# I Expansion, thermodynamics

1. Dec 18, 2017

### Paul Howard A

I was thinking about the expansion of space.

It seems clear that objects that are bound by gravitation or the strong nuclear force do not experience an increase in size as the universe continues it's expansion. However, such systems do contain abundant space.

It is argued that gravitation and the strong nuclear force "overcome" the tendency of the space within their systems to expand. If so, would not these forces be minutely diminished by the process of "overcoming" expansion? Atoms and gravitationally bound systems are also flexible. Shouldn't the expansion of space within these structures be manifest by a release of energy as these flexible systems respond to the afore mentioned spatial dynamics?

2. Dec 18, 2017

### kimbyd

I don't think "overcoming" is the right way to think about it.

The concept of expanding space stems from a simplified model of the universe: one where matter is distributed perfectly evenly throughout. In such a universe, there is expansion everywhere.

Our universe isn't like that. Our universe has regions that are much more dense than other regions. When you modify the above model to account for the fact that some regions are more dense than others, the picture you get out is slightly different: at large scales, the universe behaves like the smooth universe above. But at small scales, gravitationally-bound systems do not expand. The exact same gravitational theory is used to describe both situations, and provides a picture where overdense regions form islands of non-expanding matter, regions which move away from one another as the large-scale expansion continues.

The expansion itself isn't a force in any reasonable sense. It's just the statement that things are moving away from one another. In gravitationally-bound systems, things aren't moving away from one another, so there's no expansion, and no pull trying to separate them.

3. Dec 18, 2017

### Paul Howard A

kimbid,
Thank you for your patience with my naive assumptions. I’ve had trouble finding a good reference on this.

What about all the space inside atoms?

4. Dec 18, 2017

### kimbyd

That's a different question.

Within an atom gravity is so weak a force that it is utterly irrelevant. The force that determines most of the behavior of atoms is the electromagnetic force, which is some $10^{40}$ times stronger than gravity. Gravitational effects like the expansion of space can be utterly ignored when trying to understand the interior of atoms.

5. Dec 18, 2017

### Paul Howard A

But I’m told that atoms are 99.999999999999% empty space and that there are 1 X 10 to the 80’th power atoms...

6. Dec 18, 2017

### kimbyd

Atoms are very small. Nearly all of the space in the universe is outside of atoms. There may be a lot of atoms in the universe, but the universe is very, very big.

7. Dec 18, 2017

### Paul Howard A

...and the space BETWEEN bonded atoms in molecules and metals and plasmas etc?

8. Dec 18, 2017

### Paul Howard A

Sorry to be a pest. But it sounds like there are differing explanations for each scale?

9. Dec 18, 2017

### kimbyd

Molecules and metals are far, far too dense for gravity to be a relevant force. The electromagnetic force dominates, just as with individual atoms. Plasmas can be extremely diffuse, so the answer there is a little bit different but comes to the same thing in the end (the atoms between galaxies are in a plasma state, for example).

The expansion is an average effect on scales much, much larger than galaxies. Other physics become much more important when describing things smaller than galaxies. And atoms, no matter where they are, are much smaller than galaxies.

One way to think about it is by looking at the magnitude of the expansion, which is typically expressed in units of kilometers per second per Megaparsec, with a current value of about 68 in these units. A megaparsec is about 3.3 million light years, so 68 km/s/Mpc is 21 km/s per million light years. Typical galaxy motions relative to one another are roughly 1,000 km/s. That means you have to get to separations a few times more than 50 million light years in order to get to distances where the expansion is the most important determining factor in how things move. Typically, a distance of about 260 million light years is used as a cutoff.

So if you aren't talking about things that are more than 260 million light years apart, then the expansion probably isn't the most important factor in determining the behavior of those things. The expansion will start to matter at maybe 5-10 million light years distance, but local physics will remain important until you get into the hundreds of millions of light years.

10. Dec 18, 2017

### Paul Howard A

Very informative, and thank you.
But my question really had more to do with the effects of expanding space on thermodynamics at a local level.
If space were, indeed, “trying” to expand the distance between particles and planets, then could we not expect an increase in the kinetic energy of the bound entities?

11. Dec 18, 2017

### kimbyd

As explained above, the force that describes the expansion (gravity) also states that there is no expansion for gravitationally-bound systems. Space simply isn't expanding within our solar system, and no local experiment could possibly measure it to be expanding as a result (and yes, some physicists have actually tried to measure this and failed to do so).

12. Dec 18, 2017

### Paul Howard A

I’m getting a bit more educated and now I think I know where to look for greater insight. Thnx

13. Jan 5, 2018

### Khashishi

I'll try to explain why cosmological expansion is not relevant at small scales.

First of all, if it weren't for dark energy, expansion would be slowing down, because gravity would be pulling things together, rather than pushing them apart. The Hubble expansion would only be due to the initial velocities of everything moving apart. If you remove the initial velocity, space would contract, since things would fall toward each other. This is just regular gravity. If something is gravitationally bound, it means you've already gotten rid of the initial velocity, so it should be clear that there's no further expansion. Currently, most of the expansion of the universe is just due to the initial velocity of everything moving apart.

OK, but what about dark energy?

The accelerating expansion of the universe is only visible on super large scales, where we average over the lumps and take the mass distribution to be uniform. For Newtonian gravity, Gauss's theorem tells us that the gravitational flux over the sphere only depends on the mass inside the sphere. My understanding is that something similar holds in the case of general relativity. The gravity at the surface of the sphere is only due to the stress energy inside of the sphere. At extremely large scales, the amount of "dark energy" dominates over the matter within a giant sphere so that the gravity at the surface of the sphere points outward. The amount of dark energy outside the sphere is irrelevant, as long as it is homogeneous.

At smaller scales, like our solar system, we don't see anything that behaves like dark energy or like dark matter. We only see ordinary matter. If we draw a sphere radius 1 AU around our Sun, the gravity is clearly pointing inward. That's why the Earth orbits the Sun, instead of getting repelled. Perhaps, there is a small amount of dark energy within the sphere--we aren't sure, but it will only slightly weaken the gravity between the Earth and Sun. From Earth, it will look like the Sun is slightly less massive. But the orbit still stays stable. The orbit isn't going to grow, unless the density of dark energy between the Earth and Sun is somehow increasing in time. If dark energy is a cosmological constant, the density isn't increasing in time.

There are some conjectures that the dark energy is increasing density in time, and this could lead to a Big Rip, where everything is torn apart. But there's no evidence for this view.

14. Jan 5, 2018

### Paul Howard A

Khashishi, Thank you for your clarification. You state above that "SPACE" would contract if gravity overcame the original expansion? I have understood that space is warped by the massive bodies within it, but it never occurred to me that space, itself would contract to a singularity in a "Big Crunch" scenario! You seem to be saying that space is defined by the massive bodies within it!
I'd better let you respond before I babble on too much.

15. Jan 5, 2018

### Staff: Mentor

This is correct. More precisely: if spacetime is spherically symmetric outside of some region, the geometry of spacetime within that region depends only on the stress-energy within the region.

16. Jan 5, 2018

### kimbyd

This statement of Khashishi's isn't actually accurate.

It is strictly true if the matter in the region is perfectly-symmetric. But this basically never happens in practice. In practice, if there is no friction, the matter will enter into elliptical orbits around the center of mass of the region rather than collapsing.

Compact objects will form if the matter experiences some friction, so that it can lose energy. This is how galaxy clusters, galaxies, and star systems form. Dark matter, which doesn't experience much of any friction, tends to stay in a diffuse cloud (so that you end up with a visible galaxy sitting near the center of a huge, diffuse "halo" of dark matter).

In other words, if you're in a spherically-symmetric region inside an expanding universe where gravity overcomes the expansion, then it mostly just "freezes" rather than collapsing. Collapse happens later as friction causes the matter to lose energy over time. The "Big Crunch" only happens if the whole universe is collapsing.

17. Jan 5, 2018

### Paul Howard A

All good stuff, thank you. But I sense that this forum underestimates the depth of my ignorance. Perhaps my original query was too naïve.

I'm not so much interested in the behavior of bodies in a static space, but the thermodynamic consequences of bodies in a dynamic space.

18. Jan 5, 2018

### rootone

Newton was nearly there with that.

19. Jan 5, 2018

### Staff: Mentor

This seems like a good time to return to this opening statement and ask you for a specific reference. What textbook or peer-reviewed paper "argues" this?

I don't think space in GR is "dynamic" in the way you appear to be using this term. The "expansion of space" is not a force that other forces have to overcome. It's just a sloppy way of referring to the inertia of comoving objects in a universe like ours that started out in a very hot, dense state in which everything was moving apart very rapidly.

Dark energy, as has been mentioned, does create something that can be thought of as a "force" that tries to move things apart; a term that is sometimes used is "repulsive gravity". But that's due to the unusual form of the stress-energy tensor of dark energy. It's not due to "space".

20. Jan 6, 2018

### Paul Howard A

Peter. This is not a peer review or text book reference, but I believe Fraser Cain is respected in your field:
https://www.universetoday.com/107142/is-everything-in-the-universe-expanding/

His words:
"As space expands, it carries galaxies away from each other. From our perspective, we see galaxies moving away in every direction. The further galaxies are, the faster they’re moving".
"There are a few exceptions. The Andromeda Galaxy is actually moving towards the Milky Way, and will collide with us in about 4 billion years. In this case, the pull of gravity between the Milky Way and Andromeda is so strong that it overcomes the expansion of the Universe on a local level. Within the Milky Way, gravity holds the stars together, and same with the Solar System. The nuclear force holding atoms together is stronger than this expansion at a local scale."