How does spacetime expand?

[Schneibster]

I got a loooooooot of work to do here.

OK, here's the current most likely theory, as propounded by Leonard Susskind, considerably simplified for easy understanding:

In the beginning there was void, without time, space, matter, or energy. Since there is Heisenberg Uncertainty, there were fluctuations in this void, in time and space, having mass and energy, at random locations (whatever "location" means without space). Eventually (whatever that means in the absence of time), there was a fluctuation that happened to have internal characteristics that resulted in a large, negative cosmological constant inside it; the inside was very small (Heisenberg Uncertainty consists of quantities multiplied by one another that produce the Planck Constant, a very small number, which means that the quantities involved must also be very small). But because of the large, negative cosmological constant, that small fluctuation grew, and it grew very, very fast- a hundred billion light years at minimum, in a period of time so short that light could not cross the original size of the fluctuation. In other words, faster than light. Now, nothing can move faster than light, right? Well, not exactly nothing. Actually, no material object, and no energy, can move faster than light; but things like space, time, and dimensions, and particularly dimensional twists like so-called "domain walls" and, most importantly, since it represents the universe, the size of an unbounded area, can, since they are not material objects. This expansion lasted only for 10-42 seconds; after that, it stopped. During this time, the universe expanded from smaller than the smallest bit of an electron or quark, to at minimum ten billion light years across; this is the minimum value dictated by what we can see with our most powerful telescope, the Hubble Space Telescope. For the mathematically inclined among us, I'll note that the rate of expansion becomes exponential when the value of the cosmological constant becomes great enough (that is, when a particular ratio exceeds unity; so if it's negative, but less than one, it expands normally, if it gets greater than one, then it expands exponentially).

OK, so what's this "cosmological constant?" Well, it's a term in Einstein's original field equations of General Relativity; Einstein at first included it, because it was necessary to accommodate the then-mainstream cosmological theory called "Steady State," then after the "Big Bang" was theorized and shown to be correct by the Penzias/Wilson experiment, declared that had been a mistake; since then, cosmologists have decided that, in fact, he was right in the first place and there actually is a cosmological constant, and that it must be included in the equations even if it's value is zero (and it's not, and we can see it's not). The presence of the cosmological constant in the field equations of relativity is therefore non-controversial, no matter what its value might be conjectured to be. In the twenty-first century, we have determined that this cosmological constant is the energy of the vacuum; that is, the amount of energy that we find in free space, in what we usually refer to as "empty space" or "vacuum." This energy cannot be extracted, because it represents the minimum amount of energy it's possible for a location in spacetime to contain in our universe; we often say inaccurately that we "use up energy," but really what we do is allow it to flow from an area of high energy to one of low energy, and cause it to do work as it flows. Without this flow, there is no way to use it; and since the vacuum energy value is the lowest possible, there's nowhere for it to flow to. This is the reason that electric sockets have at minimum two prongs; the energy must come in, and it must go out, and it comes from a place of high energy and goes to a place of low energy, and the work it does in the house happens only while there is a high energy source and a low energy sink connected to the prongs of the socket outside the house. This vacuum energy is real, and can be measured and detected as the Casimir effect; but because there is nowhere at lesser energy for it to go, it is not usable (Stargate notwithstanding- their mcguffin is to extract this "zero point energy" with so-called "zero point modules" which the law of the conservation of energy says cannot exist, and which Einstein's field equations appear to indicate would cause a rip in space- vacuum decay- that would expand at the speed of light and consume our universe if it could). So we find that in fact, what we thought was "zero" is actually really not. It's not even positive; it's very slightly negative. Not only that, but the real value that underlies this cosmological constant isn't constrained to be positive; it could be either positive or negative, or (of course) zero. In our universe, it is negative, and small (that ratio I spoke of above is less than one).

The thing about the value of the cosmological constant is, the bigger its value, the more unstable it is. And the more unstable it is, the more likely it is to undergo vacuum decay, in which it abruptly jumps to a much smaller absolute value, closer to zero. When that happens, there are effects in the space where the decay occurred; those effects are that the absolute value of the energy difference between the value of the energy of the vacuum before the decay and the value after (kinda- the math gets really complicated at this point, we'd need to discuss the Einstein field equations to understand it, and that's learning General Relativity, which I assume no one here is interested in doing) gets dumped into the vacuum as real energy. And furthermore, since real energy can only be positive (that also is dictated by the term in which mass/energy appears in Einstein's field equations, called the "energy tensor"), though vacuum energy can be both positive and negative, even if the difference is negative, the energy dumped is positive.

And that's what happened in our universe; after the universe had expanded for 10-42 seconds, it underwent vacuum decay, the cosmological constant fell to a small (but still negative) value, and the leftover energy of the former large cosmological constant got dumped inside it. At this point, the universe was at minimum ten billion light years across; cosmologists believe that our universe was at least an order of magnitude larger than that, because of the non-existence, or at least extreme rarity, of topological solitons and domain walls and other topological "twists" that can occur in spacetime- it has to be big enough that we're astronomically unlikely to ever see them. And the universe was hot- hot beyond nightmares of hell, hot beyond the center of an exploding nuclear weapon, hot beyond the center of the Sun, and not an increment hotter, not even a few orders of magnitude hotter, but many orders of magnitude hotter than anything has been in this universe since that time. So hot that the very laws of nature were different; there weren't separate electromagnetism and gravity, and strong and weak nuclear forces, but a single force; there weren't hundreds of different particles, but only two, called "X" and "Y," and their antiparticles.

This is the leadup to the so-called "Big Bang." Note that a lot of shit has already happened. The shit that's already happened is called the "inflationary universe scenario of the Big Bang theory." Note also that this is creation ab initio; in fact, it is very nearly creation ex nihilo. The only thing that there has to be is a spaceless, timeless, energyless, matterless void. That's about as close to nihil as I think anyone can imagine. From here you can see far enough to understand why I'm bothering to do this; we no longer need, as atheists, to listen to the religious lying about how the super magic sky daddy made everything. We have a complete, consistent theory of the emergence of the universe from as close to "nothing" as the human mind is capable of imagining (or perhaps beyond- we can mathematically describe "nothing" better than we can visualize it, I think).

The most obvious question I've left unanswered is, "why did it expand?" The answer is, "because it had to." Einstein's equations show that a region of spacetime that has negative cosmological constant has a sort of "negative gravity" that causes every macroscopic object in it, like galaxies, to move apart; we don't yet quite understand why, any more than we understand why positive curvature results in ordinary gravity, but we know it does, and it's been confirmed by experiments (starting with Eddington's famous observation of an eclipse in Africa that showed spatial curvature around the Sun). Material objects make ordinary gravity, and so does positive spatial curvature, which is the kind associated with a positive cosmological constant. However, negative cosmological constant causes negative curvature, and that is "anti-gravity." So the answer to the question, why did the universe expand, is the same, ultimately, as the answer to the question, why do things fall when I drop them on the surface of the Earth: because of the shape of spacetime.

The universe can have three states of curvature: positive, negative, and zero. Positive curvature corresponds to a shrinking universe; zero curvature to a static universe; and negative curvature to an expanding universe. Reduced from the four dimensions of our real universe to three for pedantic purposes, we can think of positive curvature as corresponding to a sphere (the real figure is a hypersphere), zero curvature as a flat plane (representing a hyperplane), and negative curvature as an unimaginable shape of which a partial rendering in three dimensions resembles a "saddle." The hypersphere is finite but unbounded (go in one direction far enough, and you'll wind up where you started); the plane and saddle are both infinite and also unbounded (you'll keep going, always coming to new places you've never been before). The hyperspherical universe will eventually undergo a "Gnab Gib," in which it crushes down to a very high density and becomes a black hole; the flat universe will just stay the same forever; and the saddle-shaped universe will keep on expanding forever, eventually isolating every galaxy from all others, and keep on expanding after that too. Possibly spacetime will fracture eventually in a "Big Rip," but that's not clear and it would be far past the point where any kind of life like us could exist here. Of course, the hyperspherical universe would become so dense we could not live in it, eventually, too, and it would come much quicker; but "much quicker" could be, say, a quadrillion years or so. These in turn correspond to positive vacuum energy, zero vacuum energy, and negative vacuum energy.

It turns out we can measure the curvature, and not only that, but we can measure the rate at which the curvature is/was changing now and at various points in the past. We do that with the Hubble Space Telescope, and in fact, this measurement was the raison d'etre of the HST; what we built it and put it in orbit for. And we have. What we found is that at the point where the universe becomes transparent (which is as far back as we can see; before that the matter density was so high that light could not travel more than a few inches without running into something), the cosmological constant is a small negative value; as the universe expands, that value becomes smaller and smaller (a larger and larger negative value) over time. Why is this?

The answer is simple, easy, and obvious: vacuum energy is an amount of energy present in every cubic micron of space, and as space expands, there is more vacuum energy. More vacuum energy means more cosmological constant. More cosmological constant means more negative curvature. So as space expands, the rate at which it expands increases as well.

Cosmologists refer to the cosmological constant, the vacuum energy, as "dark energy," for historical reasons to do with the discovery that galaxies must, according to observations of their movements and analysis of the visible matter in them by telescope, and analysis using Einstein's field equations, have a great deal of matter in them that is not visible. Now, it's easy for matter to be invisible in space; it just has to be cold, and not radiate light, and matter will do that if it's just sitting there. So astrophysicists called it "dark matter." When they discovered something was accelerating the expansion of the universe, they automatically called it "dark energy," in analogy to the dark matter they'd already discovered; not realizing, at the time, because they're not spacetime physicists, that it was cosmological constant. As soon as relativists heard them doing that, they immediately noted that it is equivalent to the cosmological constant term of the Einstein field equation of gravity.

"Dark energy" is cosmological constant; cosmological constant is vacuum energy; vacuum energy is dark energy. The universe is a free lunch that comes from the character of the curvature of spacetime. And it comes from nothing at all; no space, no time, no matter, no energy.

Susskind goes on to show that if this is true, then there might be other universes emerging in other "places" and at other "times" (again, whatever these mean in the absence of space and time) in a "metauniverse" of some kind, composed of "the void," again, whatever that means. If this is true, and it is almost certain given the evidence we've collected over the last two decades, then other fluctuations could occur with other values of the cosmological constant, and develop into universes like (or very, very much unlike) ours. The upshot of this is that a large number of universes could exist with various values of the various physical constants, probably an infinite number; and we no longer need to worry about the source of the "fine tuning" of our universe that allows life like us to exist; it is not highly improbable, but instead inevitable, that such a universe should exist, and that we should inhabit it. No Gods needed.

Susskind develops this in the context of string physics, but it's just as applicable if string physics is completely wrong.

Questions?

You mispelled "solutions."

Thanks.

[Tero]

My intuition is that atomic radii are a fixed number. Since everything is made of these particles and lumps made of them, space can expand, up to a point. The particles have to interact. Otherwise theyare lostin space.

Signed: a lump

Sure, just ignore me withyour quantumspelling.

[FBM]

[quote="FBM »You mispelled "solutions."

Thanks.[/quote]

You're welcome. Can I consider myself a co-author of that now? Editor, at least?

[Schneibster]

Sure. Co-editor.

[Schneibster]

My intuition is that atomic radii are a fixed number. Since everything is made of these particles and lumps made of them, space can expand, up to a point. The particles have to interact. Otherwise theyare lostin space.

Signed: a lump

Sorry. I missed it.

Things in cosmology are at the megalightyear scale; the atomic diameter scale is undisturbed (at least as far as we're likely to be able to measure anytime soon).

Quadrillions of years from now, a big rip might happen, and that might change things at the atomic diameter scale; by that time, galaxies will be so far apart you won't be able to see one from another and the rate of expansion of the universe might be undergoing another transition to exponential expansion, but this time, the energy deposited by vacuum decay won't be enough to make more galaxies. It will be the heat death of the universe, and no life will be possible again in this universe.

Luckily, new universes are being created all the time, so life will go on somewhere else.

[FBM]

Sure. Co-editor.

As a team, we'll make millions.

[Schneibster]

Sure. Co-editor.

As a team, we'll make millions.

Works for me; I'm lookin' for work. Low stress work.

[PsychoSerenity]

Wow. I think I love you Schneibster! Can you have my children?

That was a terrific post. I am gobsmacked!

It all went over my head of course, but it was very interesting to read!

[Pensioner]

Wow. I think I love you Schneibster! Can you have my children?

That was a terrific post. I am gobsmacked!

It all went over my head of course, but it was very interesting to read!

Load of shite, the guy did not mention baby jebus once.

[Ronja]

Wow. I think I love you Schneibster! Can you have my children?

That was a terrific post. I am gobsmacked!

It all went over my head of course, but it was very interesting to read!

. once more. I'm not sure how much of it went over my head (some, certainly), but I did appreciate it so much I talked MiM into starting to read it (his B.Sc. and M.Sc. were in physics) - he has been conspicuously quiet for the last 10-15 minutes, and I ain't gonna do nuthin' to change that...

[MiM]

Nooo, My knowledge really doesn't go any deeper into cosmology, than that of any vaguely interested amateur.

The one question, that really intrigues me (though most people seems to think I am joking, when I post it), is whether the multi-universe theory allows universes to collide. Where and when would they be colliding (outside spacetime) and what could be the outcome of such a collision. Would it start somewhere at the "outskirts" of the universe or could it start anywhere or everywhere at once. Would it make itself known to us well in advance, or would it be a very sudden end to everything.

[Xamonas Chegwé]

Nooo, My knowledge really doesn't go any deeper into cosmology, than that of any vaguely interested amateur.

The one question, that really intrigues me (though most people seems to think I am joking, when I post it), is whether the multi-universe theory allows universes to collide. Where and when would they be colliding (outside spacetime) and what could be the outcome of such a collision. Would it start somewhere at the "outskirts" of the universe or could it start anywhere or everywhere at once. Would it make itself known to us well in advance, or would it be a very sudden end to everything.

Normally, universes are kept from colliding by strict laning laws. However, were an American and an English universe to head towards each other, each keeping to what appears, to it, to be the right side of the cosmos, the results could be catastrophic (or possibly OSSUM!)

[Schneibster]

Nooo, My knowledge really doesn't go any deeper into cosmology, than that of any vaguely interested amateur.

The one question, that really intrigues me (though most people seems to think I am joking, when I post it), is whether the multi-universe theory allows universes to collide. Where and when would they be colliding (outside spacetime) and what could be the outcome of such a collision. Would it start somewhere at the "outskirts" of the universe or could it start anywhere or everywhere at once. Would it make itself known to us well in advance, or would it be a very sudden end to everything.

There's this thingie called the "ekpyrotic hypothesis" about something very like that; the Big Bang is the sequelae of an event where the brane our universe lies on collided with another brane, and the universe will end in another such collision, with the opposite brane. It's a sort of version of the cyclical universe hypothesis. I don't know the details, but you should prolly check it out.

[JacksSmirkingRevenge]

Fuck me...

[Schneibster]

Just your mind. Hope you enjoyed it.