How does the expansion of the universe work?

[Micheth]

It is if you are looking at the motion of objects that are not bound. See below.
Yes, as long as A and B are not bound. But if A and B are bound, expansion does not introduce anything extra that the binding between them must overcome.

But if the expansion applies equally to all aspects of the universe, even bound A&B would have been further distant from each other had they not been bound, correct?
Therefore, their being bound (i.e. not being further distant from each other, = not moving apart) must have overcome what would have been the increased distance.
I don't see how that can't be the case?

 

[PeterDonis]

if the expansion applies equally to all aspects of the universe,

It doesn't. That's the point I'm making. You are trying to apply the concept to something it doesn't apply to.

 

[Micheth]

It doesn't. That's the point I'm making. You are trying to apply the concept to something it doesn't apply to.

But why wouldn't it apply equally to everything everywhere?
Wouldn't the safest assumption be that it does?

 

[PeterDonis]

why wouldn't it apply equally to everything everywhere?
Wouldn't the safest assumption be that it does?

No. The safest assumption is that it only applies where we observe it to apply--to the average motion of the matter in the universe on large scales, tens to hundreds of millions of light-years and larger. On smaller distance scales we observe systems to be bound--galaxy clusters, galaxies, solar systems, stars, planets, etc.

But that's not really the best way of asking the question. The best way of asking the question is to look at the actual model of the universe that is used in cosmology, and ask what it actually says about expansion. When you look at the actual model, you find that it treats the matter and energy in the universe as a continuous fluid, not a collection of objects. Expansion in the model corresponds to a decrease over time in the density of the fluid. But this is obviously not a correct model on all scales; the universe is not filled with a fluid of uniform density that slowly decreases over time. So we can't expect to use the concept of "expansion" on distance scales where the distribution of matter is obviously not uniform. We can only use it in an average sense, on distance scales large enough that we can view the matter as being uniform to a good enough approximation.

Furthermore, in the model, the expansion (leaving out dark energy) is not due to any force that is making space expand; it is purely due to the inertia of the matter and energy. In other words, on average, the matter and energy in the universe is flying apart because it was flying apart in the past, not because there is anything pushing it apart. So matter that is not flying apart--matter that is bound--doesn't have to overcome anything to keep from flying apart.

 

[Micheth]

Micheth said: ↑
why wouldn't it apply equally to everything everywhere?
Wouldn't the safest assumption be that it does?

No. The safest assumption is that it only applies where we observe it to apply--to the average motion of the matter in the universe on large scales, tens to hundreds of millions of light-years and larger. On smaller distance scales we observe systems to be bound--galaxy clusters, galaxies, solar systems, stars, planets, etc.

That makes me wonder, what about the "inbetween" scales...?
If there is no separation between objects (or fluids) on "smaller scales" (galaxy clusters as smaller scales hurts my brain! :-) ) but only on larger scales, then what about say, galaxies that are not technically gravitationally bound but affecting each others' movements by their mass?
Would they be flying apart only somewhat, but not by the full amount of the spatial expansion?

Furthermore, in the model, the expansion (leaving out dark energy) is not due to any force that is making space expand; it is purely due to the inertia of the matter and energy. In other words, on average, the matter and energy in the universe is flying apart because it was flying apart in the past, not because there is anything pushing it apart. So matter that is not flying apart--matter that is bound--doesn't have to overcome anything to keep from flying apart.

This is the first time I've heard that spatial expansion is due to the inertia of the matter...? (Was understanding it has a property or activity of space itself, with matter just being a passive passenger. Oh well.)
But if the expansion is due to the inertia of the matter moving out in all directions, then that begins to sound to me more like a "conventional explosion" that we're supposed to be getting out of our heads when trying to understand the Big Bang...

 

[Jorrie]

then what about say, galaxies that are not technically gravitationally bound but affecting each others' movements by their mass?
Would they be flying apart only somewhat, but not by the full amount of the spatial expansion?

Despite what Peter stated in general, yes, this is exactly why we have structure in the matter of the universe. When there is a local over-density (higher than the average), increase in distance between those objects will be slower than the 'Hubble flow' for their distance apart. Especially in a decelerating phase of expansion, at a certain distance/density regime they will start to free-fall towards each other and possibly go into orbit around a gravitational center. If the energy distribution was completely homogeneous, this could not have happened.

But if the expansion is due to the inertia of the matter moving out in all directions, then that begins to sound to me more like a "conventional explosion" that we're supposed to be getting out of our heads when trying to understand the Big Bang...

I suppose it is a case of interpretation, but as Peter said, the inertia is about the total energy content of the space, including matter, radiation and possibly dark energy. One could rather think about it as "space flying apart" and it is doing so from everywhere, not from some "point of explosion". Exactly how space started to fly apart is not certain, but there are viable theories for that.

 

[PeterDonis]

If there is no separation between objects (or fluids) on "smaller scales"

That's not what I said. I said that if we look on smaller scales, objects may be bound together (a galaxy cluster or galaxy or solar system is bound by gravity; a star or planet is bound by gravity and intermolecular forces). Objects that are bound can still be separated by some distance.

what about say, galaxies that are not technically gravitationally bound but affecting each others' movements by their mass?

The overall mass of the universe affects the motion of everything. In a model with no dark energy, the expansion gradually slows down over time (this was happening in our universe up until a few billion years ago when the effect of dark energy became significant). This gradual slowdown is due to the gravity of the matter. (The gravity of the matter is still there if dark energy is significant, like it is in our universe now; it's just that the slor wawdown due to gravity is less than the speedup due to dark energy.)

Would they be flying apart only somewhat, but not by the full amount of the spatial expansion?

Here is a better way of describing what you're trying to say here: there is an average motion of the matter in the universe, which we describe as "expansion". But individual objects or systems--galaxy clusters, galaxies, solar systems, stars, planets--might not be moving with exactly the average motion. One main reason for that is the gravitational effect of individual objects or systems on other individual objects or systems. This effect is not included in the cosmological models that describe the "average" motion, any more than the motion of the individual molecules of a fluid, due to interactions between the molecules, is included in the models that describe the fluid as a continuous substance.

This is the first time I've heard that spatial expansion is due to the inertia of the matter...?

It's not often phrased that way, but that's what the model says. (I'm about to post a response to Jorrie that elaborates on this somewhat.)

 

[PeterDonis]

One could rather think about it as "space flying apart"

But there is a problem with thinking about it this way: it leads to incorrect inferences like the one Micheth is drawing, that leads him to ask the questions he's asking, which make perfect sense given the interpretation of "space expansion" that he is using--it's just that that intepretation is not correct, given the actual physics. If you think of "space flying apart", you naturally think of that as a causal agent, something that can push objects apart, that needs to be "overcome" by bound systems in order for them to remain bound. But there is no such causal agent in the actual model that cosmologists use.

"Space expansion" is just an artifact of using a particular coordinate chart; we could, if we wanted to, set up a chart in which there was no "space expansion". The actual physics is contained in invariants, and there is no invariant in the model that corresponds to "space expansion pushing things apart". In the model, things are flying apart because they were flying apart in the past--i.e., it's purely due to inertia. As I noted previously, this model only describes the average motion of the matter in the universe; individual objects or systems can have different motions from the average motion, and those motions can be affected by the gravity of other individual objects or systems, just as you describe. But again, you can account for the motion of those individual objects purely by looking at inertia plus the gravity of other individual objects; there is no extra effect you have to include due to "space expansion".

 

[tedbmoss]

so does the universe expand to infinity? will atoms eventually fly apart?

 

[PeterDonis]

does the universe expand to infinity?

According to our best current model, the universe is already spatially infinite.

will atoms eventually fly apart?

According to our best current model, no. As I said in previous posts, the expansion itself exerts no force on bound objects. There is a very tiny force due to dark energy (which causes accelerated expansion, not expansion per se), but according to our best current model, it is constant and therefore will never cause atoms (or any bound systems we currently see) to fly apart.

 

[phinds]

so does the universe expand to infinity? will atoms eventually fly apart?

Just to add to Peter's post, if the universe is now finite then no, it could not possibly "expand to infinity" since finite things cannot becomes infinite. As Peter says, if it is already infinite then it will just continue to get bigger (but that will still be "infinite in extent")

 

[rede96]

This is the first time I've heard that spatial expansion is due to the inertia of the matter...? (Was understanding it has a property or activity of space itself, with matter just being a passive passenger. Oh well.)

"Space expansion" is just an artifact of using a particular coordinate chart; we could, if we wanted to, set up a chart in which there was no "space expansion".

For a layman, this is one thing that still confuses me. It's easier (for me) to think that expansion as simply objects, such as distant galaxies, moving apart due to some initial inertia long ago. Those objects (or energy) that were close enough to be gravitationally bound remain so. That also makes intuitive sense.

But then there are other consequences of expansion such as cosmological redshift of photons that can't be explained by inertia. The wavelength of a photon is lengthened due to expansion (which is different than Doppler shift.) and the explanation often given is that this is due the 'space' expanding as the electromagnetic wave travels through it.

So we can't really think of expansion as just inertia.

From what I understand about inflation (pre big bang expansion) the theory is that there was some very high energy scalar field (high as in compared to todays vacuum energy) which led to the universe (whatever was the universe at that time) to inflate exponentially (e-foldings) many times to almost the size it is now. In the process this field collapsed and in doing so created the particles we know from the standard model.

So my way of understanding it is that this inflation process created the initial inertia, but not only for the particles but also for what ever constitutes empty space. As it is a scalar field it wouldn't dilute as it grew. So expansion can be thought of as inertia in that sense. And that seems to have something to do with why a photon losses energy as it travels through space (Again, just my way of thinking about it!)

Also, as the FRW equations are basically energy conservation, then I would have thought that the energy that the photon loses is transferred back into this 'potential energy' of empty space or in other words, back into this expanding scalar field which we call expanding space. EDIT: I think that should be kinetic energy of expanding space, not potential. Like I have said, this is really just my way of thinking about it.

 

[PeterDonis]

there are other consequences of expansion such as cosmological redshift of photons that can't be explained by inertia

That's true; but it can't be explained by "space expansion pushing things apart" either. See below.

the explanation often given is that this is due the 'space' expanding as the electromagnetic wave travels through it.

Yes; in fact the best quick way of interpreting the redshift of an object is as a measure of the ratio of the scale factor of the universe at reception to the scale factor at emission. For example, light we are seeing with a redshift of $z = 1$ was emitted when the scale factor was $1 + z = 2$ times smaller than it is now. This is often described as the expansion of space "stretching" the waves.

However, there is a problem with this if we interpret this "stretching" as exerting some kind of actual physical force on the light: there is nothing in the model corresponding to any such force. The redshifted light we see from distant galaxies freely propagated from them to us through empty space. It wasn't confined in a waveguide or a fiber optic cable or anything of the sort--those are ways that we can "exert force" on light in the laboratory in order to change how it propagates. Nothing like that is being done to the light we see from distant galaxies, and nothing in the model corresponds to any such thing.

IMO this just illustrates that we can't always expect curved spacetime to correspond to our intuitions about how "space" and "time" work. The way to fix that is to fix our intuitions, or at least to know not to give them weight unless we can show, using the actual mathematical model, that there is actual physics that corresponds to them.

my way of understanding it is that this inflation process created the initial inertia

For the matter and energy that was hot, dense, and rapidly expanding immediately after the end of inflation, yes. See below.

but not only for the particles but also for what ever constitutes empty space

Not in the sense you mean it, no. Empty space does not have"inertia. A scalar field does, but a scalar field is not empty space. (Neither is dark energy, which according to some models is a very, very tiny bit of the inflaton field that was left over after inflation ended.)

that seems to have something to do with why a photon losses energy as it travels through space

No, it doesn't; the cosmological redshift does not have anything to do with "inertia of empty space" (since there's no such thing, see above), or with any scalar field or dark energy. The reason light from distant galaxies is redshifted when we observe it has no simple intuitive picture that corresponds to it; both of the commonly used intuitive pictures--that it's just a Doppler shift due to the galaxies moving away from us, and that it's due to the light being stretched by the expansion of space--have serious limitations (your post illustrates the limitations of the latter interpretation--the limitations of the Doppler shift interpretation become obvious when we consider redshifts large enough that the implied speed of the emitting galaxy away from us diverges significantly from the "recession velocity" that appears in the FRW cosmological models). Again, the way to fix that is to retrain your intuitions, or at least to know enough not to give them weight in this instance.

 

[rede96]

That's true; but it can't be explained by "space expansion pushing things apart" either. See below.

Sure, I agree that we shouldn't think of expansion as some force pushing things apart. But general expansion (not including dark energy) does exert a very tiny, tiny pressure. So for example an atom is very, very slightly bigger than it would be if the universe was static. Of course as you have already said that force is so small it really doesn't have any measureable effect and is no where near enough to over come the forces that hold an atom together. However if we place two atoms far enough apart in space, which are at rest wrt each other, then expansion (even without dark energy) will cause the distance between them to grow.

So how I interpret that is expansion can't be due to just past inertia (of matter) alone. This pressure, which must be coming from 'something', must also have an influence on how things move apart, especially things separated by very large distances of course. I'm just not sure what to call this 'something'. Unless its just energy density, which would make sense but it is more than just inertia.

Not in the sense you mean it, no. Empty space does not have"inertia. A scalar field does, but a scalar field is not empty space. (Neither is dark energy, which according to some models is a very, very tiny bit of the inflaton field that was left over after inflation ended.)

Ok, sure. I guess that is just my poor terminology. I think the point I was trying to make is there is something else besides inertia contributing to expansion as mentioned above.

No, it doesn't; the cosmological redshift does not have anything to do with "inertia of empty space" (since there's no such thing, see above), or with any scalar field or dark energy.

Ah ok. But by what process does the photon lose energy? If space wasn't expanding then I assume there would be no energy loss. But as space is expanding and isn't completely empty, then light must be propagating through 'something' and as this something expands slowly, then the energy from the photon is transferred into kinetic energy of the expansion of that 'something'. Does that make sense? But I just don't know what to call it :)

 

[PeterDonis]

general expansion (not including dark energy) does exert a very tiny, tiny pressure.

Please prove this claim by showing, explicitly, where in the math this very tiny, tiny pressure shows up, and how it affects the equilibrium state of a bound system. (The standard GR answer is that there is no such thing in the math, and no such very tiny, tiny pressure. So I don't expect you to be able to do this. But if you can't, you should retract your claim.)

as you have already said that force is so small it really doesn't have any measureable effect

No, that's not what I said. I said that if we exclude dark energy, there is no force at all. I also said dark energy does exert a tiny force, but your claim, quoted above, excluded that.

 

[PeterDonis]

by what process does the photon lose energy?

I think you need to read this article by Sean Carroll:

http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

 

[rede96]

Please prove this claim by showing, explicitly, where in the math this very tiny, tiny pressure shows up, and how it affects the equilibrium state of a bound system. (The standard GR answer is that there is no such thing in the math, and no such very tiny, tiny pressure. So I don't expect you to be able to do this. But if you can't, you should retract your claim.)

I got that from one of Leonard Susskind's lectures on cosmology. (See below, time index 2mins, 37seconds, watch for about 5 mins.) He is answering questions from the previous lecture where they went through the math.

 

[PeterDonis]

(See below, time index 2mins, 37seconds, watch for about 5 mins.)

His statements here are frustratingly vague. I can't tell for sure whether or not he means the effect of dark energy when he talks about a very, very tiny force--or even if he means the same thing each time he talks about it. He doesn't actually show the math that he's referring to, and he mentions dark energy several times but also mentions expansion several times without mentioning dark energy. If he did show the math, I don't think there is anything in the math that he could point to that would show a very, very tiny force in the absence of dark energy. (In the presence of dark energy, of course, there is one, and towards the end of the 5-minute segment you refer to, he does talk about the tiny effect that dark energy has on an atom.)

 

[Jorrie]

If he did show the math, I don't think there is anything in the math that he could point to that would show a very, very tiny force in the absence of dark energy. (In the presence of dark energy, of course, there is one, and towards the end of the 5-minute segment you refer to, he does talk about the tiny effect that dark energy has on an atom.)

I have before used the standard cosmic deceleration parameter to get the "cosmic tidal force" between two ends of a bound structure, based on proper distance D and cosmological time T.
$$d^2 D/dT^2= D H_0^2 (\Omega_\Lambda-\Omega_m/(2a^3))$$
This causes a small force working with or against the internal structure binding forces.
It shows that the only time there is no compression or stretching force on the structure is when $\Omega_\Lambda-\Omega_m/(2a^3) = 0$, i.e. a constant, coasting expansion rate. Long ago, when it was negative, the 'force' was compressing and today, due to Lambda, it is positive and the 'force' is stretching in nature.

Peter, do you agree with this?

 

[PeterDonis]

Peter, do you agree with this?

I agree that, if the universe is matter dominated, its expansion is decelerating, and that if it is dark energy dominated, its expansion is accelerating. That is a way of describing the math you give without using the word "force", which can be misleading.

The reason it can be misleading is that there is a key difference between the two kinds of densities you describe. The matter density $\Omega_m$ is only an average over large distance scales; it certainly does not describe the matter density in, say, the solar system, much less in the space occupied by a single atom. So viewing the deceleration in a matter dominated universe as a "force" that is compressing things is not correct if you try to apply it on small distance scales; it only works as a heuristic way of viewing the average deceleration of the expansion on large distance scales.

The dark energy density $\Omega_{\Lambda}$, OTOH, is, as far as we can tell, actually constant everywhere in the universe. So it actually is the same on the scale of the solar system, or even on the scale of a single atom, as it is on cosmological scales. So viewing the acceleration caused by dark energy as a tiny "force" even on the scale of the atom is correct, because the density of dark energy appearing in the math actually does describe the density on that scale.

So I don't entirely agree with your exposition, because you are lumping together two things--matter density and dark energy density--that actually behave very differently on small distance scales. Your exposition obscures that difference, which is crucial to the discussion we have been having. It is the reason I have been saying that expansion, in and of itself, does not cause any "force" at all on bound systems on small scales, whereas dark energy does cause a tiny "force" on those scales.

 

[Orodruin]

The dark energy density ΩΛΩΛ\Omega_{\Lambda}, OTOH, is, as far as we can tell, actually constant everywhere in the universe.

I agree with the "as far as we know", but going from there to the assertion that it really is a cosmological constant seems like a big leap of faith to me. Do you have any references on the homogeneity of dark energy?

 

[PeterDonis]

I agree with the "as far as we know", but going from there to the assertion that it really is a cosmological constant seems like a big leap of faith to me.

It might be, yes; I wasn't intending to imply that I have any special knowledge on this. I was basing my remarks on the fact that the current "best guess" model attributes it to a cosmological constant. If it turns out that it isn't--that the density of dark energy does vary--then that would make language about a "force" even more misleading, since both kinds of density involved (dark energy and matter) would be variable and both densities appearing in the math would only be large scale averages--neither would be usefully described as producing a "force" on smaller distance scales.

 

[Jorrie]

So I don't entirely agree with your exposition, because you are lumping together two things--matter density and dark energy density--that actually behave very differently on small distance scales. Your exposition obscures that difference, which is crucial to the discussion we have been having. It is the reason I have been saying that expansion, in and of itself, does not cause any "force" at all on bound systems on small scales, whereas dark energy does cause a tiny "force" on those scales.

OK, I agree that we should cut out the "force" idea, but I'm not convinced that the "cosmic tidal acceleration" plays no role in structures.

I also agree that expansion per se (non-accelerating/decelerating) will have zero effect on bounded structure sizes (essentially the orbital radii).
In the case of accelerating expansion (irrespective of which dark energy model used), I think the consensus is that the orbital radii of components of large scale bound structures are a little larger than what they would have been in a ('neutral') coasting phase of expansion.

In the case of decelerating expansion, the issue is whether the orbital radii of components of large bound structures will be a little smaller than what they would have been in a coasting phase of expansion (irrespective of the non-homogeneity model used). The 'Solution to the tethered galaxy problem' of Tamara Davis et. al seems to suggest that it does, as I interpret them. When a long tether between two galaxies is cut during a decelerating phase, the galaxies will swap positions and eventually join the Hubble flow on opposite sides of the initial middle point, even when ignoring the gravitational attraction between the two.

I understand that the effect will be totally swamped by the gravitational field of the cluster, but since we are saying that we must look at the math to understand the effect, we must be able to answer the question "does decelerating expansion cause any tidal effect of compression, however small, on gravitationally bound clusters?" Or something to this effect...

 

[rede96]

I think you need to read this article by Sean Carroll:

http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

Thanks for the link. I did already have a very basic understanding that energy is not conserved in an expanding universe and that the lost energy from the photon is translated into kinetic energy of expansion. Which is why I didn't ask where the energy went, I asked what process causes the photon to lose energy, or in other words what process causes redshift.

As you have said it is not due to inertia of empty space (as there in no such thing.) it is not due to dark energy or a scalar field, so just what does cause redshift? I know the standard answer is 'expansion', but then we go around in circles and ask what causes expansion and just what is 'expanding'

So the point I was trying to make was that there is more going on with expansion that just inertia. Which hopefully I've understood that correctly.

His statements here are frustratingly vague. I can't tell for sure whether or not he means the effect of dark energy when he talks about a very, very tiny force--or even if he means the same thing each time he talks about it. He doesn't actually show the math that he's referring to, and he mentions dark energy several times but also mentions expansion several times without mentioning dark energy. If he did show the math, I don't think there is anything in the math that he could point to that would show a very, very tiny force in the absence of dark energy. (In the presence of dark energy, of course, there is one, and towards the end of the 5-minute segment you refer to, he does talk about the tiny effect that dark energy has on an atom.)

Yes, his comments are very ambiguous. Hence why I might have interpreted them as I did. But he had gone through the math in previous lectures. Well at least how the FRW equations were derived from Newtonian cosmology and from energy conservation.

Anyway, in short what I am really struggling to understand is just what causes two bodies to recede from each other. What I mean by that is if for example I place two bodies sufficiently far apart, in such a way that they are at rest wrt each other, and the forces acting upon them to keep them together are less than the 'pressure' of expansion, then as I understand it, they will start to recede from each other at the Hubble rate. That's basically what I understand from the FRW equations, as you can't have a static universe. So they can only do one of two things, move together or move apart. Moreover I could have done this experiment at any point in time in the past and got the same result.

So there must be some component of expansion that is sort of 'pressure' acting upon these bodies that has always been present. Even if it hasn't always been the dominant component of expansion. And I understand it, we don't need dark energy in the FRW equations to make this prediction. So this pressure, what ever it is, must be different than dark energy.

 

[tedbmoss]

So if I want atoms to "fly apart", due to the "expanding" universe, entropy or age; I am free to design my own cosmology?

 

[PeterDonis]

I'm not convinced that the "cosmic tidal acceleration" plays no role in structures.

The "cosmic tidal acceleration" you refer to is based on looking at a particular family of geodesics, the "comoving" worldlines. But there are other families of geodesics besides the "comoving" ones, and most objects in the universe are traveling on one of those other, non-comoving worldlines. The math you showed only applies to "comoving" worldlines; that's why I said that, at least with regard to the matter in the universe, the math you showed only applies to large scale averages, not to individual objects.

This doesn't mean that the overall spacetime geometry of the universe has no effect on those other worldlines. It just means we have to look at its actual effect on those worldlines, rather than assuming that the effect is the same as on "comoving" worldlines.

In the case of accelerating expansion (irrespective of which dark energy model used), I think the consensus is that the orbital radii of components of large scale bound structures are a little larger than what they would have been in a ('neutral') coasting phase of expansion.

First, I think the consensus assumes that, whatever dark energy model is used, the density of dark energy does not vary very much. If dark energy "clumped" the way ordinary matter does, I think the consensus argument for it exerting a tiny force on all bound structures would not go through, nor would the consensus argument that dark energy causes accelerated expansion! Instead, I think we would expect to see a large force on bound structures (because dark energy would be clumping inside them), and a smaller effect on large distance scales.

Second, I'm not sure the comparison is with "neutral" expansion--I think the comparison is with no expansion. That is, I think the (at least implicit) comparison being made in talking about the size of bound structures is with a model of a bound structure as an isolated system embedded in a background asymptotically flat spacetime.

I'll look at the paper you linked to for the decelerating case.

 

[PeterDonis]

just what does cause redshift?

Here's what I think is the key point: the redshift is not a property of the photon by itself. It's a property of the system consisting of the emitter, the photon, and the receiver.

This is easy to see in the case of ordinary Doppler shift in flat spacetime. An emitter emits a photon. An observer moving towards the emitter sees the photon blueshifted; an observer moving away from the emitter sees it redshifted; an observer at rest with respect to the emitter sees no shift.

What I have just described is the usual way of describing the Doppler shift. But there is another way to look at it, which, unlike the way I just gave, generalizes to any spacetime. When the photon is emitted, it has a certain 4-momentum vector, which carries information about the emitter's 4-velocity (i.e., which direction the emitter is "pointing" in spacetime). The photon's 4-momentum is parallel transported (which is a technical term, but basically means "transported unchanged") along the photon's path through spacetime, until it reaches the receiver. The receiver then compares the photon's 4-momentum with its own 4-velocity (i.e., which direction it is "pointing" in spacetime) to determine whether there is any redshift/blueshift.

So in effect, what is happening is that the directions in spacetime of the emitter and the receiver are being compared by the photon. If the directions are parallel, there is no shift. If the directions diverge, there is redshift. If the directions converge, there is blueshift. What makes the flat spacetime case simple is that "parallel", "diverge", and "converge" have direct physical interpretations as "at rest relative to each other", "moving away from each other", and "moving towards each other".

The cosmological redshift is the same sort of thing, except that the geometry of spacetime isn't flat, it's curved, and the curvature isn't static, it changes with time. So there isn't a simple way to translate the comparison of "directions in spacetime" into physical interpretations as I described for flat spacetime above. But the general method I described still works fine, and you can still work out a correspondence between the comparison of "directions in spacetime" of the emitter and receiver and properties of the universe. When you work it out for the case of a photon traveling between two "comoving" objects in a universe that might be expanding, contracting, or static, using our standard cosmological models, it turns out that the correspondence works like this: "parallel" directions in spacetime for emitter and receiver corresponds to "the universe did not expand or contract during the photon's travel"; "diverging" directions means "the universe expanded during the photon's travel"; and "converging" directions means "the universe contracted during the photon's travel".

So expansion does cause redshift. But on this interpretation, it causes it by making the "directions in spacetime" of comoving objects diverge, not by "stretching" photons. The photon isn't changed at all during its travel (see "parallel transport" above). The expansion affects the emitter and receiver, not the photon. The photon just provides a physical link between emitter and receiver that allows their "directions in spacetime" to be compared.

 

[PeterDonis]

if for example I place two bodies sufficiently far apart, in such a way that they are at rest wrt each other, and the forces acting upon them to keep them together are less than the 'pressure' of expansion, then as I understand it, they will start to recede from each other at the Hubble rate

No. They will start to recede from each other, but if there is a force between them, they won't recede at the Hubble rate at first. Their recession rate will gradually approach the Hubble rate as time goes on. At least, according to the standard cosmological model, they will; but that model doesn't really apply on small distance scales (see below).

The reason this will happen, in the model, has nothing to do with "space expansion" causing a "pressure". It has to do with the rest of the matter in the universe affecting the two objects. Remember that, in the FRW model, the matter in the universe is a continuous fluid, with the same density everywhere. And the "flow lines" of this fluid are expanding--objects at rest relative to the fluid at different spatial locations will be moving apart. So when you put two objects at rest relative to each other into this fluid, at least one must be moving relative to the fluid. And if there is not enough force between the two objects, then the flow of the fluid will pull them apart, because each one is entrained in the local fluid flowing past it. But if there is at least some force between the two objects, the fluid won't pull them apart at the same rate as the fluid itself is flowing--the objects will pull on each other and counteract some of the fluid's effect. But as the objects get farther apart, the force between them will weaken, so their rate of recession will gradually approach the flow rate of the fluid in general (the Hubble rate).

But, as I've said before, there is a huge problem with all of this if you try to apply it to bound systems on small scales: the matter in the universe is not a continuous fluid! It's not even close. The intuitive model of fluid flow sweeping objects apart is simply wrong on small distance scales; that isn't what's happening. To see what might happen on small distance scales, we need a model that applies at those scales.

Here's one such model. On average, as viewed from any point, the matter in the universe is spherically symmetric. In particular, if we pick out a bound system, such as the solar system, and draw a boundary around it (say a sphere one light-year in radius centered on the Sun), the matter outside that sphere will be, on average, spherically symmetric. And there is a theorem called the "shell theorem" which says that, if the matter distribution outside some spherical shell is spherically symmetric, it has no effect on anything inside the shell--we can ignore it completely and just focus on the matter inside the shell when determining what will happen inside the shell. So we can ignore the rest of the matter in the universe when determining what the structure of the solar system will be; we only need to consider the Sun and planets and whatever other objects are large enough to be significant.

The model I just described is what I have been using in this thread. And note that in this model, if the density of dark energy really is constant everywhere, then there is dark energy inside the sphere that bounds the solar system, so it will indeed exert a tiny force and have a tiny effect on the solar system's structure. But the rest of the matter in the universe is not a continuous fluid of the same density everywhere; there isn't any "cosmological fluid" inside the solar system, so it will not exert any force inside the solar system. The only ordinary matter we have to worry about is the ordinary matter we already know is inside the solar system.

 

[PeterDonis]

So if I want atoms to "fly apart", due to the "expanding" universe, entropy or age; I am free to design my own cosmology?

Sure, you can try, but you'll need to make sure it is consistent with all the evidence we already have, and you will need it to make predictions that get verified by experiment. Good luck.

 

[rede96]

Here's what I think is the key point: the redshift is not a property of the photon by itself. It's a property of the system consisting of the emitter, the photon, and the receiver.

Thank you very much for your detailed explanation. I still have to study up on this, but that really helped. Thanks.

 

[rede96]

No. They will start to recede from each other, but if there is a force between them, they won't recede at the Hubble rate at first.

Ah ok, yes of course. And again, thanks for the detailed explanation.

The reason this will happen, in the model, has nothing to do with "space expansion" causing a "pressure". It has to do with the rest of the matter in the universe affecting the two objects.

Your explanation of shell theory got me thinking. If in the example I gave we draw a boundary around the two object's centre of mass, so there was nothing inside this boundary except the two objects placed at rest. Does this mean that everything outside this shell would have no effect? So what would happen then?

 

[PeterDonis]

If in the example I gave we draw a boundary around the two object's centre of mass, so there was nothing inside this boundary except the two objects placed at rest. Does this mean that everything outside this shell would have no effect?

Yes, assuming everything outside the shell was distributed in a spherically symmetric manner (at least to a good enough approximation).

So what would happen then?

Well, you have two massive objects in an otherwise empty space, and they are at rest relative to each other at some instant, and there is nothing else affecting their motion. What do you think would happen?

 

[rede96]

Well, you have two massive objects in an otherwise empty space, and they are at rest relative to each other at some instant, and there is nothing else affecting their motion. What do you think would happen?

I'm not sure as I guess it depends on the initial conditions.But assuming an expanding universe under today's Hubble constant then they would either attract due their gravitational pull being greater than the pull of the Hubble flow or they would recede. But if the recede, I don't know how it could be due to the rest of matter in the universe affecting the two objects as you said as there are only those two objects.

Hence why I keep thinking there must be some 'pressure' acting upon them from expansion.

 

[PeterDonis]

I'm not sure as I guess it depends on the initial conditions.

Um, what? You gave the initial conditions: the two masses are at rest relative to each other at some instant of time, there is empty space between them, and no other interactions are relevant.

assuming an expanding universe under today's Hubble constant then they would either attract due their gravitational pull being greater than the pull of the Hubble flow or they would recede.

There is no "pull of the Hubble flow". None of the rest of the matter in the universe is relevant. See above and my previous posts.

if the recede, I don't know how it could be due to the rest of matter in the universe affecting the two objects as you said as there are only those two objects.

Exactly.

Hence why I keep thinking there must be some 'pressure' acting upon them from expansion.

In other words, you agree that the only relevant interaction is between the two objects; but somehow, instead of accepting the obvious conclusion that the two objects will fall towards each other through their gravitational attraction, you think there must somehow be "pressure from expansion" acting on them? Why? Where would it come from, since we've agreed the rest of the matter in the universe has no effect?

This sort of confusion is why I keep on insisting (and I've done this in a number of threads), that "expansion", in and of itself, exerts no force. The misconception that it does is what leads to confusion like that which you are exhibiting--it makes people unwilling to accept their common sense intuition (that two masses will attract each other) in a situation where the common sense intuition is actually correct! There's enough counterintuitive stuff in relativity and cosmology already; no need to make it worse.

 

[rede96]

Um, what? You gave the initial conditions: the two masses are at rest relative to each other at some instant of time, there is empty space between them, and no other interactions are relevant.

Yes, initial conditions do matter as I didn't think I'd clearly specified them. E.g. how massive are the two objects, how far apart they are and do we assume dark energy or not. Changing those conditions would lead to a different outcome.

In other words, you agree that the only relevant interaction is between the two objects;

No: If there is dark energy present then that is an additional interaction.

you think there must somehow be "pressure from expansion" acting on them? Why? Where would it come from

Space (which includes dark energy)

it makes people unwilling to accept their common sense intuition (that two masses will attract each other) in a situation where the common sense intuition is actually correct!

Not at all, I agree that there will always be an attraction between the two objects in proportion to the inverse square law. But that attractive force does not tell me anything about the relative motion between the two bodies.

But I do agree with you that in the absence of dark energy then the only logical conclusion is that the two bodies would move towards each other BUT I am now thinking that we shouldn't talk about expansion without dark energy, as it is a real part of 'space'. That for me is where the confusion starts. One of the other big confusion factors is when people talk about recession as distant bodies being at rest wrt each other and the space growing between them.