Undergrad Light clock running faster than light?

[tagehedin]

TL;DR

Twin Paradox - Light clock speed up?

Twin Paradox.

I am on the outgoing rocket and look back at my stay at home twins light clock (two mirrors with a ray of light bouncing in between)

I get to the nearest star and on the outbound journey my twins clock apears to run slow.

When I turn around my plane of simultaneity shift and I see my twins clock run fast as I “catch up” to in respect to his plane of reference for the return trip.

Do I see the light-ray of his clock bouncing faster than the speed of light between the mirrors or do I see his clock contract so that the light-ray can bounce quicker in the shorter space?

 

[Dale]

TL;DR Summary: Twin Paradox - Light clock speed up?

Do I see the light-ray of his clock bouncing faster than the speed of light between the mirrors or do I see his clock contract so that the light-ray can bounce quicker in the shorter space?

It depends on the mathematical details of your non-inertial frame. Which you did not specify.

If you use something like radar coordinates (my preference) then the speed of light is always $c$ and there is no sudden jump in simultaneity

 

[Ibix]

Length contraction is a phenomenon between inertial frames, and you aren't using one. What you actually see is messy to compute; how you interpret it depends on your choice of non-inertial frame.

 

[PeroK]

When I turn around my plane of simultaneity shift and I see my twins clock run fast as I “catch up” to in respect to his plane of reference for the return trip.

A simultaneity shift, as you call it, is just a change of simultaneity convention. Nothing physical happens to your twin's clock. It's not a physical change to anything.

 

[PeterDonis]

When I turn around my plane of simultaneity shift and I see my twins clock run fast

These two things have nothing to do with each other.

The "simultaneity shift" is purely a convention that depends on how you choose your coordinates. No physics depends on it.

What you actually see of the other twin's clock is an invariant, independent of how you choose your coordinates: it is the result of the relativistic Doppler effect. When you turn around, you change the relativistic Doppler effect that you observe in the light signals reaching you from the stay-at-home twin.

More here:

https://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_doppler.html

Do I see the light-ray of his clock bouncing faster than the speed of light between the mirrors or do I see his clock contract so that the light-ray can bounce quicker in the shorter space?

No.

I suggest looking at the actual math of the relativistic Doppler effect.