What causes red shift in the universe?

[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?

 

[moriheru]

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

 

[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.

 

[Chalnoth]

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

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.

 

[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?

 

[Chalnoth]

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?

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.

 

[mfb]

It assumes that the universe is uniform and my question can live with that :)

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.

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

Yes.

 

[CKH]

That's one way to look at it.

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.

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.

 

[Chalnoth]

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.

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.

 

[Drakkith]

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.

 

[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.

 

[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 .

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.

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.

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.

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).

 

[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.

 

[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.

 

[Drakkith]

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'.

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

 

[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?

 

[Drakkith]

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?

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.

 

[Torbjorn_L]

a photon is the quantized interaction of the EM wave with matter.

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.

 

[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

 

[Tanelorn]

More generally, the normal concept of a Schrödinger probability wave function cannot be applied to photons:

http://en.wikipedia.org/wiki/Photon

 

[Drakkith]

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'm honestly not certain. I view even a single photon as an EM wave which has a wavelength. The wave just has only enough energy for a single photon. But I'm not an expert on quantum physics by far, so don't quote me on that.

 

[Torbjorn_L]

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 haven't studied quantum field theory, so I'm not sure how the wavefunction maps to a particle field like the QED (EM) field with its photons. My naive idea is that they have to start use operators that creates and destroys particles, because the field has an infinite degree of freedom (as many particles as you want) and you have to abandon some simpler math for operators in so called Hilbert spaces. I'm sure the wavefunction maps into that in some form, but have to throw up my hands on the rest. Sorry that I can't help more.

But the cosmological redshift is foremost concerned with the photon wavelength. I can grok wavelengths.:)

 

[presto]

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.

Very nice, but the FLWR metic is not a part of GR, unfortunately.
It just was assumed at hot that the spatial component of the metric can be time-dependent.

BTW: Mathematically this is not an expansion of space, but a scale change only.
And more: I 'assume' just the energy is conserved, and the idea about the stretching of photons, ends in a world of fairy tales.

 

[mfb]

Very nice, but the FLWR metic is not a part of GR, unfortunately.

Certainly a metric that satisfies the GR equations is a model within that theory.

BTW: Mathematically this is not an expansion of space, but a scale change only.

No difference.

And more: I 'assume' just the energy is conserved

And your assumption is wrong. There is not even a clear way to define such a thing as a global energy of the universe.

 

[presto]

The assumption about non-conservation are wrong, because these are just the principles... and Noether proved also.

Therefore the assumption about non-conservation must be just false.

Hence the problem with the perception of the light stretching -
it is impossible because this idea conflicts with the strongest fundamental principles!

"There is not even a clear way to define such a thing as a global energy of the universe."

I don't see any problem with this... and this is done already.

 

[Drakkith]

The assumption about non-conservation are wrong, because these are just the principles... and Noether proved also.

Therefore the assumption about non-conservation must be just false.

Nonsense, the issue with energy conservation is a well known fact of cosmological models using GR (which all of them do). It's not just some assumption.

Hence the problem with the perception of the light stretching -
it is impossible because this idea conflicts with the strongest fundamental principles!

No, it does not. Energy conservation applies locally, not globally. Again, this is well known to cosmologists.

"There is not even a clear way to define such a thing as a global energy of the universe."

I don't see any problem with this... and this is done already.

Please provide a reliable reference then.

 

[presto]

Nonsense, the issue with energy conservation is a well known fact of cosmological models using GR (which all of them do). It's not just some assumption.

There is none of GR in the concept of space expansion.

GR preserves energy very well, what just Neother showed and proved long ago,
therefore yours imaginations contradicts the GR also!

No, it does not. Energy conservation applies locally, not globally. Again, this is well known to cosmologists.

There is impossible to change the global energy, without change of the local energy.

Please provide a reliable reference then.

You should to provide reference, together with these illuminated cosmologists, about disproof of the energy-momentum conservation principle.

Once proven, remains proven forever...

 

[Torbjorn_L]

I'm not sure if it helps to respond to this, the erroneous and unsupported claims just keep coming despite that an encyclopedia can easily inform and despite that valid answers have been posted. But let me try again:

There is none of GR in the concept of space expansion.

Already responded to:

Certainly a metric that satisfies the GR equations is a model within that theory [of space expansion].

This was Einstein's achievement in cosmology, nearly 80 years ago, space expansion is about GR and GR only. (As we now know for sure since WMAP -04 produced the first self-consistent cosmology on GR basis.)

"The framework for the Big Bang model relies on Albert Einstein's theory of general relativity ..." [ http://en.wikipedia.org/wiki/Big_Bang ]

Read more in that reference, and if anything is unclear, please ask here. Hopefully someone with GR chops can answer.

GR preserves energy very well, what just Neother showed and proved long ago,

Already responded to:

There is not even a clear way to define such a thing as a global energy of the universe.

Since there is no global energy concept in GR, there is no problem and no inconsistency with Noether's theorems. The problem, as I understand it (not having studied it), is that GR is non-linear and too hard to solve generally:

"In general relativity and allied theories, the distribution of the mass, momentum, and stress due to matter and to any non-gravitational fields is described by the energy-momentum tensor (or matter tensor) T^{ab}. However, the Einstein field equation is not very choosy about what kinds of states of matter or nongravitational fields are admissible in a spacetime model. This is both a strength, since a good general theory of gravitation should be maximally independent of any assumptions concerning nongravitational physics, and a weakness, because without some further criterion, the Einstein field equation admits putative solutions with properties most physicists regard as unphysical, i.e. too weird to resemble anything in the real universe even approximately.

The energy conditions represent such criteria. Roughly speaking, they crudely describe properties common to all (or almost all) states of matter and all nongravitational fields which are well-established in physics, while being sufficiently strong to rule out many unphysical "solutions" of the Einstein field equation." *

[ https://www.physicsforums.com/threads/explanation-of-red-shift.775390/page-2#post-4894004 ]

I don't see any problem with this... and this is done already.

If you had read through the thread, you can see that we already have covered this:

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).

Meaning that if you introduce some energy condition over large enough volumes, you will also see that cosmological redshift obeys it.

(If the energy of the universe is zero as it seems, well then, redshift doesn't change that. But if you want to pick the system apart, you will have to tediously calculate the energy for each part.)

*This is very like the description of quantization in quantum field theory. That too will generate unphysical (there non-relativistic) solutions it is claimed, so they have to check that specifically afterwards.

Meaning there is nothing special about having, and solving, such difficulties.

 

[Drakkith]

There is none of GR in the concept of space expansion.

...what? The metric expansion of space is only described by GR. There is no other theory that explains it.

GR preserves energy very well, what just Neother showed and proved long ago,
therefore yours imaginations contradicts the GR also!

That is incorrect, just as Torbjorn explained.

You should to provide reference, together with these illuminated cosmologists, about disproof of the energy-momentum conservation principle.

Once proven, remains proven forever...

Here's an excellent explanation by Michael Weiss and John Baez: http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html
And one by Sean Carroll: http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

 

[Bandersnatch]

You should to provide reference, together with these illuminated cosmologists, about disproof of the energy-momentum conservation principle.

Isn't that what Noether's 2nd theorem in her Invariante Variationsprobleme does?

 

[presto]

I see you have a great problem with the energy conservation, because of the gravitational redshift effect.

There is none problem with this!

Just an emitter placed lower - in a stronger gravity (lower potential),
radiates lower energy at start already, thus we get the lower energy,
and it's exactly what was emitted by the source, not less!
Eout = Ein = inv.

 

[presto]

Here's an excellent explanation by Michael Weiss and John Baez: http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

This looks like a proof of the energy conservation in the expanding universe.
Therefore this is automatically a disproof of any light stretching in a fly, wrongly presupposed by the astro...logists. :)

 

[Drakkith]

This looks like a proof of the energy conservation in the expanding universe.
Therefore this is automatically a disproof of any light stretching in a fly, wrongly presupposed by the astro...logists. :)

Then you should re-read the article again, as it most definitely does not prove that energy conservation exists in GR in all circumstances. In fact, the very first line gives us an idea of the difficulties when it says, "In general — it depends on what you mean by "energy", and what you mean by "conserved". It also does not say that light does not stretch in an expanding universe. In fact, one of the main sections of the article deals with this redshift. I recommend you actually make an attempt to read and understand the article completely before trying to use it as evidence for your own point of view.

Note that it's not accurate to say that energy isn't conserved in GR. The fact is that energy conservation in GR is a complicated issue and you may or may not have energy conservation depending on what you mean by energy and by conservation, along with how you do the math.

 

[Drakkith]

I see you have a great problem with the energy conservation, because of the gravitational redshift effect.

That is incorrect. Gravitational redshift and cosmological redshift are two different things.

 

[ricardo81]

Well :) I came across something that had mentioned that the maths is well understood, though physicists have a hard time agreeing on the wording of it. I can relate to that being a programmer.

Perhaps one day I'll brush of my understanding of mathematical notation and the symbols for well-known constants to try and have a stab for my own understanding.

It is fascinating, for me I think the answers are towards the Planck length and as a Layman it seems to be that there's two separate scales, down there, one larger than the other. Relativity is sometimes described as a matrix of clocks with their own time frame... I like the idea of it actually being a matrix of processors processing the information across space-time. It seems like things like redshift perhaps hint towards a computational ceiling. Anyways, that's just some blurry thoughts from an amateur :) (the two scales would be one processor sized one and the smaller one would be 1 bit of information within)