# Global observations from Rindler frame

Gold Member

## Main Question or Discussion Point

Basically I want to understand what Rindler observer will see if he looks out the window in direction that is perpendicular to direction of acceleration.

As I understand there are at least three effects (as analyzed from perspective of Minkowski observer):
1) accelerated motion relative to inertial objects;
2) increasing aberration that creates apparent motion of inertial objects in direction of acceleration;
3) increasing length contraction of Rindler observer that creates apparent motion of inertial objects toward plane that is perpendicular to direction of motion and goes trough Rindler observer.

For the first effect distance to object changes speed of observed angular motion (acceleration) but for other two effects distance to the object does not affect angular motion (acceleration) of object.

Any thoughts? Does it seems right so far?

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pervect
Staff Emeritus
Taking this question literally, I would suggest doing a ray-trace, sending out a light ray perpendicular to the motion of the accelerating observer. The traced ray would be past directed (I hope that makes sense, it's an easy hack and a standard way of doing ray tracing outside the context of GR).

. IT appears this is actually called ray-casting if you don't deal with specular reflections and the like. The ray is just "cast" from the eye, into the scene, and you trace it's trajectory , backwards in time, until it hits something. And whatever it hits, that's what you see.

The metric is time symmetric, in geometric with the acceleration in the z direction the metric is:

(1+gz)^2 dt^2 - dx^2 - dy^2 - dz^2

And it's easy to solve for the null geodesics, because ds = 0

Last edited:
Gold Member
Thanks, pervect! But somehow I don't see solution along the lines of your suggestion. Probably you need some experience with the method to use it reliably. And I don't have.

I see it that way.
To see some dynamics I would need to find out couple of points where body is seen. I can imagine how to find that out in flat spacetime. Light rays would be straight there and I can replace accelerated observer with inertial one that has the same speed (well, to get couple of points I would need couple of inertial observers with different speeds). The tricky part in this case is that I see the object in the past so I have to back-trace trajectory of object to find out at what position it is observed. And because relative speed is constantly changing it should be recalculated for each point.