Jun. 27, 2021

This little special relativity problem occured to me today.

As usual Einstein is conducting an experiment in a moving rail carriage.

He is observed by Jyotirmoy who is sitting on the platform. The carriage is moving from left to right.

Here is what the experiment looks like from Einsten’s point of view.

He has a powerful computer with all kinds of fancy peripherals sitting at the middle of his desk. He also has two wheeled clocks which can travel on rails.

At the start of the experiment (from Einstein’s point of view) the two clocks are at equal distances from the central computer and approaching it at equal speed.

As the moment the clocks cross each other in front of the computer the computer sends them a signal synchronizing them.

The clock keeps travelling (from E’s point of view) at their equal and constant speed. After they are somewhat separated the computer sends them a command saying “report your time” using a laser. When the clocks get the command they reply back with their current time, again using lasers.

Einstein, sitting at the computer, observes that both clocks report the same time, which was to be expected from the symmetry of the situation from his point of view.

Now what does the experiment look like to Jyotirmoy?

The clocks are synchronized when they are at the same place, so there are no relativity of simultaneity problems here. At the moment they pass in front of the computer Jyotirmoy too would agree that they show the same time.

But later when the computer sends the command “report your time” using its lasers, in Jyotirmoy’s reference frame the clock on the left would get the command before the clock on the right because of the constancy of the speed of light.

So how does Jyotirmoy then explain Einstein getting the same time reported from both clocks?

[I think I know the answer, but this post is my attempt to check my answer against the Internet. Feeling too lazy to calculate and verify.]