# I Inverse results in special relativity

#### 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.

#### Kairos

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 $c$.

• Kairos

#### Kairos

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.

"Inverse results in special relativity"

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