Does universe expansion separate photons, traveling parallel?

[art pletcher]

I understand that the force of gravity prevents galaxies from expanding, as space increases. However, I question if universal expansion separates photons (electromagnetism), as they are traveling along parallel paths (Would the normal distance between them increase over time)? Thank you.

 

[valenumr]

That's an interesting proposition and I don't know whether it has been considered or not, but over large distances it would be measurable if true.

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.

 

[Chalnoth]

I understand that the force of gravity prevents galaxies from expanding, as space increases. However, I question if universal expansion separates photons (electromagnetism), as they are traveling along parallel paths (Would the normal distance between them increase over time)? Thank you.

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.

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 long time to become apparent.

 

[art pletcher]

So outside of the pull of gravity, which decreases rapidly, the two photons drift apart from each other? Just reiterating, to be certain.
I value your expertise. Thanks.

 

[Chronos]

The notion of parallelism is coordinate system dependent. Parallel paths in spherical coordinates are obviously different than those is cartesian coordinates. The universe is usually assumed to be best represented in spherical coordinates.

 

[Chalnoth]

The notion of parallelism is coordinate system dependent. Parallel paths in spherical coordinates are obviously different than those is cartesian coordinates. The universe is usually assumed to be best represented in spherical coordinates.

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.

 

[art pletcher]

I am changing this question to:
Would two photons, unbounded by gravity, become separated from the universal expansion?
Thank you

 

[marcus]

I understand that the force of gravity prevents galaxies from expanding, as space increases. However, I question if universal expansion separates photons (electromagnetism), as they are traveling along parallel paths (Would the normal distance between them increase over time)? Thank you.

I am changing this question to:
Would two photons, unbounded by gravity, become separated from the universal expansion?
Thank you

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.

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.
It is going to eventually arrive at B and at D because it was aimed at them.
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.

 

[ChrisVer]

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?

 

[art pletcher]

Thank you Marcus. You have provided the exact information that I sought. May I also ask:
Would the photons, which were aimed at B and D before expansion, intersect them after some (n) amount of expansion? Thx.

 

[Chalnoth]

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?

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]

In that case you care about geodesic deviations?

 

[cosmik debris]

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 long time 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.

 

[Chalnoth]

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.

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.

 

[Emreth]

Just google tolman gravitation of light. Some relevant work shows up starting with the original 1931 paper.

 

[cosmik debris]

Just google tolman gravitation of light. Some relevant work shows up starting with the original 1931 paper.

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?