Tuesday, August 15, 2017

You don’t expand just because the universe does. Here’s why.

Not how it works.
It’s tough to wrap your head around four dimensions.

We have known that the universe expands since the 1930s, but whether we expand with it is still one of the questions I am asked most frequently. The less self-conscious simply inform me that the universe doesn’t expand but everything in it shrinks – because how could we tell the difference?

The best answer to these questions is, as usual, a lot of math. But it’s hard to find a decent answer online that is not a pile of equations, so here’s a verbal take on it.

The first clue you need to understand the expansion of the universe is that general relativity is a theory for space-time, not for space. As Herman Minkowski put it in 1908:
“Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.”
Speaking about the expansion of space, hence, requires to undo this union.

The second clue is that in science a question must be answerable by measurement, at least in principle. We cannot observe space and neither can we observe space-time. We merely observe how space-time affects matter and radiation, which we can measure in our detectors.

The third clue is that the word “relativity” in “general relativity” means that every observer can chose to describe space-time whatever way he or she wishes. While each observer’s calculation will then differ, they will come to the same conclusion.

Armed with these three knowledge bites, let us see what we can say about the universe’s expansion.

Cosmologists describe the universe with a model known as Friedmann-Robertson-Walker (named after its inventors). The underlying assumption is that space (yes, space) is filled with matter and radiation that has the same density everywhere and in every direction. It is, as the terminology has it, homogeneous and isotropic. This assumption is called the “Cosmological Principle.”

While the Cosmological Principle originally was merely a plausible ad-hoc assumption, it is meanwhile supported by evidence. On large scales – much larger than the typical intergalactic distances – matter is indeed distributed almost the same everywhere.

But clearly, that’s not the case on shorter distances, like inside our galaxy. The Milky Way is disk-shaped with most of the (visible) mass in the center bulge, and this matter isn’t distributed homogeneously at all. The cosmological Friedmann-Robertson-Walker model, therefore, just does not describe galaxies.

This is a key point and missing it is origin of much confusion about the expansion of the universe: The solution of general relativity that describes the expanding universe is a solution on average; it is good only on very large distances. But the solutions that describe galaxies are different – and just don’t expand. It’s not that galaxies expand unnoticeably, they just don’t. The full solution, then, is both stitched together: Expanding space between non-expanding galaxies. (Though these solutions are usually only dealt with by computer simulations due to their mathematical complexity.)

You might then ask, at what distance does the expansion start to take over? That happens when you average over a volume so large that the density of matter inside the volume has a gravitational self-attraction weaker than the expansion’s pull. From atomic nuclei up, the larger the volume you average over, the smaller the average density. But it is only somewhere beyond the scales of galaxy clusters that expansion takes over. On very short distances, when the nuclear and electromagnetic forces aren’t neutralized, these also act against the pull of gravity. This safely prevents atoms and molecules from being torn apart by the universe’s expansion.

But here’s the thing. All I just told you relies on a certain, “natural” way to divide up space in space and time. It’s the cosmic microwave background (CMB) that helps us do it. There is only one way to split space and time so that the CMB looks on average the same in all direction. After that, you can still pick your time-labels, but the split is done.

Breaking up Minkowski’s union between space and time in this way is called a space-time “slicing.” Indeed, it’s much like slicing bread, where each slice is space at some moment of time. There are many ways to slice bread and there are also many ways to slice space-time. Which, as number 3 clued you, are all perfectly allowed.

The reason that physicists chose one slicing over another is usually that calculations can be greatly simplified with a smart choice of slicing. But if you really insist, there are ways to slice the universe so that space does not expand. However, these slicing are awkward: they are hard to interpret and make calculations very difficult. In such a slicing, for example, going forward in time necessarily pushes you around in space – it’s anything but intuitive.

Indeed, you can do this also with space-time around planet Earth. You could slice space-time so that space around us remains flat. Again though, this slicing is awkward and physically meaningless.

This brings us to the relevance of clue #2. We really shouldn’t be talking about space to begin with. Just as you could insist on defining space so that the universe doesn’t expand, by willpower you could also define space so that Brooklyn does expand. Let’s say a block down is a mile. You could simply insist on using units of length in which tomorrow a block down is two miles, and next week it’s ten miles, and so on. That’s pretty idiotic – and yet nobody could stop you from doing this.

But now consider you make a measurement. Say, you bounce a laser-beam back between the ends of the block, at fixed altitude, and use atomic clocks to measure the time that passes between two bounces. You would find that the time-intervals are always the same.

Atomic clocks rely on the constancy of atomic transition frequencies. The gravitational force inside an atom is entirely negligible relative to the electromagnetic force – its about 40 orders of magnitude smaller – and fixing the altitude prevents gravitational redshift caused by the Earth’s gravitational pull. It doesn’t matter which coordinates you used, you’d always find the same and unambiguous measurement result: The time elapsed between bounces of the laser remains the same.

It is similar in cosmology. We don’t measure the size of space between galaxies – how would we do that? We measure the light that comes from distant galaxies. And it turns out to be systematically red-shifted regardless of where we look. A simple way to describe this – a space-time slicing that makes calculations and interpretations easy – is that space between the galaxies expands.

So, the brief answer is: No, Brooklyn doesn’t expand. But the more accurate answer is that you should ask only for the outcome of clearly stated measurement procedures. Light from distant galaxies is shifted to the red meaning they are retreating from us. Light collected from the edges of Brooklyn isn’t redshifted. If we use a space-time slicing in which matter is at rest on the average, then the matter density of the universe is decreasing and was much higher in the past. To the extent that the density of Brooklyn has changed in the past, this can be explained without invoking general relativity.

It may be tough to wrap your head around four dimensions, but it’s always worth the effort.

[This post previously appeared on Starts With A Bang.]


IGNACIO GC said...

Thank you very much for your blog, it is inspiring.
For neophytes like me, who pretend to grasp the matter without posthumous mathematics: spacetime is expanding but it is only measurable and testable for very large cosmological distances; Then the fact is that spacetime is stretching in certain fields beyond the great intergalactic distances does not imply that there is a stretch for any place and scale, it could be said therefore that the expansion is not isotropic and therefore reproduces in some parts of the cosmos, in others not. Is it so?
On the other hand: what really expands, spacetime itself? But what is deformed ?, or rather, what is stretched in turn is the same underlying structure that allows space-time to deform in virtue of gravity, etc., what then underlies deformed space-time? Or is it phenomenologically assumed that spacetime is itself something essential without any structure underneath from which it deforms?

Ambi Valent said...

Could you explain which circumstance decides whether there is or isn't expansion? Spacetime wouldn't know whether it's inside or outside a galaxy.

There are a lot of situations: first, two stars in the same galaxy. Then, the second star is in a globular cluster in the halo. Then it's in a dwarf galaxy orbiting the first galaxy. Then in another galaxy in the same cluster. Then in a galaxy in the neighboting cluster within the same supercluster. I think Laniakea is accelerated to a common center, but will never meet there since the expansion is already stronger. So, what decides whether there can be expansion?

Andrew Wells said...

I don't know Sabiane, sometimes I try to lose weight and I still get bigger. ¯\_(ツ)_/¯

dlb said...

Typo: "The gravitational force inside an atom is entirely negligible relative to the gravitational force".

Bill said...

If everything expands proportionally we'd never have a way of measuring it. It seems that the work of Hermann Weyl, the German mathematical physicist who in 1918 pioneered the concept of arbitrary vector length and the related notion of scale (or conformal) invariance should be re-examined in light of this issue.

zben said...

Thank you. This is indeed an excellent explanation, very accessible to the educated layman.

Louis Tagliaferro said...

Dear Bee,

Although not intuitive at first over a period of time I personally could imagine four dimensions, and an inseparable space-time, that seemed logical, intuitive, and appeared to fit the evidence/descriptions I read. It relied on viewing space-time strictly as a displacement and the time unit being a “slice” of a displacement. Even though to me the latter still appears to be empirically correct, I’ve since realized physics doesn’t consider that at all. I always thought the idea has probably been considered and abandoned at some point; yet I couldn’t find any information. If you have any knowledge if such a presumption was considered and discarded perhaps you can point me to it? The thought has troubled me for some time.

Uncle Al said...

"Brooklyn...Let’s say a block down is a mile" About 7 blocks/mile, within an order of magnitude being physics' "close enough." 40.632803, -73.92235 is my olde home sewage outflow into Jamaica Bay, source of beach whistles and Coney Island whitefish (now syringes and crack bottles).

"The gravitational force inside an atom is entirely negligible relative to the gravitational force" Electromagnetic, of course.

naivetheorist said...

you might want to identify the video clip as being taken from "Annie Hall" (a great movie). i also like his other physics quotes:

"I'm astounded by people who want to 'know' the universe when it's hard enough to find your way around Chinatown."

"What I do know about physics is that to a man standing on the shore, time passes quicker than to a man on a boat - especially if the man on the boat is with his wife."

"Interestingly, according to modern astronomers, space is finite. This is a very comforting thought—particularly for people who can never remember where they have left things. "

"It is impossible to travel faster than light, and certainly not desirable, as one’s hat keeps blowing off."

and my favorite,

"formerly unsolvable equations are dealt with by threats of reprisals."



John Anderson said...

Expansion and the Arrow of Time: The block universe model (Brian Greene’s expanding loaf of raisin bread) says all spacetime exists together, right now (in some sense that doesn’t violate simultaneity). That bothers me because it seems to pre/post-ordain history and is fatalistic. So I worry about the arrow of time.

Imagine a typical hourglass filled with sand. Run the film backwards and it does NOT work because gravity is asymmetric. So perhaps gravity is a (the) factor in the arrow of time.

Has anyone thought about the exercise of an “hourglass” with a photon gas in a strong gravitational field. Can one see an irreversible flow of time with that? Seems hard to get all the photons into the bottom chamber.

Regarding Woody Allen and fatalism, “It's not that I'm afraid to die, I just don't want to be there when it happens.”

P.S. Warning - "Atomic Blonde" is not a biography of Marie Curie; boy, was I disappointed!

Sabine Hossenfelder said...


Thanks, I've fixed that.

Sabine Hossenfelder said...


But we do measure that it expands.

Sabine Hossenfelder said...

Ambi Valent,

I did explain it. It expands if the average matter density is so small that the gravitational self-atttraction becomes smaller than the outward pull from the expansion. That's a rough estimate. To be precise you'd have to do a numerical calculation with the exact matter distribution of some region of space-time and there's no general statement that can be made. But since galaxies are stable, we know they're gravitationally bound and don't expand. It's somewhere beyond the scale of galaxy clusters that expansion takes over.

Sabine Hossenfelder said...


Sorry, I don't understand that question.

Sabine Hossenfelder said...


Yes, that's correct. The expansion isn't actually homogeneous and isotropic, it's homogeneous and isotropic only on the average. It's like matter distribution too isn't actually homogeneous and isotropic, it's only so on the average.

Sabine Hossenfelder said...


The movie looks the same backwards as forwards also with gravity, I don't know why you think otherwise. You would of course have to give the particles the suitable inverted initial conditions, ie finely tuned upwards momenta, which is exceedingly unlikely to happen by chance. Sand doesn't fall up in an hourglass for the same reason eggs don't unscramble etc etc, because it's very improbable. If something falls down, its momentum is dispersed quickly into whatever medium it hits, and you'll not get it back easily. The only thing that is *really* irreversible in general relativity is falling into a singularity, hence the wide-spread belief that singularities don't exist. Best,


Phillip Helbig said...

Those interested in this should check out this nice review of the concept of expanding space, which emphasized understanding apparent paradoxes, confusing issues, etc. Also, by the same authors plus a co-author, and also related to expansion, is the discussion of the chained-galaxy problem. There is also another take by different authors and some some discussion on Peter Coles's (yes, that is the correct genitive) blog.

And, of course, as almost always, whatever the question, the answer is to read Edward Harrison's Textbook Cosmology: The Science of the Universe. It is more accessible than other books without dumbing down---quite the opposite, he spends much time discussing things which are presented confusingly, glossed over, or just wrongly by other authors.

Ambi Valent said...

my brain seems to be in a knot...

Either I think expansion and attraction between masses are independent from each other, in which case space inside a galaxy would expand (but only a little).

Or I accept that the attaction between masses can counteract expansion, and then I get non-expansion only at a thin borderline, and inside that borderline I would get contraction (that wouldn't make much sense either).

Or is there yet another phenomenon involved?

Phillip Helbig said...

Maybe what John means is that, in the absence of gravity, a uniform state has the highest entropy, but with gravity, states of higher entropy are possible via gravitational collapse. There is a puzzle as to why the universe started out with a low entropy (this is the case even for a very uniform beginning due to the presence of gravity).

The low-entropy state at the beginning seems to be the basis for the arrow of time. Sure, there are more ways to scramble an egg than unscramble it, to have a broken rather than an assembled glass, etc, but this in itself can't explain the arrow of time. If I drop an egg and it breaks, but the reverse doesn't happen in practice, one can't argue that there are more broken states than unbroken ones, hence the arrow of time from unbroken to broken, since by the same token one could argue that the previous state of an unbroken egg must also be broken. One can't make a distinction based on past and future because that is what one is trying to explain. The correct answer is that the previous state had even-lower entropy, etc, all the way back to the big bang.

Sabine Hossenfelder said...

Ambi Valent,

I don't know what you mean. Look, there are a lot of things that space-time can do. What it does depends on the distribution of masses and pressures and momentum flows and all that. General Relativity tells you what space-time does if you put in matter. Some of these solutions have an expanding space (properly defined), some don't. The Schwarzschild solution, for example, is non-expanding. It just doesn't expand. Now, galaxies aren't spherically symmetric, but disk shaped, but to some approximation you can think of it this way. You take the local non-expanding solutions, then you need some boundary condition to stich them to the global expanding solution. It is a reasonable interpretation then that space does not expand in the galaxy, but between the galaxies. Though, again, keep in mind that this depends on how you define space.

Really if this causes you brain knot, forget all the stuff about expanding space and merely talk about things that can be measured. Best,


Theophanes Raptis said...

* Expansion is single signed
* Gravity is single signed
* Time's monodromy is single signed
A three-sided coin perhaps?

“Praise not day until evening, no wife until buried, no sword until tested, no maid until bedded, no ice until crossed, no ale until drunk.”

Ambi Valent said...


it would seem to me that if you feed into the math that a galaxy hasn't expanded in the past, then it would result in the galaxy not expanding in the future as well. That's just math. But can I be sure this non-expanding galaxy is an accurate representation of the Milky Way?

I think if you started with a galaxy in which space expands only very little while attaction between masses is very dominant and feed it into the math, then it would continue to do so - and our measurements aren't yet good enough to tell whether the galaxy expands very little or not at all.

But I'm just a layman.

Sabine Hossenfelder said...


This isn't how general relativity works. You don't get to chose what space-time does. You put in matter and the equations that govern the behavior of matter, and this tells you what space-time does. You could of course assume that you have a galaxy that hasn't yet reached a quasi-stable equilibrium, one that has, say, recently undergone a collision or something like that, and in this case pretty much all bets are off - can't solve the equations other than numerically. But take the simplest case as example, a stable spherically-symmetric distribution of matter (and pressure - it won't be stable without pressure), and it will not expand, at least not in the most intuitive space-time slicing. That's still so in the presence of a cosmological constant.

As I emphasized above, however, you can chose some other space-time slicing as you please and then space can do a lot of other things. Best,


Shantanu said...

Sabine great article and Philip, thanks for the links. Amother nice (old) paper on this is

However, I don't think this issue is completely resolved. Sergei has been arguing for many years that one can see signatures of Hubble expansions on local scales also.

Sabine Hossenfelder said...


Well, if you count one guy believing otherwise, then nothing is ever completely resolved.

glueShoe said...

If the math is analogous to belt size then I've certainly expanded AND contracted over the years, and relative to my view of food at various positions in space-time.

Uncle Al said...

Bee said, "Well, if you count one guy believing otherwise, then nothing is ever completely resolved." That assassinates the future!

To observed 14 significant figures no composition of matter, field; quantum mechanical, relativistic, gravitational observable, or combination violates the Equivalence Principle. Physics is thus defined.

Test spacetime geometry with enantiomorphic atomic mass distribution geometries. Opposite shoes Einstein-Cartan violate the Equivalence Principle, sourcing baryogenesis, Milgrom acceleration, physics' unending chiral woes.

Green’s function Newtonian potential excludes chiral gravitation. Euclid versus Thurston’s E³ (plane), S³ (elliptic), H³ (hyperbolic), S² × R, H² × R, SL(2, R), Nil, and Solv three-space geometries. Look. Dark energy and dark matter are parameters not facts.

CapitalistImperialistPig said...

Oh my gosh - if those are the twins, they are really growing up!

Unknown said...

Popular accounts of "dark energy" claim that the apparently accelerating expansion of universe *Will* eventually rip apart atoms & subatomic particles.
Is that claim consistent or not with your explanations above?
Thx, Tom

Jorma said...

For a nice discussion aimed at undergraduate physics majors see

http://aapt.scitation.org/doi/full/10.1119/1.3699245 (paywall)

https://arxiv.org/abs/gr-qc/0508052v2 (eprint)


Kaleberg said...

It seems like we can ignore the expansion "force" of the universe at the scale of an individual galaxy or galactic cluster the same way we can ignore the electric charge on a planet when studying its solar orbit or the strong force in the nucleus when studying the electrons around an atom. It's a matter of scale.

Nate Guimond said...

This block universe of Brian Greene's seems ridiculous to me if considered to be anything more than a thought experiment. An intelligent observer might be able to create a mathematical model of universe that perfectly fits ours up until this moment but it would still be violently chaotic concerning future implications. This might be called emergence or novelty, but really it is having very little data on important parameters such as whether universe density fluctuates wildly beyond the limited visibility window since the beginning of expansion. I assume that we will receive information about very distant parts of the unobserved universe in a very long time, but that all messages will have been pulled so far into the microwave range that we will have to build bigger and bigger microwave telescopes and eventually the universe will fizzle out because it will be even more cold and empty. But relax, it's trillions of years from now.

As to the photon-gas-glass, I think that since no-one can tell the difference between acceleration and proximity to a gravitational field, you might be able to create some rather ambiguous situations, but in general, if you wait long enough, you always see more entropy in the forward time-direction.

except always it would show a slight deviation toward exhibiting greater entropy.

Dr. Strangelove said...

Dear Sabine,

The universe started with the Big Bang so we were told. It started the size of an atom. If the Milky Way does not expand because the gravitational attraction of the stars is strong enough to resist space expansion, how did the early universe the size of an atom expanded? Surely the electromagnetic and gravitational forces are orders of magnitudes stronger than the present Milky Way. How about when the universe was the size of the solar system? Gravitational attraction was still orders of magnitudes stronger than our galaxy.

Your answer to this may be better than mine but here’s my answer. It’s not just space that’s expanding. It’s space and time. They are expanding at the same rate. When this is taken into account, spacetime expansion does not require a change in energy. It doesn’t matter if the expansion is fast or slow, accelerating or decelerating. No change in energy. Here lies the answer to dark energy. It appears only when we slice spacetime in such a way that space is expanding but not time. When we slice spacetime so that space and time are expanding, dark energy disappears. Remember, no change in energy. No need to postulate a mysterious dark energy.

Incredible assertion? I have an unpublished paper that mathematically proves what I just described. I don’t know if you can understand it but journal editors cannot. I have shown in my paper that the total potential and kinetic energy of gravitating bodies remains unchanged in spacetime expansion.

I can share the paper with you if you want. So that’s my answer. What is your answer?

Phillip Helbig said...

"An intelligent observer might be able to create a mathematical model of universe that perfectly fits ours up until this moment but it would still be violently chaotic concerning future implications."

Chaotic systems are still deterministic. Chaotic means that detailed future behaviour is difficult to predict in practice, but not in principle.

Phillip Helbig said...

Popular accounts of "dark energy" claim that the apparently accelerating expansion of universe *Will* eventually rip apart atoms & subatomic particles.

Yes, I have seen such claims.

Simple answer: they are wrong if the "dark energy" is the cosmological constant. And there is not one shred of evidence to suggest that it is not.

Longer answer: This "big rip" is possible for so-called phantom dark energy (a hypothetical form of dark energy satisfying the equation of state with w < − 1). There is, however, zero observational evidence, and as far as I know no convincing theoretical evidence, that any such thing exists, much less that the observed dark energy is phantom energy.

Sabine Hossenfelder said...

Dr Strangelove,

My answer is that it's pretty obvious you understand very little of general relativity and I strongly recommend you learn the rules before you break them.

Sabine Hossenfelder said...


The block universe isn't Brian Greene's.

Sabine Hossenfelder said...


As Phillip says, dark energy won't rip apart atoms, ever. There are a lot of wild stories about the ultimate fate of the universe out there and frankly I think they are all bullshit. Who the heck knows what can happen in 10^10 billion years?

Dr. Strangelove said...


Since you're the expert in general relativity, you can start by pointing out what is wrong with my answer. I'm sorry to say you're answer is just hand waving and appeal to your authority (I know this and you don't) I expected more from you. Is that your best answer?

Sabine Hossenfelder said...

Dr Strangelove:

I have neither the time nor the patience to give free GR lessons to each random person who comes up with some ingenious improvement to general relativity. If you are serious about improving your argument, you can talk to a physicist for $50/20 mins, the terms and conditions are here.

Dr. Strangelove said...

I'm not after your free lessons. I'm sure they're good and you're not after my $50. I had enough GR lessons and feedback from physicists who reviewed my paper. If you don't want to say why I'm totally wrong, fine. But we want to hear your answer to my question. Not just for me but for your readers. Thanks.

Sabine Hossenfelder said...

Dr Strangelove,
Not worth my time and effort. Bye.

Phillip Helbig said...

@Dr Strangelove: I too am sceptical. But you could stick the paper on the web and anyone could look at it and send you comments.

Louis Tagliaferro said...

Sabine Said:

Sorry, I don't understand that question.
12:50 AM, August 16, 2017"

Unfortunately, and understandably I worried you might say that. Regardless the picture of the girls was great, they are both adorable. It looked like they were pretending to be pregnant, as a father of two grown girls it made me think about your previous blog post. I wonder how much, if any of that behavior comes from our upbringing as parents, exposure to society, and if there is any instinctive component. It all points to an issue that is complex and not so easy to define as some would have you believe. Enjoy them as much as you can at that age, you’ll always love them and have new ways to be proud, but you’ll miss that care-free innocent stage when it’s gone.

I’ll make this last attempt at trying to clarify what I asked about. I asked you, because in reading your blog you demonstrate a great capacity to often see things as they are and not how you want or believed them to be. Of course you know what a displacement is in physics therefore,” 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom”, would be a slice or a defined part of that radiation displacement (the microwave emission in general being an undefined displacement); analogous to a gram being a defined part or quantity of a mass. That ,appears to be empirical, because of that I often wondered why it is not considered or was abandoned as an empirical way to define time and the interpretations for the malleability of space-time?

Rob van Son (Not a physicist, just an amateur) said...

"But you could stick the paper on the web and anyone could look at it and send you comments."

Or if they don't want it

Koenraad Van Spaendonck said...

@Dr Strangelove,

"If the Milky Way does not expand because the gravitational attraction of the stars is strong enough to resist space expansion, how did the early universe the size of an atom expand? "

Exactly. I have often wondered and asked (but haven't gotten satisfactory answers sofar) about how matter would have the capability in the first place, to counter an expansion of space. Supposedly by its gravitationally attracting nature, but how does that make sense ? Matter attracting space ? So I agree with you that something about this current picture is incomplete.

Your proposal is fascinating as a breeding ground for new solutions, but I don't necessarily agree, and would suggest another solution, which is in a way related, a testable one.
I'd be more than happy to exchange papers with you on this subject.

And obviously with anyone else also, and debate the subject.

Best, Koenraad

Zack Yezek said...

Could photons lose energy when the propagate over extremely large distances, say due to some sort of friction-like interaction with the vacuum, that would generate the observed red-shift without ongoing expansion? I remember hearing this basic 'tired light' hypothesis years ago but not what became of it. Or, since to see this redshift we must detect light emitted millions & billions of years ago from other galaxies, could a time-varying fine structure constant replicate the observations?

I only ask because it seems like expanding space (really space-time) between galaxies isn't the only obvious way to explain what astronomers see. And those alternatives seem like they'd be more testable- you could look for extremely tiny spectrum shifts in light propagating over modest distances or tiny fluctuations in the fine structure constant in a lab, whereas the expansion of space can only be inferred from astronomy.

Sabine Hossenfelder said...


To begin with, the early universe didn't have the size of an atom. It's the part that's observable now that had some size at some time.

More importantly, as I explained in my post, the cosmological solution - the one that describes the expansion of the universe - is that which describes galaxies. It just isn't. The jump you make from one mathematical solution to another is not warranted. It's wrong. Don't do it. It's wrong.

Besides that, initial values matter. Galaxies are pretty much in a stable state (or at least quasi-stable over billions of years). The early universe clearly isn't. If you'd take all the stuff that's in galaxies and give it very large initial velocities, it would also blow apart.

Sabine Hossenfelder said...


I think this idea never really died. But please understand that redshift isn't the only cosmological observable. There are a lot of other observables that also tell us the universe is expanding. Anything from the CMB to gravitational lensing to structure formation says the same. You can try and find an alternative explanation for any one effect, but no one has been able to come up with a convincing alternative for all observations taken together.

It is possibly the case that the vacuum isn't entirely transparent to photons or slightly affects frequencies because it's strictly impossible to rule it out. Hence there are bounds on this saying if there's any such effect it's small and hasn't been seen.

Dr. Strangelove said...

“If you'd take all the stuff that's in galaxies and give it very large initial velocities, it would also blow apart.”

Yes that would work but that’s not spacetime expansion. It’s just matter moving at high velocities. That solution would work even in a static universe. It’s a property of matter not of spacetime. Gravitationally bounded objects prevent space between them from expanding. However, when the objects are moving apart, they allow space between them to expand. Since we cannot directly measure spacetime expansion, it becomes indistinguishable from motion of matter in space. When two concepts are indistinguishable, they are one and the same.

Yes CMB and Hubble constant prove spacetime expansion empirically. But without these observations, can GR and FLW model distinguish the two concepts? Are they really describing spacetime expansion? The cosmological constant may be just the average initial velocities of all matter in the early universe. Think about it for a long time. My theory distinguishes the two concepts and explains dark energy by combining Newtonian mechanics, special relativity and quantum mechanics.

Koenraad Van Spaendonck said...

Also: I would not bring up some new model if I hadn't been constructing a way to practically test a major consequence of it. Which is a specific deviation from the gravitational time dilatation factor. My problem was callibrating the universal new formula to known vonstants, in order to perform a test with atom clock to discern the tiny differences which become bigger with increasing height. I solved that proble recently. This test costs peanurs compared to some of the sofisticated concepts out there. An atom cclock also has the advantage of serving as a magnufying glass if you keep it going for weeks, on identical increments of successive heights here that is. It helps discern the tiny deviations for an earth bound experiment, as opposed to the huge differences at cosmological distances.


Sabine Hossenfelder said...

Dr Strangelove,

Read what I wrote. We make statement about observations. You cannot observe the expansion of space. Or time. Your statements are irrelevant confusions of interpretation. A theory either describes observations, or it doesn't. General Relativity describes observations. That's all there is to say about it.

Koenraad Van Spaendonck said...

Excuse me for the spelling mistakes, as I wrote from my cell phone.

JimV said...

"Matter attracting space ?"

As I understand it, General Relativity (Theory of) says that matter (matter/energy) bends space and time. As matter moves it must follow the bends. If it bends into an extreme inward curvature, then matter objects tend to get closer together, which makes it seems as "space is contracting". If pressure (dark energy) bends space outwards instead of inwards, matter tends to move apart, which makes it seems as if "space is expanding". That's how I (try to) understand the concept - I hope it helps.

Anyway, I trust GR (as our best current model) because of all its many successes: Mercury's precession, GPS, red-shift, gravity waves, etc.

Phillip Helbig said...

"I think this idea never really died."

I don't think any serious cosmologist takes the tired-light theory seriously.

Koenraad Van Spaendonck said...


Thank you for that explanation, interpretation.

But as you can assess from your own explanation, there is no expansion/bending/contraction (be it real or apparent) over a longer period of TIME here. Just the effect of matter on space: an effect over SPACE , which 'settles', which is a thus a static picture, an equilibrium, determined by a given central mass M.

Hence my earlier extrapoçation that matter cannot be a counter-effect of an interpreted accelerated expansion over time. Hence a question mark for that interpretation of redshift as expansion of space over the course of the universe's history.

Best, Koenraad

JimV said...

KVS "there is no expansion/bending/contraction (be it real or apparent) over a longer period of TIME"

I am already trying to work above my paygrade here, so this will be my last comment (assuming it passes moderation). My understanding is that GR says there is (expansion over a longer period of time), which has caused the red-shift (between distant galaxies). Perhaps a better way to say that is that GR says under certain conditions the universe will expand (or contract) and that this in turn will cause red-shift (or blue-shift) in the light going from one distant galaxy to another.

I have seen two papers calculating this effect in ArXive, unfortunately with a disagreement between them (but both accepting GR). One, by Bunn and Hodges, calculates the red-shift by (I think) integrating incremental relativistic-doppler effects. This models an interpretation that spacial expansion does not actually stretch light waves, but causes a velocity change between the source and destination which causes the doppler effect. The other, whose authors I forget, was in response, saying, no, with a different GR calculation we can arrive at a valid (according to GR) result in which spacial expansion does stretch the light waves.

Koenraad Van Spaendonck said...

JimV, and orhers,

That is interesting.
I see those papers give 2 interpretations.

Here's the well known story of the history behind it in a nutshell :


We read here a.o.:

"Albert Einstein added a positive cosmological constant to his equations of general relativity to counteract the attractive effects of gravity on ordinary matter, which would otherwise cause a spatially finite universe to either collapse or expand forever."

I have a question here concerning this part: Does that mean that Einstein called the clumping together over a longer period of time of matter due to gravitation, 'a collapse of the universe' ? I mean it is pretty important to know what we are talking about and how to interpret words.

Because a collapse of the universe nowadays stands for the contraction of space itself, no ?

Does anybody have a clear view on this ?

Best, Koenraad

john schultz said...

Am I missing the point? Or are you saying that curved space can't expand. It's only the "flat" (flat to some suitable number of digits of accuracy) parts that can expand.

Sabine Hossenfelder said...


Not sure who your comment was addressed to, but I definitely didn't say that curved space can't expand.

john schultz said...

Thanks for your answer. I'm still groping for understanding. How can a (portion of a) space have enough gravity to inhibit the expansion, without being curved? (& vice versa)

Ambi Valent said...


could it be said this way? The model of a galaxy as stable and isolated is a very good approximation of the physical reality, so the calculated expansion resulting from this model (zero) is a very good approximation to what could be expected to be measured in the actual universe on the local level. The further out one would get, the less the approximation would apply.

That way, the local expansion inside a galaxy could be approximated to zero for all practical purposes, but there wouldn't be an actual border between expanding and non-expanding regions.

Sabine Hossenfelder said...


No, there's no actual "border". I suspect that there must be closed hypersurfaces on which the two forces exactly cancel though. Don't know if anyone has calculated details.

Sabine Hossenfelder said...


I don't know how you come to that conclusion. As I explained in my post, there are many ways to define "space". Some of them expand, some don't. The whole concept, really, is pretty meaningless. I strongly recommend you think about what's observable and all your confusions will resolve.

JimV said...

I see I should clarify what I have been trying to say a bit more. I used the word "bend" in previous comments, but I think "deform" would have been better, so as to include stretching and shrinking as well as bending or curving.

As I see it, and as I think Dr. Bee has been saying, GR is a mathematical model for space and time deforming due to matter-energy local density and to an innate outwards pressure (dark energy). The model was intended to give math that would be able to calculate all known (observed) gravitational effects, as well as predict some new ones, and it has so far succeeded to a very high level of precision. When you throw a ball into the air and watch it come back down, the gravitational part of that motion is accurately predicted by GR as the deformation of local space and time.

As Dr. Bee has said, we can't see the space deforming. We can only see the radiation that travels through space and how it seems to twist and turn (gravitational lensing) due to matter accumulations. There might be other ways to interpret that motion, and the motion of different distant galaxies away from us, but the math of GR works and was developed from the notion of space and time deforming. So as far as the standard interpretation is concerned, there is no difference between saying, for example, that matter is flying apart or that the part of the universe that contains the matter is expanding.

In this model, as it turns out, there is no stability. Einstein mistakenly thought the universe was static but it isn't - which he eventually realized. Matter wants to clump together, but pressure wants to make the space between matter objects increase. Fortunately, the battle between them is taking many billions of years in this universe, and things will look pretty much the same for probably longer than the human race will survive. After which, we won't be around to care about what happens. (The Andromeda galaxy is going to clump together with our galaxy, for one thing, devastating lots of solar systems.)

I apologize for submitting yet another final comment on this subject.

ajitjadhav said...

"While each observer’s calculation will then differ, they will come to the same conclusion."

A poor way to put it. The conclusion itself is quantitative, and hence, involving calculations.

A vector's components may be calculated as coming out differently in different rotationally invariant systems (i.e. ignoring the other invariances). That a given vector still stays the same vector also is a matter of calculations: "invariance" refers to calculations.

You physicist guys ought to improve your _conceptual_ skills. Take a leaf off Resnick and Halliday, for instance.

But in your popular writings, you guys confused me---an engineer---a lot in the past. I won't take it any longer if you continue doing so. I may not protest (let alone with a (lit) candle); but I will sure note a bit here and there. [... Who even cares if none notices.]



john schultz said...

Well Sabine, if this is too thick-witted, there is no need to answer. BUT..., you say several things along the lines of:

"You might then ask, at what distance does the expansion start to take over? That happens when you average over a volume so large that the density of matter inside the volume has a gravitational self-attraction weaker than the expansion’s pull"

But (at least to an armchair philosopher) GR says that gravity is not a force, or attraction. It's just geometry, specifically: it is curvature. So..., weak-attraction (below some threshold) should be the same as lack-of-curvature (below the equivalent threshold)

I have no trouble believing there's something wrong with the above thinking, but I'm awfully curious just what it might be. Thanks.

Sabine Hossenfelder said...


The "conclusion" is the prediction for a measurement outcome. Of course the conclusion involves calculations. Stop blaming others for your misunderstandings.

So you "won't take it any longer" that I write for free? I shiver in fear thinking about the consequences this will have for my meager income.

Sabine Hossenfelder said...


What you say is correct, but the case I discuss in the paragraph you quote is for one particular case of how to define space. And with that definition, space is not flat inside galaxies. There are other ways to define space that you can use to make space flat. This isn't generally always possible, but it's possible in certain cases. In that case, however, interpreting gravity even approximately as a usual force isn't possible any longer. Basically that's because you mix up what was formerly space and time.

Phillip Helbig said...

"Albert Einstein added a positive cosmological constant to his equations of general relativity to counteract the attractive effects of gravity on ordinary matter, which would otherwise cause a spatially finite universe to either collapse or expand forever."

I have a question here concerning this part: Does that mean that Einstein called the clumping together over a longer period of time of matter due to gravitation, 'a collapse of the universe' ? I mean it is pretty important to know what we are talking about and how to interpret words.

Because a collapse of the universe nowadays stands for the contraction of space itself, no ?

Does anybody have a clear view on this ?

First, do you have an actual quote on this from Einstein?

Einstein believed that observations indicated that the universe is static on large scales. They do, but that is the scale of the Galaxy. On larger scales they are not. Without the cosmological constant, the universe will expand or contract. So, he added a precisely tuned value of the cosmological constant to make it static.

Two important points. First, he could have (some will say "should have") formulated GR with the cosmological constant from the beginning. Second, in general the cosmological constant does not imply a static universe; only a precisely tuned value does.

The "finite universe" is an unnecessary restriction in the Wikipedia quote.

General note: The quality of Wikipedia articles is highly variable.

Koenraad Van Spaendonck said...

Thank you all for these clarifications, certainly helpfull.

Jason said...

I'm confused by a thought experiment, which came to me when reading through this post: suppose you have a thin spherical shell of matter, which is massive enough (or sticky enough) that it is stable against the expansion of space. In particular, it should have constant radius over time, and should be structured to be robust to small perturbations. If I recall correctly from freshman physics, the gravitational force inside the shell should be uniformly zero.

Now fill the sphere with uniformly dense matter of a low enough density that self-attraction does not overcome the expansion of space. The space inside the sphere should thusbe expanding. In particular, the low-density "soup" of matter should thin out as it's particles get further and further away from each other. This surprises me. The video in my head is of this soup thinning out uniformly without losing any mass, and somehow maintaining constant volume when viewed from the outside.

The only way I have of making this video consistent is by having mass somehow collect around the inner surface of the shell. (As an aside, this is roughly the video that I would expect from a different situation, without gravity: if the inner surface of the sphere were sticky, then the random motions of particles would lead to a state where the only high-velocity particles not captured would be far away and moving outwards, most medium velocity particles would either be very close and moving towards us, or moving away, and very low velocity particles would be distributed roughly at random.)

Is this what happens? Did I get something wrong?

Sabine Hossenfelder said...


First a rather general comment. There are a lot of things that can go wrong when arguing with words. The way to clarify the situation is to do a calculation.

Second, I'm not sure even your premise is correct. A shell of matter in non-expanding space needs infinite pressure to stabilize it. It's an utterly pathological system that I generally don't recommend using.

Third, leaving aside the pathologies of shells, the scenario you speak of is the most commonly used collapse scenario. You take the FRW metric (that's the one for cosmology) and patch it inside some volume. Whether it'll expand or contract depends on the initial values. Hence, it is indeed not stable. It's also not a static solution, so of course you expect space to generically be time-dependent (though that depends on the definition, as pointed out above).

Fourth, again leaving aside the pathological shells, there are static and stable configurations for the spherical case. You can obtain these by use of the Tolmann-Oppenheimer-Volkoff equations. They are stable only for certain density/pressure profiles that have to match the equation of state. It's the commonly used solutions for stellar equilibrium.



john schultz said...


As a parenthetical comment, in a non-Euclidean spacetime, there should be nothing odd about the volume of a fixed sphere increasing with time..., although I guess it would be odd to have increasing curvature without gravity.

But that's just a passing comment because, on a far more basic level, why would a shell of matter trap space within it? If you reflect that the shell could be moving through space, it's clear that space is not trapped by it.

akidbelle said...

Hi Sabine,

I though Lemaitre was also honorable member of this gang... (FRW)


Nate Guimond said...

Sorry, at the time I was thinking, "this block universe, which Brian Greene makes reference to in some of his books, and explains using the allegory of the Raison Loaf" but I just put "of."

I meant "of," as in "to which he subscribes," and the "of" of invention was not my intention.

piein skee said...

John shultz "...on a more basic level why would a shell of matter trsp space within it?

Because he defined the situation that it did.

piein skee said...

Phillip says '...Einstein could/should jave had the cosmological constant built in at the start...'

Really? The reason he didn't was the highly elegant and hard-to-vary status of the field equations. The cc has many variants - which translate directly over to the field equations leaving it radiczlly weaker

john schultz said...

piein skee
The sphere traps its physical contents, but it doesn't trap space. In fact, it can travel freely in space, including the space that may be (at any given moment) coincide with the location of its interior.