Momentum of light in gravity field and other mediums

[jartsa]

Let's say 1 Kilogram of matter is converted into light, and all this light is reflected into one direction.

What is the momentum of the light? Mass of 1 kg times velocity c ?

Let's say the same light enters a piece of glass where the speed of light is 1/2 c. What is the momentum of the light now? 1 kg times 1/2 c ? And did the piece of glass absorb half of the momentum?

Let's say the light enters a gravity field where the gravitational time dilation factor is 1/2. Does the light give half of its momentum to the gravitating thing, similarly as light perhaps gave half of its momentum to the piece of glass?

 

[clamtrox]

Let's say 1 Kilogram of matter is converted into light, and all this light is reflected into one direction.

What is the momentum of the light? Mass of 1 kg times velocity c ?

Indeed, mc^2 = pc.

Let's say the same light enters a piece of glass where the speed of light is 1/2 c. What is the momentum of the light now? 1 kg times 1/2 c ? And did the piece of glass absorb half of the momentum?

Yeah, that seems reasonable too.

Let's say the light enters a gravity field where the gravitational time dilation factor is 1/2. Does the light give half of its momentum to the gravitating thing, similarly as light perhaps gave half of its momentum to the piece of glass?

So you are thinking about a photon climbing out of a potential well and losing it's momentum? See, the situation is a little different here as the incoming photon does not give its momentum away, but instead robs some from the gravitating body. Likewise, an escaping photon gives some of its momentum to the massive object.

 

[jartsa]

So you are thinking about a photon climbing out of a potential well and losing it's momentum? See, the situation is a little different here as the incoming photon does not give its momentum away, but instead robs some from the gravitating body. Likewise, an escaping photon gives some of its momentum to the massive object.

Let us consider a spot light in a gravity well, aimed straight up. Let's say time dilation factor is 1/2 at the location of the spot light. An observer far away will say that light is accelerated to velocity 1/2 c in the spot light, and when light leaves the gravity well the velocity of the light increases by 1/2 c.

I would guess that the light source experiences a force when it accelerates the light to velocity 1/2 c, and the gravity source experiences an equal force when light accelerates from 1/2 c to c, when leaving the gravity field.

The pull of gravity on the light can be ignored, because there isn't any. There is no energy change of light caused by pull of gravity. That is discussed here: https://www.physicsforums.com/showthread.php?t=601102
For light energy and momentum are very much proportional things, so no change of energy of light -> no change of momentum of light -> no pulling of light.