# Does Space Expand?

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What do you think? When Cosmologist talk about the expansion of the universe, it is often phrased as space itself expanding. For instance, interpreting cosmological redshifts as due to the photons being 'stretched' as they pass through expanding space, rather than being due to a doppler shift (since for instance at cosmological distances galaxies can be receding at greater than c and hence the doppler formula breaks down).

People use analogies to dots on a balloon or raisins in bread but this seems to imply that the expansion of space (the rubber or the bread) is what carries the galaxies (the dots or raisins) apart.

The idea the space expands has been attacked by various people, including the well respected John Peacock. See http://www.roe.ac.uk/~jap/book/additions.html" [Broken], click on the link 'Expanding Space'

Do people agree with this? Is Expanding Space a 'dangerous idea' or a necessary interpretation of the GR equations for FRW universes? The maths is not in dispute, but the interpretation seems to be.

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## Answers and Replies

I don't know that there's anything particularly controversial about this. In the RW metric, objects which remain at constant coordinate positions find that the physical distances (constant-time intervals) between them change over time. Since inertia will keep initially unmoving objects at constant coordinate position in a homogeneous, isotropic universe, the interpretation that space is expanding seems pretty clear.

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Sure, that's a pretty clear argument you present and I agree with you. However, there are many, including Peacock, as well as Martin Reese and Steven Wienberg who wrote a New Scientist article about this some years ago who contend that thinking in this way misleads you and it's better to just think kinematically.

The classic test case is this. Imagine you are in an expanding universe and hold a galaxy at rest with respect to you but at a cosmological distance. According to Hubbles law a galaxy at that distance should be receding but you prevent this by using a chain or rockets or something to hold it in place. If you let go of the galaxy, what does it do?

[THINK ABOUT THIS FIRST THEN READ ON]

The answer you may assume is that since space is expanding the galaxy will start moving away from you, joining the Hubble flow eventually. However in a decelerating (but still expanding) universe the particle actually comes towards you! If you think about it it becomes clear why but Peacock argues in the link I posted that it is the idea of expanding space that leads to these misconceptions and hence should be abandoned.

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In the RW metric, objects which remain at constant coordinate positions find that the physical distances (constant-time intervals) between them change over time.
Pardon me for being so blunt Parlyne, but what is that supposed to prove?

By all means we should avoid using coordinates as if they were some physical background of general relativity.

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Science Advisor
By all means we should avoid using coordinates as if they were some physical background of general relativity.

This is a good attitude, since co-ordinates are so slippery in GR and we have to be careful how we go from co-ordinates to what we actually observe. However we do need to have some physical interpretation of what the co-ordinate solutions tell us, the question is is thinking about the expanding universe as something where space itself expands useful or misleading?

I've read that distant galaxies are receding faster than light and the only way to explain this is the expansion of space. I know there is debate about the doppler shift and even the speed of light being constant. But relativity has been around a long time, and has been tested many different ways, so I will go with it until there is more consensus with regard to the newer theories.

marcus
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... relativity has been around a long time, and has been tested many different ways, so I will go with it until there is more consensus...
relativity comes in two flavors, general and special.
general (the 1915 theory) trumps special (the 1905 theory)
both have been around a long time and have triumphantly passed many tests.

general allows the distance between two things to increase faster than the speed of light

general allows the distance between two things to increase faster than the speed of light
If you make such statements then it is only fair that you provide a definion of distance in general relativity. Do you agree?

If so, then what is the definition of distance in general relativity?

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Science Advisor
Take the proper distance, which is defined at the length of the interval between events in a frame of reference in which all events are simultaneous. In the case of an expanding universe, co-moving observers have synchronized clocks and hence taking slices through space-time of constant t is straightforward.

What we find is that the proper distance between objects can increase at a rate with respect to proper time (which is also equal to the tick rate of the co-moving observers clocks) that is greater than c.

In any case, regardless of how you choose to define distance in GR, since there are different ways, there is no in-built limit on the rate of change of that distance with time, contrary to what one might expect if you had only studied special relativity.

marcus
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OOPS, WALLACE ALREADY REPLIED! I had to be away from computer for a while and didnt see his answer. Should I edit this down or eliminate it?

If you make such statements then it is only fair that you provide a definion of distance in general relativity.

Do you agree?
No. I don't agree that I am obliged to explain GR basics, each time I make a statement that everyone familiar with the theory knows to be true. In many situations that might be impractical.

...what is the definition of distance in general relativity?

I don't think that I am forced or obliged to respond, Jennifer, but since you ask, I'll take a go at that, for fun.

Gen Rel is about distance and its relation to matter. More precisely it is about geometry and its relation to matter, but the metric or distance function is the core idea in geometry.

Different geometries---different metrics---arise as solutions to the GR equation. In order to define distance one must choose a metric, the distance will be defined in that metric.

One very popular and useful metric is called the FRW metric. Among several convenient and intuitive features, it has a universal time parameter---and thus a notion of simultaneity---providing for a foliation into spatial slices. Moreover in a universe governed by the FRW metric, one can say what it means for an object to be at rest.

GR teaches us that we have no right to expect that the distance between two stationary points should always be the same. Commonly, solutions to the GR equation are metrics with the feature that distances either increase or decrease. Distances can change very dynamically and be increasing in one place and decreasing somewhere else. The FRW metric is simple and convenient in this regard because the increase is uniform across the board according to the time-dependent "scale factor" a(t).

In a lifesize universe (excluding toy model cases) whenever you have distances increasing with that kind of uniformity, you will find superluminal recession speeds. You just have to go far enough out and the rate of increase of distance will be superluminal. I would say that General Relativity welcomes this, since it is a feature of a vast number of metrics which the theory permits, as solutions of the main equation.

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GR teaches us that we have no right to expect that the distance between two stationary points should always be the same.
The distance between two stationary points?

You are right Marcus you are not obliged to explain GR basics.

marcus
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...
The classic test case is this. Imagine you are in an expanding universe and hold a galaxy at rest with respect to you but at a cosmological distance. According to Hubbles law a galaxy at that distance should be receding but you prevent this by using a chain or rockets or something to hold it in place. If you let go of the galaxy, what does it do?
..

nice example.
my guess was that if the Hubble parameter was decreasing it would continue coasting towards you even after the rockets were shut off.
I think that's roughly the same as what you said.

===============

BTW Wallace does it help if one focuses on the idea of distances increasing rather than space expanding---to get people's minds away from the raisin-dough or stretchy-rubber idea?

It could be that "space expands" is an unfortunate popularization choice of words because space is not a substance that can expand.

Ontologically, all we have is the metric or an equivalence class thereof----namely the gravitational field itself---so we don't have some kind of material medium that can expand. All we have is distance and at least for now it happens to be increasing.

I wonder sometimes if "Expanding Universe" wasn't a really unfortunate picture to use in getting an idea across to the general public.

I think if one focuses on very gradual percentagewise increases in distance then the extension of wavelength we see in cosm. redshift can be fairly intuitive

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marcus
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The distance between two stationary points?
.

Yes dear Jennifer
You do not need to use the rolleyes smilie here!
this is maybe the point you need most to understand. The distance between two stationary objects can increase

indeed if they are widely enough separated so as not to be bound by physical forces, the distance normally DOES increase.

read my post about the FRW metric (its idea of rest corresponds to the idea of being at rest with respect to the Hubble flow, or if you prefer the CMB, and so one can say when two objects are stationary)

The distance between two stationary objects can increase
Right, I suppose they must be bolted on the space-time frame of the universe while the frame itself is expanding right?

Perhaps another patronizing posting, but this time for you, about the basics of background independence in general relativity might be fitting here.

Anyway, sorry but I lost my interest in this "discussion" with you.

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Science Advisor

nice example.
my guess was that if the Hubble parameter was decreasing it would continue coasting towards you even after the rockets were shut off.
I think that's roughly the same as what you said.

careful, it is easy to say 'decrease' when you mean 'decelerate' and 'increase' when you mean 'accelerate' and vice versa. In the example I gave an increasing but decellerating universe leads to the test particle coming towards you. If you try and think about this situation by picturing a balloon with dots on it you will say the particle moves away even if the rate at which the balloon is expanding is decreasing. This prediction is wrong however. Basically the issue is that the recession of galaxies causes space to expand, not the other way around which people often get confused about if they have taken the balloon or bread baking analogies too far.

BTW Wallace does it help if one focuses on the idea of distances increasing rather than space expanding---to get people's minds away from the raisin-dough or stretchy-rubber idea?

Perhaps, although it is important that people realize that distances only increase because they did so in the past, i.e. that expansion is a kinematical initial condition, rather than galaxies receding because space is endowed with some mysterious property the causes distances between things to increase.

It could be that "space expands" is an unfortunate popularization choice of words because space is not a substance that can expand.

Ontologically, all we have is the metric or an equivalence class thereof----namely the gravitational field itself---so we don't have some kind of material medium that can expand. All we have is distance and at least for now it happens to be increasing.

Agreed, in the end we have the maths, in this case the knowledge of how the metric changes. The trick is coming up with a suitable picture to explain this to people who do not yet have (if they are students) or will never have (if they are interested general public) the mathematical skills to gain any insight from staring at the FRW metric! In this case the balloon and raisin analogies are useful devices to explain what an expanding universe looks like, but somehow it needs to be made clear that the rising of the bread or the inflating of the balloon is not the driver of the expansion.

I wonder sometimes if "Expanding Universe" wasn't a really unfortunate picture to use in getting an idea across to the general public.

I think if one focuses on very gradual percentagewise increases in distance then the extension of wavelength we see in cosm. redshift can be fairly intuitive

Personally I don't like the gradual red shifting picture. You can image cosmologically redshift as a series of doppler shifts arising from the photon passing through a series of receding rest frames and this is somewhat better than imaging a wave stretching as it passes over an expanding rubbery surface. However I think the clearest explanation is that photons are not redshifted during travel at all. They are redshifted when we observe them in a different frame to that from which they were emitted. This then links directly to SR, i.e. in SR we are familiar with quantities being frame dependant and the same goes for the energy of a photon (and hence it's wavelength) in GR. It also connects this to doppler shifts, which are another way in which the energy is different due to the different frames of emission and reception. In the case of the doppler shift the difference is a relative velocity whereas for a cosmological redshift the difference is a different a(t) in the metric.

But how do you explain this in a cartoon, without leading to a different misconception than the balloon types analogies lead to?? This is what I cannot work out..

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Right, I suppose they must be bolted on the space-time frame of the universe while the frame itself is expanding right?

Apart from the rolly eyes, this is pretty much what the FRW metric implies

Perhaps another patronizing posting, but this time for you, about the basics of background independence in general relativity might be fitting here.

I'm not quite sure what you mean by 'background independence' in this context. Could you explain?

Anyway, sorry but I lost my interest in this "discussion" with you.

Would you consider continuing the discussion with me then? I would value any input

marcus
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...But how do you explain this in a cartoon, without leading to a different misconception than the balloon types analogies lead to?? This is what I cannot work out..
I see the communication problem you are posing. No immediate ideas, although a "cartoon" or animated drawing is suggestive. Will think about it.

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StuMyers
If the rate of expansion is constant, and you boost an unbound object to be at rest with your frame, it will remain there indefinitely.

If the rate of expansion is anything else, the object should move towards or away from you.

I'm missing the problem...

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The problem, or I guess the trick is the rate of expansion is irrelevant. It is the acceleration of the expansion that tells you what happens. So in a contracting universe the particle could move away, or in an expanding universe the particle could comes towards you. You don't intuitively expect this behavior if you think of the universe as a loaf of rising bread filled with raisins!

StuMyers
So, it falls under the category of 'hey, that's cool', rather than 'something's amiss'. Got it, thanks.

Science Advisor
Right, but there is something amiss in that the devices used to explain to people how the universe works leads the intuition astray. It's a question of pedagogy rather than physics admittedly.

I think the problem is in the teaching.

Those people who teach that things like "cosmological time", "preferred space-time hyperplanes", "spatial distance", "time", "preferred coordinate systems", "preferred metrics (even with cross terms)", "expansion", "Hubble flows" etc are absolute properties of the universe as modeled by general relativity.

Only, IMHO, to confuse even more.

These things are dissections or space-time, very useful for analysis, but once these things start living a life of their own and represent "The Universe" the recipients of all this will completely miss the point.

Furthermore:

"An expanding balloon with coins stuck on it that do not expand themselves", is about the worst model I have ever encountered.

"A wavelength stretching apart due to the expansion of space", is a close second.

Anyway I am sure many will completely disagree with me.

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marcus
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Those people who teach that things like "cosmological time", "preferred space-time hyperplanes", "spatial distance", "time", "preferred coordinate systems", "preferred metrics (even with cross terms)", "expansion", "Hubble flows" etc are absolute properties of the universe as modeled by general relativity.

.

I havent encountered such people. Would you allow that it is possible you may be misunderstanding others and imagining that they are saying what they are not?
The properties you mention seem to be by and large to be properties of a particular solution to the Einstein equation. They are not absolute.

Once one has narrowed down to a particular metric, which is a particular solution, then there may well be a preferred time, an idea of being at rest with respect to Hubble flow, a preferred foliation or spatial slicing etc. These things are not absolute, but depend on one's choice of metric---and hopefully the metric will be a reasonably good fit to observation.
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You said something about "background independence" which I think needs clarifying. Many people use this term to describe GR and other theories which can be constructed without using a prior-choice of background metric
QFT is NOT background independent because at the very start, in constructing it, you have to commit to some rigid geometry---can be curved but typically is just flat Minkowski space.
GR IS background independent because you start with a continuum with no fixed geometry. You can define the theory without resorting to a background metric. Background independence is a fairly unusual property for theories to have. Quantum gravitists generally want their theories to have this property because they are aiming at getting a quantum theory with the main features of GR.

But once you HAVE a solution to the Einstein equation, a metric, say like the FRW metric-----or the flat Minkowski metric (also a solution, just a different solution obtained with zero matter)----then there is no more expectation that there will be background independence!

Solutions to the Einstein equation typically do not have Poincaré symmetry either. The flat (empty universe) solution DOES have the global symmetry one learns about in Special Relativity. But generic solutions do not

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"An expanding balloon with coins stuck on it that do not expand themselves", is about the worst model I have ever encountered.

What is wrong about thinking of a "balloon", if you think of it as an HyperSphere and not a 3D balloon ?

What is wrong about thinking of a "balloon", if you think of it as an HyperSphere and not a 3D balloon ?
"Expansion of space" is a completely wrong terminology.
It implies that space is some sort of a substance that can expand and contract.

That an observer measures a change in distance is perfectly valid in relativity but it has nothing to do with an expansion or contraction of space.

"Photon's being streched by exanding space" is another one these absurd phrases.

That an emitter and an absorber of a photon measures a different frequency is perfectly valid in relativity but it has nothing to do with a change in the state of the photon.

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Garth
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"Expansion of space" is a completely wrong terminology.
It implies that space is some sort of a substance that can expand and contract.

That an observer measures a change in distance is perfectly valid in relativity but it has nothing to do with an expansion or contraction of space.

"Photon's being streched by exanding space" is another one these absurd phrases.

That an emitter and an absorber of a photon measures a different frequency is perfectly valid in relativity but it has nothing to do with a change in the state of the photon.
The problem is observers do not measure a change in distance, we are not paying out a tape measure stretching to the Virgo cluster, for example.

What we do measure is red shift, primarily, and then the angular diameter of 'standard rulers' and the apparent magnitude of 'standard candles' etc. and use GR to interpret such observations as the expansion of space.

Using a metre metal rule as the standard of length measurement, a red-shifted photon has increased in wavelength and it has 'lost' energy.
As $\lambda(t) \propto$ a(t), where $\lambda(t)$ is the wavelength of a cosmological photon such as one sampled from the peak intensity of the CMB at cosmological time t, it might be said that "Photon's are being stretched by expanding space"

Those statements are theory dependent, i.e. dependent on the theory of GR.

Garth

Those statements are theory dependent, i.e. dependent on the theory of GR.
A photon's frequency is a eigenstate of a photon.

Observing a redshift phenomenon is due to a different position in curved space-time of the emitter and the observer, it has nothing to do with the eigenstates of the photon.

I think this is a good example on how the FRW metric can confuse coordinate effects with physical effects!

If you think I am wrong, could you please direct me to a publication that claims that the space-time curvature of a particle traveling on a geodesic path can influence that particle's properties.
Because I believe this would be completely counter to the principle of equivalence.

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Garth
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A photon's frequency is an eigenstate of a photon.
Is not a photon a supposition of the eigenstates of the electron that emitted the photon? And a measurement of its wavelength a determination of the eigenstate of the electron that absorbed the photon?
Observing a redshift phenomenon is due to a different position in curved space-time of the emitter and the observer, it has nothing to do with the eigenstates of the photon.

I think this is a good example on how the FRW metric can confuse coordinate effects with physical effects!
Does the photon itself have eigenstates?

Or are the only eigenstates involved those of emitter and absorber?

What about the Doppler shift of the photons measuring my speed in a radar speed trap? How do they gain/lose frequency?

Garth

What about the Doppler shift of the photons measuring my speed in a radar speed trap? How do they gain/lose frequency?
They don't!
Absolutely nothing happens to the photons.

The relative motion between the emitter and absorber causes the effect, it has nothing to do with the photons.

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Garth
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They don't!
Absolutely nothing happens to the photons.

The relative motion between the emitter and absorber causes the effect, it has nothing to do with the photons.

Absolutely, the only eigenstates involved are those of emitter and absorber.

Garth