Ask Ethan #64: What happens to matter as the Universe expands? (Synopsis)

Hi Ethan,
So you've explained what happens to individual particles, but what about collections of atoms?
If space is expanding does that also mean that matter becomes less dense over time? Are we all slowly spreading apart?

Could never quite get my head around this question.

Please read my comments from my Weblog.
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Thank you, Pierre

@ Bogdan

collections of atoms... or let's call them molecules :) ... are held together by chemical bonds. Some of them are extremely strong (think diamond). As long as the strength of the chemical bond is stronger than the force of expansion.... matter that is already "connected" will remain to be so.

@Bogdan #1: This question gets asked by at least one person in every single posting by Ethan on the cosmological expansion. Sinisa (#3) gave the right answer, which applies to gravity as well as chemical bonds.

Matter which is bound together is "decoupled" from the cosmological expansion, because the effective force involved in the expansion is too small, by dozens of orders of magnitude. You can do the arithmetic yourself. The current expansion rate is 70 km/s per megaparsec. A megaparsec is 3.26 light years, or 3.1 x 10^16 meters. With those numbers, calculate the hypothetical expansion speed for two atoms in a molecule (separated by about 10^-10 meters). Then compare that to the corresponding speed which the electrostatic force between the atoms at that distance would produce.

Hello Ethan.
Regarding what happens to the matter as the universe expands : In 1993 I published in " Physics Essays" an article called " the proprtional expansion of each and every celestial as the cause of Gravitation" in which I argue that the expansion of a celestial body is proportional to its density.
Following this "density proportional" expansion ,gravity wouldn't be explained by "universal attraction" ( which call for an action- at - distance) but simply by the accelerated expansion of each and every celestial body , following the expansion of the universe. It may bring a different light on how one looks at gravity and the cohesion of matter.
Ref: " physics Essays" , Vol 4 , May 1993.

Michael Kelsey @4 :
Sinisa (#3) gave the right answer, which applies to gravity as well as chemical bonds.

I appreciate the effect of expanding space may be vanishingly small, but is there not at least an important theoretical difference between no effect at all and an effect to small to measure? What happens to a single hydrogen atom isolated in space. Does the electron slowly edge away from the proton, hiding its change of energy in Heisenberg uncertainty, until after billions or trillions of years it spontaneously emits a photon and falls back to a lower energy state at the proper distance from the proton?

David, the forces that pull the atom together are far stronger (at the moment) than spacetime expansion.

It's like asking "When I pull on the rod, it expands, a little, yes, BUT SOME, so why doesn't it just fall apart when I pull on it?".

As time goes on, the acceleration of spacetime expansion will mean that the forces between the components of atoms will at some point be smaller than the speed of expansion over the distance these parts are, um, apart.

And that will be the end of atomic matter.

Then some time later, the expansion of space over the distance between gluons will be bigger than their attractive forces.

End of all baryonic matter.

If is really like stretching a rod, does that not reinforce my point? It will come apart if I pull it hard enough, but if it doesn't, then energy is stored by stretching the bonds between atoms.

If the space inside an atom cannot stretch, does that not mean that the space immediately outside has an increase in its expansion rate? How do we tell one outcome from the other where only a measurement many times smaller then experimental accuracy is required?

I appreciate the effect of expanding space may be vanishingly small, but is there not at least an important theoretical difference between no effect at all and an effect to small to measure?

There is no calculable difference when the effect you are talking about is smaller than the system noise or what we might call kinetic background (maybe not the best terms, but thats the way I think about it). Atoms are constantly buffeted and pushed around by other atoms as well as interacting photons. The expansive force is much much smaller than these. So we would not expect it to have any effect on things like rods because its effect is swamped out by the larger random pushes and pulls the rod feels from things like gas molecules around it. Heck, its probably swamped out by the effect of literal acoustic noise on a steel rod. I'm just guessing, but if you speak an 'ode to a steel rod' to your steel rod, you've probably just compressed the atoms together with more force than the expansive force will put on it in a span of hundreds of thousands of years.

then energy is stored by stretching the bonds between atoms.

Bonds are constantly fluctuating; energy is constantly being transferred between them and other modes (rotational states, kinetic energy, etc.). The effect we're talking about is smaller than this constant sea of other effects, so its not going to change the molecular system at all.

@David L #6, #8: The description from eric (#9) is appropriate here. Atoms, molecules, etc. are not static objects. They, and their constituents, are in constant motion and constantly under the influence of many forces acting in many directions.

I wrote that such bound objects (which also includes planets, solar systems, and even individual galaxies!) are _decoupled_ from the cosmic expansion. This is just what I was talking about, using technical shorthand.

You raised the "in principle" question about my "too small to measure" description, but really, that's a bit of a red herring. Any conceivable net motion induced by the cosmic expansion is tiny compared to the already present constant random motions. The "stretching" due to cosmic expansion won't accumulate over time because all those other motions will overwhelm it, and those other motions are driven by the local binding forces which reverse them and hold the object in some local average state.

If all of space-time is expanding but gravity keeps our local group bound together, wouldn't they be dragging through space-time in some way? Wouldn't there be a wake made by the mass that isn't going with the flow, so to speak?

(I should add, I'm not asking because I doubt any of the expansion or anything, I just had this thought this morning and was wondering if there is some effect like this in addition to everything else we can observe about it).

@Thomas #11: Now that is a very interesting question! I am not enough of a theorist to feel comfortable trying to answer it in detail (I'm just an experimental particle physicist).

Naively, I would think that, in principle, you can treat the decoupling of matter from the expanding FLRW metric in the same way that you'd treat a finite blob of matter moving uniformly through a static GR spacetime (that's just an instance of special relativity, after all).

In that case, I do not believe there should be a "wake" effect. That would correspond to gravitational waves being emitted by uniformly moving (i.e., non-accelerated) matter. But if the blob is radiating energy, then it must be slowing down, which contradicts basic inertia (there are no forces acting on the matter, so it shouldn't change momentum).

I'd feel more comfortable if a real cosmologist (hey, Ethan!) either worked through the field equations or pointed me at a reference. However, that's what my physics intuition tells me, for whatever it's worth.

@ Michael and eric

You're not telling me anything I don't already know (I am a physics graduate, practicing Engineer), but you both seem to be missing the point. Firstly, I did not bring the rod into the discussion, I picked an atom to keep it simple. It may well be that there is a good theoretical reason for stating categorically that the space inside an atom does not expand witht the universe. But if there is, neither of you can state it, and both seem to implicitly accept it might not be the case. eric says "you’ve probably just compressed the atoms together with more force than the expansive force will put on it in a span of hundreds of thousands of years.", Michael says "The “stretching” due to cosmic expansion won’t accumulate over time because..[it is lost in noise]". How can you discriminate between the alternative hypothesis: either that the space inside an atom expands, but the expansion is too small to measure, or the space does not expand at all? Because I don't think that is a trivial difference.

If I had a kilo of gold and promosed you half, you could check you got it. Ditto for a gram, or a milligram. But keep reducing the starting amount, and at some point you would say you can't be sure you got your fair share because the amounts were too small to measure accurately. But if I said I'm down to my last 196.97 amu of gold, and you can have half, you would cry foul because of your knowledge of atomic structure without any need to resort to measurement accuracy. But hundreds of years ago you would have accepted that in principle the gold could be halved regardless of how little we began with.

David L,

I am no expert by any means, so someone may rip this response apart. I believe that there IS expansion of space inside the atom (of course it's miniscule and unmeasurable as others have stated). This extra space does not, however, result in an increase in the distance between the nucleus and the electron cloud. The attractive force between the nucleus and the electron cloud results in a constant size for the atom.

Since you have a physics degree, this thought experiment should be clear. Take your magic electron grabbers, grab an electron and move it away from the nucleus. Now let it go. What happens to the electron? It will return to its original position due to the attractive force. I think the situation with expanding space is very similar. The expansion of space tends to move the electron away from the nucleus, but that tendency is overpowered by the electromagnetic attraction.

@ David L

I will try a different approach and no rods and things like that. You asked, what happens to a single hydrogen atom and it's electron. The answer is nothing. The electron does not move away from nucleus.. even ever so slightly. And the reasons are simple.

Wrong way to look at it is, that there's some/any difference between space between proton and electron in comparison to space between earth and sun. There is no difference. Spacetime is spacetime and it's one and the same.

So what does happen? The analogy i find useful is to treat spacetime as a fluid of sorts. But simplified (no currents or any perturbations or any atomic structure)... So i.e. fluid vacuum... if you can visualize something like that. And it has in it a property of repulsion (extremely simplified). But that repulsion can be treated as a force. So what happens in atomic world... just different forces acting on things all the time. Your picture of electron moving away ever so slightly would be true if there were NO OTHER forces acting on it. But there are. There's gravity, there's electromagentic forces etc etc.. The change in velocity or position is the sum of all forces acting on the particle. The strength of EM forces in atom are many many orders of magnitude higher than the force of expansion at such a short distance. If you're a physics grad.. calculating the strength of expansion on distances of several nano meters should be easy.
So it's not that the electron moves away because that force is sill present at such small scales... it's that all other forces acting on electron but having opposite sign/direction will be slightly less. It would be i.e. same as me trying to push on a building. It's not that the building moves because there is some small force exerted by me on it.... even in billion years.. I wouldn't move it a inch... because the rest of forces holding the building in place are much stronger than my pushing. My pushing is still present, but it doesn't do anything to change the position of the building.

And that's it.. :) I hope this helps.

This extra space does not, however, result in an increase in the distance between the nucleus and the electron cloud. The attractive force between the nucleus and the electron cloud results in a constant size for the atom.

Correct, Sean.

Sometimes the same idea needs to be put again and again not because the person listening is dumb or not listening (though this can also be the case, people are people...) but because the framework the other person uses is not the same as the one being used by you (the "you" here being the plural group and indefinite article, rather than "You, Sean").

Spacetime is expanding, but the electron eigenvalues do not change their manner equivalently, therefore the "average position" that is the effective radius of the atom doesn't expand likewise.

If is really like stretching a rod, does that not reinforce my point? It will come apart if I pull it hard enough,

Yes, but you aren't, are you. You're not even CAPABLE of putting enough force into the pull to pull a steel rod apart,are you?

And neither is the expansion of space at the current epoch of the universe able to pull that electron away from the nucleus.

IF IT WERE STRONGER, it would ****BUT IT IS NOT***.

If it were stronger, then Michael's "orders of magnitude" claim would no longer apply and therefore Michael would not claim the same (since the claim is predicated on the expansion not being equivalent to the binding forces on an electron).

Sinisa, thanks for your contribution, though I don't think there is anything new to me in it. But my musings revolve around the questions of "how do we know" and of balancing the energy books.

As you seem to visualise it, ALL space is expanding, which would indeed be the obvious default (though from previous experience of QM, that which seems obvious it is most likely wrong!). As ALL space expands, some of the space that was once inside the electron's orbit slowly leaks outside it, but the EM forces keep the electron nailed at the same distance from the proton by effectively dragging it back through the expanding space. EM potential energy unchanged, books balance, everything in the garden is rosy. But if I were an observer on a neutron which started off just outside the electron's orbit, surely I would see the atom receding from me at an initial rate that suggested the tiny amount of space between us was expanding much more rapidly than the background rate. If the rate of expansion were not constant, I would see the atom accelerate with no obvious force, and even if it were constant, I would seem to somehow be gaining gravitational potential energy from the proton (absolutely miniscule agreed, but still not zero), whilst the immediately adjacent EM bound electron was not. How is this paradox resolved?

p.s. one interesting point about electron, that got neglected. If one is picky.. there is an expansion force from space beyond electron, that's actually pushing it towards the proton. Since expansion is present as outward force from every single point, with my highschool physics, I would say there is then zero net force in terms of expansion acting on electron.. actually acting on anything... Thus it's simply more of space.. it's not force pushing or tugging at something in one particular direction.

As ALL space expands, some of the space that was once inside the electron’s orbit slowly leaks outside it,

Wrong model.

Space expands, but NOTHING STOPS THINGS MOVING IN THE EXPANDED SPACE.

Ergo that electron can just move back in.

Just because managers' chairs are bigger doesn't MAKE their arse grow bigger. There's just more space for a bigger arse in it.

@ David #19

"But if I were an observer on a neutron which started off just outside the electron’s orbit, surely I would see the atom receding from me at an initial rate that suggested the tiny amount of space between us was expanding much more rapidly than the background rate."

not sure to what atom you refer, that you would see receding from you.

You wouldn't see anything moving away from you if you were standing on a neutron. Just as you don't observe sun receding from earth... and the distances are much more dramatic. Even the picture of "some space leaking" is not needed at all, since an atom is in constant motion. It's never the same space that around it or in it. Matter is not "connected" to some particle of space like a tick... If this your mental image then I can understand why the confusion.

I mean look at earth... it;s been "exposed" to expansion for over 4 billion years... and it's doing just fine.. it's not "inflating". If you can give yourself an answer as to why earth didn;t "blow up" due to expansion, then you can understand the atom. Because it's the same thing.

Ethan, from your article:

You’re still moving at 100 km/s relative to your original
location, but that’s now a kiloparsec away! It appears to be
receding at 100 km/s from you still, but part of that — 10
km/s of it — is accounted for by the expansion of the
Universe! So your speed relative to the expansion of the
Universe has slowed down; now you’re only moving at 90
km/s. And as the Universe expands farther and farther, your
velocity continues to drop.

When you say "your speed relative to the expansion of the Universe", is that equivalent to saying "your speed in local space" ? If so, wouldn't it be the case that eventually your speed in local space would be zero since your starting point is now receding at 100 km/s due to expansion. Indeed, after more time wouldn't your direction in local space eventually be reversed?!? If so, I find it interesting that this is similar to the motion of a particle trying but failing to escape a gravity well. Thanks for your article!