Angle between the orientation of a moving object and its velocity

You answered nothing with that snippy trite crap. You replied in a condescending manner, without actually addressing the points I made.

No they don't - the first set of equations is the motion of a micro facet around its axis, but it doesn't include a (-V,0) boosting for the motion of the camera in the axels frame.

Do you agree with this statement?
"If the wheel is boosted in the cameras frame by (V,0) then the Camera must be boosted by (-V,0) in the axels frame".


If you agree with that, then what part of this, precisely, deals with the motion of the camera relative to the tangent plane of the microfacet?

Answer: None of it. That is the equation of motion for a point moving in a circular orbit around some central point.

There is nothing in that that considers the direction and magnitude of the motion of the camera relative to the plane of the tangent, but that is the neccessary value, according to Pauli, for determining whether or not doppler shifting occurs.

 

No, you posted condescending snippy trite crap, that made no corrections, and offered no answers.

No it doesn't.

The second part of the post:

You open with a frame jump to the rest frame of the ground, and conclude that because the zero angle in axle frame transforms to a zero angle in the ground frame, that there is no doppler shift.

But, your conclusion is wrong because you didn't calculate the angle between the motion of the microfacet and the motion of the camera in the axles rest frame, you only calculated the motion of the microfacet.

 

Now go back and re-read what I actually said, because this isn't it.

What I said was that the second set of equations opens with that, not the post.

And what you have said is precisely my point - you start by calulating the motion of the microfacet in the axles frame, but did not calculate the angle between the motion of the microfacet and the motion of the camera in the axels frame.

Again, this is what I said, but it's beside the point that I'm making here. The point that I'm making is that in point 1 you don't consider the motion of the camera relative to the axle (you don't boost the cameras in the axles frame) but in point 2 you boost the axel in the cameras frame.

That's not what Pauli said.

Pauli said that if the mirror is moving paralell to itself in the frame of the observer, there would be no doppler shift. The corollary of Pauli's statement is that if the observer is moving paralell to the surface of the mirror there would be no doppler shift. Therefore, it is absolutely neccessary to consider the motion of the camerlative to the motion of the microfacet to establish whether or not Pauli's criterion applies to all observers in all frames and all microfacets.

So, according to Pauli the angle of the mirror wrt the angle of the motion of the camera is precisely neccessarily to know to determine in the axels rest frame whether or not doppler shifting occurs.

 

wrong.

See above.

And the corrolary of this is what, precisely?

If the Mirror is moving paralell to itself in the Camera's rest frame, what direction is the camera moving in the Mirrors rest frame (relative to the mirrors surface)?
1) Paralell?
2) Not paralell?

Yes, see above.

Your detailed math is wrong, because it is incomplete.

You use an incomplete proof and as a result of that come to a wrong conclusion.

 

That's not the question I'm asking.

Please try and stay focused and answer the question I am asking you.

I'll even reword it for you, phrase it as a yes/no question.

Does the statement "The mirror is moving paralell to its own surface in the cameras rest frame" imply the statement "The camera is moving paralell to the surface of the mirror, in the mirrors rest frame" as a corollary.

Yes, or no.

We'll move onto that, soon enough.

Let's see you give a straight yes or no answer to this question first eh? Then we'll negotiate further proofs of anything.

 

And of course you've substantialy altered your post while I've been replying. Brilliant.

 

So... If I have a mirror in 3d space, that is oriented in the plain (X,Y,0).
And I have a Camera some height Z above the plain of the mirror.
And in the cameras rest frame I boost the mirror by (0,V,0).
You're arguing that the motion of the camera in the rest frame of the mirror is something other than (0,-V,0)?

Or, to put it another way. Are you arguing that Zero angles are not preserved by a lorentz transformation?

I will, in good time, however, obviously, for what ever reason I consider establishing this neccessary before I tackle anything else.

 

Right, so then you agree that because zero angles are preserved under a lorentz transformation, stating that that the mirror is moving paralell to itself in the rest frame of the camera implies that the camera is moving paralell to the surface of the mirror in the rest frame of the mirror?

I'm trying to back up my claim, but every time you refuse to answer the questions, you make it impossible for me to present any form of proof, because the questions I am asking are pertinent to the basic assumptions that form the frame work to the maths.

 

We're not done yet. I will tell you when we are done, and when I am ready to put up the maths mmkay?

So then when you said this:

You were in error?

Good then progress.

On to the next question.

We have established that there will be no doppler shift if the motion of the observer is paralell to the surface of the mirror in the rest frame, because that is what is implied as a corollary of Pauli's statement that if a mirror is moving paralell to itself, an observer will see no doppler shift.

Now. Do you agree that, as pauli suggested if the mirror is moving perpendicular to itself, doppler shift will be observed, then by the same logic we have just agreed upon, if, in the mirrors rest frame, the observer has any motion perpendicular to the surface of the mirror, then the observer will measure a doppler shift?

 

So your argument at this point is that the motion of an observer has nothing to do with the doppler shift of objects, as measured by that observer?

Or to put it another way, that Einsteins equivalence principle was wrong to suggest that the motion of the mirror wrt a stationary observer is equivalent to the motion of an observer wrt a stationary mirror?

I have stated that I have the math.
I have demonstrated more than once that not only can I do the math, but that I understand the math well enough to be able to present the equivalent scenario as a diagram, maths, or prose.
I have also stated that I regard these questions as neccessary before we can proceed with the math.

Now, are you going to answer these questions, or are you going to keep trolling with this trite crap?