I Inverse results in special relativity

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Orodruin

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As an aside, I'm not quite sure of the details of how a wavefunction of a multi-particle system would transform. But let's stick to single particle wavefunctions for the time being.
Well, a priori you cannot do this unless you have a non-interacting theory. This is one of the beauties with QFT.

What I am talking about is essentially related to the wave solutions of the classical Klein-Gordon equation, which to some extent generalise the de Broglie relation when interpreted as one-particle states of the non-interacting theory.
 
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Again, your relationship between the wavelengths is wrong.
OK, in fact I was just thinking in term of transverse Doppler

In addition, ##\lambda/\lambda_0 = \nu_0/\nu## only holds if the speed of the wave is independent of the reference frame, which is also not the case.
I assumed ##c=\lambda \nu ##

thank you
 

Mister T

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I assumed c=λν
Huhh? Are you still talking about an object of mass ##m## moving with speed ##v##? If so, the speed is ##c## only when the mass is zero. Relations like ##E=E_o \frac{1}{\sqrt{1-(v/c)^2}}## are not valid for objects moving at speed ##c##.
 
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Now I think I understand. Thank you.
 

pervect

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Well, a priori you cannot do this unless you have a non-interacting theory. This is one of the beauties with QFT.

What I am talking about is essentially related to the wave solutions of the classical Klein-Gordon equation, which to some extent generalise the de Broglie relation when interpreted as one-particle states of the non-interacting theory.
That's more or less what I was suggesting as well. If one used the Klein-Gordon equations, a single particle wavefunction would behave more-or-less as the Original Poster expected in terms of "Lorentz contraction".

The Dirac equations might also apply, if he was doing QM with particles that had half-integral spin.

Most likely the OP is using the de-Broglie relation withtout thinking about where it came from. And he is confused by the fact that the answers when he does this are not relativistic. I suggest that the answers aren't relativistic because the theory he is using isn't relativistic. If he re-visited the problem using a relativistic version of quantum theory, such as the Klein-Gordon equation, or some other relativistic formulation, I believe he'd solve his immediate problem. Most likely he'd find some new things to be puzzled about if he got that far, but no need to borrow confusion in advance.
 

Orodruin

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But my point is that there is a relativistic analogue of the de Broglie relation. It just relates 4-frequency to 4-momentum.
 

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