# Light in an Accelerating Frame

*Most recent answer: 09/23/2012*

Q:

suppose a box,containing a man inside,is moving with a certain acceleration in an arbitrary direction far from any gravitational effect. Now a beam of light passes through the box. does the person see the beam to be bent opposite to the direction of acceleration? it may happens as such a accelerating box creates same effects like gravitation.

- Shantonu Mukherjee (age 19)

Hooghly/West Bengal/India

- Shantonu Mukherjee (age 19)

Hooghly/West Bengal/India

A:

Yes, the light does seem to bend just as it would in a gravitational field.

Mike W.

Mike W.

*(published on 09/23/2012)*

## Follow-Up #1: accelerating frames and curvature

Q:

well,you are saying that light will bend opposite to acceleration.so this means that space-time may also be curved by the accelerating box inside it. thus mass can't be the basic entity responsible for curvature of space-time.Perhaps it is not possible.Though the situation is completely hypothetical ,but may be theoretically established by laws of General Relativity.Until theory is given nothing can be said surely. please consider my words & reply me.

- Shantonu Mukherjee (age 19)

Hooghly/West Bengal/India

- Shantonu Mukherjee (age 19)

Hooghly/West Bengal/India

A:

Actually, the foundation of General Relativity is precisely this equivalence, locally, between the effects of choosing an "accelerating" reference frame and choosing one that is "not accelerating" but in a uniform gravitational field.

So is spacetime curved just by choosing a different coordinate frame? No, the curvature of spacetime has an invariant definition, unaffected by choice of coordinate frames. Any frame with an origin accelerating with respect to gravitational free-fall will give an apparent curvature of light beams, but the actual invariant curvature of the spacetime comes from non-uniformity of the gravitational field.

Let's try to picture that distinction for a simpler, purely spatial, 2-D geometry. Say that you have a flat sheet, marked off with a nice square grid of coordinates. The change in coordinates of an inertial object, including a light ray, will be the same for each second. Now use a set of curvy coordinate lines. The change in that object's coordinates each second will be different. Clearly the actual physical situation hasn't changed, so the space is still flat. You can give a definition of the invariant curvature in terms of the coordinate spacings and something called the metric tensor, but it works out that wiggling up the coordinate lines doesn't give any invariant curvature. On the other hand, you could have a bulge in the otherwise flat sheet, and it would give an invariant curvature regardless of what sort of coordinate lines were chosen. The same lesson applies to more complicated spacetime geometry.

Mike W.

So is spacetime curved just by choosing a different coordinate frame? No, the curvature of spacetime has an invariant definition, unaffected by choice of coordinate frames. Any frame with an origin accelerating with respect to gravitational free-fall will give an apparent curvature of light beams, but the actual invariant curvature of the spacetime comes from non-uniformity of the gravitational field.

Let's try to picture that distinction for a simpler, purely spatial, 2-D geometry. Say that you have a flat sheet, marked off with a nice square grid of coordinates. The change in coordinates of an inertial object, including a light ray, will be the same for each second. Now use a set of curvy coordinate lines. The change in that object's coordinates each second will be different. Clearly the actual physical situation hasn't changed, so the space is still flat. You can give a definition of the invariant curvature in terms of the coordinate spacings and something called the metric tensor, but it works out that wiggling up the coordinate lines doesn't give any invariant curvature. On the other hand, you could have a bulge in the otherwise flat sheet, and it would give an invariant curvature regardless of what sort of coordinate lines were chosen. The same lesson applies to more complicated spacetime geometry.

Mike W.

*(published on 09/25/2012)*