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While discussing this question (Does light have an unending journey?) I stumbled on the fact that light's speed is constant only in inertial frame.

What I happened to do was add up the expansion of universe to the theory. It goes as follows:

Suppose from a source we emit a photon, at the same time, we (source) are moving away from the point of launch and so is the point that too with acceleration, now lets consider the moment when we are so far from the point of fire that the distance between the 2 points (source and firing point) is so much that the space with their respect to each other is moving with speed more than speed of light, certainly since the points are also constantly being separated they have a relative velocity of separation which just happens to be more than speed of light, now by the time the fired photon must have travelled even further and its speed now with respect to the source must be greater than speed of light.

Can this be taken as a prove for the variance of speed of light from inertial frames?

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2 Answers

You're assuming, incorrectly, that general relativity has a unique and natural way of describing the velocity of cosmologically distant objects. That isn't the case. There isn't any such definition, because velocity is a vector, and parallel transport of vectors is path-dependent.

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But I am not transporting any vector, I am seeing the velocity of something while sitting in mh chair, I observe the space is expanding with more speee than distancd is increasing with more speed than c and hence speed with respect to me sitting in my chair is more than c –  rijul gupta Oct 26 '13 at 19:54
    
I am seeing the velocity of something while sitting in mh chair... One of the basic conceptual obstacles you need to get over in relativity is that idea that there is something going on "now," which you can determine by what you "see." –  Ben Crowell Oct 26 '13 at 20:44
    
Then how are we going to make the observation ? Or should we not make the observation ? –  rijul gupta Oct 26 '13 at 20:54
    
You can, for example, make optical observations. But those optical observations do not tell you what is "really" happening "now" at some distant location. –  Ben Crowell Oct 26 '13 at 23:03
    
Then what would those observations tell ? As far as I understand we would get the light from a star till it is at a point that the space between us and the star is expanding with speed less than that of light ; when the star has moved on even further its light will stop reaching us as the space would be expanding with more speed than speed of light. Similarly if the photon we fired reaches such a distance from our frame it would be moving away with speed more than c –  rijul gupta Oct 27 '13 at 2:29
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Current, standardized definition of distance is based on the assumption that speed of light is constant, inertial frame or not. (See, for instance, wikipedia's page on metre).

Nevertheless, hypothesis of variable speed of light sometimes is used in cosmology. Note, that this is one of possible explanations of observations and not the most widespread.

Edit. Upon reading OP's comments I would like to rephrase Ben Crowell's argument: For curved spacetimes distance between two objects can grow at a rate exceeding the speed of light and that in no way violates general relativity and its postulate about the universality of speed of light. One way to understand this is to look at the space-time diagrams. Let's look at the one from Ned Wright's Cosmology Tutorial

space-time diagram

Small red triangles are the light-cones for given point -- that is if we draw space-time trajectory of an object at that point it will be inside the light-cone for that point, but the slant of the trajectory (which corresponds to the growth rate of distance) could be greater than the slant of the light-cone for some other point.

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As I see your answer it seems like you are saying that it is a possible explanation, just a little thing your link has reference to speed greater than that of light for virtual photon at small distance, my theory is about actual photons that are highly separated from point of observation. –  rijul gupta Oct 27 '13 at 6:36
    
First, virtual photons traveling faster than light is definitely stretching the metaphor of virtual particles too far. The actual theories (quantum field theory) do not have FTL or VSL phenomena. –  user23660 Oct 27 '13 at 6:49
    
Second, my point is that cosmological observations do not prove variable speed of light, but could be interpreted with this concept. They can also be successfully interpreted without this concept. –  user23660 Oct 27 '13 at 6:54
    
Still what was your point ? Am I correct ? –  rijul gupta Oct 27 '13 at 6:57
    
My point is that your 'theory' is based on misunderstanding of cosmology, but the idea that speed of light is variable does have merit in the context of cosmology. –  user23660 Oct 27 '13 at 7:07
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