# Light's direction of travel, bending, and speed

1. Jan 17, 2012

### bahamagreen

Light's "direction" of travel, bending, and speed

Hoping someone can clear up a few questions...

At any particular instant in time (from anyone's perspective), is light (or a photon, if that helps) thought to have a specific direction of travel while between emission and absorption? I've read many thought experiments where this is implied, but also read that apart from the source and target nothing may be said about the nature of any path(s)...

If yes to the above; is this direction of travel at c the "tangent" to the path when it is curved by either gravity or within an accelerating frame, or does c also include the lateral (radial) component comprising the curvature?

If no to the first question; what prevents or distinguishes that the displacement curvature does not act on the light if its orientation direction of travel at that moment is radial to the gravitational source (or normal to the plane of acceleration)?

If these questions are not clear or not well formed I'll try to answer any thoughts. Basically I'm trying to understand what it means if only light's lateral component is subject to curvature (and it's longitudinal component is not because that would be slowing below c?), and the relation between the two components to ensure observed c during curvature.

2. Jan 17, 2012

### Mentz114

Re: Light's "direction" of travel, bending, and speed

I presume you're asking for something in the GR context where light travels along null geodesics which are completely specified by the metric. There is a solution of the EFE that contains only radiation ( the plane symmetric radiation spacetime ) and that has a definate direction. In Brinkmann coordinates the Einstein tensor has only the G00 = μ component where μ is the energy density. Transformed to the usual flat-space t,x,y,z, the Einstein tensor takes the form of the tensor product of a null propagation vector kβ, viz. Gβα = σkβkα.

This is by no means the full story,because in the common cosmological models the optics is fairly complicated with the curvature causing changes in subtended angles and so on. Maybe someone else can expand on that.

It's also worth mentioning that one Prof. Moeller in his 1950's book showed that optics in GR can be handled by ascribing to spacetime a refractive index which depends on the curvature and treating it somewhat as a material.

Last edited: Jan 17, 2012
3. Jan 17, 2012

### bahamagreen

Re: Light's "direction" of travel, bending, and speed

That's over my head... I can't even tell which way you answered, or if you did!?

I was thinking more about bending of star light passing the Sun...

For example, does the tangential speed of the curved light maintain c or does that component slow a little, but then the radial component of the curvature make up for it, so when the "net direction" of travel is composed of both components the observation is c?