Gravity pulls things in by causing space-time to accelerate in a particular direction. In other words we accelerate towards the Earth at 9.8 meters per second per second because that is what space-time itself does. The space-time that is in our frame of reference accelerates down, carrying us with it. The floor pushes up on us, causing us to accelerate up. Balancing things out so that we remain where we are.
A dense mass will cause flat space-time to start falling in. Enough mass, densely enough, will cause it to fall in so fast that not even light can escape. This is a black hole.
However the Big Bang wasn't a flat space-time. The space-time that was the structure of the universe was moving apart extremely quickly. There was more than enough mass around to create a black hole today. But what it did is cause the expansion rate to slow. Not to stop, reverse, and fall back in on itself into a giant black hole.
> Gravity pulls things in by causing space-time to accelerate in a particular direction.
Ok, how does this sketch work for a low-ellipticity eccentric orbit?
> "The space-time that is in our frame of reference"
Isn't throwing out general covariance (and manifold insubstantivalism) rather a high price for a simplification of Einsteinian gravitation?
> the Big Bang wasn't a flat space-time
Sure, it's a set of events in a region of the whole spacetime. If we take "Big Bang" colloquially enough to include the inflationary epoch, always assuming GR is correct, then at every point in that "Big Bang" region of the whole spacetime there is a small patch -- a subregion -- of exactly flat spacetime. However, these small patches must be small because most choices of initially-close pairs of test objects can only couple to timelike curves that wildly spread in one direction (and focus in the other).
I don't know how to understand your two final sentences: how do you connect the period just before the end of inflation and the expansion history during the radiation and matter epochs?
Yes I know it is handwavy and misleading. But I consider it less misleading than most attempts at visualizing it.
> Ok, how does this sketch work for a low-ellipticity eccentric orbit?
At what point in the orbit does it not work as a description of what's going on locally where the orbiting body is?
> Sure, it's a set of events in a region of the whole spacetime. If we take "Big Bang" colloquially enough to include the inflationary epoch, always assuming GR is correct, then at every point in that "Big Bang" region of the whole spacetime there is a small patch -- a subregion -- of exactly flat spacetime. However, these small patches must be small because most choices of initially-close pairs of test objects can only couple to timelike curves that wildly spread in one direction (and focus in the other).
No, there is no requirement of any region of locally flat spacetime existing. It is required (outside of singularities) that, when measuring things to first order, things are flat. However in curved space-time, the curvature can be theoretically revealed in any region, no matter how small, by measurements that are sufficiently precise to show the second order deviations from flatness that we call curvature.
> I don't know how to understand your two final sentences: how do you connect the period just before the end of inflation and the expansion history during the radiation and matter epochs?
I'm just referring to the fact that the Hubble parameter is believed to have been higher in the early universe than it is today. I'm not referring to periods such as the hypothesized inflation where the behavior is not described by GR.
I'd be grateful if you take me to the time stamp, because in a casual watch of the video there was nothing like your:
Gravity pulls things in by causing space-time
to accelerate in a particular direction. In
other words we accelerate towards the Earth
at 9.8 meters per second per second
because that is what space-time itself does.
The closest thing I noticed was just after the 10 minute mark, where he points at Christoffel symbols and essentially says that you can choose a set of accelerated coordinates such that to remain at the spatial origin you have to undergo proper acceleration. "Your acceleration must be equal to this curvature term ... in curved spacetime you have to accelerate just to stand still". Which is totally fine, and even finer if he made it clear that you are "standing still" at some spatial coordinate after an arbitrary splitting of spacetime into space + time. But I don't know how or if those approx 90 seconds connect to what I quoted from you above.
(Even finer still if he removed the coordinates and completed the equation: see e.g. slide 20/50 at https://slideplayer.com/slide/12694784/ - his whiteboard is the term labelled in cyan, adapted. approx 10m45s "You don't have to worry about the details here. The point is...". The point is that I'm not his intended audience, and his presentation is fine enough, so there's no good reason for me to take you up on your suggestion to contact him.)
> At what point in the orbit does it not work as a description of what's going on locally where the orbiting body is?
I don't know that it doesn't work - it's just that to me it's such an odd way of putting it that the consequences of your "describing it that way" are unclear to me. An obvious probe is solving for an eccentric orbit.
Shoot a slower timelike observer on a ~secant line hyperbolic trajectory across the quasicircular orbit, comparing proper-time-series accelerometer and chronometer logs from their first kiss before the latter's periastron to their last kiss after. How does your "accelerated spacetime" vary by position and initial velocity? How does it work as we take v->c?
I don't know enough physics to know whether the parent knows what they are talking about, but there is one piece of math that makes me think they do not.
> at every point in that "Big Bang" region of the whole spacetime there is a small patch -- a subregion -- of exactly flat spacetime
Can explain how you get a non-empty region of exactly flat space time around every point?
Patching together curved things out of not curved things happens all of the time. The Earth looks flat around the point you are standing. I'm worried that just because it looks flat in my city doesn't mean it is actually flat in my city, if I measure carefully.
I'll try to keep this understandable, but can expand or ELI5 bits of it if that would help you.
Physically, local flatness is a statement about the local validity of Special Relativity. Practically, a failure of the local validity of Special Relativty -- a Local Lorentz Invariance violation (often abbreviated LLI violation or local LIV or local LV) -- would be apparent in stellar physics and the spectral lines of white dwarfs and neutron stars and close binaries of them. Certainly we haven't been able to generate local LIV in our highest-energy particle smashers, so the Lorentz group being built into the Standard Model is on pretty safe footing.
(For example, we need tests of Special Relativity -- and notably those of the Standard Model, which bakes in the group theory of Special Relativity -- to work for material bodies in free-fall, even if that free-fall is an elliptical path around and close to a massive object. That's everything from our atomic-clock navigation satellites to gas clouds and stars near our galaxy's central black hole or distant quasars.)
It wasn't a piece of math, which would involve writing out an Einstein-Cartan or Palatini action that let one break out the local Lorentz transformations and diffeomorphisms into a mathematical statement, as one can find in modern (particularly post-Ashtekar in the late 1980s) advanced graduate textbooks. Nobody wants that scribbled out in pseudo-LaTeX here on HN. :-)
The choice quote from part 1: "[our] final interpretation says that every spacetime is locally approximately flat in the sense that near any point of any spacetime (or near sufficiently small segments of a curve), there exists a flat metric that coincides with the spacetime metric to first order at that point (or on that curve) and approximates it arbitrarily well," [emphasis mine].
You might prefer to emphasise "approximately" in that quote, but the approximation is much better than that of, say, a square millimetre of your floor.
Next, from a historical perspective: General Relativity was built with making gravitation Special-Relativistic, following Poincaré's 1905 argument about the finite-speed propagation of the gravitational interaction. Einstein (and others) had several false starts marrying gravitation and Special Relativity in various ways before ultimately arriving at spacetime curvature. (At that point, in the 1920s, one finally had the vocabularly to describe Special Relativity's Minkowski spacetime as flat; the Lorentz group theory came later). But making sure Special Relativity didn't break on around Earth -- where it had been tested aggressively for two decades -- was terribly important to Einstein. Additionally, he did not want to break what Newtonian gravitation got right. The mathematics follow somewhat from this compatibility approach where Newtonian gravitation and Special Relativity are correct in the limit where masses are moving very slowly compared to the speed of light and are not compact like white dwarfs or denser objects.
The regions in which there is no hope in many many human lifetimes for finding a deviation from Local Lorentz Invariance are huge (there are interplanetary tests with space probes in our solar system, and interstellar tests using pulsar timing arrays), even if General Relativity turns out to be slightly wrong. This is an area which invites frequent experimental investigation: <https://duckduckgo.com/?t=ffab&q=local%20lorentz%20invarianc...>.
Finally, it is precisely your intuition that big curvature must be built up from small curvature that is the point of investigating local LIV. So far, and to great precision, those intuitions are wrong. Nature builds up impressive spacetime curvature (e.g. in white dwarfs and neutron stars) without showing any signs of softening the local validity of Special Relativity (i.e., the interactions of matter within those compact stars). And that's part of why quantum gravitation is nowhere near decided.
> The choice quote from part 1: "[our] final interpretation says that every spacetime is locally approximately flat in the sense that near any point of any spacetime (or near sufficiently small segments of a curve), there exists a flat metric that coincides with the spacetime metric to first order at that point (or on that curve) and approximates it arbitrarily well," [emphasis mine].
This statement is a mathematical conclusion from GR of a similar nature to noting that for any point on a sphere, there is a map projection onto the plane where distances on the sphere coincide to first order to distances on the plane.
This no more or less means that space-time is locally flat than it means that a sphere is locally flat. To a first order approximation, it is. But when we calculate the curvature tensor, we find that it isn't flat at all.
How do you propose to measure the ultralocal Riemann curvature? I agree with you that it can be there in an exact solution, but I don't really agree that it's necessarily physical (there are many many exact solutions which aren't, for starters). Even with a broader definition of local, a Synge 5-point like process is not going to find a failure of parallel transport in a sufficiently small region. Would you be satisfied with "effectively flat" (in an EFT sense) or even "FAPP flat"?
> Nature builds up impressive spacetime curvature (e.g. in white dwarfs and neutron stars) without showing any signs of softening the local validity of Special Relativity (i.e., the interactions of matter within those compact stars).
I.e., you need to be near huge, dense masses, or on/in them to see LIV violations, but we can't see them from observing those masses.
> And that's part of why quantum gravitation is nowhere near decided.
There are also problems with quantizing curved spacetime.
> You need to be near huge, dense masses, or on/in them to see LIV violations
A sufficient LLI violation in a compact object is likely to lead to a difference in pressure/contact line broadening, thanks to a modified dispersion relation. Ok, there's optical depth issues there, but looking at metal-rich WDs is a start (it gets you to your "or on...them", at least). Neutrino fluxes probably carry some Lorentz-symmetry-related information from multmessenger events too.
Additionally, binaries and multiples might show various equivalence breakdowns if there are LLI violations, with enhanced ellipticities or periastron precessions (by altering orbital polarization and spin precession parameters in the PPN).
But also there are plenty of theories which slightly violate local Lorentz-invariance in the Newtonian limit, bulding up over distances, and PTA data and GRB data are already constraining those.
I don't understand this answer. By GR there is no possible flat space-time around a dense mass no? BC the energy will curve the space-time. Saying that the space-time was expanding very quickly is also describing the shape of the space-time. Isn't it kind of circular to say that big bang doesn't end in a singularity b/c it is curved out? You can still ask why it's curved out with so much energy and whether it is compatible with GR? But I guess the answer if GR was holding near big bang must just be that there's some solution which is compatible with GR with so much energy in a small place which doesn't end in singularity.
The Schwarzschild solution is the unique distribution in GR for nonrotating mass in a small area, in a universe that is asymptotically flat at a long distance from the mass. This is not a flat universe, but most of it is pretty darned close to flat.
As for describing the shape of space-time, that's what GR does. What we can think of as the "shape" is actually described by something called the metric. GR says that the metric satisfies a differential equation. If the universe starts close to flat, things are moving slowly, and there is a low density of mass, the solutions to this equation create an effect that, to first order, matches Newtonian gravity. But the full theory has solutions with all sorts of bizarre things in it, like waves traveling through space, made up of fluctuations in the very structure of space-time. We call those gravity waves.
And yes, those solutions do include things like expanding universes. And the effect of gravity within an expanding universe is to slow the rate of expansion.
The metric you're referring to, oddly enough is a mapping from flat spacetime to curved. This is why the Schwarzschild and Kerr solutions to the EFE have `r` values that are in flat spacetime and yield spacetime intervals. The metric is symmetric, so you can also map back from curved to flat spacetime.
> By GR there is no possible flat space-time around a dense mass no?
In standard cosmology in the super early universe there wasn't _a_ mass, like a point mass -- there was lots of mass-energy everywhere (not a point anything but a huge swath of space, and very dense), pulling on everything, yes, but at the same time stuff was flying apart with more momentum than the gravity of all the stuff because that gravity was pulling in all directions (therefore causing the gravitational potential to be huge but the net gravitational pull in any direction to be zero) but the pressure was pushing in all directions, so it all could fly apart after all.
While not a direct answer in itself, I think it's noteworthy that the big bang already requires esoteric physics, like inflation [1], that have no known explanation, source, or parallel anywhere else in existence -- and in fact contradict everything we know about known physics. It's an entirely ad-hoc hypothesis that was largely developed to solve numerous other problems with a big bang, in particular our universe not fitting what would be expected following a "normal" big bang, such as the Horizon Problem. [2]
And so looking for logical explanations for the big bang is already a nonstarter. At this point it remains highly dependent upon ad hoc constructions.
One of the theories is that the properties of the Higgs Field changed and so the laws of physics changed. And that if they ever change again that we'll likely be dead before we know to be afraid, since the change would propagate through the universe at the speed of light. We wouldn't even see the stars blink out before the molecules in our bodies stopped being the molecules in our bodies.
Well, imagine that the big bang is really something more akin to a white hole, which is a black hole running backwards: all the stuff has outward momentum, and lots of it, so it can't get pulled back. In standard cosmology the big bang happens not at a point (so it's not really like a white hole) but everywhere, but there's also really strong repellent forces that cause "inflation", which defeats the mass-energy's gravitational pull's attempt to collapse the whole thing. But still, perhaps the thought of a white hole might help you bridge the gap.
Mind you, this is a pop science, handwavy explanation.
Except that this answer does not make sense. General Relativity predicts that if you fill flat space-time with matter, it will start to contract due to gravity. It is not uniform density by itself that prevented the early Universe from forming a giant black hole.
In fact one of the proposed cosmological models for our universe is that it has sufficient density to some day reverse its expansion and then fall in on itself into a giant black hole. See https://en.wikipedia.org/wiki/Big_Crunch for more.
My theory with zero study, math, or proper explanation is that this is exactly how the universe operates.
It explodes outward until the explosion energy is cancelled out by gravity, wherein the universe then collapses on itself. The moment in which the last bit of matter and energy is consumed by the massive black hole that forms, it's enough to cause another explosion.
