# Infinity: We’ve Been Here Before

On probability, infinity and possible natures of the universe.

What is reality? How did it come to be? It is a question many people ask, but all the answers are elusive, and produce more, and harder questions than they answer.

“The universe was created by god.” — “Who, then created god?” — “He has always been there.”

“The universe was never created, it has always been there, we just live in a pocket created by its eternal inflation”

“The universe began with a Big Bang.” — “Yes? So where did the Big Bang come from?” — “From a singularity.”

A “singularity” is simply a name for a set of coordinates in a mathematical system for which equations produce nonsensical results. In case of black holes, or the big bang, the singularity is a point in time (t=0) where the size of the universe becomes 0, while density, temperature and curvature equations become infinite. In other words, the results stop making any kind of sense we can intuitively grasp. Extrapolating into the past beyond this point with the rules we know simply yields more of the same — nothing that we can deduce any meaning from.

It implies, however, that there was something there. Something that exploded and produced the universe as we know it.

# The Problem

Just like the three theories above, every creation theory or myth — that the author knows of, at least — runs into the same chicken-and-egg problem: For something to be there, there has to be something else there first. And before that. And before that… “It is turtles all the way down.”

This leaves us with a few possible, but unsatisfactory explanations:

1. There was indeed something there, but we can not observe it, e.g.
• the laws of physics changed during big bang / inflation / whatever, therefore we can’t observe or deduce the initial conditions and make the relevant conclusions.
• we are inside a computer simulation or a pocket universe, in which the laws of physics differ from those in the host universe, so we can’t observe the initial conditions and make the relevant conclusions.
• we were created by a supernatural entity on a whim

2. we are simply too dumb and too rooted in this reality to understand how it could have happened.

3. The singularity, or the proto-universe, simply appeared into existence … because it could.

Any and all of the explanations leave us with no way to prove or disprove anything, leaving us with what amounts to a belief system — a religion.

However, funnily enough, the third of the hypotheses, that sounds suspiciously like the punchline of “why did the chicken cross the road” joke, is one that makes the most sense — given our current understanding of physics and reality.

# Something out of nothing

How could anything be created from nothing? The most plausible answer at the moment seems to be, “because of quantum vacuum fluctuations”. I can not possibly accurately explain the concept from ground up — there is a great PBS Spacetime episode on the nature of empty space - — as well as a wikipedia article on that matter (beware — just like wikipedia, PBS Space Time episodes can end up in days spent following the links down the rabbit hole). Here only this much: something really weird happens in the supposedly empty vacuum of space: Pairs of particles and anti-particles come into existence for very short times, “borrowing” the energy from the surrounding space-time. The reason for this is Heisenberg’s Uncertainty principle, which is responsible for a number of other really counter-intuitive effects as well. (*see PS, as well as the above PBS Spacetime episode, for more detail). It doesn’t just apply to the well-known location and the momentum — but also to time and energy of a quantum system. The more tightly you try to constrain a time window of a measurement of a quantum system, the less certain you can be about its energy. This means, at very short time scales the energy state of any quantum system, like, e.g., empty space, is very uncertain — it can have *any* energy, even an infinitely large one. And like in a particle accelerator, high energies lead to creation of new particles (albeit for a very short time).

As counter-intuitive as this effect is, the quantum vacuum energy can be (and has been) measured using the Casimir effect : simply put, two shielded, electrically neutral (uncharged) metal plates in a vacuum very close to each will attract each other — ie, will “feel” a measurable force towards each other — because there is more possible energy states (and therefore more energy) in space outside of them, then between them. So it seems, like the quantum vacuum energy, also called “zero-point energy”, is not a figment of the mathematicians’ imagination.

Even before the discovery of the Casimir effect, an effect called the Lamb shift was measured, a difference between the energy levels of electrons that should, by the best theories of the time (1947) be the same. It was shown that the difference can be calculated with extreme precision if we assume that it stems from virtual particles aligning themselves in the electric field of the nucleous, shielding the electrons from the nucleus’ positive charge. It appears, not only are the “virtual” particles real — they influence every atom in our universe.

The energy of such quantum vacuum fluctuations and the resulting particles is limited by time and probability: the more energy such a fluctuation contains, the shorter is the amount of time it is allowed to exist — and the less probable it is.

However, given infinite time, any event with non-zero probability, no matter how improbable, *will* happen. Simply put, it doesn’t matter if something can only happen once in a million years — if you wait for three million, the event will probably have happened three times (or two, or four,…). If you wait infinite years, however, the event will have happened over, and over, and over again — infinitely often.

So it is possible, that a very, very large quantum vacuum fluctuation has occurred at some point, containing so much energy that it effectively produced our entire universe. (As it turns out, I am not the first proposing this, see PS). This would account for a “big bang” without the need of a creator.

# Something out of something

The big bang theory is, of course, not the only theory in science to explain the universe. The eternal inflation theory proposes that the universe has always been there, and is perpetually inflating at faster-than-light speeds — only small, gravitationally bound pockets of stability emerge, from time to time, due to quantum fluctuations (sounds familiar?) that might end up looking like our observable universe.

The observable universe is called that, because this is the only part of the universe we are able to observe and interact with — and the only one we will ever be able to see and interact with, since every other part of the universe is accelerating away from us at light speeds (or faster, because it is space itself expanding, not matter moving through space — a natural warp drive, if you will — and so is not limited by the speed of light.) No information can ever reach us from those parts of the universe, because it would have to travel faster than light — which, according to Einstein, is impossible. This means, no particles, no light, no fields from the non-observable universe can ever reach us. Which effectively makes our universe — and every other non-inflating bubble in the inflating universe — contain a finite amount of energy and mass.

But, since the universe is “inflating” forever, an infinite amount of such bubble universes can arise, each of them limited, each of them possibly different.

# The infinite improbability engine

If universe like ours came into being once, and if, indeed, probabilities are to blame for its existence, by doing so it has also demonstrated to us, that the probability of it happening is not zero. But if so, it has already happened infinitely often — and will happen infinitely often again (unless, of course, we are living in a computer simulation, in which it would likely be unfeasible to leave us on for infinitely long.)

Does this mean that everything would repeat itself, over, and over, and over?

Yes and no. The infinite universes, no matter which model, will probably not have the same starting parameters. Some of them will not be inhabitable. Some of them will be very cold, some of them will have too much energy. Some of them will be just like our universe. And some of them, well, some of them will be the exact copy of our universe, down to every detail.

Why? Because the reality is quantized: Everything we know about the universe says, that there is a minimum amount of space (the Planck length) and time (the Planck duration) that anything can move. Particles can only assume discrete quantum states: up-spin/down-spin, etc. They also can not occupy the same position and the same quantum state at once. Effectively, it looks like reality is pixelated. At the same time, as we have seen with the eternal inflation, there is a limited amount of particles in the observable universe — the part of the universe that we can interact with. The same is true for a big bang universe, only more so — it is “born” with a finite amount of matter. So the total amount of possible states in our universe is finite. Given infinite time, every possible combination of allowable states will have occurred. In fact, it will have occurred infinitely often.

In other words, that girl in school who didn’t reply your crush? In infinitely many universes, the other two of you got married and had kids. In some of them it plaid out exactly like here, sentence for sentence, word for word, atom for atom. In countless others, you had countless fatal accidents before you ever reached this point in your life. You have read this article an infinite amount of times. In some of them, the article might have made more sense.

In short: it looks like we have been here before.

# But wait, …

Of course, this leaves us with more questions:

• Where do the quantum vacuum fluctuations come from?
• Where do the quantum fluctuations actually happen? In other words, where IS the universe?

Any answer assuming some physical reality outside of ours has, and forever will encounter these same questions. How do we break this vicious cycle?

I will leave this question for another article. Suffice to say, it involves more probabilities … and emergence.

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