# Explanation of Red Shift

1. Oct 10, 2014

### ricardo81

Hi all,

I understand the concept of red shift, and how it helped to explain how the universe was expanding and that most of the observable universe is moving away from us. It happens due to the wavelength of light increasing due to the expansion of space.

As I understand it, it's not know how this "happens", i.e. it's not generally understood. Am I correct in saying that?

2. Oct 10, 2014

### moriheru

Well, if the universe grows by a abitary factor say x then the wavelength of light will increase by factor x.

3. Oct 10, 2014

### ricardo81

Yes, generally that makes sense but I'm thinking more at the most granular level. Perhaps there is an equation that explains how much redshift over how much time/distance.

However I'm wondering what actually happens at the highest atomicity... surely there is some thinking behind the "how" the wavelength/frequency changes rather than what's observed to happen. It's not like the light has self-awareness to change its state after a given distance.

4. Oct 10, 2014

### Chalnoth

Nope. It's understood quite well. It's just metric expansion in General Relativity. There are many ways to go about explaining how it happens in detail, but here's a rough sketch of one way:

1. Assume General Relativity is correct. For the regime of interest, General Relativity is almost certainly an accurate description given current experimental data. So we don't have to worry about this assumption being wrong.
2. Assume the universe is perfectly uniform. This severely constrains the possible metrics that can be used to describe the universe, and the FLRW metric can be proven to encompass all possible homogeneous, isotropic universes (different universes would just have different parameter values). This assumption isn't quite correct, but the deviations aren't too dramatic either.
3. Place a photon in an expanding FLRW universe and find out what happens. Turns out it redshifts.

5. Oct 10, 2014

### ricardo81

Thanks for the post, that's led me on to reading a few more pages. It assumes that the universe is uniform and my question can live with that :)

So as a photon travels over time and gradually redshifts, it *is* the expansion of space that is causing that effect?

6. Oct 10, 2014

### Chalnoth

That's one way to look at it.

That's where General Relativity gets extremely tricky. The math is clear and unambiguous (though sometimes itself tricky to figure out), but there are many ways of describing the redshift that sound exceedingly different from one another.

For example, it is possible to describe the redshift as a result of the fact that photons have pressure. That is, if I have a box with a bunch of photons bouncing around inside it, then that box will put pressure on each side of the box equal to one third the energy density of the photons. If you then expand the sides of that box by, say, doubling the length of each side at the same time, then energy density of the photons in the box will have to drop to 1/16th its previous value in order for energy to be conserved (the pressure produces work on the sides of the box, so the photon gas loses energy as the sides move outward). There is 8 times the volume, so one factor of 1/8th comes from the increase in volume, but there is an additional factor of 1/2 that comes from the loss of energy: double the sides of the box, and the wavelength of each photon has doubled.

Last edited: Oct 10, 2014
7. Oct 10, 2014

### Staff: Mentor

You don't need that assumption for redshifts. We just observe that the universe is extremely uniform, so our description of the whole universe uses this approximation.
Yes.

8. Oct 10, 2014

### CKH

You are assuming an adiabatic expansion (in which the sides are expanded slowly)? The photons in that case would lose energy to the sides lowering their frequency. In an expanding universe, there is no box (as such). It seems easier to understand part of the loss in frequency as a doppler effect. The farther the source, the faster you are receding from that source. However, as the universe expands, the gravitation potential also increases so at least some photon energy must be converted into gravitational potential.

9. Oct 10, 2014

### Chalnoth

Slow, in this case, means slow compared to the speed of light. So not really that slow.

Yes, it's an analogy. But the mathematics that are actually involved in describing the photon gas in an expanding universe are identical to this analogy. If you want to go into detail, the conservation of energy equation in the example is:

$$\Delta E = -W$$

That is, the change in energy of the gas is the negative of the amount of work it performs.

In the real situation, what you get is a change in energy for a co-moving volume that is determined by the space-time curvature. That change turns out to be exactly what you'd get if you imagined a universe filled with expanding boxes. This analogy breaks down once you start considering extremely large volumes, but then so does the concept of total energy itself.

10. Oct 10, 2014

### Staff: Mentor

I don't know about anyone else, but I like to visualize light as an EM wave and not photons in this case. An EM wave has a wavelength and thus will be spread out across space. As the space the EM wave occupies expands, different parts of the wave get moved apart, resulting in a lengthening of the wavelength and thus a redshift.

That's my understanding at least.

11. Oct 11, 2014

### ricardo81

> visualize light as an EM wave

Indeed, that's how I'm thinking, and that one hertz travels some order of magnitude of planck lengths.

I'm now left unsure what's causing the redshift, is it deemed to be the expansion of space or is it interaction with matter on its travels, causing it to gradually exchange energy with its surroundings (and increase its wavelength / reduce its frequency)... or both?

I'm 'hoping' it's the former.

12. Oct 11, 2014

### Torbjorn_L

I have found the Wikipedia page my go to resource for this, since it lists all large redshift processes - doppler, relativistic doppler, gravitational and cosmological - and give formulas: http://en.wikipedia.org/wiki/Redshift .

I don't think that works out, and the attempt is confusing cosmological redshift with doppler and gravitational. As you yourself surmise, the redshift is larger than just the intrinsic doppler shift (except for nearby galaxies).

Gravitational redshift is a loss of energy for the photon as it climbs a gravity "potential well" from lower to higher potential energies. [ http://gfm.cii.fc.ul.pt/events/lecture_series/general_relativity/gfm-general_relativity-lecture4.pdf ] And indeed, when the universe expands the gravitational potential energy increases, I think. But the cosmological redshift is simpler understood as a geometric effect, see the equations in the first link.

Yes, it is. If you also visualize the space in between as a coordinate grid, new points are inserted in the grid as space expands. That is how the photons are stretched. This parallel visualization is how Susskind does it in his youtube Standford Lectures in cosmology, highly recommended. (You would want to watch the latest series, the subject moves quickly.)

Now, if you think about it as energy exchange, you expect gravitational redshift. (See above.) But energy isn't well defined in general relativity*, and you have to think about those expanding boxes. It is easier to use the correct physics and expect that the photons will loose energy as they redshift and shrug away such consequences on general relativity grounds.

*Under very wide constraints you can see energy in GR as conserved, locally and globally, as gravitational potential energy balances other terms. I've seen a paper that claims that it works out throughout (non-quantum, classical) black holes even.

Similarly a FRW universe such as ours can be seen as zero energy, locally and globally, where energy conservation is gravitational potential energy balanced by dark energy pressure terms and other terms, et cetera, and dynamical system behavior is zero energy.

But all this is arguable - and argued. I expect that if these ideas are useful for understanding they will eventually win out for practical reasons. It would help understand cosmological redshift, I think. But we aren't there (yet).

Last edited: Oct 11, 2014
13. Oct 11, 2014

### Chronos

Matter interactions as the source of CMB redshift is ruled out by their blackbody spectrum. If CMB photons are unaffected by matter interactions, it makes little sense to apply such an effect to photons emitted by less distant galaxies.

14. Oct 11, 2014

### ricardo81

Interesting stuff, thank you.

Just for reference, my curiosity comes from reading about quantum mechanics (I'm a computer programmer though my fundamental knowledge of maths (and physics) is somewhat lacking when it comes to the equations mentioned). I end up having a vague notion/preference of Bohmian mechanics and a more deterministic answer to things.

From my understanding, it's almost as if there are designated (predetermined?) points in space that the light will travel to, and the newly created points in space cost the photon energy in 'bypassing'. I've come to learn that all theories of physics are compatible with both directions of time, and this would seem to make sense here, as it seems like there would be an issue with a photon backtracking its journey, as the compression would be "lossy"? I guess that's more of an entropy issue than anything.

15. Oct 12, 2014

### Staff: Mentor

That seems like a roundabout way of looking at it to me. The "stretching the wavelength" view seems much simpler.

16. Oct 19, 2014

### Tanelorn

Drakkith, I have always viewed red shift this way also. One thing I remain uncertain of, is the length of the photon when being viewed as a wave, and does its length matter anyway when being red shifted?

Last edited: Oct 19, 2014
17. Oct 19, 2014

### Staff: Mentor

Photons do not have a length. They are energy quanta. In other words, a photon is the quantized interaction of the EM wave with matter.

18. Oct 19, 2014

### Torbjorn_L

That is the classic quantum mechanical model, I believe. But when you switch to relativistic quantum field theory, which is the only way to make sense of cosmological redshift as I understand it (photons having a wavelength associated with the geometry), particles are ripples in its associated quantum field (and the fields it interacts with).

"Even to say a particle like an electron is a ripple purely in the electron field is an approximate statement, and sometimes the fact that it is not exactly true matters.

It turns out that since electrons carry electric charge, their very presence disturbs the electromagnetic field around them, and so electrons spend some of their time as a combination of two disturbances, one in in the electron field and one in the electromagnetic field. The disturbance in the electron field is not an electron particle, and the disturbance in the photon field is not a photon particle. However, the combination of the two is just such as to be a nice ripple, with a well-defined energy and momentum, and with an electron’s mass."

[ http://profmattstrassler.com/articl...ysics-basics/virtual-particles-what-are-they/ ]

And of course such a quantum ripple has no real "length" until it interacts with something where length is relevant. There is a number of lengths or areas or volumes that can be associated with it, in more or less fuzzy ways. The wavelength is one (diffraction), the wavefunction volume another (likelihood), et cetera, as per above when you get close to a photon you will get problems with its interactions with other fields, et cetera.

Last edited: Oct 19, 2014
19. Oct 19, 2014

### Tanelorn

Thanks Drakkith and Torbjorn. So when we talk about photons being viewed as a wave we are not talking about its wavelength, we are talking about its wave function. I still have to figure out what wave function actually is unfortunately.. Is there a simple description for wave function?

http://en.wikipedia.org/wiki/Wave–particle_duality

20. Oct 19, 2014