Describe the mechanism in GR causing *Space* expansion

[Glurth]

From what I have read, it sounds like GR predicts that under certain conditions, space itself will expand. If this is incorrect, please just let me know and ignore the below.

While I don’t know the math involved in GR, I can understand explanations of how gravity distorts space-time, to alter trajectories of objects moving in a straight space-time line, such that they appear to curve in space, around locations of higher-energy density. I can understand explanations of how a constant speed of light for all observers can lead to relative time dilation, and length contraction.

But I fail to see how either of these descriptions can result in an expanding volume of space, or even the appearance of such.

Is there a way to describe this phenomenon without math? Can you describe what conditions could induce an expansion of space and how? (Obviously, I can imagine scenarios in which the volume encompassed by “stuff” would increase, but these involve objects moving through space with some initial momentum (away from a central point), which is not the same thing as space itself expanding (no central point, no initial momentum).

Also, would the manifestation of this phenomenon be relative? So that, like time-dilation, different observers may see different results?

 

[PeterDonis]

what I have read, it sounds like GR predicts that under certain conditions, space itself will expand

No. Some predictions of GR, such as the models we use in cosmology, are often described as having "expanding space" in pop science presentations, but that's not really correct. "Expanding space" is an interpretation of what the model says; it's not the actual model. The actual model only makes predictions for observations--for example, it predicts a relationship between how far away from us in the universe a distant galaxy is and the Doppler shift we observe in its spectrum. The model itself doesn't tell you that this relationship is due to "expanding space", and there is no mechanism in the model that "makes space expand".

 

[Glurth]

Thank you, Peter, for the clarification.

So, just to clarify, GR doesn't actually predict our observation that the distance between distant galaxies will appear to increase with time, with no central point of origin? We just INSERT that into GR models to make them look like our universe? Is this why we call it DARK-energy? (I thought that was JUST for the acceleration of the expansion.)

 

[PeterDonis]

GR doesn't actually predict our observation that the distance between distant galaxies will appear to increase with time, with no central point of origin?

The distance between distant galaxies is not directly observable. But GR certainly does predict all the observations we do make of distant galaxies (their brightness, their redshift, etc., and the relationships between them), and the GR model that makes those correct predictions does have the distance between galaxies increasing with time, with no central point of origin.

What the model does not do is say that what I just described is "expansion of space". That's an interpretation.

 

[Glurth]

Throwing aside my poor use of language, I think you see what I'm asking now: Is there anyway one could describe how GR predicts those observations, without getting into the math? How/what warps space-time such that distant objects appear to move AWAY from each other, rather than TOWARDS each other like we see locally?

 

[bcrowell]

I like PeterDonis's explanation.

Although the OP asked for a nonmathematical explanation, here's a mathematical way of defining what we mean by expansion of space. A congruence is defined as a set of smooth, nonintersecting curves whose union fills all of space. A timelike congruence is one in which all the curves are timelike. Given a timelike congruence, we can define a number called the expansion scalar $\Theta$, which measures whether the curves are spreading apart. In a cosmological model, we normally have a locally defined frame in which spacetime is isotropic. This could be the frame defined by the CMB, or equivalently a frame that moves with the Hubble flow. The Hubble flow defines a congruence of timelike curves, and the expansion scalar of these curves is nonzero. I think this is really the only meaningful sense in which we can say that space is expanding, and it *isn't* really a literal statement that space is expanding.

As PeterDonis says, anything else is just words, interpretation, personal preference, or a convenient way of organizing our knowledge about various observations. For example, I sometimes find it convenient to conceptualize cosmological redshifts as the expansion of the wavelength of light that occurs while it's in flight, due to the expansion of the underlying space. But that's just one description. There are other descriptions that match equally well with the observed redshifts. The underlying math of GR is the same in all cases.

 

[PAllen]

To follow on what Bcrowell said, the same expansion scalar can apply to a congruence representing raisins in a rapidly rising (expanding) loaf of raisin bread. There is nothing in GR that says one is expansion 'in space' while the other is expansion 'of space'. The expansion scalar makes no distinction. Note, the expanding raisin congruence could be isotropic and homogeneous except at the boundary.

What is really remarkable is that GR makes it essentially impossible to have a steady state universe. The assumption of isotropy and homogeneity at cosmic scales leads inexorably to expansion of the congruence. This prediction of GR was extracted before there was observational evidence of expansion, and initially dismayed Einstein, because he was looking for steady state solutions.

 

[bcrowell]

To follow on what Bcrowell said, the same expansion scalar can apply to a congruence representing raisins in a rapidly rising (expanding) loaf of raisin bread. There is nothing in GR that says one is expansion 'in space' while the other is expansion 'of space'. The expansion scalar makes no distinction. Note, the expanding raisin congruence could be isotropic and homogeneous except at the boundary.

I don't think it's quite as arbitrary as that. The congruence representing the Hubble flow has special properties that really do make it a description of cosmological expansion. One of those properties is that the world-lines are all geodesics. Another of those properties is that it's the Hubble flow.

 

[PeterDonis]

How/what warps space-time such that distant objects appear to move AWAY from each other, rather than TOWARDS each other like we see locally?

There are two answers to this. The first is that the ordinary matter and energy in the universe acts to slow down the expansion--or, if we want to avoid the word "expansion", it acts to decrease the rate at which distant objects appear to move away from each other (and from us). In other words, ordinary matter and energy in the universe as a whole exerts attractive gravity, just as it does locally. (Remember that ordinary "gravity", what you're used to seeing locally, does not cause objects to "move towards each other"; it causes them to accelerate towards each other. If they start out moving away from each other, it causes them to move away more slowly.)

The second answer is that ordinary matter and energy is not all that is present in the universe. There is also something called "dark energy", which acts to increase the rate at which distant objects appear to move away from each other (and from us). Pop science presentations often describe this as "the expansion of the universe is accelerating". (It's only in the past few billion years that this has been happening; before that, the rate at which objects appeared to be moving apart was decreasing, not increasing.) Ordinary matter and energy can't produce this effect, which can be thought of (with appropriate caution) as "repulsive gravity"; that's why cosmologists include dark energy in our best current model of the universe.

 

[Glurth]

Peter; I must misunderstand, it sounds like you are attributing the expansion entirely to dark energy.

>> The assumption of isotropy and homogeneity at cosmic scales leads inexorably to expansion of the congruence. This prediction of GR was extracted before there was observational evidence of expansion
Ah thank you PAllen, this is what I was thinking about when positing originally. Is it possible to provide a simple visualization or conceptualization for how this works? I'm talking "bowling ball on a rubber sheet"-simple, at least to start with.

 

[PAllen]

I don't think it's quite as arbitrary as that. The congruence representing the Hubble flow has special properties that really do make it a description of cosmological expansion. One of those properties is that the world-lines are all geodesics. Another of those properties is that it's the Hubble flow.

I said the expansion scalar makes no distinction. Further, there is no mathematical object you can point to that makes such a distinction. The Hubble flow is just a name we may give to the congruence (and that galaxies approximately materialize this congruence).

As for geodesics, while my raisins would not follow geodesics, you can construct an isotropic, homogeneous, expanding congruence of geodesics in flat Minkowski space: the Milne congruence.

 

[bcrowell]

As for geodesics, while my raisins would not follow geodesics, you can construct an isotropic, homogeneous, expanding congruence of geodesics in flat Minkowski space: the Milne congruence.

I'm not sure what point you're making here. This can be considered as a special case of the FLRW spacetimes where there is no matter. In this special case, there is no way of defining a Hubble flow, and it therefore makes sense that we can't define an expansion tensor for the Hubble flow.

 

[PAllen]

I'm not sure what point you're making here. This can be considered as a special case of the FLRW spacetimes where there is no matter. In this special case, there is no way of defining a Hubble flow, and it therefore makes sense that we can't define an expansion tensor for the Hubble flow.

My point is that you can define a congruence of geodesics in Minkowski spacetime with isotropic, homogeneous expansion (as defined by the expansion scalar). If some collection of tiny objects followed these over some volume, no one would claim this is expansion 'of space' rather than 'in space'. My claim is that there is no mathematical distinction between these (expansion of space rather than in space). There is just an expansion scalar of a congruence, subject to whatever interpretation you like.

What is different about a realistic cosmological solution is that matter, on average, follows the mathematical congruence, and that (per GR) there must be spacetime curvature in a non-empty universe - the Milne congruence as cosmological model cannot actually be realized (though it can be modeled over a region).

 

[PAllen]

Peter; I must misunderstand, it sounds like you are attributing the expansion entirely to dark energy.

>> The assumption of isotropy and homogeneity at cosmic scales leads inexorably to expansion of the congruence. This prediction of GR was extracted before there was observational evidence of expansion
Ah thank you PAllen, this is what I was thinking about when positing originally. Is it possible to provide a simple visualization or conceptualization for how this works? I'm talking "bowling ball on a rubber sheet"-simple, at least to start with.

I don't really know of one. In terms of 'verbal mathematics', if you specify that matter is homogeneously distributed, and any motion (if present) is isotropic, and derive the general family of solutions in GR with this property, you find that the only solutions that are static require a constant to be introduced and set to a uniquely tuned value for a given overall matter density. Any solution with the constant not introduced, or having any value other than the uniquely tuned one, gives you an expanding congruence (that may become contracting at some point if the density is high enough).

 

[PeterDonis]

I must misunderstand, it sounds like you are attributing the expansion entirely to dark energy.

No; only the "acceleration" of the expansion (i.e., the increase in the rate of increase of distances between galaxies) is attributed to dark energy. The expansion itself (i.e,. the fact that distances between galaxies are increasing) is due to the Big Bang--i.e., the universe is expanding now because it started off in a hot, dense state that was expanding. (More precisely, it was that way at the end of inflation.)

 

[bcrowell]

My point is that you can define a congruence of geodesics in Minkowski spacetime with isotropic, homogeneous expansion (as defined by the expansion scalar). If some collection of tiny objects followed these over some volume, no one would claim this is expansion 'of space' rather than 'in space'.

I don't see the point of focusing on this exceptional case. Normally when we talk about FLRW models, we mean ones that aren't empty. The non-empty ones have different properties from the empty one. In particular, they have a well-defined Hubble flow.

If you meet someone who really loves to interpret cosmological expansion as an expansion of space, then I don't see what is accomplished by discussing this special case with that person. Of course that person will agree that there is no way to define a rate of cosmological expansion in this case. Since there is no way to define a rate of expansion, the question never even arises as to whether that rate of expansion should be referred to as an expansion of space.

My claim is that there is no mathematical distinction between these (expansion of space rather than in space).

I think we both agree that in non-empty FLRW metrics, it is arbitrary whether or not to say that there is "expansion of space." Those are just words, and we can choose to define them however we wish.

 

[Glurth]

I guess what's throwing me off is HOW gravity, which locally appears to be an attractive force, at large distances can appear to be repulsive.
Is there something else going on other than gravity (like, say... thermodynamic expansion)? Or is gravity, in particular situations, simply warping space-time so much that it acts repulsive? Or does it just APPEAR repulsive? Is there some frame of reference in which it does NOT appear repulsive?

>>In terms of 'verbal mathematics', if you specify that matter is homogeneously distributed, and any motion (if present) is isotropic, and derive the general family of solutions in GR with this property, you find that the only solutions that are static require a constant to be introduced and set to a uniquely tuned value for a given overall matter density. Any solution with the constant not introduced, or having any value other than the uniquely tuned one, gives you an expanding congruence (that may become contracting at some point if the density is high enough).

Hmm, so does that(homogeneously distributed, motion isotropic) mean the only variables left, to determine weather a model universe "expands" or "contracts", is the density of matter and energy? No other variables are a factor? Sounds like the same conditions that determine weather a black hole will form or not. Could something like that, maybe for flatlanders, be used as an imperfect analogy?

 

[PAllen]

I guess what's throwing me off is HOW gravity, which locally appears to be an attractive force, at large distances can appear to be repulsive.
Is there something else going on other than gravity (like, say... thermodynamic expansion)? Or is gravity, in particular situations, simply warping space-time so much that it acts repulsive? Or does it just APPEAR repulsive? Is there some frame of reference in which it does NOT appear repulsive?

>>In terms of 'verbal mathematics', if you specify that matter is homogeneously distributed, and any motion (if present) is isotropic, and derive the general family of solutions in GR with this property, you find that the only solutions that are static require a constant to be introduced and set to a uniquely tuned value for a given overall matter density. Any solution with the constant not introduced, or having any value other than the uniquely tuned one, gives you an expanding congruence (that may become contracting at some point if the density is high enough).

Hmm, so does that(homogeneously distributed, motion isotropic) mean the only variables left, to determine weather a model universe "expands" or "contracts", is the density of matter and energy? No other variables are a factor? Sounds like the same conditions that determine weather a black hole will form or not. Could something like that, maybe for flatlanders, be used as an imperfect analogy?

Even for a solution that ultimately collapses, there was prior expansion. Only by imagining initial conditions of 'created the universe as a whole in a contracting state' would you avoid expansion. But even then, if run the model backwards from that point (rather than presuming creation in that state), you find an expanding phase. Thus GR really is telling us that (if it is a true theory), that some form of big bang model is an inherent prediction. To my view, this is really the most remarkable prediction, perhaps unique in science, where a few very simple assumptions about gravity plus math make a wholly unexpected prediction about cosmology that is then discovered.

As for the other part of your question, there are two parameters involved in whether or not there is a collapse phase for a universe. The matter/energy density and the cosmological constant (that I referred to in my prior post about fine tuning). Together, these fully determine whether there will be a collapse phase (again, given that GR is take to be true).

[edit: I thought of a possible way to understand about why there isn't always just collapse if gravity is attractive. Consider that the inside of a spherical shell behaves as if there is no gravity - it is locally identical to if the shell weren't there. Then a homogeneous stated can be imagined as concentric shells from any point. Thus the direct attractive character becomes irrelevant, and the dynamical features of the theory dominate. ]

 

[Glurth]

>> Then a homogeneous stated can be imagined as concentric shells from any point. Thus the direct attractive character becomes irrelevant...

I love those insights that make you smack your head and say, "well, of COURSE it's that way!" Thank you!

>> the dynamical features of the theory dominate.
So, this is where the cosmological constant comes in? I thought I read that the cosmological constant acts as a repulsive force produced by empty space: I assume that is just an imperfect analogy? It sure doesn't SOUND like it's generated by gravity

 

[PeterDonis]

I guess what's throwing me off is HOW gravity, which locally appears to be an attractive force, at large distances can appear to be repulsive.

It doesn't. (At least, it doesn't if we leave out dark energy.) The gravity of the ordinary matter and energy in the universe is attractive; it makes the rate at which objects appear to move apart in the universe decrease over time. The fact that objects are moving apart does not mean gravity is repulsive. In the same way, the attractive gravity of the Earth makes the upward speed of a ball that's thrown upward decrease over time. The fact that the ball is moving upward doesn't mean Earth's gravity is repulsive.

 

[pervect]

A few of my favorite papers which might be helpful to the OP's interest in expanding space (though it will take a fair amount of time to actually read them, of course).

http://arxiv.org/abs/0707.0380 "Expanding space, the root of all evil?"

From the abstract:

While it remains the staple of virtually all cosmological teaching, the concept of expanding space in explaining the increasing separation of galaxies has recently come under fire as a dangerous idea whose application leads to the development of confusion and the establishment of misconceptions. In this paper, we develop a notion of expanding space that is completely valid as a framework for the description of the evolution of the universe and whose application allows an intuitive understanding of the influence of universal expansion. We also demonstrate how arguments against the concept in general have failed thus far, as they imbue expanding space with physical properties not consistent with the expectations of general relativity.

Note that the claims of this paper is just that the idea of "expanding space" can be interpreted in a manner whereby it gives correct qualitative physical predictions.

A more critical paper that mentions some of the usual confusions surrounding expanding space - it may be a bit more technical than the previous one though:

http://arxiv.org/abs/astro-ph/0310808 "Expanding confusion: common misconceptions of the cosmological horizon and the superluminal expansion of the universe"

We use standard general relativity to illustrate and clarify several common misconceptions about the expansion of the Universe. To show the abundance of these misconceptions we cite numerous misleading, or easily misinterpreted, statements in the literature.

In both cases I've linked to the abstract, from which one can get the PDF version of the whole paper.

My personal take is that the idea is very commonly presented in pop-sci, enough so that we have to "live with it". But (and again this is my personal opinion) the idea does it seems to generate quite a bit of confusion as to what it actually says.

 

[PAllen]

http://arxiv.org/abs/astro-ph/0310808 "Expanding confusion: common misconceptions of the cosmological horizon and the superluminal expansion of the universe"
In both cases I've linked to the abstract, from which one can get the PDF version of the whole paper.

My personal take is that the idea is very commonly presented in pop-sci, enough so that we have to "live with it". But (and again this is my personal opinion) the idea does it seems to generate quite a bit of confusion as to what it actually says.

It is worth noting, in reference to controversy on this, that Tamara Davis, co-author of this paper, largely dis-avowed it later, adopting the view (which I hold) that cosmological red shifts are fundamentally indistinguishable from kinematic red shifts.

 

[PAllen]

Can't resist one more comment on how there is nothing possible in the math of GR that distinguishes whether an expanding congruence represents expanding space versus expansion in space. Consider simply a time reversed Oppenheimer-Snyder collapse. This is a perfectly valid (though physically ridiculously implausible) solution in GR. You have an FLRW expansion into white hole Schwarzschild solution. Most anyone would see this as expansion in space, yet the description of the expanding congruence is mathematically identical to a cosmological solution.

Now don't get me wrong - I think expanding space can be useful interpretation aid, and e.g. for explaining CMB radiation frequency, it is much easier that any other interpretation I know of. I just feel it is important to understand that there is no specific 'physics of expanding space', because that helps remove the mystery of things like "why doesn't a galaxy expand?". It also helps understand why there isn't a distinguishable form (rather than pattern) of cosmologic red shift. There is mathematically only one general form of red shift in GR.

I also think the Milne congruence is very useful to understand what phenomena come from matter and curvature and what are coordinate dependent. You see that arbitrarily super-luminal recession speeds do not require curvature and are not, in any way shape or form, relative velocities. In fact, one can jump from here to realize that a super-luminal recession velocity is effectively a celerity, which 'everyone' understands has no limit in relativity. The superliminal magnitude comes from dividing growth in distance as measured by 'me' by a time that matches ticks on a clock with high red shift with ticks on my clock (that is what the cosmological time coordinate does). The result of this division is a celerity, and is trivially superluminal. Using the Milne congruence in flat spacetime you directly see how the recession velocities are mathematically nothing but celerities. That is, the flat space-time limit of an FLRW recession velocity is exactly an SR celerity not an SR relative velocity.