# Expansion of the Universe: is new space(time?) being created or does it just get stretched?

Is new space(time?) being created as the Universe expands, or does the existing spacetime just get stretched?

If it just gets stretched, why do galaxies move along with the expansion instead of just getting smeared (like a drawing on an inflatable balloon)?

• Your second question is a duplicate of Why does space expansion not expand matter? – John Rennie Jan 2 '15 at 19:01
• Oh, yes, only the second part though. The first part was not answered there – SuperCiocia Jan 2 '15 at 19:26
• The local universe seems to stay the same, all the laws of physics seem to stay the same. If things got stretched, one would expect that atomic transitions would be changing their frequencies because the spatial coordinates enter into the equations second order, while the time-like coordinate enters in first order. One can make more complex arguments of this kind, but the measurements are not consistent with changes to local physics, as far as I know. – CuriousOne Jan 2 '15 at 21:25
• Interesting paper here, looking at the mathematical parallels between GR and solid mechanics, arxiv.org/pdf/1603.07655.pdf – boyfarrell Jul 1 '18 at 16:39

Since the second part of your question is a duplicate I'll address just the first part. however I suspect you're going to be disappointed because my answer is that your question doesn't have an answer.

The problem is that spacetime isn't an object and isn't being stretched. We're all used to seeing spacetime modelled as a rubber sheet, but while this can be a useful analogy for beginners it's misleading if you stretch it too far. In general relativity spacetime is a mathematical structure not a physical object. It's a combination of a manifold and a metric. At the risk of oversimplifying, the manifold determines the dimensionality and the topology, and the metric allows us to calculate distances.

We normally approximate our universe with the FLRW metric, and one of the features of this metric is that it's time dependant. Specifically, if we use the metric to calculate the distance between two comoving points we find that the distance we calculate increases with time. This is why we say the universe is expanding. However nothing is being stretched or created in anything like the usual meaning of those words.

• "In general relativity spacetime is a mathematical structure not a physical object." So you are saying that mathematics makes things move? – bright magus Jan 3 '15 at 9:45
• @brightmagus: no. I'm saying that mathematics describes how things move. – John Rennie Jan 3 '15 at 9:55
• So why do things move the way they do in GR if this is not due to the curvature of the space? – bright magus Jan 3 '15 at 10:03
• @brightmagus: I don't know. I can tell you how to calculate their trajectory using the geodesic equation, but to find out why they move you'll need to ask a philosopher. – John Rennie Jan 3 '15 at 11:27
• @SuperCiocia: I guess that depends on what you mean by physical entity, but my view is that no they are not. But I should emphasise that this is a purely philosophical viewpoint and irrelevant to the gory business of using GR to calculate things about the real world. – John Rennie Jan 5 '15 at 15:41

Short answer: Unlike stretchy materials, spacetime lacks a measure of stretchedness.

Long answer: Let's see where the rubber sheet analogy holds and where it fails. When you stretch a rubber sheet, two points on it change distance. You can also formulate a differential version of this property by saying it about infinitesimally close points. Similar is happening for the spacetime. In fact, description how infinitesimally close points change their (infinitesimal) distance is a complete geometric description of a spacetime in general relativity (GR). Even more, it is complete description of a spacetime in GR (up to details about the matter content in it).

This is described by a quantity called metric tensor $g_{\mu\nu}$, or simply metric for short. It is $n$ by $n$ matrix, where $n$ is the number of spacetime dimensions (so it is usually 4 unless you are dealing with theories with different number of dimensions). Square of the infinitesimal distance is given by: $$ds^2=\sum_\mu \sum_\nu g_{\mu\nu}dx^\mu dx^\nu$$

In Einstein summation convention, summation over repeated indices is assumed, so this is usually written simply as $ds^2=g_{\mu\nu}dx^\mu dx^\nu$.

For flat spacetime $g_{\mu\nu}$ is a diagonal matrix with -1 followed by 1s or 1 followed by -1s, depending on the convention (it gives the same physics in the end). For a flat Euclidean space, metric tensor is simply a unit matrix, so for 3-dimensional space this gives: $$ds^2=dx^2+dy^2+dz^2$$ which is just a differential expression for Pythagorean theorem.

Where does the analogy fail?

Well, as I said before, metric is a complete description of the spacetime in GR. This means that the spacetime doesn't have any additional property. Rubber, on the other hand, has a measure of how much it has been stretched. This is closely related to rubber having a measure amount of rubber per unit space. But there is no such thing as "amount of space per unit space", so once you stretch the spacetime, it won't go back. Or you could say that stretching and creating spacetime is the same thing, because you end up with more volume "for free" (meaning that, unlike rubber, it has no way to "remember" it used to have less volume).

Expansion of space means simply that distances between the points become larger, without any movement implied. It is simpler that with stretchy materials, but less intuitive, because our intuition forces us to imply additional properties which are not there.

• "... so once you stretch the spacetime, it won't go back" Which only suggests that spacetime isn't elastic, and not that it does not stretch. On the other hand, spacetime curvature due due to gravity could be understood as "elastic" - once you remove the source of gravity, the spacetime goes back to (nearly) flat, doesn't it? – bright magus Jan 3 '15 at 14:06
• @brightmagus In a way it's "even less than not elastic". Unlike non-elastic substances, it doesn't get "less dense" (or something like that) with stretching. It can't because it isn't a substance. Curvature in GR is gravitational analogue of electromagnetic field in electromagnetism, so it is justified to call it elastic as it is justified to call EM field elastic, as both tend to "go away" once you remove their respective sources. – Varin Esan Jan 3 '15 at 22:02
• "It can't because it isn't a substance." I won't even ask what it is. Apparently it is whatever physicists need it to be. – bright magus Jan 3 '15 at 22:40
• @brightmagus Usually, the right question isn't "What something is?", but "What properties does it have?". I've sketched some of it's properties in my answer, and also pointed out which properties it doesn't have (properties that are hidden assumptions forced by intuition). – Varin Esan Jan 4 '15 at 9:57
• Apparently, you sketched the properties (concerning stretching) incorrectly, as you agreed. – bright magus Jan 4 '15 at 10:09

If the stretching analogy were to be more than that, and was something actually happening to expanding spacetime, that would result in an increase either in elastic potential energy or elastic tension. That increasing tension would result in an increase of the speed of gravitational waves and a reduction in the effective mass of objects, none of which have been observed

The expansion of the universe is just the relative motion of objects in it. There's no definable difference in general relativity between ordinary relative motion of two objects and those objects being "stationary while space expands between them". At best, they're descriptions of the same phenomenon in different coordinates.

Some sources that talk about expanding space are just using it as alternate description of the same physics. This isn't strictly wrong but I think it's unnecessarily confusing. It leads to questions like yours which would probably never arise if people understood that the motion of galactic superclusters is the same as any other motion.

Some sources explicitly say that the expansion of the universe is different from other kinds of motion because it's due to the expansion of space itself. They're just plain wrong, and you should be suspicious of everything else they say about cosmology.

• "Some sources explicitly say that the expansion of the universe is different from other kinds of motion because it's due to the expansion of space itself. They're just plain wrong, and you should be suspicious of everything else they say about cosmology." Similar discussion here: physics.stackexchange.com/questions/442986/… – D. Halsey Oct 18 at 21:38
• How does this explain galaxies receding faster than light? – safesphere Oct 19 at 5:43
• @safesphere See this and this. In short, metric distances between objects can expand arbitrarily quickly even in special relativity. – benrg Oct 19 at 16:40
• In that link you derive superluminal speed as distance measured in one frame per time measured in a different frame. This is not a valid procedure in SR or anywhere. I like the Milne model a lot, but sorry, no properly defined velocities in it or in SR are superluminal. In contrast to your example, superluminal velocities in FLRW are (hypothetically) measured properly in the same frame. The expansion of space without acceleration is equivalent to relative motion only locally, but not globally with the (unconfirmed) existence of the particle horizon and superluminal velocities. – safesphere Oct 19 at 22:41
• @safesphere The Milne model is an FLRW cosmology (the $\Omega=0$, $\dot a>0$ case). The recessional velocity coincides in this case with the SR rapidity (times $c$). FLRW coordinates don't define an inertial frame. Note also that the lines of constant cosmological time along which FLRW distance is measured are not spacetime geodesics, except when $\dot a=0$. – benrg Oct 20 at 3:03