# Is expansion meaningless where it is not measurably happening?

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On 9/23/2022 at 12:59 PM, MigL said:

The fact is, the universe is only expanding at certain scales; below those scales, galaxies may actually be coming together, such as our galaxy and Andromeda, because the gravitational coupling exceeds the 'dark energy' of the expansion.

IOW, expansion is distance ( scale ) dependent.

I was about to reply to this saying basically that I think that space is expanding at all scales, but on smaller scales (even between Milky Way and Andromeda), gravity overwhelms expansion so that the galaxies are "moving through" space relative to each other faster than expansion can separate them. A google search shows only results that disagree with my view, and seem to suggest that if two things (in an otherwise empty universe, say) aren't separating, then I guess there's no meaningful way to say that that space is expanding? If two more-distant galaxies are separating at an increasing rate due to expansion, people use phrases like, "gravity has no effect at those distances" due to expansion, which is also not what I thought.

Say for example you have 2 masses in an empty universe where their gravitational attraction exactly balances expansion of space between them, so they remain at a fixed distance.

Would you say, space is expanding between them, but gravity accelerates them through that space at a rate that keeps them at the same distance? Maybe even there is a measurement that shows that gravity still applies and that expansion is also happening.

Or would you say there is no expansion of space and no gravitational effect between the 2 masses in this system? It's nonsense to say the masses are moving through space or accelerating, because those only make sense relative to something else, and they're not moving relative to anything. There is no way to distinguish expansion and gravity, because any effect (like redshift) of expansion that would otherwise cause the 2 masses to separate, would be exactly cancelled out by an opposite effect of gravity that would otherwise cause the 2 masses to converge, and so no such effects are measurable.

Is either correct?

Could you also say that "gravitational effect" and "expansion" are just emergent effects of the metric, and are not fundamental and separate parts of the metric or the universe? It is the metric that has these two masses relatively stationary, and gravitational attraction and expansion are simply zero for these 2 masses? If so, then I think you could model or label the system so there is both a gravitational effect and expansion of space between the 2 masses, but you would only do that if you had a reason to separate them, otherwise it is simply an unnecessary complication.

It seems, I shouldn't think of expansion as some intrinsic process that's happening throughout the universe, but is just a measurement that is a consequence of our universe's particular metric tensor?

Edited by md65536
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My take on this, is that expansion is due to some effect like the Cosmological Constant, an 'add-on' to the EFE, such that gravity is 'modified' by it, and the two are linked.
It acts like a 'step' potential such that when gravity ( the terms other than the CC ) exceed that 'step', at close distances, gravity prevails.
If gravity (terms other than the CC ) is below the 'step', at large distances,then expansion prevails.

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The cosmological constant (CC) is associated with vacuum energy and its corresponding expansion, which is the accelerating expansion that dominates on the largest scales. There's also expansion (or contraction) in the Einstein field equation (EFE) without the CC (as in the original form of the EFE which didn't have the CC. The CC was first added to try to avoid expansion/contraction and allow for a steady-state universe). So, not all of expansion is an 'add-on'.

That might provide the answer I was looking for. If the vacuum energy is contributing an expanding influence to the curvature of spacetime that is still present even at small scales, but the Einstein tensor overwhelms it and the net effect is no expansion or even contraction at small scales (eg. within a galaxy), then there's simply no expansion. So expansion is the end result, meaning space between comoving stuff is actually increasing, rather than just a component such as the influence of vacuum energy alone.

I think my mistake is in thinking of space as a thing that is independent of the stuff in it, where for example the vacuum can expand without the stuff moving apart. I think I should consider it just as coordinates, but quickly get lost trying to think of expansion that way.

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My take (my probably overvalued \$0.02) is that the expansion is more or less constant at large scale...so using that reference frame most objects are moving gravitationally through that space. I don't see the expansion "overwhelmed" by gravitationally bound objects any more than I would see it that way if I jumped off a truck...

So essentially I think similar to first thoughts in the original post, but I realize there are other ways of considering it and defining a reference frame, inertial or otherwise.

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I read once that expansion is everywhere, even 'pushing' apart the atoms in your body, but of course to an unmeasurable extent. This happens because the expansion energy exists whether or not there is matter present.

The analogy I use (don't know if it is necessarily a good one...) is imaging a ball bearing on a table with a magnet to the right of it and them representing the two masses, and a fan to the right of both and blowing toward them. The breeze is analogous to expansion and it always has an effect on the ball bearing, trying to push it away. The closeness of the magnet and ball bearing determine whether the ball bearing moves away, remains in place, or rolls toward the magnet.

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4 hours ago, zapatos said:

The analogy I use (don't know if it is necessarily a good one...) is imaging a ball bearing on a table with a magnet to the right of it and them representing the two masses, and a fan to the right of both and blowing toward them. The breeze is analogous to expansion and it always has an effect on the ball bearing, trying to push it away. The closeness of the magnet and ball bearing determine whether the ball bearing moves away, remains in place, or rolls toward the magnet.

I think it's confusing because the expansion "breeze" would have to blow in all directions and not push on the ball bearing at all. But, the idea of expansion contributing and gravity contributing to the whole, makes sense.

As for atoms expanding, what I've read is that that would only happen if the vacuum energy increased boundlessly, so that the scale at which expansion dominates gets smaller over time, approaching zero. But that would be speculative.

I thought of 2 analogies that help me make sense of this.

1. Imagine the Earth is a perfect sphere and it's expanding uniformly. A rigid tectonic plate or island could represent a gravitationally bound region. This is analogous to universal expansion at all scales, since even though the island doesn't change in size, the underlying size of the Earth's surface does. Note that for the island to stay a fixed size, some other part of the crust would have to expand more than the average expansion, for the whole Earth to expand uniformly.

2. Imagine a patch of live skin cells that all slowly divide over time, so that any given area of skin doubles over some long time. A scab or patch of dead cells on it could represent a gravitationally bound region. In this case it's not needed for another area to expand faster to make up for the scab, because the whole isn't expanding with global uniformity and the distortion caused by the scab would be like curvature of spacetime.

I think the second is a closer analogy to expansion in the universe, because it's attributed to local vacuum energy rather than some global expansion of the volume of space. I think the island analogy is wrong in that it confusingly represents space both as the crust (including the island) but also as some extra underlying thing that doesn't have a real analog in the universe.

But beyond analogies as thought experiments, I think the technical answer needs to be based on the actual definition of expansion. Expansion refers to "metric expansion" which is a change in the measure of distance itself, rather than just a change in the distance between specific things. Well that's not helpful to think about, but what does it mean? The closest I've seen to a description of the technical meaning of expansion is that it involves a divergence of geodesics over time. I think in the case of a static gravitationally bound region, geodesics wouldn't diverge. It wouldn't matter how the rest of the universe was expanding, it would be like tattooed lines on a rigid scab.

The geodesics would be like the fan and magnet contributing to a whole, or vacuum energy and gravity contributing to one metric. It would not be like the Earth analogy where one could imagine separate geodesics for an expanding Earth and a static island through the same place.

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Well I changed my mind again. Geodesics aren't some set of lines that remain fixed relative to absolute space, because there is no such thing. Whether something's moving or not will always (I think) involve a choice of coordinates. Also, whether 2 masses are gravitationally bound depends not just on their locations, but their relative velocity. So for example, two comoving fairly distant galaxies can be unbound and separating due to expansion, while two similarly located galaxies can be gravitationally bound just by giving them enough velocity toward each other (basically an "unescape" velocity to overcome expansion).

So I think the answer to whether some specific effect is expansion or not, can depend on a choice, and doesn't have a single answer. To get around that, the definition exists only where it is applicable, eg. per wikipedia "The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time." As well, to say whether something is moving or not, "comoving coordinates" are used, not because that represents absolute motion or anything, but because most of the observable universe approximately fits them pretty well.

I think whether expansion is occurring on smaller scales between gravitationally bound masses is literally undefined, and a definitive answer would require some extra definitions and that would necessarily involve making some arbitrary choices of what's moving and what's not.

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1 hour ago, md65536 said:

I think whether expansion is occurring on smaller scales between gravitationally bound masses is literally undefined, and a definitive answer would require some extra definitions and that would necessarily involve making some arbitrary choices of what's moving and what's not.

But expansion involves space, not matter, correct? Matter is not moved by expansion. For expansion to not occur on smaller scales seems to imply that matter is stopping expansion. Just because gravitationally bound objects don't separate due to expansion, I don't think we can conclude that space in that area is not experiencing expansion.

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<Preliminary>

I think one thing is how the motion of galaxies would be perceived by typical "galactic observers" (those people sharing the same galaxy and observing whatever other galaxies there are around), and another thing is how they would observe gravitation to work within their own galaxy. Yet another thing is what they would make of any other "components" of gravity (vacuum energy, spatial curvature) if there is nothing around as a reference. There's also the question whether that model of universe is consistent with Einstein's equations. It's an interesting question.

</end Preliminary>

My best guess is that your universe would be mathematically consistent, the galactic observers would notice nothing peculiar about gravitation in their own galaxy, but they would see a point in the sky that's always there, with no receding velocity of any kind, and  changing in luminosity and features as it evolves, as both galaxies grow old, with the natural delay that we all know. But they would be clueless as to what keeps it there, assuming they would ever get to extrapolate that gravity was also valid for cosmic objects.

The main problem I see is that this universe would be unstable, so the situation wouldn't last --in cosmological times. This is similar to Einstein's initial proposal of a static universe with a cosmological constant that's just so tuned to keep everything in place at large scales. I'm not sure if that's what @MigL means by "step" solution. There would certainly be a jump in the sign under even the slightest pertubation --let's say a bunch of more photons than average escape in the direction opposite to the "neighbouring" galaxy, and bam, the galaxies start separating forever.

I've been playing with the model mathematically a little bit, and it seems to be consistent. I've taken as a basis the FRWL universe at large scales. Because the universe is mostly nothing (just two galaxies), assuming there's no radiation background, no DM, just k (spatial curvature) and vacuum energy. Don't forget that k, the spatial curvature, is an observational piece of input, as well as the vacuum energy and the density of different stuff. If you feed k=0 (which is what we observe in our universe), it certainly gives a static universe. Of course, you can't see the galaxies in the model, because the FRWL model is valid as an average for enormous scales of this mostly empty space-time that keeps expanding and expanding. So, as @zapatos says, who is to tell spacetime isn't expanding even when there's nothing in it?

But I wouldn't worry too much, because one cannot measure empty space expanding with mostly nothing in it.

All this, of course, is just my take, and presented as contingencies based on the models we know and how I understand them.

1 minute ago, joigus said:

--let's say a bunch of more photons than average escape in the direction opposite to the "neighbouring" galaxy, and bam, the galaxies start separating forever.

LOL. Ok. A bunch of more photons than average escape in the direction towards the "neighbouring" galaxy, and bam, the galaxies start separating forever.

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21 hours ago, zapatos said:

But expansion involves space, not matter, correct? Matter is not moved by expansion. For expansion to not occur on smaller scales seems to imply that matter is stopping expansion. Just because gravitationally bound objects don't separate due to expansion, I don't think we can conclude that space in that area is not experiencing expansion.

But what is space without matter? Isn't it just distance, and specifically distance between things? Isn't the vacuum itself observer-dependent? Space isn't made of some "stuff" that is measurable independent of other things, I think.

Anyway I think scientific answers don't depend on those questions, because science deals with definitions and measurements. If expansion is defined as "expansion of the metric", and not of "space", then it doesn't matter what space is. If expansion is defined only for gravitationally unbound objects, and defined as their increasing separation, then I think there's no expansion without that separation, and no way to apply it to gravitationally bound masses.

But yes, it doesn't make sense that matter would "stop" expansion. For example, consider 2 comoving distant galaxies that are separating due to expansion. Then say there are 2 gravitationally bound small masses somewhere between them. There is metric expansion between the 2 galaxies. It seems fine to say that space is expanding everywhere throughout the distance between them. What is happening between the 2 small masses? The definitions can answer that! In comoving coordinates, the galaxies have fixed coordinates, and the measure of distance itself is increasing. In these coordinates, for the 2 smaller masses to remain a fixed distance from each other in their local coordinates, one or both must be changing location in comoving coordinates. That gives the answer, that space is expanding between the gravitationally bound masses and they're moving through that space (at the very least mathematically!).

But then, we can also consider the local coordinates of the gravitationally bound masses, where in this example they're stationary. You really can say that the masses aren't moving through space (which means nothing more than that they're not changing location in these coordinates).

The metric is covariant but I'm still not sure if expansion would be something that is an absolute part of the metric, or dependent on the coordinates.

I think it's reasonable to say "space is still expanding here" but with the implication that it's referring to space generally, or in other coordinates, not space in local coordinates.

19 hours ago, joigus said:

A bunch of more photons than average escape in the direction towards the "neighbouring" galaxy, and bam, the galaxies start separating forever.

Interesting, I hadn't thought of the physics of the model beyond being an example. I think that even a bunch of photons scattered in all directions would start separation because of decreased mass density.

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10 minutes ago, md65536 said:

Interesting, I hadn't thought of the physics of the model beyond being an example. I think that even a bunch of photons scattered in all directions would start separation because of decreased mass density.

Absolutely.  Good point. In the small scale, the solution would be unstable, and galactic observers would be able to tell there is expansion IMO.

On second thought, you would need the minutest assymetry, and appealing to conservation of momentum. If it's just photons being lost in every direction, I think you could prove, based on the equivalence pple. that if either one of the galaxies is loosing them isotropically, as the CM of both would be placed exactly the same.

Does that makes sense to you? I would have to go over the arguments more carefully. I'm using Newtonian approximation for the galaxies in my reasoning.

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I would think that if we draw a gravittional potential vs radial separation graph, we would get a curve asymptotic to the GP ( y axis ) and RS ( x axis ) of the 1/x type.
Similarly, a dark energy plot on the same graph, would be a GP =CosmologicalConstant horizontal line ( y= Const ).

Where the two plots cross, would be the radial separation where expansion becomes dominant and overwhelms gravity.

( disregarding  any initial velocities/accelerations )

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11 hours ago, joigus said:

the CM of both would be placed exactly the same.

Yes, but the effect of gravity would diminish as the energy was carried away. This is what I thought you were talking about when you first mentioned photons. In a Newtonian analysis, a symmetric "shell" of outbound photons (or an expanding shell with mass equivalent to the photons' energy) would stop attracting a mass to the center of the shell as soon as the mass was inside the shell (shell theorem, which also implies the gravitational effect would not diminish before that happened). Based on that, you could reason something like, the photons from the first mass that pass by the second mass stop attracting the second mass toward the first, and start attracting it away.

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5 hours ago, md65536 said:

Yes, but the effect of gravity would diminish as the energy was carried away. This is what I thought you were talking about when you first mentioned photons. In a Newtonian analysis, a symmetric "shell" of outbound photons (or an expanding shell with mass equivalent to the photons' energy) would stop attracting a mass to the center of the shell as soon as the mass was inside the shell (shell theorem, which also implies the gravitational effect would not diminish before that happened). Based on that, you could reason something like, the photons from the first mass that pass by the second mass stop attracting the second mass toward the first, and start attracting it away.

Right. You've convinced me. The EP is only valid locally, so I didn't apply it correctly. Now matter how you look at it --once you consider the galaxies are not constant-- the situation would be unstable for the two galaxies.

If not for the loss of mass, the slightest anisotropy, or assymetry between both, would be enough to make the situation unstable for the galaxies, and they would be able to tell --eventually-- that spacetime is expanding.

11 hours ago, MigL said:

I would think that if we draw a gravittional potential vs radial separation graph, we would get a curve asymptotic to the GP ( y axis ) and RS ( x axis ) of the 1/x type.
Similarly, a dark energy plot on the same graph, would be a GP =CosmologicalConstant horizontal line ( y= Const ).

Where the two plots cross, would be the radial separation where expansion becomes dominant and overwhelms gravity.

( disregarding  any initial velocities/accelerations )

Ah, got it. That's what you mean by "step" right?

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6 hours ago, joigus said:

If not for the loss of mass, the slightest anisotropy, or assymetry between both, would be enough to make the situation unstable for the galaxies, and they would be able to tell --eventually-- that spacetime is expanding.

I agree, but then the topic's question could be reframed by that. Our universe and this toy universe are expanding due to vacuum energy or dark energy, but it would collapse if gravity was increased (put everything closer together, and/or add more mass). So if there was still this vacuum "expanding" influence on everything, but the universe collapsed, is there any way in which it could be said that the space itself is still expanding? Or is the metric still expanding?

I no longer think this is a scientific question because the definition of expansion (as far as I know it) just doesn't apply. I think the question might be philosophical, and similar to asking "what is the true nature of the universe beyond what can be measured?"

Conversely, for example say you have a toy universe with vacuum energy but where everything is gravitationally bound and collapses, except for one particle that is distant and not gravitationally bound, and separates at an ever-increasing rate. This fits the definition of expansion and I'd say that the space between the particle and the rest of the universe is expanding. This might be a stretch because the definitions are based on a universe that appears homogeneous.

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49 minutes ago, md65536 said:

[...] is there any way in which it could be said that the space itself is still expanding? Or is the metric still expanding?

The metric itself is not a proper observable, really. What's a proper observable is the combination of derivatives of the metric and the metric coefficients themselves that makes up the components of the Einstein tensor.

I still think this expansion would make sense in that it would reflect deviations from a model of universe with just matter density and spatial curvature. That, of course, provided the denizens of this universe had an individual --say Alf-- who was capable of deriving Alf's equations by just sitting and thinking about people falling in a gravitational field. That's what it took Einstein, if you think about it.

Denizens of this universe, would be able to infer that Alf's equations allow for the addition of a term (constant)x(metric) that doesn't make any difference in the equations. So they would start thinking about this and at some point propose measuring this constant by measuring deviations from pure matter-density and spatial curvature solutions, perhaps by sending "people" far away and making measurements. The fact that something is very difficult to measure doesn't necessarily mean it cannot be measured, at least in principle.

If you do have that other galaxy, perhaps you could devise high-precision methods to measure that deviation.

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On 9/30/2022 at 2:32 PM, joigus said:

I still think this expansion would make sense in that it would reflect deviations from a model of universe with just matter density and spatial curvature. [...] The fact that something is very difficult to measure doesn't necessarily mean it cannot be measured, at least in principle.

Yes, that seems valid. It doesn't matter whether they would measure it or find meaning in it, just that it's possible they could. It seems their meaning would basically be, "if there were other things not bound by gravity, the space between them is expanding."

Just to add to what it all means: From https://en.wikipedia.org/wiki/Expansion_of_the_universe

Quote

A metric defines the concept of distance, by stating in mathematical terms how distances between two nearby points in space are measured, in terms of the coordinate system.

[few paragraphs later...]

Specification of a metric requires that one first specify the coordinates used.

Expansion of our universe is stated in terms of comoving coordinates where general galaxies (or "comoving observers") that have not been accelerated by forces or gravity, have fixed spatial coordinates. Their distances would be considered at a common comoving time, where "The comoving time coordinate is the elapsed time since the Big Bang according to a clock of a comoving observer and is a measure of cosmological time."

So for example if you had 2 galaxies not gravitationally bound to each other, on a line, one located at (0) in comoving coordinates and the other at (1), we say their locations are fixed and that the measure of distance between them is increasing. Say we call the distance between them "one intergalactic unit", which I just made up. Here, the meaning of "the measure of distance itself (in these coordinates) is increasing" is that an intergalactic unit is equal to an increasing number of lightyears, over time. The measure of a lightyear can remain fixed. It doesn't mean that every possible measure of distance is increasing, which would be meaningless (see several other threads) because a change in a measure of distance is relative to something else.

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