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art pletcher

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In summary: B and it takes a certain amount of time for the photon to get there. Now let's say the expansion of the universe is happening faster than the speed of light. So the photon that observer B receives when it arrives at A is older than the one that observer A receives when it arrives at B. Now, what happens when the two photons are compared to each other? They would be found to be different in some way (maybe they had different directions of travel, or they were in different parts of the universe when they were measured). But since the expansion of the universe is happening faster than the speed of light, the difference between the two photons will grow over time. So over the long term, the distance

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art pletcher

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valenumr

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Imagine there were a single star in the universe, which would be surrounded by a spherical cloud of it's own radiation that dims (or cools) with respect to distance classically (here I mean inverse square law). If that spherical space were expanding, there would I think, be an measurable amount of excessive cooling at large distances due to the expanding volume.

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Chalnoth

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There are a few things that make this question hard to answer. First, the concept of parallel lines in General Relativity is a bit complicated. To get parallel lines in curved space-time, you have to move a vector from point a on line A to point b, but the eventual direction of that vector can depend upon the path from a to b. So there's no one single answer to which line at point a is parallel to which line at point b.art pletcher said:

The second issue is that photons do actually experience gravity, so their mutual gravitation will tend to pull them together, while the cosmological constant will push them apart. Which of these two effects wins depends upon how far apart the photons are. This is a small effect, though, so it takes a

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art pletcher

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I value your expertise. Thanks.

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Chronos

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Chalnoth

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It's not coordinate dependent as long as you use parallel transport, but it is dependent upon the path you choose between the two lines. The problem is that parallel transport is ambiguous except in the special case of flat space-time.Chronos said:

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art pletcher

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Would two photons, unbounded by gravity, become separated from the universal expansion?

Thank you

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marcus

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art pletcher said:

Hi Art, I don't see what's so hard about the question. the way you stated it first seems clear enough. Excuse me for not responding earlier, I was busy and I don't always read everything as soon as it's posted. BTW I'm not an expert---just an amateur on-looker who likes Cosmology and Quantum Gravity research a lot.art pletcher said:

Would two photons, unbounded by gravity, become separated from the universal expansion?

Thank you

You know in cosmology there is a CMB rest criterion and a universe time also called Friedmann time. that's how one can define proper distance. the distance you'd measure if you could pause the expansion process at a particular moment of universe time to allow you to measure it.

Ned Wright describes measuring proper distance with a string of observers all at CMB rest, with their clocks synchronized, all at one agreed on moment measuring the distances between them. that's another way to think of it. In any case it's well-defined.

My point is the concept of "parallel" can be made meaningful in cosmology using universe time (the standard time the Friedmann model runs on, and which everybody in cosmology uses) and proper distance (also a standard construct that everybody uses---the Hubble law is defined in terms of proper time)

Anyway just for concreteness imagine you have 4 galaxies which are widely separated and at a particular moment of universe time they form a SQUARE, call them A, B, C, and D and they have observers A, B, C, and D stationed at them. the observers can check that the angles are 90 degrees. (assuming spatial flatness) or (assuming uniform curvature and near flatness) at least that the proper distances are all something, say 1 billion LY, along the sides.

So at that moment in time observer A sends a flash of light aimed at B and observer C sends a flash of light aimed at D.

Clearly the light beams start out parallel.

the light is traveling along geodesics, shortest distance paths from A to B and from C to D.

And when the light flashes arrive at the two destinations they will be farther apart than they were at the start, due to distance expansion.

So everything is well-defined and the answer to your question is yes, expansion does increase the distance between parallel light beams.

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ChrisVer

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Chalnoth said:but it is dependent upon the path you choose between the two lines

Well you can't randomly choose any path possible... The light will follow geodesics, and so its path is predetermined by the spacetime metric, no?

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art pletcher

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Would the photons, which were aimed at B and D before expansion, intersect them after some (n) amount of expansion? Thx.

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Chalnoth

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In this case, the path is a fictitious thing used to link the two light beams, to see if it makes sense to say that they are both traveling in the same direction.ChrisVer said:Well you can't randomly choose any path possible... The light will follow geodesics, and so its path is predetermined by the spacetime metric, no?

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ChrisVer

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In that case you care about geodesic deviations?

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cosmik debris

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Chalnoth said:The second issue is that photons do actually experience gravity, so their mutual gravitation will tend to pull them together, while the cosmological constant will push them apart. Which of these two effects wins depends upon how far apart the photons are. This is a small effect, though, so it takes alongtime to become apparent.

I think that photons traveling parallel and in the same direction do not attract each other, they do if they are traveling in opposite directions.

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Chalnoth

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Ahh, yes, I think you're right. I'd have to look it up again to be sure, but I do think that's accurate.cosmik debris said:I think that photons traveling parallel and in the same direction do not attract each other, they do if they are traveling in opposite directions.

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Emreth

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cosmik debris

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Emreth said:

So it seems the answer is "it depends". The naiive calculation using the energy of the photon or light beam would suggest attraction, but there are two terms, an attraction and a repulsion, in the em tensor which cancel out in the case of parallel same direction photons/light beams. Is that what they are saying?

No, the speed of photons is constant and is not affected by the expansion of the universe. The expansion of the universe only affects the space through which the photons are traveling.

No, the expansion of the universe does not physically separate photons that are traveling parallel to each other. While the space between them may increase, the photons themselves remain on the same path.

The expansion of the universe causes the distance between two points in space to increase over time. This means that photons traveling through the expanding universe will travel a greater distance compared to the same journey in a non-expanding universe.

Yes, the expansion of the universe can cause photons to redshift. As the space between the source of the photons and the observer expands, the wavelength of the photons also increases, resulting in a redshift.

No, the path of photons can also be affected by other factors such as gravitational lensing, which can bend the path of photons as they travel through space. However, the expansion of the universe does not directly alter the path of photons.

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