# Local effects of universal expansion

First let me apologize for asking these questions. So much has been devoted to discussing the expansion of space both on the internet in general and this forum that the answers to my question are probably out there, but there is a lot to wade through. A lot. I found this forum and thought what a great place that a laymen like me could just pose my questions, so I am ...

Almost all of the materials I have read about the expansion of space deal with galaxies and distant objects, but I presume this expansion is happening locally also. Right? The distance between any two spots on my arm are also stretch and trying to increase but the chemical bonds that hold my cells together are keeping them in a relative stable configuration with relation to each other. Just like the distance between any two random spots on the ground is stretching but the Earth's gravity is continually pulling things back away from that "new" expanded space into another relative stable configuration. Do I have that right?

If electrons in hydrogen atoms orbit the proton at a fixed distance, this expansion is also increasing the distance between the electron and proton, but the EM force is also constantly pulling the electron into a consistent orbit distance.

If I have that understood correctly, then does that mean that electrons are a little easier to strip away from atoms than if the universe wasn't expanding? Or for that matter can the space shuttle achieve orbit just a little easier? Is the expansion causing constant "stress" on any forces trying to attract two particles?

Thanks for indulging me.

marcus
Gold Member
Dearly Missed
I like the way you describe it--in very concrete terms. I agree with the picture. Smallscale local distances stabilized by forces---crystal bonds in rock, gravity binding larger systems like solar system and galaxy.

So it's only very largescale distances that we observe expanding, and percentagewise that expansion is very slow. About 1/140 of a percent every million years.

I suspect that you are right about the space shuttle. It is just slightly easier for it to get into orbit than it would be in, say, a gradually contracting universe, all else being equal. But I'm not confident in saying that. I'm not sure I fully understand how the clear visible expansion of large distance is related to our small-scale geometry.

Maybe the curvature is, so-to-speak, irregular. Maybe our space shuttle doesn't know about the expansion, but somebody else's space shuttle more at the fringe of the galaxy catches more than their share of the effect. Maybe it doesn't play out in a perfectly linear fashion with everybody getting their precise percentagewise share.

1/140 of one percent, per million years. It's such a tiny rate.

Sorry about the unsatisfactory response. Maybe someone with more expertise will reply more definitely.

Ich
Almost all of the materials I have read about the expansion of space deal with galaxies and distant objects, but I presume this expansion is happening locally also. Right?
Wrong. On small scales, expansion is nothing else than the divergent motion of things. If things aren't moving away from each other, there's no expansion.
The distance between any two spots on my arm are also stretch and trying to increase but the chemical bonds that hold my cells together are keeping them in a relative stable configuration with relation to each other.
No. Nothing stretching there. If those spots aren't moving away from each other now, they won't do so in the future.
Talking about gravity, they will be attracted towards each other by the gravity of your arm.
Discounting your arm, they will be attracted towards each other by the gravity of dark matter around here.
Discounting Dark Matter, they will be pushed away from each other by the gravity of dark energy.
All this is independent of whether the universe is expanding or collapsing.
And of course, taking other forces into account, the chemical bonds win by a huge margin.
Is the expansion causing constant "stress" on any forces trying to attract two particles?
No. Mathematically, "expansion" means something like the Hubble parameter, velocity per distance. This is irrelevant for local physics.
The relevant thing in a homogeneous universe that you have to take into account is how the Hubble parameter changes with time*, acceleration per distance. But this is nothing else than the gravity of all the things around, including Dark Matter and Dark Energy. (see e.g. chapter 3.2 of Peacock's "Cosmological Physics".)
(*) To be exact, I'm really talking about the second time derivative of the scale factor. If "scale factor" means nothing to you, forget this remark.

Wrong. On small scales, expansion is nothing else than the divergent motion of things. If things aren't moving away from each other, there's no expansion.

So is space only expanding in certain parts of space? What keeps it from expanding right here in front of me?

Ich
So is space only expanding in certain parts of space? What keeps it from expanding right here in front of me?
Space in GR is defined by its metric properties, as the distance between things.
If the big things in the whole universe have increasing distances to each other in a very ordered manner, you'll call this phenomenon "expansion of space".
If you don't go for the global picture, but look at some local neighbourhood only, you might as well say that the things are moving away from each other. That's different words for exactly the same phenomenon.
But it makes clear that if you stop that motion somehow, those things are then at rest wrt each other and will stay so until something (gravity or forces) act on them. There is no tendency to resume the motion besides that.
The difference between expanding and non-expanding space is a choice of words rather than a physically measurable fact. In that sense, to stop space from expanding, you simply have to stop things from moving (which might be a problem on cosmological scales for different - not only practical - reasons).

bcrowell
Staff Emeritus
Gold Member
So is space only expanding in certain parts of space? What keeps it from expanding right here in front of me?

I don't think Ich's #5 in reply to this was quite right.

What keeps hydrogen atoms and the solar system from expanding is that they're bound by forces. A hydrogen atom is bound by electrical forces. The solar system is bound by gravitational forces.

This may be relevant: http://www.lightandmatter.com/html_books/genrel/ch08/ch08.html#Section8.2 [Broken]

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Ich
I don't think Ich's #5 in reply to this was quite right.
Hmm..
so, in normal coordinates, you're saying there are terms proportional to $\dot a$ in the equation of motion? (At least to leading order in a perturbational analysis)
The $\ddot a$-term represents gravity with the effective source $\rho + 3 p$.
I'm saying that in the absence of $\ddot a$, there's no effect on local motion to leading order, which I think is a standard result.
The interpretation of the $\ddot a$-term as gravity may not be spelled out in many treatments, but it's IMHO obvious from the Friedmann equations and Birkhoff's theorem.

BillSaltLake
Gold Member
The product H0t0 determines whether ä is presently positive or negative. H0t0-1 has the same sign as ä, and this is presently about .99-1 = -.01, so you might think that the "expansion" is slightly reducing the radius of interacting systems. This is counterintuitive. However, a much bigger effect on local systems probably comes from da/dt, which is positive. Just guessing here, but I would say that the fractional change in r of an orbit due to expansion is the same as the fractional change in 'a' that occurs in the time required for 1 radian of orbit.

Ich
H0t0-1 has the same sign as ä
No, ä is positive since 6 bn years.
a much bigger effect on local systems probably comes from da/dt
No.
The effect on local systems is an additional term $\frac{\ddot a}{a} \, r$, see e.g. http://arxiv.org/abs/gr-qc/0602098" [Broken]. $\dot a$ is quite irrelevant.

Further, if you look for the source of the term in the Friedmann equations, $\frac{\ddot a}{a} \, r$ turns out to be the same as
$$-\frac{4 \pi G}{3} (\rho - 3p) x,$$
if x is proper distance.
Which is simply he "Newtonian" (there's an additioinal pressure term) gravity of a homogeneous fluid. Which makes perfect sense, why should it act differently on galaxy clusters than on planets or electrons?

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BillSaltLake
Gold Member
Yep, Ich got me on that. I was simplifying that 'a' was proportional to tn where n = H0t0. The correct LDCM expression is [sinh(1.28t/t0)]2/3 (assuming H0t0 = .99), which has a 2d derivative that goes positive at about t=.51t0 and later. Obviously with positive ä, an extra force that is repulsive will act on orbiting masses and on atoms within a solid, trying to expand things.

Just realized that this ä force will(?) expand solids composed of heavier atoms more than light atom solids (given the same chemical bond strength), although the fact that there's a difference doesn't seem right. It's still way too weak to measure directly, anyway.

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Ich
although the fact that there's a difference doesn't seem right
It's gravity, not a force. More mass = more weight = more force = more effect at same material strength.

Well, this quickly went beyond my understanding, but thanks for the responses. I think I got confirmation on my understanding.

I was wondering if this expansion might possible effect things like radioactive decay rates (making it slightly easier for particles to decide it's their time to leave), or perhaps even have some effect on electrical conductance as it would seem to be slightly pushing electrons out to a more excited state. But of course, very slight.

So how fast is this expansion happening? How long does it take 1 unit of space distance to double?

BillSaltLake
Gold Member
Scale should double in just over 10 billion years (10.4 billion years using the LCDM expression).

bcrowell
Staff Emeritus
Gold Member
Hmm..
so, in normal coordinates, you're saying there are terms proportional to $\dot a$ in the equation of motion? (At least to leading order in a perturbational analysis)
The $\ddot a$-term represents gravity with the effective source $\rho + 3 p$.
I'm saying that in the absence of $\ddot a$, there's no effect on local motion to leading order, which I think is a standard result.
The interpretation of the $\ddot a$-term as gravity may not be spelled out in many treatments, but it's IMHO obvious from the Friedmann equations and Birkhoff's theorem.

I don't understand the relevance of discussing $\ddot a=0$ here. That would be the Milne universe, not a general FRW solution or the real universe.

In the real universe, you can't answer the OP's question without considering the dynamics of the system (atom, solar system). Here is a paper that does some of the estimates: http://arxiv.org/abs/astro-ph/9803097v1

Ich
bcrowell said:
I don't understand the relevance of discussing ä=0 here.
That's not what I did. In #3, I explicitly stated the ä-dependence. In #5, I said:
Ich said:
But it makes clear that if you stop that motion somehow, those things are then at rest wrt each other and will stay so until something (gravity or forces) act on them. There is no tendency to resume the motion besides that.
where I called this dependency "gravity", which I explained in #9.

bcrowell said:
In the real universe, you can't answer the OP's question without considering the dynamics of the system (atom, solar system). Here is a paper that does some of the estimates
I think this is the fourth time we start discussing this paper. I claim that it is completely in accordance with my explanation in #3, though the authors fail to give an interpretation of their result.
If you're interested, I'll start a new thread to back up my claim. Just let me know.

Chronos
Gold Member
Expansion is not unilateral. We perceive distant galaxies are increasingly redshifted and observational evidence is consistent with this hypothesis. There is no inarguable evidence any galaxy exhibits redshift wholly inconsistent with independent distance indicators [standard candles], and no credible evidence whatsoever suggesting a systematic trend to this effect. If physics, as we know it [e.g., newtonian gravity] is not invariant over time, the differences should be most pronounced right here on earth - given we are at the temporal edge of the universe. The evidence to date does not support this conjecture.

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If we look at gravitationally bound structures like the largest superclusters or perhaps the great wall, is it correct to say that galaxies at the opposite edges of these structures, despite being very very far apart, are not experiencing this 1/140 of a percent expansion every million years or at least noticably less because they are gravitationally bound?

bcrowell
Staff Emeritus
Gold Member
If we look at gravitationally bound structures like the largest superclusters or perhaps the great wall, is it correct to say that galaxies at the opposite edges of these structures, despite being very very far apart, are not experiencing this 1/140 of a percent expansion every million years or at least noticably less because they are gravitationally bound?

Yes, I think that's right. As you go to larger and larger scales, you interpolate smoothly between the case of a solar system (ridiculously small expansion) and the whole universe.

Ich
As you go to larger and larger scales, you interpolate smoothly between the case of a solar system (ridiculously small expansion) and the whole universe.
Not really, it's a rather abrupt difference between gravitationally bound to one or another cluster. Most galaxies will "soon" be a part of a super cluster and stick with it for almost an eternity. This decision is a rather digital one.
Bound structures will in the end not follow the expansion at all. That's the definition of "bound".

Not really, it's a rather abrupt difference between gravitationally bound to one or another cluster. Most galaxies will "soon" be a part of a super cluster and stick with it for almost an eternity. This decision is a rather digital one.
Bound structures will in the end not follow the expansion at all. That's the definition of "bound".
From: http://arxiv.org/PS_cache/arxiv/pdf/0704/0704.0221v3.pdf" [Broken] by Lawrence M. Krauss and Robert J. Scherrer
Both analytic [7] and numerical [10] calculations indicate that the Local
Group remains gravitationally bound in the face of the accelerated Hubble expansion. All
more distant structures will be driven outside of the de Sitter event horizon in a timescale on
the order of 100 billion years ([4], see also Refs. [8, 9]). While objects will not be observed
to cross the event horizon, light from them will be exponentially redshifted, so that within
a time frame comparable to the longest lived main sequence stars all objects outside of our
local cluster will truly become invisible

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Has anyone checked that the rate of expansion is, on average, equal in every direction of the sky?

bapowell