Speed Constancy of Light Implication

[jaketodd]

Scenario 1: Imagine you are in an inertial reference frame and a planet is moving past you very quickly. A photon is coming towards you and will also pass the planet. The photon is not on a collision-course with you.

Scenario 2: You are at rest relative to a planet and a photon is coming towards you. The photon, on the same trajectory as in Scenario 1, will pass you and the planet. Both you and the planet are in inertial reference frames.

In Scenario 1, from your reference frame, will the photon spend more time near the planet than in your reference frame in Scenario 2 because of the constancy of the speed of light in all reference frames?

Thanks,

Jake

 

[JesseM]

What do you mean by "near"--like within a certain radius? Also, in scenario 1 is the photon traveling in the same direction as the planet from your point of view, or in the opposite direction? (if they're going in opposite directions the distance between them will increase more rapidly in your frame than if they're going in the same direction)

 

[jaketodd]

What do you mean by "near"--like within a certain radius? Also, in scenario 1 is the photon traveling in the same direction as the planet from your point of view, or in the opposite direction? (if they're going in opposite directions the distance between them will increase more rapidly in your frame than if they're going in the same direction)

By "near" I mean close enough for gravity to have an noticeable effect. But, for what we are talking about, I think the distance does not matter as long as it is the same for both scenarios.

Yes, the photon is traveling in the same direction as the planet in Scenario 1.

So am I correct in my assumption: In Scenario 1, from your reference frame, will the photon spend more time near the planet than in your reference frame in Scenario 2 because of the constancy of the speed of light in all reference frames?

Thanks,

Jake

 

[Dale]

So am I correct in my assumption: In Scenario 1, from your reference frame, will the photon spend more time near the planet than in your reference frame in Scenario 2 because of the constancy of the speed of light in all reference frames?

Yes.

 

[jaketodd]

Thanks guys

 

[JesseM]

By "near" I mean close enough for gravity to have an noticeable effect.

The problem is that gravity requires general relativity, and I don't think it'd drop off the same way for a planet that's moving in an approximately inertial coordinate system as it would for a planet that's at rest in such a coordinate system (see for example this post by pervect, who is very knowledgeable about GR, where he says 'The gravitational field of a movng mass is an interesting question which deserves a topic in its own right- and has been previously discussed. The very short version is that it is very wrong to substitute some value of 'm' into a Newtonian formula and to expect to get correct results. Much like the electric field of a moving charge, the gravitational field of a moving mass is not even spherically symmetrical.' Also see the links in this post for more on the question of the gravitational field of a moving object). So the problem is easy to address if you're just talking about distance in an SR sense, but not so easy if gravity is essential to the problem.

Yes, the photon is traveling in the same direction as the planet in Scenario 1.

So am I correct in my assumption: In Scenario 1, from your reference frame, will the photon spend more time near the planet than in your reference frame in Scenario 2 because of the constancy of the speed of light in all reference frames?

In a purely SR sense, if the photon is going in the same direction as the planet the distance between the photon and the planet changes at a speed less than c in your frame, so you do see the photon spending more time within a given radius than it spends within the same radius in a frame where the planet is at rest.