One universe is not enough + The "what does the universe expand into?" Q (Sabine H.)

C C Offline
One Universe Is Not Enough

EXCERPT: . . . Again, so far, so good. We have one Universe, it inflates, inflation ends, we get the hot Big Bang, and everyone's happy.

Until you remember one important caveat that we've ignored thus far: everything that physically exists, including all particles and fields, must be inherently quantum in nature. Quantum particles are strange, counterintuitive entities that don't always act like particles, but also have wave-like properties. And one of the most important things that quantum particles do, whenever you put one of them anywhere in the Universe, is that their positions are no longer fixed, but rather are described by a probability distribution. And the longer you wait, the more the wavefunction that describes where a particle is spreads out.

As time goes on, even for a simple, single particle, its quantum wavefunction that describes its position will spread out, spontaneously, over time. This happens for all quantum particles.

This isn't a big deal for a free electron in our Universe today, but it's an awfully big deal for inflation! Imagine you're up atop this hill, and you're rolling slowly towards the valley. At the same time, your position has a probability of spreading out, and while there's a finite chance that you'll wind up closer to the valley than you would have otherwise, there's also a chance that you'll wind up further up the hill than you started.

Now, here's the kicker: because your space is expanding and inflating, different regions of space can have different things happen. Let's imagine we let enough time pass that five different regions, each now the same size as the original region, now exist. What happens if we allow them to randomly spread out?

If inflation is a quantum field, then the field value spreads out over time, with different regions of space taking different realizations of the field value. In many regions, the field value will wind up in the bottom of the valley, ending inflation, but in many more, inflation will continue, arbitrarily far into the future.

[...] When you work out the probabilities, for practically all viable models of inflation, you find that the amount of space where inflation occurs and doesn't end always increases over time. There will inevitably be regions where inflation does end, and where it does, you get a hot Big Bang. But outside of each of those regions, there will be a place where inflation didn't end, and space continues inflating there. With each new instant that time brings, there's a finite chance that inflation will end, but an even better chance that it will continue on, farther into the future.

What we wind up with, therefore, is a spacetime where, at any time, inflation ends in a few regions, and we get a hot Big Bang where it does. Each of those regions will be surrounded by a broader spacetime that continues to inflate, where in each of the inflating regions, a few small patches will see inflation end and a hot Big Bang ensue. These various hot Big Bangs will each give rise to their own observable Universe, just like ours, with a different starting point and different specific initial conditions for each region. They will be separated by more inflating space, and no two Universes will ever collide or interact with one another.

This is where the concepts of eternal inflation, the multiverse, and the existence of many disconnected Universes come from.

If you accept that inflation is a stage that occurred in the Universe's past prior to the hot Big Bang, and that the Universe itself is inherently quantum in nature, the existence of a multiverse is unavoidable. Even though we cannot observe these other Universes, we can observe a huge amount of evidence for inflation, indirectly pointing to its inevitability. We can also observe a huge amount of evidence that the Universe itself is quantum, even though we have no proof that inflation itself behaves as a quantum field. If you put these pieces together, it unambiguously leads to the prediction that our Universe should be only one of countlessly many Universes, all embedded in an eternally inflating, expanding background. One Universe is not enough. Even though we cannot detect it, the prediction of a multiverse is unavoidable....


The "What does the universe expand into?" question (Sabine Hossenfelder)

EXCERPT: . . . It is, I believe, to no small part caused by the common illustrations of a curved universe: it’s a rubber-sheet with a bowling-ball on it, it’s an inflating balloon, or – in the rarer case that someone tries to illustrate negative curvature, it’s a potato chip (because really I have no idea what a saddle looks like).

But in each of these cases what the illustration actually shows is a two-dimensional surface embedded in a non-curved (“flat”) three-dimensional space. That’s good because you can draw it, but it’s bad because it raises the impression that to speak of curvature you need to put the surface into a larger space. That, however, isn’t so [...] Curvature [...] is an intrinsic property of the surface – you do not need the embedding space to define it and to measure it. Also note that the curvature is a local property; it can change from one place to the next, just that a ball has constant curvature.

General relativity uses the same notion of local, intrinsic curvature, just that in this case we aren’t dealing with two dimensions of space and ants crawling on it, but with three dimensions of space, one dimension of time, and humans crawling around in it. So the math is more complicated [...] but that is still an entirely internal construct. We can measure it by tracking the motion of particles, and it’s this curvature that creates the effect we usually refer to as gravity.

Now, what cosmologists mean when they speak of the expansion of the universe is a trend of certain measurement results that, using Einstein’s equations, can be interpreted as being due to an increasing distance between galaxies. Again, this expansion is an entirely internal notion. It is defined and measured in our universe. You do not have to embed this four dimensional space-time into anything else to quantify it....

Ostronomos Offline
So inward expansion is mainstream science now. I have to take immediate note of this.

The embedding space is four dimensional and does not extend into further dimensions? Thus there is no option for external growth? But would there be a maximum number of dimensions in which to embed a universe of incredibly large size? Are the dimensions dependent on the size?


The article on the inflation model is intriguing. For it relates the quantum wavefunction to the size of the universe as something known by the name of "field value". This would appear on the surface to contradict the latter article's claim of no embedding space. But when considered in a broader context, the idea of outward contraction can be likened to inward extension on a 4-Dimensional surface, such that inflation is the inward creation of spacetime in a mathematically extensional sense. And because it is Quantum in nature, the wavefunction of the universe spreads out.
C C Offline
By "embedded" she's just referring to how any drawing or graphic depiction of an object needs an "outside" to depict it with a surface and configuration (make a thing of appearance rather than abstract description). In the case of either an exemplar of a static universe or one with temporal differences / changes added to it, the extra dimension(s) or "external environment" which the representation is placed in for illustration / mapping purposes in an imaginary convenience. Since there is no "outside" (at least for the institutional enterprise's widely-accepted, buttoned-down conceptions of what's "going on").


Edit won't work -- the "in" between "purposes" and "an" should be "is". I would have also added that while "internal" might still have a practical language function in everyday discourse about the subject, its is arguably also defunct or unnecessary in a strict context if its counterpart is not the case. Kind of like aquatic people swimming about calling themselves "non-terrestrials" on a water planet that never had any land and land dwellers, except as an imagined possibility.

Zinjanthropos Online
Maybe we're the first of many universes. Regardless, where did that first one come from?
Syne Offline
(Aug 29, 2018 12:30 AM)Zinjanthropos Wrote: Maybe we're the first of many universes. Regardless, where did that first one come from?

That's just it. Once you postulate multiple universes, it's just an infinite regress that forever avoids the inconvenient question of origin. IOW, completely unsatisfying.

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