Neddy Bate
Valued Senior Member
Angle between the orientation of a moving object and its velocity
- Thread starter Pete
- Start date
My argument is that you got the Pauli explanation all wrong, all along. Why is it so hard for you to admit that you were wrong?
You now have the correct writeup on what it means, I suggest that you spend some time understanding it.
The person who has been trolling all along is you. You simply did not understand that the angle wrt the observer, while it plays a role in the Doppler effect it plays no role in the Doppler effect from moving mirrors. This is what the math of the Bateman paper (reprised by Pauli , in his book) teaches you:
-Velocity of the mirror perpendicular to the normal to the mirror => zero Doppler shift
-Velocity of the mirror has a non-zero component along the normal to the mirror => Doppler shift.
-NOTHING to do with the motion of the observer, ok? And, before you ask again, since the statement is expressed in coordinate-free format, nothing to do with any frame of reference be that "the camera", "the observer" or whatever. It is a relationship between two vectors, valid in any system of coordinates (this is why it is "coordinate-independent").
BTW: it is not "Einsteins equivalence principle", it is the "Principle of Relativity". And it isn't "Einsteins" since it predates Einstein by hundreds of years. EEP is something totally different, it has to do with the equivalence between uniformly accelerated frames and uniform gravitational fields. More importantly, as you can see from the Bateman/Pauli explanation, neither of the two principles has anything to do with the problem, the direction of the observer does not factor in the Doppler shift off moving mirrors, period.
Now, at this point you can do the honest thing and admit that you were wrong all along or you can continue to troll my posts on the subject as you have been doing for quite a while. If it is the latter, I will no longer respond.
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But mainstream science says that you are wrong.
Because I don't have it wrong.
I understood it back in Post 46, which you subssequently agreed to:
The only thing I have done is apply the equivalence principle to it, in other words, a moving mirror is equivalent to a moving observer watching a stationary mirror.
Yes, I got it 9 pages and 176 posts ago, thankyou.
Now, apply the principle of relativity.
Let me put it another way.
Post 212 I said this:
That was for paralell motion. Now we're talking about perpendicular motion.
As I said yesterday:
Which is the post we're discussing, I applied the equivalence principle to come to this:
In other words, to use the formalism in post 212, boosting the mirror by (0,0,V) is equivalent to boosting an observer by (0,0,-V) in the mirrors rest frame.
In other words, the statement:
Is implied as a corollary when considering Pauli's statement in light of the equivalence of inertial frames.
Now, at this point you can do the honest thing and admit that you were wrong all along or you can continue to troll my posts on the subject as you have been doing for quite a while. If it is the latter, I will no longer respond.[/QUOTE]
I have not trolled you. I have simply tried to engage you in a reasonable, rational discussion, as I am now. All I am asking is if we apply the principle of relativity, is if a mirror moving perpendicular to its surface is equivalent to an observer moving perpendicular to the mirrors surface - or to rephrase it, is boosting a mirror by (0,0,V) the same as boosting an observer by (0,0,-V)?
It's a straight forward yes or no question.
For the last time, the boost is irrelevant, the result is completely determined be the angle between the velocity of the mirror and the direction of its own normal. Since the problem is stated in coordinate-independent terms (vectors), the way you boost the mirror wrt the observer or the way you boost the observer wrt the mirror play absolutely NO role in the outcome (yes, the two boosts are perfectly equivalent and, no, neither of the has anything to do with the zero Doppler shift off mirrors moving parallel to themselves). Neither does the principle of relativity, for the same exact reasons. You are repeating the same error AN made much earlier in this thread (but he has not since repeated). Pete and I fully understand this issue and we are engaged in a debate that deals exclusively with zero-angle invariance. This is how the problem is formulated in correct terms.
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So then your argument, using your original scenario is that the motion of the camera in the mirrors rest frame is irrelevant in determining whether or not the camera measures doppler shifting in light that is reflected from a mirror?
I'd appreciate you admitting to your errors before I answer more of your questions. Do you understand your errors now?
And I'd appreciate you answering my questions, as you agreed you would.
It's a simple yes/no answer, and it's a relevant follow on from the discussion.
I have answered a lot of questions, admit that you were wrong all along by misinterpreting the Bateman paper and I'll answer your latest one. BTW: the way you are phrasing your latest question points out that you still don't understand the paper, nor what I have been telling you about the coordinate-independent formulation and about the specifics of the mirror motion.
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This is one of the things about your "discussions" that is frustrating. You have obviously failed to clarify things and yet demand that others admit errors, before you do clarify them!
I understand the issue in the orginal form, a flat ideal mirror, whose flat surface is in uniform motion relative to the plane of a light source and camera.
I am also still having some difficulty in seeing you translate that to the mirrored rim of a wheel rolling along a path parallel to the plane of the light source and camera.
And answers to questions like Trippy has asked are relevant, if not to your understanding, then at least to reaching some consensus with respects to the exact conditions, represented by the rolling wheel variation.
Even if you don't believe the questions and answers are important to your solution, they should not be difficult to answer in a clear and concise manner.
It is not an honest discussion when you demand agreement without fully establishing the foundation.
My original contention was that your math was incomplete because it failed to consider the motion of the camera in the rest frame of the mirror, and that this was nececssary as a corollary of Paulis conditions when we apply relativity to them (gallilean or otherwise).
Your contention is that the motion of the camera is irrelevant.
The questions are me trying to understand why you think it is irrelevant given that you have simply asserted it without presenting any proof mathmatical, logical or otherwise (demonstrating, for example that it leads to some kind of contradiction).
So either answer the questions, or pony up with some proof that the motion of the camera in the reference frame of the mirror is irrelevant to determining whether or not the camera observes doppler shifting of the mirror.
The proof can be found in Bateman's paper as well as in Pauli's book as well as in my writeup on the subject. The bottom line is expressed in post 217 and reiterated in post 222.
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See, you don't want to admit to error and you pile up questions upon questions that reflect the same exact misunderstandings. The scenario in discussion has several stipulations that you are missing:
-the camera is at rest wrt the source
-the mirror moves perpendicular on its normal , hence your repeated attempts at boosting the camera along the normal are in error
-the mirror moves between the source and the camera
Under the above conditions, the Doppler shift between the frequency at the source and the frequency received by the camera is exactly zero.
Do you understand your errors now ?
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Really? Because my posting history suggests otherwise. My posting history suggests I am perfectly willing to admit an error where it has been demonstrated. You should know that - in the thread with the question regarding GPE between two seperated bodies, and the work done in seperating them, I made an error that resulted in a sign change in the answer. When my error was demonstrated, I freely admitted it and was able to subsequently explain why I made the error.
Nothing I have said suggests other wise.
You seem to have misunderstood what I am asking, which is the point of asking questions - it is the only way to establish where miscommunications have occured.
First we agreed that Pauli's criteria is that the mirror is moving paralell to itself (or, perpendicular to its normal).
Then we agreed that the mirror moving paralell to itself (or, perpendicular to its normal) was equivalent to the camera moving paralell to the surface of the mirror.
We had previously agreed that demonstrating that the motion of the mirror has a component perpendicular to the surface of the mirror was sufficient to prove that doppler shifting would be observed in light reflected by the mirror.
Now, what I am asking, is whether or not this is equivalent to demonstrating that the camera has a component of motion perpendicular to the surface of the mirror.
We'll get to these bits once we've finished discussing the second criterion of your setup, and what it implies.
We did not "agree", I had to drag you to understand that. As late of post 222 , you still did not understand this feature correctly.
The mere fact that you keep wanting to bring the "camera" into the picture demonstrates that you still don't understand the conditions for zero Doppler shift. You claim you do, but you don't.
I explained that to you, it is good that now you agree with me.
Nope, wrong again. To get the non-zero doppler shift you must have a non-null projection of the mirror velocity onto the normal to the mirror plane. Vectors are coordinate-independent entities, you get the same results independent of any system of coordinates you choose. Why is this so difficult to understand in terms of coordinate independent description? Why do you keep insisting in bringing in the camera into the picture? Do you not understand the coordinate independent formalisms?
You did not have to drag me to understand anything, because nothing I have said has changed that is:
By the principle of relativity a mirror moving paralell to itself is equivalent to a camera moving paralell to the surface of the mirror, and that as a corollary of Pauli's hypothesis, it then follows that this is an equivalent requirement for zero doppler shifting to occur in light reflected off that mirror, as observed by the camera.
You're the one that set the experiment up to include the camera in the first place, not me.
Right. In order to get a doppler shift, the mirror must have motion perpendicular to it's surface. That is precisely what I said, and said 117 posts ago.
It's not.
Because you included it in your experimental setup, and I insist on .
Your argument amounts to the fact that because the motion of a mirror placed in the tangent plain to a circle is neccessarily in its own plain, and that because all similar mirrors at all points on the circumference of a circle neccessarily behave in this fashion, then there is neccessarily no doppler shift, at any point on the circles surface, and this is true of all observers.
My response to that is that such is true only for observers measuring the portion of the circle along a radial line of sight, which is only true at two locations on the circumference, and that at all other points on the circumference of the circle, and for all other observers some degree of doppler shifting must exist. I also contend that not only can this be proven in the case of a wheel rolling with no slip, but in the case of a stationary wheel, and in a coordinate independent description, and that it is still consistent with Pauli's description.
BUT, before I invest any of my time in typing up LaTeX and preparing diagrams with one arm in a cast, I believe it is neccessary to have an honest, earnest and frank discussion in good faith about the implications and corollaries that follow from Pauli's criteria for no doppler shift off a moving mirror when we apply the principles of relativity and equivalence to it, and how it relates to your experimental setup.
Now, are you capable of having an honest, earnest and frank discussion in good faith or not?
You may want to fix that - you seem to have inadvertantly attributed my question to Tach.
Done and thanks!
But it doesn't , it is moving parallel to itself, so you are simply repeating the same error you made 117 posts ago. Actually AN made the same mistake in one of the posts, I pointed it out to him and he did not repeat it.
I know that you made this claim, it is just as wrong now as it was then. You claimed that you have additional math to prove your case, where is it?
You received all the explanations to your ongoing misconceptions, so where is the beef? where is your math that completes my allegedly incomplete math?
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