Discussion: Zero Doppler effect for reflected light from a rolling wheel
- Thread starter James R
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Correction: for the rolling wheel case. You need to be specific.
It is very simple, really. Let's try a different way, since you either cannot or will not understand any of the other proofs. We agreed that in the frame of the axle each elementary mirror moves parallel to itself while the wheel is spinning. Yes or no?
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First, I know that this goes beyond your above statement...
The problem I keep having with this is that without further definition, "the frame of the axle" suggests an observer in that frame. We all know what a wheel looks like and that it has an axle. The question of Doppler effects as has been discussed using a light source and camera is always from the frame of the camera and that can be viewing the wheel from many different perspectives.
In almost all of those a camera/observer will "see" a Doppler shift in the reflected light. Only in a few special cases would there be no Doppler shift observable by the camera/observer.
That said.., if you are speaking of the mirrored surface being the edge of the rim when viewed from 90 degrees to the wheel's rotation, the whole rim edge mirror, remains parallel to itself, while the wheel spins.
Good, try explaining this to pete and scores of the others. BTW, you don't need any viewing from 90 degrees angle.
That's true. It was however necessisary to be certain that what I was describing was that mirrored edge and no part of the tread surface that would be visible from any other angle.
Tach, it seems, has changed tack.
Heh. Yes.
The scenario where we have a section of stainless steel pipe of zero thickness:
And a stainless steel washer of zero width:
Both of which display perfect specular reflection, and are moving between a light source and a camera, with some velocity $$ v \leq \omega r$$, while rotating about their C[sub]n[/sub] axis, with some angular velocity $$\omega$$, oriented so that the plane containing their nC[sub]2[/sub] axes also contains the light source and the camera (or. alternatively, oriented so that the vector of motion is perpendicular to the C[sub]n[/sub] axis - same thing, different wording).
And now that the problem has been defined unambiguously, sensible discussion of the two seperate problems, or components of the problem, can begin.
Source
Tach, it seems, is now talking about the second scenario (a washer of zero width), where everything in the debate, and the discussion so far, including the material provided by Tach to support his argument, appears to have been discussing the first scenario (pipe of zero thickness).
You know, if you don't understand things, just ask. This problem has been previously defined in mathematical terms and nowhere was any discussion about thickness. The reflection is off a circle, you only need to follow the drawing. While creating your own drawings might be fun, it doesn't add anything to the description, especially when it is not accompanied by any mathematical formalism.
Having said that, the same exact formalism applies to BOTH "tube" and "washer". If you did the math accompanying your pretty drawings, you would have found that out. So, it isn't clear why you have created the "washer" case. Can you post the math formalisms explaining the difference(s)? That would be a lot more interesting.
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Actually, the zero Doppler effect applies not only to the circumference but to the "sidewall" and the spokes as well. I think I have mentioned the spokes before, actually I am quite sure I did. The same exact formalism as the one applied to the rim applies to the other parts of the wheel, be it shiny or matte.
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:roll eyes:
Haven't you learned anything yet?
If nothing else, you should have figured out by now that prose literacy is every bit as important as quantitative literacy. The biggest problem faced by science in this day and age is poor communicators.
I'm familiar with your drawings, and several people have commented that they muddy the issue. I'm fairly confident that OnlyMe was refering to the second style of scenario - a washer of zero width, and I'm equally confident that OnlyMe, Pete, Alphanumeric, RJBeery, James R, and several others understand why specifying zero width for the washer, and zero thickness for the cylinder might be important to avoid ambiguity.
The thing is. I understand the discussion, I understand the math, I understand the problem, and I understand how to break down the problem into its components. Equally, I have taken enough time to understand what people other than you have said, to understand where sources of confusion have arisen.
I also understand how these posts (to specify a few):
The above sketch has only one light source, only one camera, and only one wheel rolling between the two.
Do you notice how the length of the optical path changes from 5.829 to 5.656 between the first and second slides? As the length of the optical path becomes shorter, the frequency of the reflected light must become greater. Surely you must agree with that simple principle?
Then do you see how the length of the optical path changes from 5.656 to 5.829 between the second and third slides? As the length of the optical path becomes longer, the frequency of the reflected light must become lower, surely?
Tach, would you casre to tell me how the above diagram is incorrect?
What in "valid for only a part of the wheel only" did you not understand? The equations are valid for the entire circumference of the wheel. This is the second time I point this to you. There is only one light source , only one camera and one wheel rolling between the two. The LHS and RHS of the drawing bellow represent two SEPARATE scenarios. This is explained clearly in the text. There is only ONE light source in each scenario.
Relate to what I have proposed.
Are you capable of having a civil discussion>
Isn't it?
You can't see how a three dimensional wheel might be related to a tube and washers?
Is it more obvious if I post an image of a trolley wheel in lieu of a car wheel?
Perhaps, later in the day, or later in the week, if I can find time to sit down with a pen and some paper.
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Perhaps, later in the day, or later in the week, if I can find time to sit down with a pen and some paper.
Please find the time, I would be most interested in your formalism(s).
Out of curiosity, why did you post the repeated errors by Neddy Bate? Is there any connection with your formalism?
In an idealized hypothetical, it may apply to any flat and ideally mirrored surface, which is moving parallel to the plane of the light source and camera. However, this will only be true for what ever "time" the light from the source reflects off of the mirrored surface, and to the camera. And this will only be the case when that reflecting surface is midway between the source and camera in its path of travel parallel to the plane of the source and camera.
For a flat mirror this will occur of some time equivalent to the length of the mirror in the direction of its motion divided by its velocity. In the case of a wheel the time that the light reflects between the source and camera is diminished by the reduction in the length of the mirrored surface in the direction of the wheel's motion.
If you assume that the light can reflect off of a wheel that is moving parallel to the plane of the light source and the camera, at any point other than that point midway between the source and camera, the light path between the source and wheel and the light path between the wheel and camera will not be equal.., and the speed of the wheel relative to the source and the speed of the wheel relative to the camera will also not be equal. And there will in practical terms be a detectable Doppler effect.
If any other result were true, we could not explain the cosmological redshift, as resulting from an expansion of space. Where in this case, the instantaneous expansion of space at the instantaneous location of a photon, affects the wavelength of the photon.
In practice light is not reflected instantaneously from any reflective surface. As a result the velocity of any reflective surface relative to a camera or observer, must result in a Doppler effect.
The special case of an ideal mirror with a velocity parallel to the plane of the light source and camera.., may be seen as an exception, but only in an idealized hypothetical thought experiment.
Now the question is, not whether others understand you, but rather do you understand anyone else? If you did there are numerous times your responses should have begun with, "OK I see your point, but what I was referring to...
Posting Neddy Bates' images was about the experimental setup, not the formalism.
This is false, it applies for any reflective surface whose velocity is parallel to the said surface. I have already recommended that you read Pauli or, even better, Bateman on the subject.
The solution does not involve the "length of the mirror" in any form or fashion.
Word salad.
The solution is not dependent on the mirror moving "parallel to the plane of the light source and the camera", it is much more general than that. Again, read Pauli and/or Bateman.
The light path(s) length(s) have nothing to do with to do with the solution. I have already flagged this error in Neddy Bate's thinking.
The above is trivially false, the camera and the the source are in the same frame of reference.
You are now way in the left field.
Again, take some time to read Pauli.
Yes, I understand very well.
You realize that the claims embedded in his posts/figures have been shown to be false, right?
I repeat. My posting the other two images is about the experimental setup not the conclusions he reached from that setup.
You do realize the difference between the experimental setup, and the conclusions reached based on that experimental setup, don't you?
Yes, I do. I don't see any "experimental setup", I see just a bunch of (incorrect) pictures. Perhaps you will also add the experimental setups when you find the time to post your formalism. I would be most interested in both.
Really? That's interesting. Not surprising, but still interesting. Because when I look at those three images, I see what appears to be the same experimental setup, with the minor (and frankly irrelevant) illustrative difference that one of them contains an extra light source.
No matter.
Perhaps you will also add the experimental setups when you find the time to post your formalism. I would be most interested in both.[/QUOTE]
Before I expend my time doing anything, do you agree that this:
Along with the repetition of the experiment, with the pipe and the washer painted, is an accurate summation of your experiment, and that it accurately breaks your experimental setup down into its components - with the proviso that your 'no slip' condition implies $$ v = \omega r$$, rather than $$ v \leq \omega r$$. My time is both precious and expensive, and I have no wish to sit down and perform any form of analysis for you to turn around at the end of it and claim the experimental setup was wrong to begin with.
Let us agree on the setup first.
Sure, make it even simpler, post only the study for the case $$ v = \omega r$$. You are going to have the tube/washer roll between the source and the camera, right? Let's not waste the time with having both the source and the camera on the same side of the wheel.
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