Suppose we have two mirrors in a gravity free vacuum.

Both are shaped identically and ,why not circular  and extremely thin.(and rigid)

 

They are very close to each other (separation is zero for practical purposes)

 

Mirror A emits a signal (any practical kind that would work in a vacuum) from its cog in the direction of Mirror B's cog.

The signal is reflected back and forth between the two mirrors cross  from that point onwards

 

The 2 mirrors move apart as a consequence. (the signal carries energy)

 

Is there a mathematical /physical description of this increasing separation over time as a function of the speed of the signal  ?

Is this a very complex problem ?

Can it be answered in as simple a way as possible so that I can understand what is involved?

Even better ,has it been brought up before somewhere?

Edited March 31, 20187 yr by geordief

Here are some thoughts to kick off your analysis.

 

Initially the mirrors (call them A and B) are co moving, so it does not matter which mirror frame you choose to work in.

At the instant mirror A emits a photon, momentum balance requires it to start moving away from mirror B and the photon starts travelling towards B.

From this point on frame A and Frame B are not the same.

 

So the first decision is, which frame do you wish to work in?

Mirror B's and I would want to know  the "state of play" after it had twice  received the signal.

I would also be interested in other stages of the scenario(would that be termed after x re-ransmissions?) and in the limit.