round, of radius R, per AXLE" ...

FIGURE 3: Rotating disk in 4 dimensional spacetime. Note the atoms of a single rotating radial per axle are CURVED per ground ...

FIGURE 2: Non-rotating translating disk in 4 dimensional spacetime. Note the atoms of a single rotating radial per axle are LINEAR per ground ...

Both figures possess the very same AXLE translation rate.

The radials are linear per ground if a non-rotating disk, and generally curved for a rotating disk. It's the rotation that curves them, and if this did not occur, then forces would be induced into the disk per ground that do not exist in the disk per axle, which of course would make any theory unreasonable and invalid. As such the disk solns are not the same for both cases, even though the general shape and size of the perimeters are the very same. The "configuration of the disk's atoms" differs for these 2 cases, per ground.

Anyone can see at a glance why the shapes of these 2 cases are the very same, per any POV, including the ground POV.
Spacetime diagrams model the LTs verbatum.

Thank You,

57. Nice work, SYA. Here is another way of demonstrating essentially the same thing that you just demonstrated:

Originally Posted by cincirob
cinci: The one of the relativists here should figure out why a rotating wheel and a non-rotating wheel give identical answers and show an analysis that proves it. So far, no luck.
These things are self-evident, and true by definition:
1. According to the axle frame, no part of the circular disk is ever located outside of the geometric circle represented by (r')ē = (x')ē + (y')ē where r' is the radius of the circular disk, as measured by the axle frame.
2. According to the axle frame, there is never a space between the edge of the circular disk and the geometric circle represented by (r')ē = (x')ē + (y')ē where r' is the radius of the circular disk, as measured by the axle frame.
3. Note that #1 and #2 hold true regardless of whether the circular disk is rotating or non-rotating.

This is self-evident, and true according to SR:
4. According to the road frame, the x' axis is moving and contracted by a factor of √(1 - (vē/cē)), so the above geometric circle is contracted by a factor of √(1 - (vē/cē)) to a geometric ellipse.

Thus, these things are also self-evident, and true according to SR:
5. According to the road frame, no part of the disk is ever located outside of the geometric ellipse represented by (r')ē = (x')ē + (y')ē where the x' axis is contracted by a factor of √(1 - (vē/cē)).
6. According to the road frame, there is never a space between the edge of the disk and the geometric ellipse represented by (r')ē = (x')ē + (y')ē where the x' axis is contracted by a factor of √(1 - (vē/cē)).
7. Note that #5 and #6 hold true regardless of whether the disk is rotating or non-rotating.

Q.E.D.

58. cinci: Everything the three of you say is absolutely correct for a Born rigid disk. How do I know? Because I did this analysis years ago at the same time JT did, curved spokes, curved chords, 2piR/(1 - (v/c)^2)^.5 roll out, and all, despite anybody's claims to the contrary. It's all over on the old site for anyone who wants to know the truth. (People who want to know the truth seem to be in short supply here.) If you still want to claim I don't understand it..............pants on fire!

Now when you can prove that you can build one of these at speed, let me know. That's why I think the thing is bogus.

59. Originally Posted by cincirob
cinci: Everything the three of you say is absolutely correct for a Born rigid disk. How do I know? Because I did this analysis years ago at the same time JT did, curved spokes, curved chords, 2piR/(1 - (v/c)^2)^.5 roll out, and all, despite anybody's claims to the contrary. It's all over on the old site for anyone who wants to know the truth. (People who want to know the truth seem to be in short supply here.) If you still want to claim I don't understand it..............pants on fire!
You did the analysis in an odd way, because you did not understand how RoS applied using the LTs. You had the fortune of seeing the correct solns produced by others first. You did not understand what the solns meant, because you remain unclear on some basics of SR, eg spacetime events.

Originally Posted by cincirob
Now when you can prove that you can build one of these at speed, let me know. That's why I think the thing is bogus.
(Yet) Again, no one cares. When you prove you understand relativity, you will then know why all your arguments that Gron's work is false, are mistaken. No one cares to help you build magic wheels with wonderous wheel building procedures, or start from a ground POV while ignoring an axle POV to relate the non-inertial POV of the rotating disk, until you first learn spacetime events & why the LTs can be used to model points that move in both systems. It would be a waste of time, otherwise. And, we've been trying to help you with these matters for many years now, so. Maybe you should try something new, and work a basic all inertial scenario until you understand how events work in LTs.

Thank You,

You did the analysis in an odd way, because you did not understand how RoS applied using the LTs. You had the fortune of seeing the correct solns produced by others first. You did not understand what the solns meant, because you remain unclear on some basics of SR, eg spacetime events.

(Yet) Again, no one cares. When you prove you understand relativity, you will then know why all your arguments that Gron's work is false, are mistaken. No one cares to help you build magic wheels with wonderous wheel building procedures, or start from a ground POV while ignoring an axle POV to relate the non-inertial POV of the rotating disk, until you first learn spacetime events & why the LTs can be used to model points that move in both systems. It would be a waste of time, otherwise. And, we've been trying to help you with these matters for many years now, so. Maybe you should try something new, and work a basic all inertial scenario until you understand how events work in LTs.

Thank You,
Good idea. I want to see how Cinci handles a moving pole, how coordinates of two simultaneous events per frame A transform to a frame B, by using Lorentz tranformations.
Cinci still does not know how to do it. Cinci knows only gamma and the LCF formula, and he probably thinks they mean the same as Lorentz Tranformations. That's why Cinci erroneously sees in Gron's Lorentz Tranformations only length contraction of a non-rotating wheel, even with rotation velocity w in the equations! And if he is in a good mood and does see rotation he will never admit it's the physical wheel rotating, but only abstract points rotating over a non-rotating wheel. Painful. To be honest, Cinci should write poetry. He has lots of imagination, but unfortunately after all those years he has still no knowledge at all of Einstein relativity.

61. cinci: Everything the three of you say is absolutely correct for a Born rigid disk. How do I know? Because I did this analysis years ago at the same time JT did, curved spokes, curved chords, 2piR/(1 - (v/c)^2)^.5 roll out, and all, despite anybody's claims to the contrary. It's all over on the old site for anyone who wants to know the truth. (People who want to know the truth seem to be in short supply here.) If you still want to claim I don't understand it..............pants on fire!

SYA: You did the analysis in an odd way, because you did not understand how RoS applied using the LTs. You had the fortune of seeing the correct solns produced by others first. You did not understand what the solns meant, because you remain unclear on some basics of SR, eg spacetime events.

cinci: Well no, this is just you trying to justify all your insulting comments. Actually, I don't think one can do the analysis without understanding RoS and if you understood relativity, you would know that. Further, nobody did the curved chords before I did so I couldn't have copied that.

As for seeing the solutions of others before I did it, well so did everybody else here. But it's not quite true because I don't think Gron had any numbers in his paper. I made my own numbers independently of Gron's equations and of anybody here. What I got from Gron's paper was the hint that Ros caused the curvature. From there it's all my own solution. I didn't just copy his equations as you did.

And the space-time events issue is nonsense because Gron didn't describe it that way. So the fact that I don't doesn't mean I don't understand it.

cinci: Now when you can prove that you can build one of these at speed, let me know. That's why I think the thing is bogus.

SYA: (Yet) Again, no one cares.

cinci: Then stop posting about it.

SYA: When you prove you understand relativity, you will then know why all your arguments that Gron's work is false, are mistaken.

cinci: This isn't an argument. It was a challenge for you to put some analysis on the Born rigid wheel and this response proves you can't do it.

SYA: No one cares to help you build magic wheels with wonderous wheel building procedures, or start from a ground POV while ignoring an axle POV to relate the non-inertial POV of the rotating disk, until you first learn spacetime events & why the LTs can be used to model points that move in both systems. It would be a waste of time, otherwise. And, we've been trying to help you with these matters for many years now, so.

cinci: In other words, you don't know how to build a wheel at speed and make it make sense.

SYA: Maybe you should try something new, and work a basic all inertial scenario until you understand how events work in LTs.

cinci: And maybe you should grow up and stop trying to prove I haven't done an analysis that I obviously have done. In fact, there's no evidence that shows you did the analysis before JT and I did. Back on the old site you simply posted Gron's paper and left. JT and I did the analysis ourselves. Now you just copy what JT did or blindly plug into Gron's equations.

62. VeeDee: Good idea. I want to see how Cinci handles a moving pole, how coordinates of two simultaneous events per frame A transform to a frame B, by using Lorentz tranformations.

cinci: As I remember, I showed you how to do it.

VeeDee: Cinci still does not know how to do it. Cinci knows only gamma and the LCF formula, and he probably thinks they mean the same as Lorentz Tranformations.

cinci: And you think they don't? ;-)

VeeDee: That's why Cinci erroneously sees in Gron's Lorentz Tranformations only length contraction of a non-rotating wheel, even with rotation velocity w in the equations!

cinci: OK smart guy. Did you realize that Gron's analysis works for a non-rotating disk with points constrained to move around it before I told you? Or maybe you still think that isn't a fact? Let's see you prove otherwise.

VeeDee: And if he is in a good mood and does see rotation he will never admit it's the physical wheel rotating, but only abstract points rotating over a non-rotating wheel. Painful.

cinci: Let's see you prove otherwise.

VeeDee: To be honest, Cinci should write poetry. He has lots of imagination, but unfortunately after all those years he has still no knowledge at all of Einstein relativity.

cinci: I'll cop to the imagination.................. I had a career as a designer. It comes in handy. On the relativity, I explained to you a different way to think about the wheel analysis and you didn't get it. If you were as good as you think you are, you would have.

63. VeeDee: The shape of the wheel rim in the road frame is in both cases an ellips.
But in both cases the events the ellips is made of at a t road time are different.
Unfortunately you won't be able to understand this because you don't know what events are.

cinci: An event would be when you wake up and realize I know as much about the wheel analysis as you do. and I knew it a long time before you showed up.

64. Originally Posted by cincirob
cinci: In other words, you don't know how to build a wheel at speed and make it make sense.
So now that it has been proven that the rotating disk has the same shape as the non-rotating disk, (contrary to your 5 year claim otherwise), you are changing your tune and claiming the wheel cannot be built at speed. How clever.

Instead of starting a new argument that you are bound to lose, (again), why not use your imagination to invent a method that works? First off, I would not recommend building it out of inertial poles, because they are going to have to accelerate into the rotating state, and that would probably cause some stresses. I would start with a pole already rotating with angular velocity ω in the axle frame, whose midpoint is located at the axle, and then gradually move the pole out to the edge of the wheel. Like this:

There. See how easy that was?

65. Originally Posted by VeeDee
Good idea. I want to see how Cinci handles a moving pole, how coordinates of two simultaneous events per frame A transform to a frame B, by using Lorentz tranformations.
Cinci still does not know how to do it. Cinci knows only gamma and the LCF formula, and he probably thinks they mean the same as Lorentz Tranformations. That's why Cinci erroneously sees in Gron's Lorentz Tranformations only length contraction of a non-rotating wheel, even with rotation velocity w in the equations! And if he is in a good mood and does see rotation he will never admit it's the physical wheel rotating, but only abstract points rotating over a non-rotating wheel. Painful. To be honest, Cinci should write poetry. He has lots of imagination, but unfortunately after all those years he has still no knowledge at all of Einstein relativity.
This was essentially done here by JT, in the first Relativistically Rolling Wheel thread ... between posts #477 & #503. I asked for JT to run the analysis in post #477, and JT's various posts from #483 -> #503 covered the analysis, and graphically as well. Went right over cincirob's head though.

For reference ...

Post #477 ... http://www.thephysicsforum.com/speci...html#post11346

Post #483 ... http://www.thephysicsforum.com/speci...html#post11360

Post #503 ... http://www.thephysicsforum.com/speci...html#post11417

It's been recovered with cinci's rod and barn scenario, by JT, if I recall correctly. But each time cinci gets backed into a corner on basic aspects of relativity, the need to add real material to rotating wheels during roll-up, pears, skipping axle POVs, the desire to build a magic wheel on the fly, and LTs not being able to aid in the handling of entities that move in both systems. Sigh.

Thank You,

66. Originally Posted by cincirob
VeeDee: Good idea. I want to see how Cinci handles a moving pole, how coordinates of two simultaneous events per frame A transform to a frame B, by using Lorentz tranformations.

cinci: As I remember, I showed you how to do it.

VeeDee: Cinci still does not know how to do it. Cinci knows only gamma and the LCF formula, and he probably thinks they mean the same as Lorentz Tranformations.

cinci: And you think they don't? ;-)
No, they don't.
Amazing isn't it? ,
The LCF gives you the contracted length between simultaneous events in the road frame, i.o.w. for equal road t coordinate. Not necessariliy Lorentz transformations. Lortenz transformations gives you new coordinates (including t coordinate) of events not taking care whether they have to end up, same t or not.

I knew you don't have a clue what Lorentz tranformations do and don't do.

The LCF formula is derived from (i.o.w. they are not the 'same' as...) Lorentz Transformations applied to a linear moving physical object.
Simultaneous events in one frame end up non simultaneous in another frame, but by taking care of which events do end up as simultaneous in the road frame the LCF calculates the contracted distance. You cannot use the LCF for your rotating chord, because the LCF are not formulated to do that: a rotating chord, part of the wheel atoms is not an linear moving rod. Engineers should know that difference, but you obviously don't.

You tried to save your *ss by telling everybody your chord is a coincident abstract chord moving linear at .866 level. Unfortunately you don't know special relativity deals with coordinates of real physical spacetime events of wheel atoms. We deal with rotating chord atoms, not linear moving abstract points. I.o.w. forget LCF, use Lorentz Transformations.

You are a complete zero as far as Einstein relativity is concerned. Your pretentiousness sticking to your absurd relativity interpretation is hilarious. You simply make a fool of yourself defending your nonsense for so many years. You blame us for not working with a rotating wheel but in fact it's YOU that is not working with a rotating wheel by stubornly sticking to your LCF formula for the chord calculation. Adding a small talk about RoS that nobody understand will not help.

VeeDee: That's why Cinci erroneously sees in Gron's Lorentz Tranformations only length contraction of a non-rotating wheel, even with rotation velocity w in the equations!

cinci: OK smart guy. Did you realize that Gron's analysis works for a non-rotating disk with points constrained to move around it before I told you? Or maybe you still think that isn't a fact? Let's see you prove otherwise.

VeeDee: And if he is in a good mood and does see rotation he will never admit it's the physical wheel rotating, but only abstract points rotating over a non-rotating wheel. Painful.

cinci: Let's see you prove otherwise.

VeeDee: To be honest, Cinci should write poetry. He has lots of imagination, but unfortunately after all those years he has still no knowledge at all of Einstein relativity.

cinci: I'll cop to the imagination.................. I had a career as a designer. It comes in handy. On the relativity, I explained to you a different way to think about the wheel analysis and you didn't get it.
I'm not interested in getting it if it gives wrong results. And your imagnination does give wrong results. A pear is not an ellips.

If you were as good as you think you are, you would have. [/B]

67. VeeDee: Amazing isn't it?

cinci: Yes, a coordinate distance times (1 - (v/c)^2)^.5 is different that any other distance times (1 - (v/c)^2)^.5. Now I get it. :-)

68. Originally Posted by cincirob
cinci: Yes, a coordinate distance times (1 - (v/c)^2)^.5 is different that any other distance times (1 - (v/c)^2)^.5. Now I get it. :-)
No, clearly you do not get it.

You apply the LCF to the rest length of your pole and find its length in the road frame is 0.152. So you figure the right edge of your pole is located at x=0.152 at t=0.000 in the road frame, which is correct, but it does not have anything to do with the wheel.

Everyone else applies the full LT to the right edge of your pole at the time when it is coincident with the right edge of the wheel, and we find that the right edge of your pole would be coincident with the right edge of the wheel at x=1.000 at t=0.866 in the road frame.

If the two methods were the same, they would not produce different results, now would they.

69. Just for kicks and giggles, I decided to derive my own formula to find the coordinates of the endpoints of a pole simultaneously in the road frame. Unlike cincirob, I do not enjoy calculating rest lengths, composed velocities, and different gamma factors. So, my method is designed to avoid doing it that way.

I won't show the derivation here, because cincirob would probably say it is easier to do it his way. But my end result is actually quite simple:

x'R = ((u't'L) + L') / (1 + (u'v/c))
Where:
x'R is the spacial coordinate of the Right edge of the pole in the axle frame
u' is the velocity of the pole as measured by the axle frame
t'L is the temporal coordinate of the Left edge of the pole in the axle frame
L' is the length of the pole as measured by the axle frame
v is the relative velocity of the axle frame as measured by the road frame

And
t'R = (-vx'R / c) + t'L
Where:
t'R is the temporal coordinate of the Right edge of the pole in the axle frame
v is the relative velocity of the axle frame as measured by the road frame
x'R is the spacial coordinate of the Right edge of the pole in the axle frame
t'L is the temporal coordinate of the Left edge of the pole in the axle frame

---

So, let's work an example using cincirob's pole. We know its Left edge is located at x'L=0.000 t'L=0.000 and that transforms to the road frame as xL=0.000 tL=0.000. So, to find the Right edge simultaneously in the road frame, we do this:
x'R = ((u't'L) + L') / (1 + (u'v/c))
x'R = ((0.750*0.000) + 0.500) / (1 + (0.750*0.866))
x'R = 0.303

And
t'R = (-vx'R / c) + t'L
t'R = (-0.866*0.303) + 0.000
t'R = -0.263

Just apply the LT as usual, and you will find x'R=0.303 and t'R=-0.263 transform to the road frame as xR=0.152 and tR=0.000 just like cincirob's beloved LCF results.

70. Note: The above formulas only work if x'L = 0.000 but I am working on a more general solution....

71. Originally Posted by cincirob
VeeDee: Amazing isn't it?

cinci: Yes, a coordinate distance times (1 - (v/c)^2)^.5 is different that any other distance times (1 - (v/c)^2)^.5. Now I get it. :-)
In other words: you are still a complete illiterate as far as relativity is concerned ... and apparently you enjoy it a lot..

72. Originally Posted by cincirob
VeeDee: Amazing isn't it?

cinci: Yes, a coordinate distance times (1 - (v/c)^2)^.5 is different that any other distance times (1 - (v/c)^2)^.5. Now I get it. :-)
OK then cinci, so what do you think after reading JTyesthatJT's most recent posts? After careful consideration of that, what is you position now then?

Thank You,

73. JT: You apply the LCF to the rest length of your pole and find its length in the road frame is 0.152. So you figure the right edge of your pole is located at x=0.152 at t=0.000 in the road frame, which is correct, but it does not have anything to do with the wheel.

cinci: I acknowledged some time ago that the pear didn't work. But let me ask you this. Don't you see any reason at all to make the comparison between a chord and such a pole?

Despite anything SYA babbles about on the subject, there are physicists who say the Gron wheel must be constructed at speed. And you know that's true because you can't slow the wheel down or accelerate it without adding or subtracting material. The comparison with the pole started out as an attempt to build the wheel at speed and it doesn't work. So how would you build it at speed?

74. JT: Just apply the LT as usual, and you will find x'R=0.303 and t'R=-0.263 transform to the road frame as xR=0.152 and tR=0.000 just like cincirob's beloved LCF results.

cinci: So I was right all along, right?

JT: I won't show the derivation here, because cincirob would probably say it is easier to do it his way.

[B}cinci: And I was right about that too, right? And it's not only easier, it gives you a physical feel for why it comes about. [/B]

75. Originally Posted by JTyesthatJT
Just for kicks and giggles, I decided to derive my own formula to find the coordinates of the endpoints of a pole simultaneously in the road frame. Unlike cincirob, I do not enjoy calculating rest lengths, composed velocities, and different gamma factors. So, my method is designed to avoid doing it that way.

I won't show the derivation here, because cincirob would probably say it is easier to do it his way. But my end result is actually quite simple:

x'R = ((u't'L) + L') / (1 + (u'v/c))
Where:
x'R is the spacial coordinate of the Right edge of the pole in the axle frame
u' is the velocity of the pole as measured by the axle frame
t'L is the temporal coordinate of the Left edge of the pole in the axle frame
L' is the length of the pole as measured by the axle frame
v is the relative velocity of the axle frame as measured by the road frame

And
t'R = (-vx'R / c) + t'L
Where:
t'R is the temporal coordinate of the Right edge of the pole in the axle frame
v is the relative velocity of the axle frame as measured by the road frame
x'R is the spacial coordinate of the Right edge of the pole in the axle frame
t'L is the temporal coordinate of the Left edge of the pole in the axle frame

---

So, let's work an example using cincirob's pole. We know its Left edge is located at x'L=0.000 t'L=0.000 and that transforms to the road frame as xL=0.000 tL=0.000. So, to find the Right edge simultaneously in the road frame, we do this:
x'R = ((u't'L) + L') / (1 + (u'v/c))
x'R = ((0.750*0.000) + 0.500) / (1 + (0.750*0.866))
x'R = 0.303

And
t'R = (-vx'R / c) + t'L
t'R = (-0.866*0.303) + 0.000
t'R = -0.263

Just apply the LT as usual, and you will find x'R=0.303 and t'R=-0.263 transform to the road frame as xR=0.152 and tR=0.000 just like cincirob's beloved LCF results.
Very good job, JT.

I did a quick loedel diagram check for your t'R equation ;-)

Loedel diagrams (same unit scale on all axes!) are O.K. for two frames, but it also does work for the pole moving per axle frame without having to introduce the pole rest frame! Watch this:

Edit: diagram update.

76. Originally Posted by cincirob
cinci: Don't you see any reason at all to make the comparison between a chord and such a pole?
Not really, because the pole only approximates the chord. The pole travels along a straight line at a velocity of 0.750c through the axle frame, whereas the chord travels along a circular path of various radii from 0.866 to 1.000 at various velocities from 0.750c to 0.866c. That's like comparing apples to oranges.

The only usefulness of the pole was that it intersected the right edge of the wheel at x'=0.500 t'=0.000 which transforms to the road as x=1.000 t=0.866. That tells us the shape of the wheel in the road frame must be an ellipse. But we could have determined that from any event located at x'=0.500 t'=0.000 coordinates in the axle frame. For example, the firecracker popping in that location tells us the same thing.

Originally Posted by cincirob
cinci: Despite anything SYA babbles about on the subject, there are physicists who say the Gron wheel must be constructed at speed. And you know that's true because you can't slow the wheel down or accelerate it without adding or subtracting material. The comparison with the pole started out as an attempt to build the wheel at speed and it doesn't work. So how would you build it at speed?
Your contracting/shrinking wheel does not have to be built at speed, so this is a non-issue. But if I wanted to build a wheel at speed, I would build it the way I described in my post #264 above.

Originally Posted by cincirob
JT: Just apply the LT as usual, and you will find x'R=0.303 and t'R=-0.263 transform to the road frame as xR=0.152 and tR=0.000 just like cincirob's beloved LCF results.

cinci: So I was right all along, right?
Nope. Road coordinates x=0.152 t=0.000 are not the correct coordinates for the right edge of the wheel, even though they are correct coordinates for the right edge of the pole.

Originally Posted by cincirob
JT: I won't show the derivation here, because cincirob would probably say it is easier to do it his way.

cinci: And I was right about that too, right? And it's not only easier, it gives you a physical feel for why it comes about.
Being able to easily calculate the length of the pole in the road frame is nice. But by itself, it doesn't tell you anything about the location of the right edge of the wheel.

77. Originally Posted by cinci to JT
Don't you see any reason at all to make the comparison between a chord and such a pole?
We have made that comparison for years, just for you. The comparison showed that the linear string of atoms comprising the momentarily horizontal rotating cord per axle (at y'=0.866) IS NOT the same string of atoms that constitute a momentarily horizontal rolling cord per ground (at y=y'=0.866). They are an entirely different set of atoms (except the atoms at the endpoints on the rim), and thus are different cords altogether. The inertial rod at that height (y'=y=0.866) are the very same atoms in both the axle and ground systems, because they do not rotate. That's what the analysis told everyone. The length of the rotating disk cord and rod must differ, per ground. To understand that, one must use the LTs and understand spacetime events. JT presented that very well, long ago, for you.

Originally Posted by cinci to JT
Despite anything SYA babbles about on the subject, there are physicists who say the Gron wheel must be constructed at speed. And you know that's true because you can't slow the wheel down or accelerate it without adding or subtracting material. The comparison with the pole started out as an attempt to build the wheel at speed and it doesn't work. So how would you build it at speed? [/B]
Building a disk at speed is a wonderous thought experiment. It's no more practical or possible than rolling a disk up to a relativistic rotation rate. It's impossible. I can say that building a disk at speed is impossible, and thus one should just roll the wheel up to speed. Or, I can say that rolling a wheel up to speed is impossible, and thus one should build a wheel at speed. All, impossible.

You say material needs added or subtracted from the disk as its rotation rate changes. Another can argue that the atoms of the disk may be defined to deform such that atoms from adjacent planes wrt the z-axis move into the voids created by the circumferential contraction. A deformation to recipe, that always keeps the disk round and of radius R' with a virtual Born rigid structure.

What's important, is that one understands how to apply the LTs, that LT coordinates are 0-dimensional points in spacetime, not points in space alone. That if an atom is HERE at x',y',z',t' per axle (moving or not), then per the LTs it also exists THERE at coordinate x,y,z,t per ground (moving). HERE >>> IS <<< THERE, even though they are quantified differently per the 2 differing inertial frames of reference. That is, observers are allowed to disagree on the measure of space and time, but all agree on the event. An event might be described as the mutual flyby of 2 clocks, one reading 11:32 and the other 7:24 on flyby. All in the cosmos agree the clocks read as such at that event, even though observers can disagree on when and where that event took place by there own clocks and rulers.

Thank You,

78. cinci: Don't you see any reason at all to make the comparison between a chord and such a pole?

Not really, because the pole only approximates the chord. The pole travels along a straight line at a velocity of 0.750c through the axle frame, whereas the chord travels along a circular path of various radii from 0.866 to 1.000 at various velocities from 0.750c to 0.866c. That's like comparing apples to oranges.

cinci: YOu can't say "Not really" and follow that it "approximates it". That's the whole idea.

cinci: Despite anything SYA babbles about on the subject, there are physicists who say the Gron wheel must be constructed at speed. And you know that's true because you can't slow the wheel down or accelerate it without adding or subtracting material. The comparison with the pole started out as an attempt to build the wheel at speed and it doesn't work. So how would you build it at speed?

JT: Your contracting/shrinking wheel does not have to be built at speed, so this is a non-issue. But if I wanted to build a wheel at speed, I would build it the way I described in my post #264 above.

cinci: Everybody can construct it in that frame. Construct it in the road frame.

JT: Just apply the LT as usual, and you will find x'R=0.303 and t'R=-0.263 transform to the road frame as xR=0.152 and tR=0.000 just like cincirob's beloved LCF results.

cinci: So I was right all along, right?

JT: Nope. Road coordinates x=0.152 t=0.000 are not the correct coordinates for the right edge of the wheel, even though they are correct coordinates for the right edge of the pole.

cinci: Your calculation was for the pole and I got the same answer. Do you get points for saying I'm wrong about everything even when I'm not. So your "Nope" is wrong.

JT: I won't show the derivation here, because cincirob would probably say it is easier to do it his way.

cinci: And I was right about that too, right? And it's not only easier, it gives you a physical feel for why it comes about.

JT: Being able to easily calculate the length of the pole in the road frame is nice. But by itself, it doesn't tell you anything about the location of the right edge of the wheel.

cinci: It doesn't tell you when the sun will come up tomorrow but it's still correct and it's still easier.

79. cinci: Don't you see any reason at all to make the comparison between a chord and such a pole?

SYA: We have made that comparison for years, just for you.

cinci: Actually that isn't anywhere near the truth. On the other forum and here also you avoided that question dozens of times.

SYA: You say material needs added or subtracted from the disk as its rotation rate changes. Another can argue that the atoms of the disk may be defined to deform such that atoms from adjacent planes wrt the z-axis move into the voids created by the circumferential contraction. A deformation to recipe, that always keeps the disk round and of radius R' with a virtual Born rigid structure.

cinci: For a rack and pinion, you have to change the number of teeth. There isn't any way around adding material. Your other arguments amount to majic.

80. Cinci doesn't know the difference between a rotating set of atoms (chord) and a linear moving set of atoms. This means for Cinci the chord atoms and the pole atoms should follow the same 4D spacetime paths (worldline of events)...? Poor cinci...

81. Originally Posted by cincirob
cinci: Don't you see any reason at all to make the comparison between a chord and such a pole?

SYA: We have made that comparison for years, just for you.

cinci: Actually that isn't anywhere near the truth. On the other forum and here also you avoided that question dozens of times.

Originally Posted by cincirob
SYA: You say material needs added or subtracted from the disk as its rotation rate changes. Another can argue that the atoms of the disk may be defined to deform such that atoms from adjacent planes wrt the z-axis move into the voids created by the circumferential contraction. A deformation to recipe, that always keeps the disk round and of radius R' with a virtual Born rigid structure.

cinci: For a rack and pinion, you have to change the number of teeth. There isn't any way around adding material. Your other arguments amount to magic.
Correct, it's all magic in the case of rotating bodies at relativistic rate, including at-speed magic wheel building procedures. (Yet again) The Gron analysis never suggested any Born rigid disk could spin as such, but rather simply assumed it did. It did however explorer the implications of relativistic effects in the case of rotation. What does it all mean? It means that if one slowly accelerated the spin rate of Gron's disk, that disk would eventually deform and break up as the result of 2 composite effects ...

(1) centrifugal force, and
(2) circumferential contraction

although the latter (2) would be rather negligible to the former (1) even though it must exist. As such, a disk should shatter just a tiny bit sooner than it normally would had classical mechanics alone governed existence, but could only be measured if stress-sensing-equipment were accurate enough to measure such.

OK, so you cannot understand why Gron's model is the generally accepted one. You long argued that Gron's analysis was false. Later, you changed your position to Gron's analysis being mathematically proper, but false as far as a real disk goes. When told that Gron's disk was never assumed to be real (no real wheel can exist as such), that it was simply assumed as existent in thought experiment for the sake of exploring the relativistic effects of rotation for relativistic rotation rates, you argue his theory is false because it does not model real material. When you were retold many times over the years that Gron never considered any real disk could exist as such, you then argue that "a few other physicists claim real disks may be constructed at steady relativistic rotation rate". When you are then told that said physicists did not mean to imply real wheels could be built as such, that it was merely a wonderous disk-building thought experiment, you yourself "choose not to believe that". Then you switch gears altogether, and argue that rack and pinion fails during roll-up, as though that somehow supports your mistaken positions. Round and round we forever go, where cinci ends up, everybody knows ... adding material during roll-up, rack and pinion failing during roll-up, and magical wheel building procedures at speed. Good grief ...

Take a break, learn about spacetime events, and try and use the LTs in a simple all inertial scenario. This is the only hope in which your issues can vanish cinci. I recommend you learn spacetime diagrams, given the years you have had help on all these relativity matters and never having come to grips with them. It cannot hurt to try.

Thank You,

82. Originally Posted by VeeDee
Cinci doesn't know the difference between a rotating set of atoms (chord) and a linear moving set of atoms. This means for Cinci the chord atoms and the pole atoms should follow the same 4D spacetime paths (worldline of events)...? Poor cinci...
Yes, I must have explained 50 times to cinci that the rotating cord atoms follow types of cycloids, but since he does not understand that the LTs can map an atom in both systems, no matter if it moves in both systems or not, ... he is completely stuck, and will not be told.

Thank You

83. Originally Posted by VeeDee
Very good job, JT.

I did a quick loedel diagram check for your t'R equation ;-)

Loedel diagrams (same unit scale on all axes!) are O.K. for two frames, but it also does work for the pole moving per axle frame without having to introduce the pole rest frame! Watch this:

Edit: diagram update.

Wow, thank you. That looks great. I tried to draw a Minkowski diagram of cinci's pole, but with its puny length of 0.152 in the road frame, it doesn't make for a very nice Minkowski diagram. At least not the way I draw them.

Another way to calculate x'R=0.304 and t'R=-0.263 is to first do cincirob's rest length and composed velocity calculations, then simply plug xR=0.152 and tR=0.000 into these equations:
x'R = γ(xR - vtR) = 0.304
t'R = γ(tR - (vxR / cē)) = -0.263
Where
v = 0.866c
γ = 2.000

But I prefer not to do cincirob's rest length and composed velocity calculations, which is why I derived those equations in post #269. After working on the derivations some more, it turns out those equations should look like this:
x'R = (cēu't'L + u'vx'L + cēL') / (cē + u'v)
t'R = (-vx'R / cē) + (t'L) + (vx'L / cē)
or
t'R = t'L + v(x'L - x'R) / cē

And those equations should work for the pole at any time, not just when x'L=0.000 at t'L=0.000.

84. Originally Posted by cincirob
cinci: YOu can't say "Not really" and follow that it "approximates it". That's the whole idea.
It is a pretty poor approximation. The pole and the chord have almost nothing in common.

Originally Posted by cincirob
cinci: Everybody can construct it in that frame. Construct it in the road frame.
That is the kind of comment that makes people think that you might not understand the Gron model, or relativity in general. If one can construct the wheel on-the-fly in the axle frame, surely all frames must agree that the wheel can be constructed on-the-fly.

Just take the animation I provided you, change the shape of the wheel from circular to elliptical, make the spokes all curve upward, and then make the rim segment curve dynamically as it moves out to the rim. It will be just like Gron's ellipse model, which you claim you understand. So this should not be a problem.

85. SYA: Correct, it's all magic in the case of rotating bodies at relativistic rate, including at-speed magic wheel building procedures. (Yet again) The Gron analysis never suggested any Born rigid disk could spin as such, but rather simply assumed it did.

cinci: Yes, it is an assumption and what I've been trying to do is test that assumption. It's called scientific curiosity.

SYA: OK, so you cannot understand why Gron's model is the generally accepted one.

cinci: An unfounded....correction, another unfounded assumption on your part. It's works fine if you assume a Born rigid wheel. And it results in the curved spokes which is an interesting RoS effect.

What you're missing is that nobody really understands a Born rigid disk.

86. cinci: YOu can't say "Not really" and follow that it "approximates it". That's the whole idea.

JT: It is a pretty poor approximation. The pole and the chord have almost nothing in common.

cinci: Same length, same x-direction velocity.

cinci: Everybody can construct it in that frame. Construct it in the road frame.

JT: That is the kind of comment that makes people think that you might not understand the Gron model, or relativity in general. If one can construct the wheel on-the-fly in the axle frame, surely all frames must agree that the wheel can be constructed on-the-fly.

cinci: That's the kind of comment that makes me think you can't construct it in the road frame.

JT: Just take the animation I provided you, change the shape of the wheel from circular to elliptical, make the spokes all curve upward, and then make the rim segment curve dynamically as it moves out to the rim. It will be just like Gron's ellipse model, which you claim you understand. So this should not be a problem.

cinci: And that's the kind of comment that makes me think that any cartoon you draw is hard science.

87. SYA: Yes, I must have explained 50 times to cinci that the rotating cord atoms follow types of cycloids,...

cinci: Nonsense. I had to tell you what the correct shape was. You misnamed it. Besides, you don't use those velocities in Gron's analysis. I do use them to get the pear.

88. Originally Posted by cincirob
SYA: Yes, I must have explained 50 times to cinci that the rotating cord atoms follow types of cycloids,...

cinci: Nonsense. I had to tell you what the correct shape was. You misnamed it.
LOL, alrighty then. Whatever makes ya happier today. They're all cycloids, no matter how they might be further qualified.

Originally Posted by cincirob
Besides, you don't use those velocities in Gron's analysis. I do use them to get the pear.
Gron's analysis uses v, because the LTs use v. The atoms of the linear spoke per axle are (generally) curved per ground, because of the other velocity Gron uses which you claim he does not ... ω. Gron's usage of ω, in conjunction with the LTs which use v, allow him to know how to map rotating disk atoms in the axle system to their respective location "as simultaneous" in the ground system. Gron does not use the composition of velocities because it is not required, just to say it simply as possible here. You have never understood why, and you won't be told. If you get a pear shape, that should be a hint that your analysis is flawed. The disk is defined "as round", and Born rigid, per axle.

Thank You,

89. Originally Posted by cincirob
cinci: YOu can't say "Not really" and follow that it "approximates it". That's the whole idea.

JT: It is a pretty poor approximation. The pole and the chord have almost nothing in common.

cinci: Same length, same x-direction velocity.
The atoms of the rotating cord move along different axes of motion than do the atoms of the inertial rod. You cannot assume the rotating cord to be the same length as the rod, per ground. How can they, if they move along entirely different paths thru space over duration? The Fitzgerald LCF works only for motion where the body length is aligned with the propagation path, the body moving in uniform linear translation. All the atoms at any y=y' value are always on that same axis of motion, per both the axle and ground POVs. The cord has atoms traveling at different velocities, along different types of cycloid paths. It's an apple and an orange. Yet, Gron has enough knowns in his analysis to map any moving atom of the axle system into the ground system (in which it also moves), using (in part) the LTs.

Learn about spacetime events, and you'll understand why it all works very nicely.

Thank You,

90. Originally Posted by cincirob
JT: It is a pretty poor approximation. The pole and the chord have almost nothing in common.

cinci: Same length...
In the axle frame, yes.

Originally Posted by cincirob
cinci: ...same x-direction velocity.
Yes, in the axle frame that is true, but only in the instant when the wheel chord is parallel to the road. For example, that happens at t'=0.000 but not at t'=-0.263. Yet at t=0.000 in the road frame, your 0.152 long pole spans from axle time t'=0.000 (at its left edge) to t'=-0.263 (at its right edge). You are neglecting to consider where the chord would be at t'=-0.263. It is not even coincident with the pole yet.

Originally Posted by cincirob
JT: That is the kind of comment that makes people think that you might not understand the Gron model, or relativity in general. If one can construct the wheel on-the-fly in the axle frame, surely all frames must agree that the wheel can be constructed on-the-fly.

cinci: That's the kind of comment that makes me think you can't construct it in the road frame.
If I can construct it in the axle frame, then by that very fact, it is also constructed in all frames. Only an anti-relativist would think otherwise.

The atoms of the rotating cord move along different axes of motion than do the atoms of the inertial rod. You cannot assume the rotating cord to be the same length as the rod, per ground. How can they, if they move along entirely different paths thru space over duration? The Fitzgerald LCF works only for motion where the body length is aligned with the propagation path, the body moving in uniform linear translation. All the atoms at any y=y' value are always on that same axis of motion, per both the axle and ground POVs. The cord has atoms traveling at different velocities, along different types of cycloid paths.
I already told Cinci about this (post #266) but instead of thinking about it he prefers nitpicking abnout a non-issue. Cinci doesn't understand why the LCF is only for linear movcing object. And you know why? The LCF is derived from the Lorentz Transformations. But Cinci doesn't understand Lorentz Transformations, because he doesn't understand what events in 4D spacetime are. If cinci would understand the LCF are derived from Lorentz transformations of a linar moving object, he would immediately see the LCF is not meant for rotating chords.
Contraction occurs because of RoS. RoS deals with objects moving over time. Not just an object at a split second in time. Because the chord rotates, the RoS of its events, and the LT calculations will not give same contraction for chord and pole.

It's an apple and an orange. Yet, Gron has enough knowns in his analysis to map any moving atom of the axle system into the ground system (in which it also moves), using (in part) the LTs.

Learn about spacetime events, and you'll understand why it all works very nicely.
I'm afraid he needs more. As long as he sticks his head in the sand by not willing to learn about spacetime events in spacetime diagrams, he will never understand it...

Thank You,

92. Originally Posted by JTyesthatJT
Yet at t=0.000 in the road frame, your 0.152 long pole spans from axle time t'=0.000 (at its left edge) to t'=-0.263 (at its right edge). You are neglecting to consider where the chord would be at t'=-0.263. It is not even coincident with the pole yet.
The pole in the road frame is made of events from different t' poles per axle frame. That's how the RoS contraction works.
Hope this helps to make cinci see the light:

All in the cosmos agree the clocks read as such at that event, even though observers can disagree on when and where that event took place by there own clocks and rulers.
Correct. That's why I prefer discussing events 'containing' wristwatch time, real physical wristwatch time indication. And then spot where these events pop up in the different frames. Hence RECIPROCAL time dilation becomes a piece of cake... RoS is such a beauty... But it will take some(?) time until cinci is ready to discuss reciprocal time dilation, let alone reciprocal length contraction :-D

94. cincirob: Besides, you don't use those velocities in Gron's analysis. I do use them to get the pear.

SYA: Gron's analysis uses v, because the LTs use v.

cinci: So all your talk about cycloid velocities is just hot air.

95. Originally Posted by cincirob
cincirob: Besides, you don't use those velocities in Gron's analysis. I do use them to get the pear.

SYA: Gron's analysis uses v, because the LTs use v.

cinci: So all your talk about cycloid velocities is just hot air.
Well, can you maybe explain why you would say such a thing? That might help get to the bottom of this.

Thank You,

Well, can you maybe explain why you would say such a thing? That might help get to the bottom of this.
I think cincirob wants someone to use all the different velocities of all the points on the elongated cycloid, then length-contract each point (lol) according to its corresponding gamma factor. Because he likes to solve relativity problems using the LCF instead of the LT equations which he does not trust because they only use v. Or something like that.

Oh, and I also think cincirob wants someone to show that the rim can be built on-the-fly as the wheel rolls through the road frame, using all the different velocities and length-contractions involved. Because doing it in the axle frame is too easy. Or something like that.

97. When you talk about the road frame are you meaning from a stationary point on the road? (say from a hedgehog's frame)

98. Originally Posted by Jilan
When you talk about the road frame are you meaning from a stationary point on the road? (say from a hedgehog's frame)
Yes, the road frame is the reference frame in which the road is stationary. The wheel rolls along the road, which means the wheel rotates and also moves linearly (translational motion) through the road frame.

The axle frame, as we discussed earlier, is the reference frame in which the wheel only rotates, but does not move linearly, (no translational motion).

Both the axle frame and the road frame are inertial reference frames, (which means they are non-rotating, non-accelerating reference frames).

99. Thanks for clearing that up. So from a hedgehogs point of view there would be no difference in the shape of the wheel whether it were rolling or skidding on ice?

100. Originally Posted by Jilan
Thanks for clearing that up. So from a hedgehogs point of view there would be no difference in the shape of the wheel whether it were rolling or skidding on ice?
Yes, assuming a constant radius as measured by the axle frame, and assuming a constant translational velocity as measured by the road frame, there would be no difference in the wheel's shape or size, whether rotating or not.

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