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I have looked at the other questions (ie "why does space expansion affect matter") but can't find the answer I am looking for.

My question: There is always mention of space expanding when we talk about the speed of galaxies relative to ours.

Why, if space is expanding, does matter not also expand? If a circle is drawn on balloon (2d plane), and the balloon expands, then the circle also expands. If matter is an object with 3 spatial dimensions, then when those 3 dimensions expand, so should the object.

If that was the case, we wouldn't see the universe as expanding at all, because we would be expanding (spatially) with it.

I have a few potential answers for this, which raise their own problems:

  1. Fundamental particles are 'point sized' objects. They cannot expand because they do not have spatial dimension to begin with. The problem with this is that while the particles would not expand, the space between them would, leading to a point where the 3 non-gravity forces would no longer hold matter together due to distance

  2. Fundamental particles are curled up in additional dimensions ala string theory. These dimensions are not expanding. Same problems as 1, with the added problem of being a bit unsatisfying.

  3. The answer seems to be (from Marek in the previous question) that the gravitational force is so much weaker than the other forces that large (macro) objects move apart, but small (micro) objects stay together. However, this simple explanation seems to imply that expansion of space is a 'force' that can be overcome by a greater one. That doesn't sound right to me.

I think some of the problems in this question verge into metaphysics, but I think from his (?) previous answer, Marek can probably explain the physical side of things a bit more thoroughly. I will leave it there cos anything else I write sounds rambling!

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OK... well, it seems to me that your question and the earlier question are actually polar opposites. You're asking why matter doesn't move along with space, and the other poster was asking why matter does move along with space. And you can actually use either description validly. Either way, I think you'd just get essentially the same answers to this question as are already on the other one, and that's why I closed it. –  David Z Dec 21 '10 at 7:20
This problem has been extensively studied. These are some references that I think answer various aspects of your question. I would say that it is not exactly a solved problem. 1 2 3 4 5 and this review (Rev.Mod.Phys.) is free from arXiv. (mod edit: titles omitted for brevity) –  Vagelford Dec 22 '10 at 2:03
related: physics.stackexchange.com/q/70047 –  Ben Crowell Aug 6 '13 at 5:44
I am not impressed by the answers here. Let's consider the galaxy (as asked here). How are the stars affected by the smoothed spacetime geometry outside? Does the rest of the universe exert a net outward force? In other words, can anyone describe the spacetime curvature in, for example, an empty region (or an overdense region like a galaxy) in an otherwise uniform expanding universe? –  akrasia Aug 14 '14 at 20:15
It's not actually true that cosmological expansion doesn't expand matter. For example, GR does predict a secular trend in the size of the earth's orbit due to the varying rate of cosmological expansion, but it's much too small to detect. There is certainly a significant effect on some systems, such as unbound superclusters. There is theoretically a strain on a block of wood due to cosmological expansion, but it's much too small to measure. See physics.stackexchange.com/q/70047 . –  Ben Crowell Nov 4 '14 at 23:42

7 Answers 7

Let's talk about the balloon first because it provides a pretty good model for the expanding universe.

It's true that if you draw a big circle then it will quickly expand as you blow into the balloon. Actually, the apparent speed with which two of the points on the circle in a distance $D$ of each other would move relative to each other will be $v = H_0 D$ where $H_0$ is the speed the balloon itself is expanding. This simple relation is known as Hubble's law and $H_0$ is the famous Hubble constant. The moral of this story is that the expansion effect is dependent on the distance between objects and really only apparent for the space-time on the biggest scales.

Still, this is only part of the full picture because even on small distances objects should expand (just slower). Let us consider galaxies for the moment. According to wikipedia, $H_0 \approx 70\, {\rm km \cdot s^{-1} \cdot {Mpc}^-1}$ so for Milky way which has a diameter of $D \approx 30\, {\rm kPc}$ this would give $v \approx 2\,{\rm km \cdot s^{-1}}$. You can see that the effect is not terribly big but the given enough time, our galaxy should grow. But it doesn't.

To understand why, we have to remember that space expansion isn't the only important thing that happens in our universe. There are other forces like electromagnetism. But most importantly, we have forgotten about good old Newtonian gravity that holds big massive objects together.

You see, when equations of space-time expansion are derived, nothing of the above is taken into account because all of it is negligible on the macroscopic scale. One assumes that universe is a homogenous fluid where microscopic fluid particles are the size of the galaxies (it takes some getting used to to think about galaxies as being microscopic). So it shouldn't be surprising that this model doesn't tell us anything about the stability of galaxies; not to mention planets, houses or tables. And conversely, when investigating stability of objects you don't really need to account for space-time expansion unless you get to the scale of galaxies and even there the effect isn't that big.

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@SoulmanZ: sure, it's called inflation. But these conditions won't happen again in a foreseeable future :-) –  Marek Dec 22 '10 at 0:40
@SoulmanZ: it's not a pseudo-force. It's a completely usual force and the basic point about forces is that it doesn't matter where they are coming from. If you pull an object with a force of $10N$ to the one side using gravitation and to the other with a force of $10N$ using electromagnetism, it wouldn't move. So it's only important how big a force is and it shouldn't be surprising that certain forces are more important than others in certain situations. We use just gravitation to describe Solar System but we use electromagnetism to describe electric circuits. –  Marek Dec 22 '10 at 0:44
@SoulmanZ: maybe I didn't make it clear enough that both big-scale expansion and standard short-scale Newtonian attraction are effects predicted by General Relativity. They are just an apparent forces that have a deeper reasons in the way space-time is curved and its dynamics. But on a classical level you can consider them as full fledged forces on par with EM and others. Just on different scales. –  Marek Dec 22 '10 at 0:47
@SoulmanZ: expansion is just an apparent force arising from GR, as described in my previous comment. But for the purposes of local observers it's a completely usual force. You look at the sky and you see galaxies speeding away from you, accelerating even. So there must be some force acting on them, you tell yourself. This is just an illusion created by GR though. In the same way, when you jump, something pulls you down, so you'd imagine there must be gravitation. But in fact, there are no forces acting on you, it's just that you are moving in the curved space-time. –  Marek Dec 22 '10 at 0:59
@SoulmanZ: I am not sure how much sense is this making to you. Depending on your exposition to GR, this might appear to be a complete blabbering. Nevertheless, the moral of the story is that GR reduces all of the gravitational effects to movement in and movement of space-time. There are no gravitational forces in that description. But often it is very convenient to describe some of those GR phenomena as forces and work with simplified picture. –  Marek Dec 22 '10 at 1:02

If the question is interpreted as why don't atoms and other bound systems expand the answer is that the general expansion of space cannot do continuous work against the electromagnetic force that holds an atom together or any other force that holds a bound system together.

However the accelerating expansion of the universe can exert a small "constant" negative force between the electrons and nucleus and make the atom very very slightly bigger than it would have been in a non-accelerating expanding universe. But in the current best theory of dark energy which is that it is a constant vacuum energy, this effect will be constant and the atoms have already expanded as much as they ever would.

There are theoretical speculations of an acceleration of the accelerating expansion of the universe where this effect increases with time such that eventually in an exponential way the universe ends in a big rip where atoms and eventually nuclei would be ripped apart.

On another website, I answered a question about whether we could extract energy from the expanding universe and this is the answer I wrote which I think will be helpful in understanding this issue:

The universe is expanding at 74 km/sec/Mpc (Mpc is a mega parsec which is 3.26 million light years). So let's take two heavy objects and place them far from any galaxy cluster or other influence and space them just one parsec apart (3.26 light years).  Then they will effectively be moving apart at 7.4 cm/sec.  Now imagine that your monomolecular filament rope between the objects puts a force on the objects that will decelerate the objects.  Then during the time that they are decelerating you can extract work from the objects. That work per second comes from the force the rope is exerting being applied over the 7.4 cm/sec that the objects are moving apart. However, once the force causes their relative velocity to drop to 0, you won't be able to get any more energy from the objects since they are no longer moving apart.  There will still be a constant force on your rope but you need to have a force applied over a distance to get work.

Now this is all from just the "Big Bang" expansion of space.  Once the rope's force has gotten their relative velocity to zero, the two objects are like a gravitational bound system and it will stop "expanding".  However, in addition to the "standard" expansion of space, we now know that there is dark energy which is causing an accelerating expansion of the universe.  This means that the two objects are not just "moving" apart at constant 7.4 cm/sec but that this velocity is actually increasing with time.  So if you setup your rope such that the force it is exerting on the objects results in an deceleration that is slightly smaller than this cosmic acceleration, you can extract work continuously and indefinitely.  Unfortunately, I have not been able to convert the dark energy measurements into units of acceleration in this particular case of objects at one parsec.  I suspect it is a small number but current estimates are that it is definitely positive.  Note that if your rope exerts more force that causes a deceleration larger than the cosmic acceleration then the objects will eventually stop moving apart and the work you can extract will drop to zero again.

Note that from just the normal expansion of the universe you can only extract a finite total amount of energy, but that with the accelerated expansion you can extract a small but positive amount of energy per second forever.  However, your rope needs to get longer and longer with time (at the rate of 7.4 cm/sec, in this example), so, as they say TANSTAFL (there ain't no such thing as a free lunch). The rope needs to get longer because you have to have your very small force applied to continuously moving objects to get work done.  Since it will take continuous energy to make a continuously lengthening rope, and you cannot win this battle by starting with objects that are further apart since then the rope is lengthening at an even faster rate than the 7.4 cm/sec of this example.  You can increase the energy per second you extract by making the objects more massive, but then the force on the rope increases so you need to make a thicker rope.

The bottom line is that I think this free energy project is impractical, even though it is theoretically possible.  The problem that needs to be solved is the energy cost of the continuously lengthening rope.

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What about two objects connected with a spring? It sounds like the 'outward' movement would be accelerated by the expansion factor, while the inward movement would be retarded by the same amount. Not disagreeing that it's impractical, but still interesting that it's even possible in theory. –  kbelder Mar 12 '13 at 15:59
@kbelder Two objects connected by a spring, when all oscillations die away due to friction (in the spring itself if not due to air etc) will have an equilibrium separation that would be very very slightly larger appart in an accelerated expanding universe and when there is oscillation out and back, they would just oscillate around that new equilibrium location. –  FrankH Mar 12 '13 at 17:17
Your text is helpful for a layman like me. But I am wondering about a point. When the kinetic energy of object 2 has been collected by object 1 through the rope, you state thet there is still a force on the rope that produces no work for lack of relative motion. I do not see why there should be a force, or why it could not have an effect if existing. Object 2 has acquired a velocity towards object 1 that exactly compensate the expansion velocity for their distance. There can be a force only if expansion rate increases. - - - Typo: TANSTAAFL –  babou Aug 21 '14 at 22:54
A second point is that, if you have unbounded rope, you can extract energy continuously without accelerated expansion. You simply extract energy slowly enough so that object 2 keeps receding from object 1, though not as fast as expansion would do it. Till you reach the end of your rope. Normally objects recede at an accelerated speed since it is proportional to distance. So if you maintain constant recession speed, you can collect the energy of the acceleration. I have not done the calculation ... it is probably not very much ... but with a very big mass :) –  babou Aug 21 '14 at 23:51
This is basically right, but in realistic cosmological models it is not true that the effect of the acceleration vanishes. The secular trend goes like $(d/dt)(\ddot{a}/a)$, which is not zero in realistic cosmological models (although it will asymptotically approach zero for a model dominated by a cosmological constant). More info here: physics.stackexchange.com/a/70056/4552 –  Ben Crowell Nov 4 '14 at 23:48

This was written for a question that closed during my composition of this. The question is how does the CC effect atomic physics, by Ashton.

Dark energy has the mass-energy equivalent of a proton every 1-10 cubic meters. That is a pretty diffuse energy. An atom is on the scale of $10^{-8}$cm in length or has a volume of about $10^{-30}m^3$. So about that proportion of a proton’s mass-energy worth of dark energy acts on an atom, or perturbs its atomic levels. That is about $10^{-21}$ Gev or $10^{-12}$ev. That is very small.

Now your question is not entirely without merit. Some very sensitive atomic measurements get atomic level splittings to within $10^{-6}$ev. I will not say for certain, but these atomic-quantum optics people can be quite clever on the bench. It is not entirely unimaginable that with squeezed states, entangled squeezed states of photons and electrons and so forth that this might be measured. If there is an EM response due to a level splitting the wave would be around the sub Hertzian range.

The interaction Hamiltonian for the cosmological constant would be an inverted harmonic oscillator potential $H_{cc}~=~\Lambda r^2/3$. Some analysis for avoided crossings of energy levels and states and the rest might not be an unreasonable thing to work on.

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Well, according to the answer given to this question: At which point of the universe $R_{\mu \nu}=0$ if there is a source of gravitation (point mass), the universe expansion refers actually to matter expansion:

"So Einstein's equations in vacuum mean exactly that: that $G_{\mu \nu} = 8\pi T_{\mu \nu} = 0$ in a region without mass-energy. That is far from saying that there is no gravity, just as it would be silly to say there is no electric field in the exterior of a charged ball."

So if this is true that the Einstein's equation:

$$R_{\mu\nu}-\frac {1}{2}g_{\mu\nu}R+g_{\mu\nu}\Lambda=\frac {8\pi G}{c^4}T_{\mu\nu}$$

(if not null) is restricted to matter only (because if the $T_{\mu\nu}=0$ then the left hand side of the equation also vanishes), and since it contains the cosmological constant $\Lambda$, the logical conclusion is that matter must be expanding.

Summing up: the vacuum Einstein's equation requires that either (1) the universe under consideration must always be all void of matter, or (2) matter is expanding (or (3) Einstein's equation is wrong). Since (1) is considered not true, and (3) is not claimed by mainstream physics, then we have only (2) left - i.e. matter is expanding.

P.S. You can also formulate it differently - gravity ($T_{\mu\nu} \neq0$) is the source of universe expansion within matter.

EDIT: It should be obvious, that $\Lambda$ is not just a force that can be overcome (and therefore not apparent). It is on the side of the equation that shows actual curvature.

EDIT2: As I wrote elsewhere, (possible) expansion would keep relative values (of various "constants, planck's constant, electron mass, speed of light, elementary charge, and permitivity of free space") intact. It's like with the time dilatation and length contraction in SR - for the moving frame nothing changes, and local observer wouldn't notice. The difference being here that the outside observer also wouldn't notice, because the change would be taking place everywhere, at the same time, and with equal acceleration.

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wrong conclusion because expansion of space is not the only phenomenon in nature. There exists the strong force and the electromagnetic which hold the atoms together which are orders of magnitude stronger than any effective force breaking them apart from the expansion. The effective gravitational force ( in the limit newtonian and GR effects have to be consistent) is stronger than the expansion. en.wikipedia.org/wiki/… –  anna v May 7 '14 at 10:02
Expansion of matter does not necessarily mean braking it apart - just like expansion of the universe is not considered to break it apart. It might simply mean a proportionate growth of all matter, with all associated phenomena, which therefore would not be apparent. But if you still oppose, than you should admit that either (1) or (3) is true. Or answer the question: Why is $\Lambda$ included in an equation which is considered non-zero for matter only? –  bright magus May 7 '14 at 10:10
In addition if everything were expanding as the GR equation says, then we would not be able to see the expansion of the universe. It would be like a change of nominal units. –  anna v May 7 '14 at 10:47
Well, Anna, incompleteness does not explain $\Lambda$ referring to matter and yet saying there is no matter expansion. If so, than there is something inherently wrong, either with the claims that Einstein's equation refers to matter only or with the equation itself. As to your other comment: there can be two (separate) expansions actually, and what we see (presuming we correctly interpret the redshift) is not the phenomenon associated with $\Lambda$. Or $\Lambda$ refers to both phenomena and we can perceive one, but not the other. Perhaps it's not only dark matter that proved we were wrong ... –  bright magus May 7 '14 at 11:01
If we thought that maxwel's equations should describe atoms, we would be wrong, because atoms are controlled by more than classical electromagnetic forces. That is why the Bohr atom was incomplete and Schrodinger's equations were necessary. In a similar way, to think GR describes matter as is, can only be wrong, because matter is much more than its gravitational interactions. –  anna v May 7 '14 at 11:46

Quick fun analogy:

If we think of the expansion of space as a sheet stretching, particles of matter move away from each other. Hooray, as explained several times before.

Extending this to 3D, we're basically stretching objects at a very slow rate. 1.62038964 × 10^-17 m/s / meter, to be precise. Thus, a typical person is stretched at about 3x10^-17 meters per second. I couldn't find any good estimates on the ideal spring constant of the human body but you'd probably be stretched by within 10 orders of magnitude of 10^-15 meters.

(Due to the electromagnetic force being so strong, your tensile strength is very high.)

Thus, with Hubble expansion you're about 0.0000000000001% taller. Congrats!

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To accept that the space is expanding you have to admit that the ruler, made of atoms, is invariant, i.e. it has always the same length, and no one has provided a convincing argument of this. The space expantion relies in the belief that this is a fact. If atoms are expanding at the same rate we were not able to measure any expantion. If, on the contrary, the atoms are shrinking thru time we can measure a space expantion without any de facto happening to the space. I dont know why the space is expanding except that we measure it. The matter may be contracting because the gravitoelectric fields have energy that is expanding and are sourced by the particles since matter is born and, obviously, we are not able to measure this fact in the lab. Un discussed model, out of academia, un-peer-reviewed, is 'A self-similar model of the Universe unveils the nature of dark energy' that does not need any Dark Energy, Inflation, etc.

Concluding: to the question 'Why does space expansion not expand matter?': if matter expanded at the same rate no one would be able to measure any variation. The measuring act is to obtain a ratio between two quantities and both the numerator or the denominator (the standard) can change to obtain a specific measured value. But the standard is based in the 'atom' properties (in the first link and in this recent one The physical basis of natural units and truly fundamental constants) that we presume invariables.

Both links provide an inside about units, but the first link is much more interesting because it provides an insight on the rationale of the measuring act.

EDIT add:
Usually it is accepted that there are no effects on Solar system scale of the space expansion, but recently it was reported, i.e. measured, that the SUN-Earth distance is increasing much more than expected:
Experimental measurement of growth patterns on fossil corals: Secular variation in ancient Earth-Sun distances by Weijia Zhang , 2010 (behind paywall)

Experimental results indicate a special expansion with an average expansion coefficient of $0.57H_0$

Secular increase of astronomical unit from analysis of the major planet motions, and its interpretation by G. A. Krasinsky, 2004 (behind paywall)

measured $\fraq{dAU,dt}=15 \pm 4 m/cy .. at present there is no satisfactory explanation of the detected secular increase of AU

-- not peer reviewed by Weijia pdf of 'A test of the suggestion of an eternally constant Earth orbit in both Phanerozoic and Cryptozoic from astronomical observations and geological rhythms' (on http://www.paper.edu.cn )

The author reviewed all developments in lunar system research and paleontology since 1963, found three contradictions between different methods: ... This means that the ancient Earth is closer to the Sun. .. The revolution period of Earth is increasing, recorded by NASA. The semimajor axis of Earth is increasing, recorded by JPL.

in the page 13 we find a table with the measured values of length of a sidereal year (increasing) after 1900.

The increasing distance is deduced in the presented model, as seen at eq. 35), pag 10 of the preliminary paper of 2002 (arxiv) by Alfredo Oliveira
A relativistic time variation of matter/space fits both local and cosmic data

So, to the question 'Why does space expansion not expand matter?'
the answer is because 'the space expansion is the result of the evanescence of matter' i.e. matter is shrinking.

As an exercise: imagine you are siting in the midlle of a room and you start to see the walls moving away of you. When wake of that dream, or hallucination if you are doped, how would you describe it? :
I was sh-shr-shri-shrinking, as Alice in the Wonderland naturally did, or that the house is getting bigger-BIGGER ?

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Answer to this question is only by understanding and not proof. If the Universe is expanding then I say Yes, to that the Matter is also expanding. Explanation for this is, all the Matter is expanding means, even the scale to measure the Matter is also expanding. Consider a small Example: A rectangular wooden block is expanding, Measure the initial dimensions of the block, say they are x,y,z after expansion of only the wooden block, measure again, then it is x+a,y+b,z+c. But what if the scale is also expanding at the same rate as of the wooden block, then measure it any time you will get its dimensions as x,y,z only and not x+a,y+b,z+c. Coming back to reality, the same thing is happenning in the Universe. i.e. Universe is expanding along with it everything else is also expanding. Only thing is that we cannot notice the small things. We can notice for larger things such as Galaxies, Planets, Stars etc.

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