[jazzyjackson]

Hold up, so the flat-earthers just need to think a little bigger?

(Legit tho I've been trying to understand the 'shape' of the universe for a while now -- in the sense of, when I look at stars and galaxies in the sky above me, what direction am I looking as it relates to where things are in the universe relative to each other? As a kid I took Bill Nyes word for it: everything is on the surface of a balloon, expanding from the center. But do I ever see the far side of the balloon? Or is everywhere I look somehow constrained to the surface in every direction away from me, such that the 'other side of the balloon' is infinitely far away... but if I could see far enough, my own spot on the surface of this sphere would be visible to me, minus a few billion years... I want to understand this but I am very confused! This looks like an informative website so I'll keep reading ... thank you)

[roywiggins]

The balloon-surface model works if the universe is actually positively curved. It bends around in on itself and comes back. So you would be able to see yourself (eventually) after light made its way around the surface and back to you.

As far as anyone can tell, though, the universe is flat. So photons traveling outwards from you will never come back around- they'll just keep going.

I'm partial to the raisin bread model of the universe:

https://www.loc.gov/rr/scitech/mysteries/universe.html

It's a tad misleading: the raisin bread is, probably, infinite in extent. As a practical matter, we can only see a finite portion of the raisin bread. As we gaze more deeply into the sky, we're looking further into the raisin bread. Because light only travels at a finite speed, the further something is away, the older the image we see of it is. At a certain point, all we can see is the goopy bread batter that the raisin bread used to be: that's (sort of, kinda) the Cosmic Microwave Background: it's the oldest light in the universe, and we can't see anything older than it.

So the universe looks like a bunch of galaxies, with us at the center, and a sphere of microwave radiation at the edge. But every single observer sees a similar sphere around their exact location, so it's a kind of illusion.

[eridius]

Does the expansion of the universe mean that galaxies that are too far away from us are seemingly moving faster than the speed of light, and this is why we can't see any galaxies past a given point (because that's where they "accelerate" faster than light)?

[roywiggins]

A lot of the visible universe actually appears to be receding faster than the speed of light:

https://phys.org/news/2015-10-galaxies-faster.html

It's because the space inbetween is getting bigger. But light keeps moving towards us from those galaxies, so we see those photons eventually anyway. You can still hear things that are going above the speed of sound, as long as they're headed away from you- if they're headed toward you, you'll not hear them (probably?). But the waves they throw off will expand behind them just fine.

[acqq]

> if they're headed toward you, you'll not hear them (probably?)

Actually, you would not have much time to hear, but what you would hear (among the other effects) would be the sound “in reverse”(!)

https://physics.stackexchange.com/questions/14880/hearing-a-...

[rcxdude]

For a practical (if dangerous!) example, see supersonic rounds: if one is shot towards you, you hear the bullet whizzing by before you hear the gunshot.

[LgWoodenBadger]

Well, a supersonic round wouldn't whizz until it drops down to subsonic speeds.

You'd hear the crack of the round then the crack from the original shot.

[simonh]

If the universe originated with the big bang and then expanded, then unless it expanded infinitely fast it must be bounded. But if it's bounded, how can it be flat?

[roywiggins]

The math indicates that the singularity was infinitely dense and infinitely hot... if you're already allowing that something infinitely dense could be real, then infinitely fast expansion doesn't seem less crazy. Going from an infinite temperature to a finite temperature is an infinite amount of cooling, which also seems impossible; likewise, an infinite density to a finite one.

You'd need infinite expansion to do that- if it was merely finite, you'd still end up with an infinite density. Expanding an infinitely dense point to a bowling ball still gets you an infinite density; you need to expand it out "infinitely far" (whatever that means) to spread stuff out enough to get a merely finite density.

https://en.wikipedia.org/wiki/Initial_singularity

It seems more likely that the singularity at t=0 in general relativity isn't physical- what does an infinite density even mean?

[raattgift]

Now I'll take a not-very-rigorous stab at your exact question:

> what does an infinite density even mean?

In the previous reply I asked what does t=0 mean and under time-reversal marched some late time test objects towards a big-bang style singularity. Infinite density means that you can put any amount of matter down as initial values on a spacelike hypersurface at a time far from the singularity, evolve that surface in time towards the singularity, and eventually up at the singularity. The problem of the singularity is that a spacelike hypersurface there doesn't admit a sensible set of initial values, so you can't predict much about what comes out of the singularity when marching forward towards late times.

I also talked briefly about the pressure components of the stress-energy tensor.

Let's treat the stress-energy tensor as a 4x4 matrix describing the flux of i-momentum in the i-direction, and slice up spacetime into time-indexed 3-spaces. If we make a little 3d "cell" (being a little loose with terminology) then T^{00} encodes the amount of momentum sourced within the cell at t_{now} and staying within the cell at t_{immediately adjacent to now}.

Let's look at only one spatial dimension.

T^{11} encodes the amount of momentum originating to our left or right entering and leaving the cell to the left or right. Lets send rightward-going momentum into the cell from the left and mostly bounce out again to the left as leftward-going momentum, with some of the sent-in momentum sticking behind in the cell as energy (T^{00}) and some leaking out as rightward-going momentum to the next cell to the right. This is how pressure works, and shows how the stress-energy tensor can evolve as you squash things together. Momentum that is sent into a region (a cell being a sort of region) can stick around as energy. The question is, "how does it stick around"? Perhaps by increasing the frequency of the particle(s) occupying the cell.

Since T^00 usually dominates the stress-energy tensor T, and that in turn usually determines the Einstein tensor G, as more momentum-energy enters the cell without leaving, local curvature around the cell also increases. That in turn drives the split of momentum reflected back out of the cell, momentum retained within the cell, and momentum passed in another direction. This is essentially the root of the nonlinearity of the Einstein Field Equations.

The split of what energy-momentum reflects back out, flows right through, or remains within a cell depends essentially on paths of least resistance, and those depend on how the contents of the cell behave locally and also on the geometrical background. Grossly, momentum will tend to exit a cell in a downwards direction if it can, and downwards is in the direction of cells with greater energy (T^00).

At ever higher density around a cell, practically any kind of momentum entering the cell stays in the cell. As we move towards infinite density, all the "higher" (in a gravitational potential sense) cells eventually lose all of their energy (and any newly arriving momentum) in the direction of the "lowest" cell, even as we take the sizes of all cells to zero.

(For black holes rather than collapsing whole universes (or time-reversed expanding universes) only the cells inside the horizon are guaranteed to leak their entire energy and future momentum-energy towards the lowest cell.)

Unanswered questions: what quantum numbers are found in the lowest cell, especially as we shrink cell sizes? If you have a lowest infinitesimal cell holding all the sources of stress-energy, do quantum effects transfer momentum-energy from it to neighbouring higher infinitesimal cells? What quantum numbers escape the singularity? Can this happen hierarchically so as to form jets or other structures?

[raattgift]

> what does an infinite density even mean?

What does t=0 even mean? If we switch to some coordinates where t_0 \def t_now = 0 and t_past \gt 0, as with the scale factor in cosmology, we don't have a special time coordinate at t_past ~ 13.8 Gyr, so we can still think about the stress-energy (and the mechanisms that generate it) and the curvature it sources locally.

We can also think about things under time-reversal:

A comoving test observer in vacuum just free falls without end. Our test observer is a point with no charges (including "active" gravitational charge) and no internal structure, so it feels no tidal effects.

If we have two such observers starting at arbitrarily large space-like separation, they eventually they come close to each other and ultimately end up freely falling on the same trajectory, forever.

If we complicate the test observers from this no-repulsive-interaction picture, we develop pressure (represented in the stress-energy tensor, T^11 T^22 T^33). The local increase in pressure generates local curvature in response, and if the repulsive interaction is finite then eventually the two interacting test observers end up freely falling on the same trajectory, forever. The eventuality is because the background has infinite curvature, and that and the contribution from the self-gravitation of pressure wins out over any finite repulsion.

We can complicate test object interactions further by introducing: repulsive and attractive interactions; extended observers that are composites of these test observers; and even have these objects obey the statistics for bosons and fermions. Same-charged fermions in effect resist being pushed onto the same trajectory, but the resistance is almost certainly finite. Eventually some daughter product free-falls forever.

(We can see some of this in sufficiently massive objects that repulsion or exclusion is overcome, as in the cores of stars or in neutron stars, where internal pressure tends to dominate the local stress-energy.)

What the daughter products of squashed-together Standard Model particles might be is a matter of research, both in terrestrial laboratories and in astrophysical processes (including black holes). Conversely, mirroring the time-reversal thinking above, the Standard Model particles have to freeze out of something hotter and denser that exists at greater lookback time. (cf. electroweak symmetry breaking).

Worse, at a(t_0) ("now") there is a lot of dark matter, and we don't know the details of how that interacts with the Standard Model. Those details will almost certainly matter in the time-reversal picture above.

Consequently we don't know that repulsion/exclusion is finite. Perhaps some crystalline structure develops in the time-reverse picture (or in black holes), and things just accumulate in that. Or perhaps there is a sudden drop in pressure where daughter products fly away from some ultrastrong squashing-together (cf. pair-instability supernovae).

There are quite a few options. And of course the Robertson-Walker background is already just an approximation; the real metric is likely to be very different at high lookback times.

Finally, Carroll has a nice deck (and it's filled with references) at https://www.slideshare.net/seanmcarroll/what-we-dont-know-ab...