# Discussion:Zero Doppler effect for reflected light from a rolling wheel

And we're already off to a poor start.

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.

Allow me to repeat myself:

Before I expend my time doing anything, do you agree that this:

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).

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.

But this time, I have emphasized the salient clause for you.

And we're already off to a poor start.

Allow me to repeat myself:

But this time, I have emphasized the salient clause for you.

Yes, we are saying the same thing. Go ahead.

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.

Only in an idealized and theoretical hypothetical. (BTW I did not wind up having Pauli's book and the Bateman reference is not readily available. I put both on my list but the list is not short.)

What you have been arguing can only occur in practice when there is no difference in the speed of the reflecting surface relative to the light source and camera. Again assuming the reflecting surface is moving parallel to the plane of the source and camera. If not moving parallel any relative velocity will result in a Doppler effect. (Have to keep stating this so it is clear.)

Again,
OnlyMe said:
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.

You keep saying you understand what others are saying but I have yet to see anything in your posts that demonstrates that.

Tach said:
Yes, I understand very well.

Tach, sometimes what you call word salad is necessisary to make clear the involved conditions. You seem to continually address an idealized hypothetical with only extremely limited aplication to any practical situation. All the while any reference to any praticale example, seems to be ignored.

Again, light is never reflected from any surface instantaneously. There are no real world ideal mirrors that do reflect light instantaneously. If the parallel motion of an object relative to an observer is small, yes the Doppler effect will be trivial. That in no way suggests that it will not occur, IN A REAL WORLD PRACTICAL SITUATION.

Correction: for the rolling wheel case. You need to be specific.
No, your logic is quite general. You said so explicitly in [post=2860270]post 195[/post]:
Theorem: Given a function defined parametrically as :

$$x=f(t)$$
$$y=g(t)$$

where f and g are continuous with continuous first order derivatives and $$\frac{df}{dt}\ne 0$$ and $$\frac{dg}{dt}\ne 0$$ then any elementary mirror moving tangent to the above curve has the same direction as its velocity along the curve in any point. [...] This is a generalization of the previous discussions about Doppler effect produced by moving mirrors, now you have been given the generalization to arbitrary trajectories.

Your angle transformation argument is also general enough to apply to an arbitrary plane mirror.

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?

Yes, in the rest frame of the axle, each element of the spinning mirror wheel moves parallel to itself.

We can also agree that for a plane mirror aligned with the y-axis, each elementary mirror moves parallel to itself in a reference frame in which the mirror is moving parallel with with y-axis. Yes or no?

Think through the consequences carefully before you continue, Tach.
Have you derived how to properly transform the angle between a surface and an arbitrary velocity vector yet, or would you like me to post mine?

Last edited:
Yes, in the rest frame of the axle, each element of the spinning mirror wheel moves parallel to itself.

Good, so we agree that in the axle frame the plane of the mirror makes a zero angle with its velocity. Next step: do you agree that the zero angle as measured in the axle frame transforms into a zero angle in the ground frame? Yes or no?

Only in an idealized and theoretical hypothetical. (BTW I did not wind up having Pauli's book and the Bateman reference is not readily available. I put both on my list but the list is not short.)

But you have already given ample proof that you don't understand the idealized case, why would you engage in a more complicated case that you know nothing about?

Tach, sometimes what you call word salad is necessisary to make clear the involved conditions. You seem to continually address an idealized hypothetical with only extremely limited aplication to any practical situation. All the while any reference to any praticale example, seems to be ignored.

I ignore your word salads because they are a mix of innuendo with downright errors and misunderstandings. This is what I call "mixed greens".

Again, light is never reflected from any surface instantaneously.

So, how does this result into a Doppler effect? Can you write down the formalism explaining it? You pretend to have studied physics.

There are no real world ideal mirrors that do reflect light instantaneously. If the parallel motion of an object relative to an observer is small, yes the Doppler effect will be trivial. That in no way suggests that it will not occur, IN A REAL WORLD PRACTICAL SITUATION.

Prove it.

So Tach,

You are saying that a Doppler effect only occurs when there is relative motion between the light source and observer? And is unaffected by the motion of an object in motion, parallel to the plane of the source and observer?

I ignore your word salads because they are a mix of innuendo with downright errors and misunderstandings. This is what I call "mixed greens".
And you wonder why people are rude to you?

And you wonder why people are rude to you?

I don't think he does. But really it does not matter. I am just having fun with him.

He hates that I won't get into the math. And I wonder if he actually fully understands English.

So Tach,

You are saying that a Doppler effect only occurs when there is relative motion between the light source and observer? And is unaffected by the motion of an object in motion, parallel to the plane of the source and observer?

Tach has also stipulated that the object must be moving between the light source and the camera. He doesn't like it when the light source and the camera are both on the same side of the moving object. I think he added that stipulation some time after James R's rebuttal, though.

I don't think he does. But really it does not matter. I am just having fun with him.

He hates that I won't get into the math.

Actually it amuses me. Especially since you pretend to have studied physics, yet you cannot quantify any of your statements.

Actually it amuses me. Especially since you pretend to have studied physics, yet you cannot quantify any of your statements.

How could that make any difference with you Tach? How many threads and total posts have been centered on this hypothetical with you now? There has been a lot of people who have argued the math with you and you either don't understand them or are unable to make sense yourself.

At least four, five.., maybe six, (I lose track) of your "opponents" seem to know their math. At least two have degrees in math. You don't seem to understand them! And they obviously have problems with your reasoning and at times your math...

Really, I have been watching from the sidelines and decided maybe a try at English, but no.., no "discussion" there either.

How could that make any difference with you Tach? How many threads and total posts have been centered on this hypothetical with you now?

Well, at least the people arguing intelligently with me (like pete) for example:

-understand the parameters of the discussion (as you don't)
-do not make vague references to "practical" considerations that cannot be quantified (as you do)
-are able to cast their position in a formal way (as you cannot)

So far there have been two debates and two threads. People who understand physics and can talk intelligently about it, are starting to understand the subject.

So Tach,

You are saying that a Doppler effect only occurs when there is relative motion between the light source and observer?

Is this what you understood from the two threads and two debates? Or are you just in the process of building a strawman in preparation for beating it to death?

And is unaffected by the motion of an object in motion, parallel to the plane of the source and observer?

You really, really need to learn what is being discussed. Questions like this show that you don't even understand the basics. Why don't you try the local library for the Pauli book or for the Bateman paper? I think that this must be the 4-th or 5-th time I am recommending you reading them in order to clear your misconceptions.

Is this what you understood from the two threads and two debates? Or are you just in the process of building a strawman in preparation for beating it to death?

This was a simple question you could have answered.., I think.

And the discussion began in a thead before either debate or discussion thread. That's five threads... I don't think you ever understood the original discussion and it led off and into the debate/discussions here.

You really, really need to learn what is being discussed. Questions like this show that you don't even understand the basics. Why don't you try the local library for the Pauli book or for the Bateman paper? I think that this must be the 4-th or 5-th time I am recommending you reading them in order to clear your misconceptions.

Why when I can just ask questions of authorities like yourself?

I really cannot believe that you are this slow... I have already posted that I was just messing with you and you keep on biting..

T
Why when I can just ask questions of authorities like yourself?

Because you are too lazy to learn and when I explain the same exact things that you could have learned if you weren't so lazy, you argue.

I really cannot believe that you are this slow... I have already posted that I was just messing with you and you keep on biting..

So, you are just trolling.

So, you are just trolling.

I never thought of it that way and I am not sure since I don't know what that means.

I can say that had you been so inclined it could have been a discussion. As it turned out .... Maybe. Someone else will have to say. Like I said I don't even know what it is.

But I do have to say I was having fun. Then again that is always what I am doing.

Good, so we agree that in the axle frame the plane of the mirror makes a zero angle with its velocity. Next step: do you agree that the zero angle as measured in the axle frame transforms into a zero angle in the ground frame? Yes or no?
No, not for an angle between a surface and a velocity vector.

This is painfully obvious if you consider a flat surface in uniform motion.

Have you derived how to properly transform the angle between a surface and an arbitrary velocity vector yet, or would you like me to post mine?

No, not for an angle between a surface and a velocity vector.

I showed you through two methods that your claim is wrong. How do you define the "angle between a surface and a velocity vector"? You realize that we are talking about the velocity of the surface , not about some arbitrary velocity, right?

This is painfully obvious if you consider a flat surface in uniform motion.

Have you derived how to properly transform the angle between a surface and an arbitrary velocity vector yet,

Yes, I actually did, so please don't talk down to me. If you are getting a different result, you must have made an error. Because, if you are saying is true, then the aberration formula, expressing the frame invariance of the zero angle between two co-linear vectors, would be falsified.
If what you are claiming were true, you would be performing the amazing feat of transforming a zero angle into a non-zero angle by simply changing frames. This would be a fantastic experimental refutation of POR.

or would you like me to post mine?

I am curious to see what you did, so go ahead, post it.

Last edited:
I showed you through two methods that your claim is wrong.
The methods you presented are wrong.
How do you define the "angle between a surface and a velocity vector"?
Does this really need explaining?
Try here

Yes, I actually did, so please don't talk down to me.
No, you did not.

If you are getting a different result, you must have made an error. Because, if you are saying is true, then the aberration formula, expressing the frame invariance of the zero angle between two co-linear vectors, would be falsified.
No, this is a qualitatively different situation to that described by the aberration formula.
If what you are claiming were true, you would be performing the amazing feat of transforming a zero angle into a non-zero angle by simply changing frames. This would be a fantastic experimental refutation of POR.
POR?
It's not amazing at all.

Look:
A zero angle between two spacelike manifolds (eg rods or surfaces) is zero in all frames.
It is true that a zero angle between two timelike worldlines (eg a velocity vector) is zero in all frames.

But, we're talking about an angle between a spacelike manifold (the mirror surface) and a timelike worldline (it's velocity).

You have nowhere shown how to transform such an angle between frames.