# The physical meaning of expansion in cosmology

1. Jul 24, 2008

### marcus

The aim of the thread is to offer a non-technical concrete way of understanding the standard model. Usual metric, equations, parameters are in the background but the focus here is on unmathematical presentation, indicating how key physical quantities could (ideally!) be measured.

When I talk about distances I mostly mean distance between stationary observers--that is stationary wrt the CMB. Stationary is an approximate notion (as most ideas are): the observer's microwave sky is nearly the same temp in all directions. What I mean by the present moment--now--is all the observers for whom the sky has the same temperature.

This is my recipe for intuitively understanding standard expansion cosmology, other people can have different ways to go about it. As long as everybody understands that space is just a bunch of distances, then it is perfectly fine to say space expands.

The key thing is not to objectify space---think of it as if it were a thing or a material substance. If I suspect there are people in the room who are apt objectify space in their heads, then I try to refrain from saying those exact words "space expands", because it might encourage the idea that it is a thing or material. Instead, I say something that means the same, like "distances increase in a regular pattern." But if I am in the coffee room at the astronomy building with nobody around but some grad students, then I have no compunction about referring to space as expanding because everybody knows it's just a network of geometric relations---basically just a bunch of distances.

Saying space expands is just a quick way of stating Hubble Law, which is an empirical observed approximately regular pattern of increase of distances. It's as true as anything ever is in science. It talks about current (now) distances between contemporary stationary observers and it says that on large scale they are currently increasing at a percentage rate of 1/140 of a percent every million years.

It's important to mention that the rate changes, it used to be a lot bigger in the past, and it is decreasing asymptotically to about 1/160 percent per million years in the far future. According to the standard model, it will always decrease but at a more and more gradual rate so that it kind of levels out at 1/160 of a percent in the late universe.

There is some random variation in the pattern which averages out and it applies to largescale distance outside the range of gravitationally bound systems. It's both empirical and what the standard (Friedmann) model says ought to happen---and it's what is meant by saying space expands.

I want to say a bit more about measuring the current distance between stationary observers, but that can wait for another post.

2. Jul 24, 2008

### marcus

Just a word about General Relativity. It is our best theory of geometry/gravity so far.
We know it's wrong because it breaks down at places---develops singularities at the center of a hole or the moment of a bang. Improved theories that get rid of these singularities are under construction but not yet empirically tested. Actually quantum cosmology is progressing remarkably fast at the moment so it is becoming almost routine to run computer models back to before the bang and to model what's down the hole past where singularity used to be. So there's a quantum revolution going on in GR.

But the improved quantum models being constructed reproduce GR if you stay sufficiently away from the classical singularities. What I have to say assumes GR but also in a sense includes the revolution.

Geometry tells us how distances behave---and other geometric stuff like angles. If you go out and construct a large triangle with surveyor instruments and find that when perfectly measured the angles don't add to 180 degrees then you say the space here is curved. If you construct a right triangle and measure the sides and they don't satisfy a certain algebraic rule then again you say the space is curved. Or if you measure the distance between stationary objects and later find it has changed, well OK it has changed.

GR teaches us not to expect that triangles always sum to 180 degrees, or obey pythagoras formula. And it teaches us not to expect distances to always stay the same. The beautiful thing is that, as a highly successful theory of geometry, GR predicts the deviations from Greek expectation. (It also predicts deviations from the framework of special relativity, which has some of the same rigidity as the Greek version.) The deviations are according to a regular rule (the Einstein equation) which governs geometry.

This post is admittedly vague---it is merely meant to convey my attitude about GR. Briefly, my attitude is don't live in a straight-jacket of Greek expectations about geometry.

GR tells us to expect approximate flatness (un-curved-ness, approximate Greek-ness) in our daily geometry because the gravitational field is weak. And it says to expect other geometric realities over large distances and time intervals, or near high density. And what is so nice, it tells us how to calculate what to expect in the way of differences.

Also curvature is an internal experience---the angles not adding up to what the Greeks told us. Curvature does not presuppose any extra dimensions.

3. Jul 24, 2008

### marcus

A word on how to think of measuring distance, ideally.
I saw this some years back at Ned Wright's website, but when I looked recently I didn't find it.
He pictured a chain of contemporary stationary observers stretching from here to there.

The distances between neighboring observers are short, so they can measure the radar distance between neighbors very quickly. The idea is to be able to measure a distance at the present moment, before it changes.

All the observers are at rest wrt the CMB---that is the important thing. That lets them synchronize their clocks. Differences in gravitational potential are neglected, they are mostly pretty even in that regard. So they synchronize their clocks and at the same moment--now--they all measure the radar distance to their neighbors. And we add it up.
So that's the real physical distance along the chain of observers.

Pick the distance along the shortest chain and that's the distance from here to there.

In the real world astronomers have a distance ladder of different methods of estimating, and they check one method against the other. No one method is perfect but the end result is they give a way to estimate and approximate the ideal present-day physical distance to some remote stationary observer (in the vicinity of some remote galaxy, say) corresponding to the distance in the usual Friedmann model. That's how I think of, for example, the particle horizon----current distance of about 46 billion lightyears---present day distance to the farthest thing we could in principle see or detect.

and it is this kind of physical today distance which is increasing---the rate of increase is what is meant by recession speed.

I guess it's obvious that this rate of increase can be very much larger than c without violating the rule that nothing can catch up with and pass a proton. Have to go soon for an appointment. Will discuss this further as time permits.

4. Jul 24, 2008

### MeJennifer

I think the phrase "expansion of space" should be completely avoided as it is technically wrong and confusing. I disagree with you that it is "perfectly fine". If you disagree then explain to me what it is that expands?

I think that is a good phrase as it accurately explains what happens in to distances between objects in a particular coordinate chart.

5. Jul 24, 2008

### paw

Nicely said Marcus. From reading many of the posts here and in the SR & GR forum it's clear to me that many people do exactly that, objectify the notion of space time.

I'd like to add to your post a little. Another common misconception is that the mathemetical model under discussion must, of necessity, describe reality. Just because GR describes spacetime in terms of 'curvature' doesn't necessarily mean that it does in fact 'curve'. This is just the best model we have at this time. It works in terms of calculating motion of masses in its region of applicability and is therefore very useful but it's still just a mathematical model of reality. Same with the expanding universe, it's the best model we have but still a model.

Another point I'd like to make. Argument via analogy is probably the worst possible way to make a point in cosmology, GR, SR or quantum physics. Analogy relies on there being a similar and common shared experience but the afforementioned sciences are completely out of common experience. There are no analogies by definition. You pretty much need to stick to math or at the least to well defined scientific terms.

6. Jul 24, 2008

### MeJennifer

Note that it is very important to distinguish between space and spacetime in these discussions. Spacetime does not expand and distances between events never increase or decrease.

7. Jul 24, 2008

### paw

Good point, thanks. I'm guilty of poor choice of words myself at times. However I do try to get it right which is something I guess....

8. Jul 24, 2008

### robertm

I sure your efforts will be greatly appreciated by many here in the Cosmology forum, the questions you are answering come up in almost every thread.

A pre-emptive attack huh?

9. Jul 24, 2008

### starkind

Typo in post 3, you wrote proton instead of photon. I'll delete this on correction. Good stuff, marcus.

10. Jul 28, 2008

### yuiop

Hi Marcus,

I suspect this thread is partly in answer to a question I asked you in another thread, but you have not really addressed the question directly. Basically the question was what fo you mean by the distance between galaxies is increasing? Do you mean galaxies are moving through space or space is expanding and carrying the galaxies along with it.

In post #1 you said:
which seems to indicate that that you tend towards the galaxies moving through space rather than space expanding and that is the impression I get from other posts of yours. However, the problem with galaxies moving through space is that they would be subject to time dilation, length conctraction and momentum as per Special Relativity as well as recession velocities being restricted to below c. You have not adressed this issue at all in this thread. One of the links you posted in another recent thread actually says the opposite to what you are saying. It is the sciam article http://www.astro.princeton.edu/~aes/AST105/Readings/misconceptionsBigBang.pdf [Broken] on popular misconceptions that you recommended to artie in the "Does the fabric of space-time move faster than the speed of light?" thread it clearly says "The solution is that special relativity applies only to “normal” velocities—motion through space. The velocity in Hubble’s law is a recession velocity caused by the expansion of space, not a motion through space." The sciam article you recommended in fact implies that you are suffering from a misconception if you do not accept that "space itself expands". You admit you do not like the description of "space itself expanding" because it implies that the vacuum of space is a substance, implying some sort of ether and you are right to be concerned because that is exactly what it implies. If the vacuum of space is exactly nothing then it can not be curved, stretched or expanding. The expanding space interpretation is used because it elliminates the time dilation of SR and the restriction of velocities to less than c. This in turn implies that it is motion relative to the substance of space that causes time dilation rather than motion relative to other observers which contradicts what we have been told for a long time in Special Relativity. It also implies that the speed of light is not a restriction relative to observers but a restriction relative to the local fabric of space. So cosmologists are on the horns of a dilemna. They want to use the space expanding explanation because it gets rid of speed restrictions and time dilation but at the same time they don't want to admit the vacuum of space is a substance and it the substance of space that regulates relative velocities and time dilation rather than motion relative to other observers as implied by SR. The trouble is they can't have it both ways.

P.S. I am playing Devil's advocate here because I am not sure myself which interpretation is correct. If anything I lean towards galaxies moving through space rather than space expanding and suspect that observations can be accounted for by a basically SR model with gravity and rapid inflation in the early stages thrown in. By the way, SR and GR can happily co-exist, because rapidly moving objects in a gravitational field experience both gravitational time dilation and SR kinetic time dilation. Purists would say GR includes the SR time dilation due to rapid motion but I split them up to make the effects clear.

Last edited by a moderator: May 3, 2017
11. Jul 28, 2008

### MeJennifer

One of the first things to realize in relativity is that motion is always relative. From that perspective the whole "motion through space" or "expansion of space" dichotomy is pretty absurd IMHO.

As to special relativity being compatible with general relativity that is only true for spacetimes without a cosmological constant.

12. Jul 29, 2008

### oldman

Well, I think that laudable as this aim is, Marcus, I fear it is rather like trying to light a match on a piece of wet soap. The trouble lies with the concept of 'understanding', which I take as a synonym for 'placing new knowledge in the context of your own experience'.

When it comes to understanding what has come to be called the 'expansion' of the universe, there is sadly no such context or, worse still, misleading contexts of balloons inflating, of an impossibly hypothetical "chain of contemporary stationary observers stretching from here to there", or thoughts of heated objects swelling up. Remember that someone (I can't remember Her name, but She talks in bold...) once said: For my thoughts are not your thoughts, neither are your ways my ways. This is in fact talk about General Relativity.

Expansion is simply a metaphor for GR change. Thole it.

Perhaps if the match were made of Sodium.......

13. Jul 29, 2008

### mysearch

An excellent goal worthy of support, but who will judge the success of this understanding, the experts or the students? As an interested student of this subject, albeit a very old one, statements without explanation are not always helpful, e.g.

Fine, but please qualify or quantify such statement so that the ‘student’ can understand the context, as almost every introductory text on cosmology talks about the expansion of space. Most mention the balloon analogy, which is then often qualified but not always rationalised, other than to say the ‘big bang’ should not be modelled as an explosion. Post #10 has already highlighted some confusion with respect to special relativity, which may or may not just be with the definition of expansion or non-expansion in question.

With all due respect, while the absurdity may be obvious to the experts, I thought the whole point about the expansion of space was to avoid the issue of relative motion through space, which might then violate SR. Please accept that these comments are not intended as a criticism, but rather seek to support the stated goal above.

14. Jul 29, 2008

### MeJennifer

I don't see the issue, special relativity's applicability is limited to flat spacetimes.

15. Jul 29, 2008

### marcus

I think neither of your two alternatives is correct, kev. You are putting words in my mouth.
It is fine to say space expands as long as you do not objectify space and imagine it is a substance.

If you treat space as the sum total of all the distance relations between CMB stationary observers then all it means to say space expands is that there is a regular pattern of increase of distances. This pattern of increase is called Hubble Law. And it is all that is meant by saying space expands. And the law appears to be correct. And it is fine to say space expands. It is an intelligent concise way of describing what we see happening.

To say space expands does not logically imply that space is a substance. It has the unfortunate side effect of suggesting that to people who are new to the discussion, or who aren't thinking carefully.

Around here, at PF cosmology, there are a lot of noobs so you might want to refrain from putting it that way. What I often do is say pattern of increasing distances (which means the same) so as to emphasize that we don't want to objectify space.

The other thing you should try to avoid is thinking of galaxies as moving through space. (That also, in a different way, tends to objectify space in the listener's mind.) Galaxies typically have only rather small local speeds relative to the CMB as far as we can tell. A few hundred km/s. This is not their recession speed and has nothing to do with recession speed.

Recession speed is not a physical property of the galaxy itself. It is a rate of increase in the distance between us and them. It isn't even defined except from our standpoint or until you say who us is. With recession speed you should focus on the distance between two stationary observers, and focus on the distance itself, and the percentage rate of increase. Like 1/140 of a percent per million years.

I have some things to do, don't have time to edit this or make it clearer. Maybe later today. Hope it does some good as it is. Remember that the new geometry we have been living with since 1915 is not the same as rigid Greek geometry. You have no right to expect distances between stationary objects to remain constant. The best you can hope for is some pattern to the change in distances.

Last edited: Jul 29, 2008
16. Jul 29, 2008

### BoomBoom

Not if your view of space is that it is nothing at all. It is quite easy to imagine galaxies moving through it. In fact, it is the only way that expansion of space can make any lick of sense at all IMO....otherwise you need an explanation of where all the extra empty space is coming from. It doesn't push or pull anything, it is simply created by things moving farther apart.

17. Jul 29, 2008

### marcus

I want to say belated thanks for all the feedback, including kind expressions of approval. And to Starkind for catching a typo. I did mean photon, not proton! Some posts were responding to others like MeJennifer's. Apologies if I missed anyone. All the feedback helps (sometimes if only to show what people find most difficult to understand, but often to suggest points left out.) Thanks all!

I'm trying to think how I could continue this thread. Something else has come up but will get back to this in a few minutes.

18. Jul 30, 2008

### mysearch

Response to #14

If, on the very large scale, the universe is assumed to be homogeneous with no centre of gravity, where matter, inclusive of any dark matter, can be modelled as ‘dust’, what causes spacetime curvature on this scale?

If the measurement of [k], to-date, suggests a value that is effectively zero, then FRW metric appears to reduce to a form:

$$- c^2 \mathrm{d}\tau^2 = - c^2 \mathrm{d}t^2 + {a(t)}^2 \left( \frac{\mathrm{d}r^2}{1-k r^2}\right) = - c^2 \mathrm{d}t^2 + {a(t)}^2 \mathrm{d}r^2$$

This seems to be similar to the Minkowski or SR spacetime metric, other than the terms $$a(t)$$. Now I am assuming the rate of change of this conceptual or real expansion with time might be modelled as a constant or decelerating or accelerating value or more likely a mixture of all over time. However, today $$a(t)=1$$, so what does the equation above say about the curvature of spacetime at any given point in time?

Putting aside any ideas about whether spacetime has any inherent structure or not, if two objects in spacetime appear to be moving apart within a given frame of reference, what laws of physics, i.e. energy, forces or curvature, can be used to account for the apparent recession velocity?

Please note these are questions not assertions of fact.

19. Jul 30, 2008

### MeJennifer

Re: Response to #14

Right, so it is conformally flat but, conformally flat is not equal to flat and thus it is very unsimilar to Minkowski spacetime.

20. Jul 30, 2008

### mysearch

Response to #19

I assume that the inference is that the answer to my questions in #18 can only be addressed by introducing the complexity of conformal flatness plus all the mathematical complexity that goes along with this idea? Not sure this is in the spirit of what this thread set out to achieve:

However, it might be a perfectly valid response to my questions, as several sources concur that FRW universes are also conformally flat. In an attempt to understand the implications of this complexity I found the following abstract to an article entitled: Coordinate confusion in conformal cosmology

I guess I should timeout at this point having hopefully returned to the main issue of this thread The physical meaning of expansion in cosmology albeit without necessarily understanding why “the question of whether space really expands is a futile exercise”. I look forward to another concise answer to this question.

Last edited: Jul 30, 2008
21. Jul 30, 2008

### marcus

Is the USA really a democracy? :-)

Questions with the word really in them can often seem to be futile. I think what one needs to do is remove the word really (which seems to have no meaning in the context) and consider the question.

Is the USA a democracy? Well, OK, that's not futile to ask: we define what we are going to mean by a democracy and try to answer. Does that polity or society satisfy those conditions? It might be a hard question but it is not necessarily a futile one.

Does space expand? Yes it does if one views space at the present moment as a bunch of distances between observers stationary wrt CMB. Then space expanding is just a regular pattern of increasing distance specified by Hubble's Law.

So the question is does Hubble's Law apply?---and how well does it fit the data? Successful predictions? That's a substantive scientific question, not futile.

As a rule, all scientific questions come down to questions of how well some model fits observation----instead of asking is some model REALLY true, we ask how well it fits and if it can be refuted by empirical means, and also is it perhaps significantly simpler than alternative models if there are some equally good fits.

So I would emend that paper's abstract merely by deleting the futility clause at the end, so that it says:
If the authors had asked my advice, I would have suggested that editorial change---just cut out the last twelve words which I think distract from the rest because they evoke a separate issue.

I think that there's this separate issue of trying to reform our language, that keeps coming up. Should we or should we not try to discourage people from using the phrase "expansion of space"?

I think the essential concern here is that if people hear you say expansion of space they will mentally objectify space as a physical material, instead of just a collection of geometric relationships. Attributing physical reality.

I think the correct response to this danger is not to try to stamp out the phrase (attempted language reform can be a cure worse than the disease), but to emphasize that what it means is a patter of increasing distances.

I think trying to censor out that phrase also presents real dangers of confusion. If you start saying "Let's not say space expands." somebody will inevitably think you are saying "Space does not expand." (this has happened! I have been misquoted that way myself in fact )
And then somebody else will say "Oh good it is possible that space does not expand. Let's try to think of arguments to show this, and alternative explanations of redshift and recession speeds!" This can cause confusion and considerable wasted effort.

As far as I can see, from regularly scanning the research literature, the expansion of space is not controversial (as long as you are clear about what you mean and don't attribute physical reality to space.) The danger of attempting to reform language in this case is that one can create the delusion of taking part in a major controversy about something which in fact is not to any major extent controversial.

So I've changed my position on language reform in this area! For a few months I was avoiding using the phrase expansion of space and saying something else that means the same thing. Now the downside of doing that has been demonstrated. So I think it is an excellent way of describing the universe, and that it is potentially harmful to try to stamp out that language usage.

In other words, hurrah for expansion!

Last edited: Jul 30, 2008
22. Jul 30, 2008

### Ynaught?

Hey Marcus,

I have a quick question...

Why? What is the evil that results from "objectifying space"?

23. Jul 30, 2008

### marcus

actually BTW this is not my crusade. Several other people have made the point more forcefully about not objectifying space and over the past couple of years I have been adapting. I already had that point of view but it wasn't epecially an urgent message with me.

Also BTW, Ynaught, I've noticed when people do this, they seem, after living with the misconception for a while, to end up dreadfully confused. And they come around and ask questions like when space expands what makes the new space? they think there has to be some new space created to fill in the gaps. And how can it be created? out of what? Or if two blobs of space are receding from each other where did they get the energy to do this and wouldn't their speed be limited by c according to SR. And what is space made of? since it is some kind of material. And if space is expanding what is there outside it that it is pushing out into? Is it a different kind of space? I wouldn't call that evil, just unnecessary detours. they make life harder for themselves by objectifying something that is merely relational and wasn't meant to be objectified.

So you ask, what evil results? Well maybe there is no EVIL. Maybe the point is that as far as we know it is wrong, an intellectual dead-end. Occam Razor says don't make up unnecessary entities and long experience validates the principle.

You may know those 1915 quotes from Einstein where he says that (as far as General Relativity goes) spacetime has been deprived of the last vestige of objective physical reality. He said that several times in various ways. He came to GeneralRelativity thinking of space as a bunch of distances (something learned from Mach) and not as some kind of graph paper with its own independent existence.

that spirit---that space and spacetime have no objective reality---infuses Gen Rel, because that is how he was thinking when he developed it. So if you take that point of view it helps with understanding. I think at least.
=================================
=================================

that's really all I have to say. the rest is just extra. I want to try and suggest how it is done mathematically.

the principle of general covariance alias diffeomorphism invariance: you can push the matter and geomety all around and totally remodel the situation and it still describes the same world.

mathematically, what is important is not WHERE the humps are, but where the humps are in relation to the matter and more generally to events. events have significance. they have no fixed points where they are located, anywhere will do as long as relationships are preserved.

this is a very personal way of saying it. If you don't like my way, get somebody else to say it a different way.

In classic GR a key step is to use a blank continuum (limp, with no initial background geometry) to set things up and then in effect you solve for the geometry and then throw the continuum away. Only the relationships (that arise as a solution to the equations) are left---like the smile when the cat is gone.

The gravitational field is ultimately not just one particular metric on one particular continuum but an equivalence class of metrics under diffeomorphisms (smooth morphings).

One way to say it is that the less reality you can attribute mentally to the points of the continuum and the more you can focus on the field (the dynamical geometry) the easier to understand and the fewer philosophical pitfalls.
==============

Last edited: Jul 30, 2008
24. Jul 30, 2008

### Ynaught?

All wonderful philosophical questions... Along with: "What existed before the Big Bang? Where did all the mass and energy in the Universe come from? If entropy generally increases, what made it so low to begin with?"

I am not trying to be confrontational. I am simply at a loss to see what the big deal with imbuing "space" with objectivity is.

How? How do "they" make it harder for themselves?

EDIT**
Are there scientific pitfalls or just philosophic ones? That is the question I should have asked to begin with!

Last edited: Jul 30, 2008
25. Jul 31, 2008

### oldman

Above (my emphasis in bold) is just about the best definition of space I've yet come across.

But it ain't perfect. Here you are talking about space in a special context. One needs a smattering of GR and a bit of background to appreciate the part played by the "CMB": , what is meant by "now" and indeed the whole current comological consensus. It would certainly puzzle anyone new to cosmology. Saying that this space expands could badly confuse someone who regards space as lebensraum to walk a dog in.

There are several sorts of space. One is the sort of space that pervades the intertices between atoms in a crystal. A crystal may expand, but one doesn't imagine any expansion of space. The crystal together with its interstitial spaces expands into external space.

Then there is the space between trigonometric beacons set up by surveyors, who can safely assume that their 'bunch of distances' won't change (ignoring earthquakes and continental drift, that is). Brooklyn doesn't expand.

Or a science-fiction writer might imagine a rigid space-station falling freely in deep space where tidal forces are imperceptible. In an FRW universe there is no reason to suppose that its internal spaces with their 'bunch of distances' would ever change, even over cosmic times (provided they're spanned by a constant rate of expansion).

So the space you defined is quite unlike the ordinary space we are familiar with, although one could in principle measure its 'bunch of distances' by regular methods, say radar or measuring rods, suitably set up.

It would help to distinguish the 'space that expands', which you define so clearly, from ordinary space with a suitable qualifier.

Don't finalise your position on language yet! Choose a qualifier. (I like Hubble space).

Last edited: Jul 31, 2008