# Confusion with relativity of simultaneity

• I
No. He would observe the rear clock being activated first; then the front clock some time later.
Why?

PS note that an accelerating train would have an internal time dilation similar to gravitational time dilation. A clock at the front of the train would run faster than a clock at the rear, as observed from onboard the train. That's essentially why clocks don't stay in sync in an accelerating reference frame.
I thought the train was in constant motion in this thought experiment.

PeroK
Homework Helper
Gold Member
Why?
Clocks cannot be synchronised in two different reference frames. That's what the previous posts have been explaining.

Synchonised in one frame + invariant speed of light implies not synchronised in other frames.

The simple thought experiments we have been discussing show this.

PeroK
Homework Helper
Gold Member
I thought the train was in constant motion in this thought experiment.
Yes, but you introduced the idea of synchronising the clocks before the train departed, while it was at rest on the platform. That led to a discussion of the acceleration needed to get the train moving.

Janus
Staff Emeritus
Gold Member
Thank you. I will look into that.

Okay. Let's say that the clocks are synchronised inside the train when the train is in constant motion. But let's say they were synchronized MECHANICALLY, by a very precise machine that pressed the "start" buttons of both clocks at the exact same time.

Now, would the clocks still appear to be out of sync to the platform observer?
Yes. It doesn't matter how the clocks are synced. In reference to your diagram in a later post. You have a device with two arms attached to it. When the device triggers the two arms press the buttons on the clock. However, you are assuming that the triggering of the device and the pressing of the buttons are simultaneous in the device's own frame, and they are not. The impulse generated at the trigger can't travel down either arm faster than the speed of sound for the material the arm is made of. Let's call this "S". In the platform frame, the speed of those impulses relative to the platform is subject to the relativistic addition of velocities.
If v is the relative velocity between platform and train, the impulse traveling in the direction of the train will be moving at
$$V_1 = \frac{v+S}{1+\frac{vS}{c^2}}$$
relative to the platform.

The impulse traveling along the opposite arm will have a velocity of
$$V_2 = \frac{v-S}{1-\frac{vS}{c^2}}$$
relative to the platform.
So let's assume that the arms are made of of a very stiff material in which the speed of sound is equal to 0.5 c, and the train-platform relative velocity is equal to 0.9c
then V1 = 0.9655c
which means that in the platform rest frame, this impulse travels at .0655c with respect to the triggering device.
and V2 = 0.7273c
which means that this impulse travels at 0.1727c with respect to the triggering device according to the platform frame. Since the arms are equal in length, the rearward moving impulse will reach the end of its arm and push the button before the forward moving impulse reaches the end of its arm, and the clocks will start at different times according to the platform.