And there's a good metaphor: The surface of Earth has no center. Therefore we can imagine that space similarly has no center if we imagine it having 4 dimensions.
But what proof is there that universe is actually 4-dimensional? Or > 3 dimensional in general?
The thing is that you don't need to imagine extra dimensions. Th surface of a sphere remains 2-dimensional in this metaphor, even if the actual sphere is 3-dimensional. The Universe is not stretched on anything though, and whatever number of dimesion it exhibits, the stretching relies on them only.
The explanation isn't very satisfying to me. If you expand the surface of a sphere, you're still expanding a 2-manifold in 3 dimensions. When you expand the sphere, you're expanding into the empty part of 3-space.
You can describe any 2d shape using 3 dimensions, just imagine that it's set askew or bent. From the perspective of the inhabitant of such a flatland, it's undetectable and irrelevant. So is it from the perspective of the topology of the shape.
Describing the universe's shape is similarly done from within, so we can't see the outside and don't need any "outside" to see that the Universe is expanding. It's a description of how our 3d world is behaving, seen from within, and not relying on any "outside".
The word "expand" is not describing the exact same physical phenomenon as what we are used to seeing, because when we expand something, we typically cause it from the outside. That's why it can't be satisfying: it's a similar but different thing.
Right so the expansion of our 3-D universe would need to be happening into the 4th or more dimensions for the analogue to make sense. But is that really what they are saying that when cosmologists speak of the expansion of the universe they mean it is expanding to the other 3+ (spatial) dimensions?.
Note the title of the article "What is our Universe Expanding Into? Is it expanding into the 4th spatial dimension?
AIUI, strictly speaking, the universe could be "stretched on something". The manifold could be embedded in a higher dimensional space, like the 2D surface of a balloon being embedded in 3D space. However, the maths is the same whether it's embedded like that (in any of an infinity of possible ways) or the manifold is all there is. My understanding is that physicists assume the latter simply because there's no practical benefit to doing otherwise, rather than because they have any evidence the universe isn't embedded in a higher space.
(I believe this is a different thing to the various higher dimensional cosmological theories that exist - branes and the like - but such things are beyond me.)
In general relativity space-time is a 4-dimensional (3 space + 1 time) surface that itself can expand, contract, or move around. It's perfectly reasonable in GR to have a distance be L at time t, then L+dL at time t+dt. No extra spatial dimensions needed.
Is there an "edge" in the sense that, if you lived there and looked in your telescope in one direction, you see galaxies, but if you turned it around, you'd see nothing?
The evidence strongly indicates a flat, infinite, isomorphic universe. You are correct of course that we do not and cannot know, but anything else would require extraordinary evidence to the contrary.
Flat universe theory sounds like flat earth theory in the 14th century. How could the earth be round at that point? It would take extraordinary evidence to the contrary. That doesn't mean flat earth theory was true.. just that everyone accepts that answer now.
Wouldn’t this evidence also be consistent with being “not near enough to the edge to perceive an edge”? And also consistent with that, because of the expansion of the universe we will never be able to get a signal from the “edge” to know anyway?
My problem with an infinite isomorphic universe is that it implies infinite mass. I don’t know enough about cosmology or other physics to understand all the implications, but to me it seems like it would make models of the early universe janky - ie why would it not just immediately collapse in on itself?
As I understand it, the standard cosmology includes inflation, which stretched out the "full" universe to much larger than the observable universe. This also made the observable universe very, very close to flat, which makes it almost impossible to observe the difference between "flat" and "not flat, but very close to flat in the observable part of the universe".
So if you think there's evidence that strongly indicates "truly flat", I'd like to hear what it is. Ditto for evidence that strongly indicates "infinite" as opposed to "finite, but considerably larger than the observable portion".
[Edit: If you want to say that inflation is a just-so story, I'm not sure I will disagree. And if you say that inflation looks like it was specifically designed to be untestable, I could probably agree with that, too. But those are different from saying that you have sufficient evidence to rule out inflation.]
> We now know (as of 2013) that the universe is flat with only a 0.4% margin of error. This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe.
Yeah this is what I don't understand. In order for this not to be true, space would have to be curved back in on itself like the surface of a balloon. Meaning you could eventually wind up back where you started. But do we know for sure this is how the 3D space in our universe works?
There is no edge, no. In some theories Space warps around on itself, but it would be more like a möbius strip. But the edge of our observable universe is just when the Big Bang happened, and before that we can’t detect any light, so it looks like an edge. If you were there the universe would looks much the same as it does from our own vantage as it’s self similar.
Why a Möbius strip? That would imply that if I travelled around the universe and back to Earth, everything would be like it had been reflected in a mirror.
Why do you say that? But, as to why a a strip, because you appear to walk in a straight line but end up at the same point. It could have been a sphere too, but you have more dimensions to move in, and they aren't nearly as cool.
For something to be expanding right now to be true then it must also be true that it began expanding at some point and the center of that expansion (or many centers) a point of reference for the expansion now. If time is linear with a begining at least.
If you aim at a direction in the sky and teleport past the last object or energy in that direction, you yourself becoming an edge of the universe, where will you go if you expand in the direction of the expansion of the object behind you? My answer: into nothing, your very progression has updated the boundary of reality. If you were a dot in a two dimensional window,your arrival at pixel 0x0 and attempt to move past it simply updates where 0x0 is relative to all other points.
shortly after the bigbang, when the universe was a nonzero amount of time the size of a potato, compared to its current size, how to reconcile that with 'it doesnt expand into anything'?
It wasn’t the size of a potato. It was everywhere all at once. There is no three dimensional shape of the universe, no boundary, and edge. Still, between galaxies space is expanding. That means everything below a certain amount of mass density is getting further from every other mass density. Within the mass density space does not expand. We are not getting further away from other stars. But saying the universe was the size of the potato dramatically misses what we believed the universe is today and what the article says. It abstracts the nature of things to what is familiar to you, but misses the actual nature of things.
Note the Big Bang is a point in time where all paths started, as stated in the article. It’s a mathematical singularity. It’s not an explosion as you think of it. It was a sudden expansion of all points in space creating vastly more space between the points. But since space has no boundary it didn’t get bigger, and it wasn’t smaller.
> Note the Big Bang is a point in time where all paths started, as stated in the article. It’s a mathematical singularity. It’s not an explosion as you think of it. It was a sudden expansion of all points in space creating vastly more space between the points. But since space has no boundary it didn’t get bigger, and it wasn’t smaller.
I think PBS space time does a good job explaining these things, but you’re right it doesn’t map to our understanding of how mass and space work in a Newtonian world. These videos give some explanation and link through internally to more details.
There was a point in time where everything in the visible universe was the size of a potato, but the entire universe (beyond the visible edge) is most likely just more matter in every direction indefinitely.
Because the universe follows general relativity, space itself behaves like a fluid. When the universe "expands", that's just space itself growing bigger over time.
The analogy that's usually used to help people wrap their heads around this is to think of the 3D universe as the curved 2D surface a balloon. As the balloon expands, every point becomes farther away than every other point. A bug walking on the surface of the balloon could go anywhere on the balloon and never hit an edge. That makes sense.
But also in this analogy if the bug travels long enough in what to it seems a straight line, it will wind up back where it started. Does this hold true for the universe as well?
Let's say the universe stopped expanding tomorrow, and didn't shrink. If someone got in a spaceship and traveled in (what seems to them) a straight line for long enough, would they wind up back where they started?
If not, how can the universe have no edge? How can a you always see another galaxy straight ahead, in a universe with a finite number of galaxies? The universe doesn't just create new galaxies. You have to start recycling galaxies at some point.
> But also in this analogy if the bug travels long enough in what to it seems a straight line, it will wind up back where it started. Does this hold true for the universe as well?
It's possible, but the experimental evidence have indicated that it does not - the 2D analogy that more closely matches the measurements is "infinite flat sheet", not "curved surface of a sphere."
Infinite means infinite number of galaxies, right? I watch How the Universe Works religiously. Most of the astrophysicists on that show don't seem to think the universe is infinite.
I have recently wondered about this. When we talk about the big bang, the mostly-uniform CMB, accelerated expansion, etc. aren't we always axiomatically presuming the correctness of the cosmological principle (which, in a hand-wavy way says the universe plays the same game everywhere). I would think all we can say confidently is that the principle is working out in our locale.
I thought dark energy was the reason the non-gravitational-bound galaxies are accelerating away from each other? If they are accelerating, that would be a change in velocity, which seems like a change in momentum. ?
The name "acceleration" is just as misleading as "expanding" here, but maybe useful.
Our galaxy is non-gravitationally-bound to a lot of other galaxies, and we "accelerate" away from them. Yet we don't really feel that. We also obviously can't accelerate away from all of them, when they are in random directions. That's because the "acceleration" describes the change of distance, without changing position. Without changing position, there's no change of momentum.
That "acceleration" is a consequence of the expansion/stretching described in the article.
Imagine a hotel with infinite rooms and there is a guest in each room. A bus arrives carrying infinite guests and you must assign each of these guests to a room. One solution is to ask each guest to move two rooms over and assign the new guests to the odd number rooms.
I am not a physicist, but i do visualize the universe expansion as such an infinity paradox.
> But also in this analogy if the bug travels long enough in what to it seems a straight line, it will wind up back where it started. Does this hold true for the universe as well?
That’s indeed a very important question. The shape of the universe is a subject of study in cosmology.
The property you mention relates to its curvature (hyperbolic, flat or spheric). Experimental data shows that the observable universe is flat which means the universe is either flat or sufficiently big for the observable universe to appear flat as a local area.
> If not, how can the universe have no edge?
What we see of the universe indeed as an edge. Light takes time to travel. It means that the farther you look the earlier you look and we can’t look farther than the beginning of time.
Is it true that if the universe is flat, then either it has to have an edge (meaning a place where you see galaxies in one direction and nothing in the other), or it has to have an infinite number of galaxies?
I’m not entirely sure of that to be honest with you. I seem to remember than counterintuitively you can embed a flat torus in 3D but it goes further than my knowledge.
It means it’s not a “small” hypersphere, that’s for sure.
"Experimental data shows that the observable universe is flat", agreed. However the research put a maximum bound on it's non-flatness. So it's low, but it's impossible to prove it's perfectly flat.
The thing I don't get with that analogy is the ballon IS expanding into something - eg if you put the balloon in a cup, it won't expand (unless you have REALLY strong lungs :-) ).
Also, curious where the extra energy comes from to keep the 'vacuum energy' (zero point energy?) from going down - IIRC, its remained constant even though the universe is expanding
> Also, curious where the extra energy comes from to keep the 'vacuum energy' (zero point energy?) from going down - IIRC, its remained constant even though the universe is expanding
Energy is ill-defined in a global sense: it's the conserved quantity associated with time-translation symmetry, but there's no single choice of "time translation" that can be extended to all of spacetime.
Hmm...This goes beyond what PBS space-time taught me about it :-) My understanding was we have more space (eg space is expanding) but the 'vacuum energy' is staying constant.. If I understand what you're saying, that statement depends on the time frame you measure against ?
Hmm..ok - thank you. I'm gonna have to work on that more, atm I'm having a hard time comprehending how volume can increase without density decreasing. To google!
Google won't help you here. Popsci stuff is useless at best, and more often actively misleading. You need a GR textbook. An Introduction to General Relativity, Spacetime, and Geometry (https://fma.if.usp.br/~mlima/teaching/PGF5292_2021/Carroll_S...) is relatively accessible.
This article might help: "Energy Is Not Conserved" by Sean Carroll [1]. Here are a couple of paragraphs to give you the gist of it.
> But many people have just this reaction. It’s clear that cosmologists have not done a very good job of spreading the word about something that’s been well-understood since at least the 1920’s: energy is not conserved in general relativity. (With caveats to be explained below.)
> The point is pretty simple: back when you thought energy was conserved, there was a reason why you thought that, namely time-translation invariance. A fancy way of saying “the background on which particles and forces evolve, as well as the dynamical rules governing their motions, are fixed, not changing with time.” But in general relativity that’s simply no longer true. Einstein tells us that space and time are dynamical, and in particular that they can evolve with time. When the space through which particles move is changing, the total energy of those particles is not conserved.
Yes but even in these analogy the balloon is still expanding into something. There is space around the balloon and when the balloon expands, there is less of that surrounding space.
At this point even if there was an edge you couldn't get to it because points move apart faster than the speed of light and we can't go faster. The points themselves aren't actually moving (rather space is being created in between) so there's no speed limit violation.
does the universe have a finite number of galaxies? We see the 'observable' universe. The universe is even larger than what we can see, but that light can never reach us.
I would add the connection to GR. In a Newtonian world, there would be nowhere for matter to expand into, and our intuition would be correct. But in General Relativity, space itself can grow or shrink like a fluid.
The 'big bang' is both a point in time, and in space. The boundaries of the universe are the light cone of the big bang.
It is conceivable that our 'universe' is just one regional phenomena within a much larger universe. Multiple such 'universes' in the same physical space could seem to be isolated until they expand to the point of overlap and begin to collide.
As shown in that figure, a level 1 multiverse is simply whatever other areas exist beyond our universes light cone. There could very well be 'stuff' out there that we are expanding into!
> The boundaries of the universe are the light cone of the big bang.
That "boundary" is not a spacial boundary, but simply the farthest distance we can "see".
The universe is expanding fast enough that any given space-time point can only "see" a finite region of the greater universe.
But it is all connected. We can see objects far away, whose citizens (if they exist) can see beyond our visible boundary, and so on.
And our area is not expanding "into" other areas. Think of the expansion as equally inflating every area, including our own. Pushing distant areas to be more distant. All in a smooth way across the region of the universe we can see and beyond.
Interesting. Would that larger universe also be expanding and of so, what would it be expanding into? Maybe the larger universe exists in a larger-larger universe?
Maybe the universes that are expanding inside a larger universe would not overlap but repell when they encounter each other, i.e. push each other out of the way instead changing the shape of a universe.
The article says it’s NOT a point in space btw and that it happened everywhere simultaneously. This is an interesting idea I wasn’t aware if and trying to wrap my head around it now :)
This is really interesting. Our thinking is so entrenched in 3D, we just can't develop an intuition for a universe where space itself expands and there is nothing else. Even if you say that the universe expands into something then what are the boundaries of that? Turtles all the way down.
I don’t know. Everyone can understand a change of metric.
If you decide that what used to be 1cm is now 2cm, everyone will understand that everything is now twice as far. Now, imagine that instead of suddenly going from 1cm to 2cm, you do it gradually during say, 1 minute. Well, congratulations, that’s expansion right there.
I never understood the balloon analogy. It’s just a bad one.
A great visualization, is to imagine that space remains unchanged, but everything in it is shrinking at the same rate.
The shrinking people don't perceive they are shrinking, or that anything else is shrinking. But the distances between things not held together by significant forces (like chemical or gravitational bonds) appear to be growing and growing.
And space isn't expanding >into< anything. It is just relative changes between bond forces and space, creating the experience of more space. There is no impact of this expansion "outside" the universe (that we know of, of course).
Universe is expanding in the sense that the "amount" of space is growing: there was so much space between those two stars and a year later there is more of it. Where does this space come from? And why is it only space that's expanding, why not time?
> When we say we live in an expanding universe, we’re saying that the distances between galaxies, on average, grows with time. And that’s it.
How could this be due to the expansion of space, which should expand our galaxy, and my foot-long ruler, to the same extent that it expands the empty space between our galaxy and the next?
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[ 5.1 ms ] story [ 175 ms ] threadAnd there's a good metaphor: The surface of Earth has no center. Therefore we can imagine that space similarly has no center if we imagine it having 4 dimensions.
But what proof is there that universe is actually 4-dimensional? Or > 3 dimensional in general?
Describing the universe's shape is similarly done from within, so we can't see the outside and don't need any "outside" to see that the Universe is expanding. It's a description of how our 3d world is behaving, seen from within, and not relying on any "outside".
The word "expand" is not describing the exact same physical phenomenon as what we are used to seeing, because when we expand something, we typically cause it from the outside. That's why it can't be satisfying: it's a similar but different thing.
Note the title of the article "What is our Universe Expanding Into? Is it expanding into the 4th spatial dimension?
(I believe this is a different thing to the various higher dimensional cosmological theories that exist - branes and the like - but such things are beyond me.)
My problem with an infinite isomorphic universe is that it implies infinite mass. I don’t know enough about cosmology or other physics to understand all the implications, but to me it seems like it would make models of the early universe janky - ie why would it not just immediately collapse in on itself?
As I understand it, the standard cosmology includes inflation, which stretched out the "full" universe to much larger than the observable universe. This also made the observable universe very, very close to flat, which makes it almost impossible to observe the difference between "flat" and "not flat, but very close to flat in the observable part of the universe".
So if you think there's evidence that strongly indicates "truly flat", I'd like to hear what it is. Ditto for evidence that strongly indicates "infinite" as opposed to "finite, but considerably larger than the observable portion".
[Edit: If you want to say that inflation is a just-so story, I'm not sure I will disagree. And if you say that inflation looks like it was specifically designed to be untestable, I could probably agree with that, too. But those are different from saying that you have sufficient evidence to rule out inflation.]
> We now know (as of 2013) that the universe is flat with only a 0.4% margin of error. This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe.
https://wmap.gsfc.nasa.gov/universe/uni_shape.html
Sure, why not?
> I thought the Big Bang implied a finite mass.
What makes you say that? How so?
If you aim at a direction in the sky and teleport past the last object or energy in that direction, you yourself becoming an edge of the universe, where will you go if you expand in the direction of the expansion of the object behind you? My answer: into nothing, your very progression has updated the boundary of reality. If you were a dot in a two dimensional window,your arrival at pixel 0x0 and attempt to move past it simply updates where 0x0 is relative to all other points.
As to teleporting to the edge, there is as much an edge to the Universe as to the Earth, so the answer is: you can't teleport there.
Note the Big Bang is a point in time where all paths started, as stated in the article. It’s a mathematical singularity. It’s not an explosion as you think of it. It was a sudden expansion of all points in space creating vastly more space between the points. But since space has no boundary it didn’t get bigger, and it wasn’t smaller.
This makes zero sense.
https://youtu.be/bUHZ2k9DYHY
https://youtu.be/bUHZ2k9DYHY
Because the universe follows general relativity, space itself behaves like a fluid. When the universe "expands", that's just space itself growing bigger over time.
But also in this analogy if the bug travels long enough in what to it seems a straight line, it will wind up back where it started. Does this hold true for the universe as well?
Let's say the universe stopped expanding tomorrow, and didn't shrink. If someone got in a spaceship and traveled in (what seems to them) a straight line for long enough, would they wind up back where they started?
If not, how can the universe have no edge? How can a you always see another galaxy straight ahead, in a universe with a finite number of galaxies? The universe doesn't just create new galaxies. You have to start recycling galaxies at some point.
It's possible, but the experimental evidence have indicated that it does not - the 2D analogy that more closely matches the measurements is "infinite flat sheet", not "curved surface of a sphere."
As as I know, we don’t know. As I understand it we can see ~13.9 billion light years away but not further, and so we don’t know what’s past it.
I’d love if an expert chimed in.
That, and stretching a surface intuitively imparts momentum on things on top, whereas it's not the case here.
Our galaxy is non-gravitationally-bound to a lot of other galaxies, and we "accelerate" away from them. Yet we don't really feel that. We also obviously can't accelerate away from all of them, when they are in random directions. That's because the "acceleration" describes the change of distance, without changing position. Without changing position, there's no change of momentum.
That "acceleration" is a consequence of the expansion/stretching described in the article.
This still requires the balloon to expand into 3D space.
I am not a physicist, but i do visualize the universe expansion as such an infinity paradox.
It's an analogy that works in our experience that we can visualise.
There is no reason to suppose that the universe requires something "outside" it to expand "into". It could just... get bigger.
That’s indeed a very important question. The shape of the universe is a subject of study in cosmology.
The property you mention relates to its curvature (hyperbolic, flat or spheric). Experimental data shows that the observable universe is flat which means the universe is either flat or sufficiently big for the observable universe to appear flat as a local area.
> If not, how can the universe have no edge?
What we see of the universe indeed as an edge. Light takes time to travel. It means that the farther you look the earlier you look and we can’t look farther than the beginning of time.
It means it’s not a “small” hypersphere, that’s for sure.
Also, curious where the extra energy comes from to keep the 'vacuum energy' (zero point energy?) from going down - IIRC, its remained constant even though the universe is expanding
Energy is ill-defined in a global sense: it's the conserved quantity associated with time-translation symmetry, but there's no single choice of "time translation" that can be extended to all of spacetime.
edit: s/your/you're/
Thanks!
> But many people have just this reaction. It’s clear that cosmologists have not done a very good job of spreading the word about something that’s been well-understood since at least the 1920’s: energy is not conserved in general relativity. (With caveats to be explained below.)
> The point is pretty simple: back when you thought energy was conserved, there was a reason why you thought that, namely time-translation invariance. A fancy way of saying “the background on which particles and forces evolve, as well as the dynamical rules governing their motions, are fixed, not changing with time.” But in general relativity that’s simply no longer true. Einstein tells us that space and time are dynamical, and in particular that they can evolve with time. When the space through which particles move is changing, the total energy of those particles is not conserved.
[1] https://www.preposterousuniverse.com/blog/2010/02/22/energy-...
edit: that was a good read! Thanks again
It is conceivable that our 'universe' is just one regional phenomena within a much larger universe. Multiple such 'universes' in the same physical space could seem to be isolated until they expand to the point of overlap and begin to collide.
This image from Max Tegmark illustrates this idea well: https://space.mit.edu/home/tegmark/multiverse.jpg
As shown in that figure, a level 1 multiverse is simply whatever other areas exist beyond our universes light cone. There could very well be 'stuff' out there that we are expanding into!
That "boundary" is not a spacial boundary, but simply the farthest distance we can "see".
The universe is expanding fast enough that any given space-time point can only "see" a finite region of the greater universe.
But it is all connected. We can see objects far away, whose citizens (if they exist) can see beyond our visible boundary, and so on.
And our area is not expanding "into" other areas. Think of the expansion as equally inflating every area, including our own. Pushing distant areas to be more distant. All in a smooth way across the region of the universe we can see and beyond.
Maybe the universes that are expanding inside a larger universe would not overlap but repell when they encounter each other, i.e. push each other out of the way instead changing the shape of a universe.
If you decide that what used to be 1cm is now 2cm, everyone will understand that everything is now twice as far. Now, imagine that instead of suddenly going from 1cm to 2cm, you do it gradually during say, 1 minute. Well, congratulations, that’s expansion right there.
I never understood the balloon analogy. It’s just a bad one.
The shrinking people don't perceive they are shrinking, or that anything else is shrinking. But the distances between things not held together by significant forces (like chemical or gravitational bonds) appear to be growing and growing.
And space isn't expanding >into< anything. It is just relative changes between bond forces and space, creating the experience of more space. There is no impact of this expansion "outside" the universe (that we know of, of course).
There is no "into" without the concept of "space".
The universe is space (and time).
Thus it's not expanding into anything as there is no space outside of the universe.
QED.
Every second we have another second* of time in most of the universe.
* May be less time near large amounts of mass.
https://open.spotify.com/episode/7zQsqfpx1p3fBUsqLGtHnM
How could this be due to the expansion of space, which should expand our galaxy, and my foot-long ruler, to the same extent that it expands the empty space between our galaxy and the next?
This seems to come from a Rust programmer.
Every C programmer knows that the universe expands into void and the size of void is machine and inplementation dependent.