Eh? Prove it's false!
shape of a relativistic wheel
- Thread starter DRZion
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Easily. Can you stop dodging and provide a mathematical proof? Once you do it, I'll show you why it's false. Don't worry, unlike you I will deliver the math.
Tach, can't you provide the math yourself? If so, then prove it!
I already gave one in [POST=2848877]post #93[/POST], which you never adequately addressed. I also gave an argument in [POST=2848712]post #59[/POST], which you basically dismissed out of hand (you never actually explained what was wrong with it).
You, by contrast, have nothing. Given that and the fact [POST=2643009]you were wrong last time you demanded people do calculations while refusing to do them yourself, for all your chest beating[/POST], I think it's about time we saw this "proof" of yours.
Tach, it's ridiculous for you to suggest przyk doesn't 'deliver the math', he's engaged in a great many lengthy threads involving the details of things like special relativity and electromagnetism. Perhaps the only person who consistently posts more actual algebra than przyk is Rpenner.
On the other hand you're known for doing what you do at the moment, saying you have a proof and then not providing it and demanding other people provide theirs. More than one person has commented on this tactic of yours in just this thread. This might sound insulting but that's the tactic Chinglu uses and I don't think you want to be compared to him.
I think enough people have asked you now that it's time you provided what you claim to have done, regardless of whether or not you deem przyk to have provided sufficient mathematics. You complained the mods were being slack with Chinglu so you can't complain when I'm now stepping up and asking you to lay your cards on the table.
Err, no. $$\rho \, k(v)$$ is NOT larger in the top half than in the bottom half . I'll give you a chance to remedy your proof, calculate the energy density $$k(v)$$. If you do it correctly, you will find out that it oscillates with time, sometimes it is larger for the upper half, sometimes it is higher for the lower half of the wheel. Like I told you, I did all these calculations when I claimed I did them, this is how I know your claim is false.
Since you have no calculation per se, I suggest that you start by calculating k(v). If you do it correctly, you will be disproving your own claim.
One more thing, before any of you makes any more claims for not providing the math, I have provided in this thread all the components for calculating $$k(v)$$. Actually, I have provided the math for the equation of the ellipse, of the spokes, of the tangential speed.
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No, I've seen it before. For example, it was mentioned in [post=2385907]DRZion's first Sciforums thread[/post] in 2009.
My point is that you are now disagreeing with the same material you used to support your argument a year ago.
Their motion is different, so there are different length contraction and light delay effects.
Where is the contradiction?
No, I don't, and I'm sure you wouldn't either if you actually thought it through. Why don't you "Look inside their papers", like you suggested in [post=2778963]that thread[/post]? Or at least read the accompanying text?
Try comparing the appearance of the green wheel in figures 12b and 12c.
I can't say I'm certain they are correct, but I have read their papers and thought through the various effects and don't see any absurdities.
The equation of the spokes you posted early in the thread is correct:
$$\frac{\gamma(x-vt)}{y-r}=tan(\omega \gamma (t-vx/c^2)+\phi_i)$$
where $$\phi_i=i \frac{ 2 \pi}{8} ,
i=0,1,2,...7$$
Plugging in r = 2, v = 0.8c, t = 0, quickmath gives this:
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I disagree with some of the material. DrZion, before this thread was totally hijacked, brought up an interesting point in his OP: how come that more spokes are visible on the upper side and what would happen if one covered up the lower side with a piece of paper? I think that I know the answers to both questions.
One: the equation of the spokes (for the rolling wheel) that I have derived, supports drawing (b), so that part is correct
Two: the reason that a strip of paper would not preclude the spoke "migration" from showing is a rendering error made by the paper authors. This is not really a physics error, it is a computer graphics error. We can talk about it, if you are interested.
Because you can view the rotating-only wheel as a limit case of the rolling case. If you do that, you can see the contradiction immediately, the spokes that were upturned for the rolling wheel become downturned for the rotating-only case.
I did. There is NO supporting math in any of their papers, just a a lot of prose and pictures. This is why I ended up reconstructing the math for the equation of the ellipse , for the spokes, for the tangential speed, etc.
The equation of the spokes you posted early in the thread is correct:
$$\frac{\gamma(x-vt)}{y-r}=tan(\omega \gamma (t-vx/c^2)+\phi_i)$$
where $$\phi_i=i \frac{ 2 \pi}{8} ,
i=0,1,2,...7$$
Plugging in r = 2, v = 0.8c, t = 0, quickmath gives this:
OK, I cannot disagree with this
Now , making $$v=0$$ gets us the equations of the spokes for the spinning wheel:
$$\frac{x}{y-r}=tan(\omega t+\phi_i)$$
where $$\phi_i=i \frac{ 2 \pi}{8} ,
i=0,1,2,...7$$
So, the spokes should be straight lines.
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There isn't "more mass", The raytraced image of the spokes makes them look curved as in the picture.
A simple test proves this: place a strip of paper between the wheel and the light source or between the wheel and the eye and you'll see only half the spokes. No spokes have "wandered" in the half of the wheel peeking over the fence.
Now, the final error in the paper, which is quite serious, is that at the speeds in question, one can't really see anything because the whole image is totally blurred. I do not know how the authors managed to publish in two reputable computer graphics journals. Maybe because the referees were intimidated by the physics part.
There is another very serious error: the images contradict the text. The authors claim (incorrectly) a Doppler shift in the frequency of the light reflected off the wheels while the pictures show (correctly) no such effect.
Also, the spinning wheel (the one drawn in green) is downright wrong, the spokes should be straight (see simple proof at the end of previous posts)
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You agree with this diagram for the actual shape of the spokes at t=0 in the ground frame, right?
5 spokes above y=R, 3 spokes below y=R, therefore more mass above y=R, right?
5 spokes above y=R, 3 spokes below y=R, therefore more mass above y=R, right?
The equation of the spokes you posted early in the thread is correct:
$$\frac{\gamma(x-vt)}{y-r}=tan(\omega \gamma (t-vx/c^2)+\phi_i)$$
where $$\phi_i=i \frac{ 2 \pi}{8} ,
i=0,1,2,...7$$
Plugging in r = 2, v = 0.8c, t = 0, quickmath gives this:
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I still don't see a contradiction.
- The videos are rendering visual effects, they are showing what a camera would actually record (except for light intensity changes and doppler shift color changes).
- In the camera rest frame the rolling wheel spokes are distorted while the spinning wheel spokes are straight..
- Remember Teller-Penrose - at a distance, the light-delay shape distortion of an approaching object is approximately opposite to the length-contraction shape distortion.
- With the spinning wheel in the video, there is no length contraction distortion, only light-delay distortion.
Did you notice that the spinning wheel distortion is reversed when looking at it from the other side?
Sigh.
There is no Doppler shift.
Nope, the spinning wheel spokes are bent DOWNWARDS.
You mean Terrell right? Teller is the guy with the H bomb. Yes, I know the effect very well, the spinning wheel is stationary wrt the camera so there shouldn't be any Penrose effect. The differences in light transit time from the stationary wheel to the camera are negligible, so they cannot account for the spoke curvature.
No, I missed that.
:bugeye:
No, their visual appearance is that they are bent downward, because the light from different f]parts of the wheel takes different times to reach the camera.
No, not negligible at all. The rim of that wheel is moving at 0.93c.
The whole point of that site is to demonstrate the effects of light transit times.
The reason that the spinning wheel spokes appear curved upward from one side and downward from the other side is solely due to light transit differences.
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Come on, Tach, this is really easy.
You gave the equation for the shape of the spokes in the ground frame.
Diagramming that shape at t=0 give the diagram shown.
Clearly, more of the wheel material is higher than y=R then below y=R.
Therefore, there is more mass above y=R than below.
Why the sigh?
I can prove this quite easily, there is no Doppler shift of a moving mirror.
The differences in distance are insufficient to warrant a significant effect. Think about it, if the wheel has a radius of 1m, and the wheel is at 10m from the camera, the difference in distances is $$\sqrt{101}-10$$.
If the camera is at 100m, things get even dicier. Light travels at 300,000,000m/s, translate that in a difference in arrival time. No camera can tell the difference.
Do the exercise above. Calculate the shutter speed.
I would be interested in a mathematical proof. Especially in the context of the transit time distances being what they are.
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I am not going to touch this one with a ten foot pole.
I hesitate to start another sidetrack, but feel free to post your proof.
Tach, the rim of the green wheel is moving at 0.93c relative to the camera. Figure out the scale.
Hint - this is a simulation, not a practical camera recording, and it's not real-time (unless those wheels are light-seconds wide)
Try it with a wheel 1 light second wide, and a camera 5 light-seconds away.
It's not a difficult exercise.
Really? You've invested all this time arguing about the mass distribution, and now you're suddenly just not interested?
Why?
You agreed that this is an accurate diagram of the rolling wheel in the ground frame at t=0, right?
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