What Happens to a Photon's 4 Momentum After a Lorentz Boost?

[curiouserand.]

hi there!

Just wondering... if i have a photon moving in the z direction 4 momentum given by (0,0,1,1)

and I lorentz boost it in the z direction... would I get the same original 4 momentum (0,0,1,1) because i thought that boosting something at the speed of light means that it remains at the speed of light right?

in the case of the x direction (1,0,0,1) the lorentz boost in the x direction gives (cosh, -sinh, 0,1)... which isn't the original 4 momentum

could somebody kindly explain what exactly I'm getting wrong here?

Thank you!

 

[Dale]

The magnitude (Minkowski norm) of the photon's 4 momentum is invariant, but the components of the 4 momentum do change. When you boost it in the z direction you will get a 4 momentum of the form (0,0,E/c,E/c) where E/c is not in general equal to 1 in all frames.

 

[jtbell]

The energy and momentum are not invariant between reference frames. The speed of the photon is invariant, nevertheless.

In general, v/c = pc/E. For a photon in the original reference frame, E = pc so v/c = 1. In the new reference frame, after the transformation, you should be able to show that E' = p'c so v'/c = 1 also.

 

[curiouserand.]

ok... so am i getting this right? ... since E/c can change then lorentz boosting of a photon in the direction of its travel changes its energy therefore changing its frequency/colour only? the velocity remains at c

 

[Dale]

Correct.

 

[jtbell]

Note that the change in frequency and wavelength between two reference frames is just the longitudinal relativistic Doppler shift.