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Some scenarios describing the fate of the matter vs dark energy tug of war on the universe involve the acceleration of the universe increasing to the point that it ends up ripping apart even atoms. This is called the Big Rip.

This makes no sense to me. It looks like all of these general relativity (GR) models of the universe assume it has a uniform isotropic distribution of matter and energy. This works great at long scales, but it is also clearly wrong even at the length scale of the separation of galaxies.

The density of atomic nuclei remains the same even though the universe is expanding even as we speak. I don't think the "scale" in the Friedmann equation can be interpreted so literally. Or maybe said better, it's got to break down when the cosmological horizon distance gets to the scale where the isotropic assumption breaks down, right?

How can scientists be claiming that runaway expansion will rip apart atoms?

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I think you would have to ask the Big Rip proponents because no one else believes that those scenarios are compatible with the physics we know. I have asked similar questions to the Big Rip champions and the answers never made any sense, either. So I can only say that I totally share your sentiments. – Luboš Motl Apr 9 '11 at 5:16
up vote 7 down vote accepted

Look at this paper:

"In an expanding universe, what doesn't expand?" by Richard Price

The expansion of the universe is often viewed as a uniform stretching of space that would affect compact objects, atoms and stars, as well as the separation of galaxies. One usually hears that bound systems do not take part in the general expansion, but a much more subtle question is whether bound systems expand partially. In this paper, a very definitive answer is given for a very simple system: a classical "atom" bound by electrical attraction. With a mathemical description appropriate for undergraduate physics majors, we show that this bound system either completely follows the cosmological expansion, or -- after initial transients -- completely ignores it. This "all or nothing" behavior can be understood with techniques of junior-level mechanics. Lastly, the simple description is shown to be a justifiable approximation of the relativistically correct formulation of the problem.

Short summary
All or nothing behavior: If the binding force is greater, the object does not expand significantly. If the cosmological costant is stronger, the object expands.

Hence, as the cosmological constant grows to infinity (or minus infinity, according to the usual convention), more and more strongly bound systems are ripped apart.

However, this analysis assumes the binding force (i.e. gravity or electrodynamics) decreases with distance.

The strong force, however, increases with distance.
So the cosmological constant versus the strong force is still an interesting question.

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+1, this is the correct picture. Cosmological constant (or rather expansion due to it) is negligible for microscopic scales but if it somehow manages to diverge to infinity it will naturally become relevant even at these scales and one needs to compare binding forces with this tearing due to expansion. – Marek Apr 9 '11 at 13:11
thanks for the reference – anna v Apr 9 '11 at 14:31
So to summarise this conclusion in terms of the actual question:(1) The Big Rip will happen (up to atom scale at least);(2) Cosmological isotropy assumptions dont make any difference - the basic theory is sound;(3) Nuclear Rip may or may not happen. Is this the "correct picture"? – Roy Simpson Apr 12 '11 at 18:42
@Roy Simpson: The big rip will probably not happen -- unless dark energy has the right equation of state to make it happen. – Ben Crowell Aug 5 '11 at 4:01
The paper is interesting, but it's completely classical. It's not at all obvious to me that the classical approximation is valid. A classical "atom" can have any size. A quantum-mechanical atom has a size that is fixed by fundamental constants, and likewise for a nucleus. Their definition of the "physical" distance r as a "proper distance" also seems weak to me. I don't see the justification for assuming that such a definition makes sense. The reason we are normally justified in talking about rulers, etc., is that the length of a ruler is defined by the sizes of atoms. – Ben Crowell Aug 5 '11 at 4:18

I looked at the link, and it is a general scenaria link, so I will concentrate on the isotropic part of your question.

You say:

The density of atomic nuclei remains the same even though the universe is expanding even as we speak.

Define density of a piece of metal. It is the number of atoms*(atomic mass) per cubic centimeter. Number is constant. Consider atomic mass constant too. Cubic centimeter was defined as a cm cubed, drawn on a piece of metal at some central bank. Now they take the wavelength of some atom.

The universe is expanding, from the time of big bang, at each point of space. It means as an example that the distance between these two points : is expanding at the rate of expansion of the universe , and the dots are expanding, and this page is expanding and ... The same is true for matter composed of atoms.

We would not notice the expansion, even if our senses were sensitive enough to be able to see such small cosmological changes, because of our definition of distance and units in general.

So the isotropy and uniformity do not have a role to play in an argument whether the big Rip, as expounded in the link you gave, can happen or not.

Some theory has to enter, see for example the link provided by Jim Graber above, where results are conditional to the strength of forces.

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"The same is true for matter composed of atoms." -> no. It is only true for free particles. If you have two particles bound together (imagine a spring between them for simplicity) then they will stay together even if the underlying space-time expands. That's why we observe separation of galaxies from each other but there is no expansion of stars inside galaxies themselves (because Newtonian gravity is still strong between stars inside a single galaxy but not between more galaxies which are too far away). So -1, whole answer is based on a misconception. – Marek Apr 9 '11 at 10:20
@anna v: "Define density of a piece of metal. It is the number of atoms per cubic centimeter". Nope. This is number density. Except that the answer is almost completely wrong. – user1355 Apr 9 '11 at 10:47
@Marek, what does free or bound particles have to do with the expansion of the underlying space? When the big bang happened everything was bound, and expanding. All points in our universe are expanding from all other points, is how I have been taught. – anna v Apr 9 '11 at 11:26
@sb1 I corrected it. I did not want to get involved in expanding on the units of mass, I guess. – anna v Apr 9 '11 at 11:27
@Marek Do you have a reference for your statement that is more than just words that I have found on the net? Measurements of the stars not expanding in galaxies, for example? I have found several claims like this, but no links to solid solutions or data. – anna v Apr 9 '11 at 11:51

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