Eh? Prove it's false!For you to prove your false claim.
Eh? Prove it's false!For you to prove your false claim.
Eh? Prove it's false!
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.
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).Can you stop dodging and provide a mathematical proof?
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.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.
Why don't you do it first, since you claim to have already done it?
Actually it proves quite a bit. If you choose a parameterisation of the perimeter of the wheel in the ground frame where the parameter x measures distance in a homogenous manner (e.g. it's a distance in metres), the lower half of the wheel is 0 < x < L, and the upper half is L < x < 2L, then you can express the energy difference between the two halves as
$$It's an inescapable conclusion that $$\Delta E > 0$$. The only way you could argue against this would either be to deny that
\Delta E \,=\, \int_{0}^{L} \mathrm{d}x \, \bigl( \rho(x + L) \, k[v(x+L)] \,-\, \rho(x) \, k[v(x)] \bigr) \,.
$$
- $$\rho \, k(v)$$ is larger in the top half than in the bottom half,
No, I've seen it before. For example, it was mentioned in [post=2385907]DRZion's first Sciforums thread[/post] in 2009.So, what is your point?That I have introduced you to this website about a year ago?
Their motion is different, so there are different length contraction and light delay effects.Look at the rotating-in-place wheel (in green). Contrast with the rolling wheel (in blue). Do you see a contradiction? The spokes are curved downwards for the rotating one and upwards for the rolling one. How can that be?
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?At times you can see only 3 spokes above the midline for the green wheel while you are always seeing 6 for the blue wheel. Do you see the anomaly? When the wheels overlap their spokes point in OPPOSITE directions (one upward, the other one downward). So, you don't think this is absurd?
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.What makes you so sure that the website authors are correct?
The equation of the spokes you posted early in the thread is correct:We must first agree on the equations of the spokes, I don't think yours is correct.
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.
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:
So, we're agreed that at a given instant in the moving frame there is more mass above y = R than below?
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:
I still don't see a contradiction.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.
You agree with this diagram for the actual shape of the spokes at t=0 in the moving frame, right?
5 spokes above y=R, 3 spokes below y=R, therefore more mass above y=R, right?
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.
Did you notice that the spinning wheel distortion is reversed when looking at it from the other side?
:bugeye:There is no Doppler shift.
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.Nope, the spinning wheel spokes are bent DOWNWARDS.
You mean Terrell right? Teller is the guy with the H bomb.
No, not negligible at all. The rim of that wheel is moving at 0.93c.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.
Come on, Tach, this is really easy.Sigh.
: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 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.
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 hesitate to start another sidetrack, but feel free to post your proof.I can prove this quite easily, there is no Doppler shift of a moving mirror.
Tach, the rim of the green wheel is moving at 0.93c relative to the camera. Figure out the scale.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.
Try it with a wheel 1 light second wide, and a camera 5 light-seconds away.Do the exercise above.
It's not a difficult exercise.I would be interested in a mathematical proof. Especially in the context of the transit time distances being what they are.
I am not going to touch this one with a ten foot pole.