# Light in the expanding space universe

1. Sep 7, 2015

### Gerinski

Hi PF members, I have a question about electromagnetic radiation propagating in an expanding universe.

We know that because of space expansion, light from a distant source gets redshifted, its wavelength becoming longer and its amplitude flatter.

If we move far enough from the source, we should reach a point where the space expansion rate equals precisely the speed of light propagation so the light wave becomes totally flat. There is zero amplitude and the wavelength is equal to the space expansion rate.

If we move still farther, the light wave can not catch up anymore with the space expansion. That space region has become causally disconnected from the light source.

This presents some question to me:

At the point where the space expansion equals the speed of light, the light wave has effectively disappeared. It's amplitude is zero and its wavelength equals the rate of space expansion so there is actually no physical EM wave anymore.

Where has the energy of the EM wave gone to?

In the regions where expansion has exceeded the speed of light, causality with the light source is gone. The light wave has died "before the appearance of that space". Is this a correct interpretation?

Thanks !

2. Sep 7, 2015

### mgkii

I'm sure others will jump in here and "firm up" the explanation... but I think you've got two concepts mixed. The expansion of the universe is pushing objects away from us, and the further you look the quicker they are being pushed away from us. However, light emitted from those objects is travelling "inside" this expanding universe and not being expanded by it.

I think that rather a light the wave having zero amplitude through some influence of the expanding universe, the point you describe is simply the horizon of the visible universe.

Let the corrections begin.... :-)

3. Sep 7, 2015

### Gerinski

Thanks. But the CMB is clearly redshifted in our current spacetime environment. It was less redshifted in our past and it will be more redshifted in our future.
If we would be still farther in the future, and assuming that space will keep on expanding, there should be a time when the expansion of our local space equals the speed of light relative to the CMB emission surface. At that epoch we will not be able to detect the CMB anymore, it will have become a totally flat wave with no amplitude.

4. Sep 7, 2015

### ogg

This a bit above my pay grade - so hopefully others will correct me. First you need to distinguish between a point in space (or space-time) from which no light can reach us, and what is happening AT that point. The emr wave "there" doesn't "know" that when it reaches us it will be redshifted to infinity. At that point some of its energy has gone to the Dark Energy (this is by definition, not some discovery we've made, in this way we hold to the Conservation of Energy), based on how far/long it has traveled from its source. Hmmm, why not think about it like a leak? Or maybe a "friction"? As you probably know, detecting an emr wave requires a detector of a size of the scale of its wavelength. So as wavelength lengthens, the emr becomes "one with the Universe" to wave hands around in front of mirrors with smoke generators in full gear. It becomes undetectable. And of course there are uncertainty issues involved, but perhaps not necessary to discuss here. What I haven't got my head around is the correlation between the age of the Universe and the current distance to the EH - they're roughly the same. Coincidence? I doubt it. While you're considering energy losses, consider what is happening to the gravitational Potential Energy of two particles as their separation grows. Finally, st expansion is (afaik) not relevant to bound systems (our local cluster), but ALL light IS subject to cosmological redshift - its just gotta travel distances of hundreds of millions or billions of parsecs. So, your statement that light "inside" "is not being expanded by it" is an error.

5. Sep 7, 2015

### ogg

Its gotta travel far to have MEASURABLE redshift. There's also weird and strange things "happening at the EH". Take a look at discussions of our holographic universe and (the supposed) Conservation of Information. Many physicists claim that CoI is "more fundamental" than CoE. Famously, Stephen Hawking lost his bet that CoI didn't apply to EHs. (personally, I have, in my ignorance, a real problem with CoI - especially since it seems to be an assumption and may or may not be a necessary assumption. Recently, I've read that it is a "fundamental" assumption of Quantum Mechanics, but while solutions to the wave equations seem to use it, I don't understand why its claimed that it is a necessity...)

6. Sep 7, 2015

### Staff: Mentor

No.
The wavelength just expands in the same way as the universe does: if the universe is now twice as large as at the time of emission, the wavelength doubled. If the universe is now 1000 times as large, the wavelength increased by a factor of 1000. The amplitude reduces accordingly, but there you get an additional effect simply from the larger distance. Anyway, it never gets zero.

There is a point where the calculated distance (for some way to calculate it) increases with a speed of c, but this point has no special relevance. Light emitted there doesn't come closer to us today, but as the expansion rate of the universe is changing it will do so tomorrow, and in something like 20-25 billion years (guessed) it will reach us. The actual horizon is a bit further away.
As mentioned above, the electromagnetic waves don't vanish. Their energy reduces, right. There is no global energy conservation of general relativity. The energy is simply lost.
Those regions just exist relative to us. They are not special in any way. Observers there will make the same calculations to conclude they can never see us.

No, not at all. This has nothing to do with the concept of dark energy.
Sort of. The numbers were completely different a few billion years ago, and they will be significantly different again 10 billion years in the future.

7. Sep 7, 2015

### ogg

mfb - hmm. I have heard no better explanation for the coincidence, than "coincidence", so I can only say its suspicious. As far as GR and Energy Conservation, of course you're right. But we aren't talking about GR, we're talking about the Standard Model. I am under the impression that the question of Conservation of Energy hasn't been definitively answered. IOW, the claim that the emr energy simply vanishes with redshift is no more nor less true than the claim that it is conserved (in the form of Dark Energy). Am I wrong? (of course, even if I'm right that neither has been falsified, that doesn't make my positive assertion a correct representation of our current knowledge) Thanks!

8. Sep 7, 2015

### Orodruin

Staff Emeritus
The standard model of cosmology is built upon GR so that is what you are discussing whether you realise it or not.

You seem to misunderstand the concept of the last scattering surface. It was released everywhere at the same time. The reason we see a surface now is that light that was emitted closer has already passed us and light which is from further away still has to do so. Some regions of the Universe are causally disconnected from ours and the light from there will never reach us, but there will always be light from somewhere at the time of the CMB release which will reach us.

9. Sep 8, 2015

### bapowell

What does dark energy have to do with conserving redshifted electromagnetic energy?

10. Sep 8, 2015

### Staff: Mentor

You are wrong.
- if the energy would be conserved, the evolution of the universe would have looked completely different. It would also mean GR is completely wrong, in disagreement with experiments.
- dark energy is speeding up expansion, photons are slowing it down
- there is simply no reason to expect one going to the other. It's like asking "if I hide an apple behind me so you cannot see it any more, does it become a banana?".

11. Sep 8, 2015

### Staff: Mentor

No, that's not how space expansion works. There is no privileged position in the universe. A better statement is: "because of space expansion, light everywhere in the universe is continually being redshifted, its wavelength becoming longer and its amplitude flatter". There's no difference between light at our location "now", which was emitted by a distant galaxy a long time ago, and light at the distant galaxy "now" (which could have been emitted by us a long time ago).

No. The light is the same at that distant point as it is here (see above). A galaxy currently at our cosmological horizon (the point where the "space expansion rate" equals the speed of light) emits light that is perfectly normal, when viewed by local observers; but because of the expansion of space, the light emitted in our direction doesn't move any closer to us. It does move away from the emitting galaxy at the speed of light, however, so it certainly can't be said to "vanish".

12. Sep 8, 2015

### Overstepper

Hi, I'm new here. I have a doubt, I tried googling it but it seems I don't know the right words or concepts.

Imagine a map of the universe inside a circle (I would say sphere, but I wanna make it simple). The stars are constantly "shooting" photons all over place. What happens to light that does not hit matter, and goes out of that circle? Will that light continue to go in the same direction it was before eternally? If so, since it won't come back, isn't the energy of that light "lost" by the universe? If so, should we conclude that the universe is losing energy?

13. Sep 8, 2015

### Staff: Mentor

This is not a good way to imagine it. The universe has no boundary, so you should either be imagining an infinite flat plane, or a finite but unbounded surface like a 2-sphere. See below.

There is no outside. The light stays inside the universe forever. If the universe is spatially infinite (as our best current models suggest it is), then the "circle" is really a plane with no edge anywhere. If the universe is spatially finite, then it is a 3-sphere (in your analogy, leaving out a dimension, it would be the surface of a 2-sphere), so it again has no boundary anywhere; light that travels far enough just circumnavigates the universe and returns to its starting point, and starts all over again.

14. Sep 8, 2015

### marcus

Cosmologists do their best to model the universe AS A WHOLE despite the fact that they can only see a limited portion at any one time.
With the help of assumptions (like average overall uniformity) they are able to draw some conclusions about the whole, and the standard model (called LambdaCDM) is a model of the whole thing.

The model comes in several versions---e.g. infinite (so no boundary) and e.g. finite spatial volume but curved around so that there is no boundary in that case either.
It is impossible for energy to "leak out" because there is no boundary, and no place for it to go to. By definition the universe is everything. That's the simplest way to deal with it mathematically. We have no evidence of a boundary and adding one to the model would make things a lot more complicated.

Of course there is a boundary to the observable region but it is constantly changing, the observable region keeps growing and more stuff is being included constantly. You can't just only model the observable region.

So don't worry about light leaving the universe

there is more to say though! We don't have a global energy conservation law! If you are curious keep on asking questions. Other people will jump in.
Ask yourself what about the stretching out of light's wavelengths as the universe expands. Longer wavelengths carry less energy. A packet of light loses energy as it is redshifted. Ancient light that used to be visible has now been stretched out to infrared and even microwave. Lower frequency less energy.

People will recommend papers to read about the distant future of the universe, if it keeps expanding. It might interest you,if you keep asking.
But don't worry about light actually "leaking out" across some boundary.

Hmm. I see now Peter already answered you. I had to get up for a few minutes and do a chore, halfway thru writing this, didn;t realize Peter was answering.