# Special Relativity Question

• bon
In summary, the distance between two photons traveling along the x-axis in S with constant distance L between them will appear longer in S' due to time dilation. This is connected to the Doppler effect as S' will also perceive the photons to have a longer wavelength, resulting in a slight redshift.

## Homework Statement

Two photons travel along the x-axis of S, with a constant distance L between them.
Find the distance between them as observed in S' (standard config - i.e. moving with speed v in x direction wrt S)
How is this result connected to the Doppler effect?

## The Attempt at a Solution

So normally the distance would be lorentz contracted - right? So it would be L/gamma

but i guess it is not here? and how is it related to doppler? any hints would be great ! thanks

What you see is a pair of photons pass S at speed c, S determines the distance to be L.

S', at speed v wrt to S also sees the photons pass at speed c - what length will S' measure?

Presumably S has timed them, S' gets the same time dilated, so the distance between the photons that S' measures is expanded.

Reality check:
imagine S and S' are both at x'=x=0 when the first photon arrives.
in the time it takes for the second photon to arrive at S (still at the origin) S' has moved on and has yet to see the photon pass. He has to wait a bit longer for the second photon to pass... so he measures a longer time. Longer time, same speed, means longer distance.

This also means that S' and S will disagree about the color of the photons - S' will decide the photons are a bit redder... in terms of the relativistic doppler shift, this is because the wavelength has expanded.