# Relativity of simultaneity in train experiment-doesn't Doppler effect reveal simultaneity?

In Einstein's simultaneity thought experiment with the "moving" train and lightning strikes, wouldn't the observer on the train be able to deduce the simultaneity of the lighting strikes from the fact that the lighting strike in the direction of motion would have photons of shortened wavelength and the lightning strike that the train is moving away from would have photons with longer wavelengths?

Perhaps more fundamentally, why wouldn't the microwave background radiation similarly be "blue" and "red shiftied" due to the motion of an observer?

• so now add a wind so the heated air doesn't doppler shift for the train: it doesn't change any of the timing. – JEB Sep 15 '18 at 20:15
• If the frame of a pair of moving lamps is always "preferred", what happens when one pair of lamps is moving relative to another pair? Or what happens if I, in my non-preferred frame, decide to turn a couple of lamps on? – WillO Aug 29 '19 at 5:42

If you assume the sources of the flash are stationary with respect to the ground, then you are correct in saying that on the train, the wavelengths will be red/blue shifted.

None of this contradicts relativity. Relativity says you can't tell if you are moving relative to the ground based on experiments that only take place inside the train. It does NOT say you can't tell if you are moving relative to the ground when you look out a window.

And this also does not define a special frame. Someone can say "I am moving relative to the ground and that is why I see red/blue shift," and someone else can still say "the ground is moving relative to me, and that is why the flashes are red/blue shifted," and both are equally correct, and will never make a physical prediction that contradicts the other person.

• I thought that the train experiment concluded that the two strikes could be determined to be simultaneous by one observer and not simultaneous by another observer. But there IS a preferred inertial frame in this case. The one in which the spectra of both lightning bolts is the same-which is also a chemical reality. – Joseph Hirsch Aug 19 '19 at 22:47
• @JosephHirsch You're just saying that there exists a frame in which the lightning bolts are stationary. That's true! That frame isn't PREFERRED, though. The laws of physics are obeyed in every frame. Maybe you prefer the frame where the lightning bolts are stationary, maybe you prefer the frame where you are stationary, maybe you prefer a different frame altogether. And again, it's not miraculous that you can figure out the frame in which the lightning bolts are stationary, given that you are observing the lightning! You can also find the frame a car is stationary in by looking at the car! – Jahan Claes Aug 20 '19 at 1:09

Assuming that the lightnings emit photons of the same wavelengths you are right.

But the thought experiment is not about whether it's possible to determine if events occur simultaneously in another frame of reference. The thought experiment shows that different frames of reference have different conception of simultaneity.

The Doppler shift does not alter the train “thought experiment” because the determination depends only on the speed of light. The Doppler shift changes both the wavelength and the frequency such that the speed is unchanged and hence the thought experiment is unchanged.

Regarding your second question, the microwave background radiation is blue and red shifted. It is called the dipole anisotropy and it enables us to determine our velocity with respect to “comoving” cosmological coordinates.

• Does dipole anisotrophy result in a resistance to acceleration in the direction of relative motion? – Joseph Hirsch Sep 15 '18 at 20:11
• @JosephHirsch No, it does not. You can't feel the direction of your motion relative to the CMB frame by trying to accelerate in various directions. You can only determine the anisotropy of the CMB by looking at it (with an instrument that can detect those microwave frequencies). – PM 2Ring Sep 15 '18 at 20:20
• Why won’t the more blue shifted photons exert a greater pressure than the more red shifted ones? – Joseph Hirsch Sep 15 '18 at 21:51
• Fair enough, but the differential radiation pressure is small so its effect on the motion of bodies is also small. – PM 2Ring Sep 16 '18 at 6:09
• @PM2Ring if your motion changes, particularly your velocity, then the background radiation in your "face" is getting blue shifted while the background radiation into your "tail" is getting red shifted. Now you have a disequilibrium relative to your initial state which would get bigger and bigger the faster you move. In effect, there could be some inertial frames relative to the background radiation where the radiation would reach an impenetrable level of energy. – Joseph Hirsch Aug 19 '19 at 22:52