Can a light beam stay trapped in a moving cart with ideal mirrors indefinitely?

[birulami]

Consider a light clock, i.e. two ideal mirrors, mounted in parallel with a vacuum in between, such that, in principle, a beam of light or just a single photon will keep bouncing between the two forever.

Now consider the light clock on a cart. If the cart, from the beginning, has constant velocity, be it zero or not, just constant, the beam will keep bouncing. But now we start pulling the cart gently --- or not so gently, because I think this does not matter. My question is: is there any chance that the photon will be accelerated along with the cart and the mirrors, or will it fall behind and eventually "fall out" of the light clock?

I assume the latter, i.e. the light beam or photon will "fall out" at the back of the light clock.

Now I take into account that the Earth is rotating, moving in an ellipse around the sun and with it circling the center of the galaxy and what-not. So my cart, here on Earth in the lab, is not moving at all with constant velocity, but is accelerated according to the mix of centripedal forces keeping it on the mix of circular paths.

Consequently the beam of light will fall out at the back pretty soon in any lab on earth. True? Or will gravitation, acting on the photon in same way as on the the mirrors, make sure I can keep it in between the mirrors --- assuming that this is technically feasible in principle?

Harald.

 

[yuiop]

Now consider the light clock on a cart. If the cart, from the beginning, has constant velocity, be it zero or not, just constant, the beam will keep bouncing. But now we start pulling the cart gently --- or not so gently, because I think this does not matter. My question is: is there any chance that the photon will be accelerated along with the cart and the mirrors, or will it fall behind and eventually "fall out" of the light clock?

No it won't. If it did, you would be able to determine absolute motion. If to the person on cart the light beam hits the top mirror and returns to the bottom mirror, then the same must be true for all observers even when they are moving relative to the cart or the cart is moving relative to them (same thing). However, the cart is accelerating all the time (which on second reading is probably what you meant) then it possible with great enough acceleration that the photon will miss the upper mirror (and the deflection of the light beam in the clock is effectively acting as an accelerometer) but in this case the photon will miss the mirror according to all observers.

In the orbital case, the light is falling as fast as the mirrors so it still hits the mirrors and the light clock behaves as it does in flat space (for a sufficiently small light clock). Recall that an orbiting satellite is in free fall.

If the light clock is stationary in a very strong gravitational field and is horizontally orientated then the light beam could visibly curve (and miss the mirror) and the same is true in a very rapidly accelerating rocket. It is O.K. for light paths to curve in such extreme conditions.

 

[birulami]

It was maybe not clear from my initial post: the cart should be tugged in a direction orthogonal to the beam of light bouncing between the mirrors.

Assuming you understood the same: how would the acceleration of the cart be transmitted to the light beam bouncing between the mirrors?

And no, I don't think this helps to get to absolute motion. The beam "falls out" in the back if you change the velocity of the cart. All you can detect then is the change, i.e. an acceleration.

Harald.

 

[yuiop]

It was maybe not clear from my initial post: the cart should be tugged in a direction orthogonal to the beam of light bouncing between the mirrors.

Assuming you understood the same: how would the acceleration of the cart be transmitted to the light beam bouncing between the mirrors?

And no, I don't think this helps to get to absolute motion. The beam "falls out" in the back if you change the velocity of the cart. All you can detect then is the change, i.e. an acceleration.

Harald.

Yes, I was assuming the light beam is orthogonal to the motion. The velocity of the light clock deflects the beam so that under constant velocity conditions it normally hits the far mirror, but you are right that under accelerating conditions, the beam can fall out the clock. I added that in edit, but you posted in the meantime.

 

[birulami]

In the orbital case, the light is falling as fast as the mirrors so it still hits the mirrors and the light clock behaves as it does in flat space (for a sufficiently small light clock). Recall that an orbiting satellite is in free fall.

So in principle I could go to the lab, set up the two mirrors, flash a light and have a photon keep bouncing while the lab rotates around with the Earth --- given ideal conditions with regard to the mirrors, their angle being zero, the vacuum and other obstacles to the photon, the photons angle being 90 degrees to mirrors? Hmm,

 

[ghwellsjr]

If you could make a light clock that would bounce light back and forth forever with no regeneration and you accelerated it, then yes, the light would fall out of the light clock. But any realizable light clock would be designed to detect each bounce and regenerate (and realign) the bouncing flash so that it would continue to work under any reasonable acceleration.

 

[birulami]

I added that in edit, but you posted in the meantime.

Yes, I saw it too late. Thanks for the clarification. With these kind of thought experiment, I often struggle to describe it so clear that no misunderstanding is possible.

Harald.