Quantum Wavefunctions Without Space

Question

A handful of physicists have a rather peculiar definition of 'nothing' in terms of cosmology. Their claim is that the Universe, assuming it has 0 total energy, could have arisen from nothing but quantum vacuum fluctuations of virtual particle-pairs. As per the $\text{time/energy uncertainty principle}$, the less energy a system has, the more time it can exist. If the Universe has, what is essentially, a total energy of 0, the Big Bang may have been an effect of virtual quantum particle pair creation.

However, how can there be a probability wave of a [virtual] particle's existence if there is no space (assuming 'before' the Universe there was no space). Through what space would the probability wave propagate?

Edit: A more simple way of asking this question is as follows:

How can quantum fluctuations be responsible for the Universe if they occur within it?

Answer 1

Your idea that a quantum fluctuation created the universe is a misinterpretation of the suggestions that I have heard. Explaining why requires introducing a few ideas, so bear with me while I do this.

The object we think of as the universe is made up of two bits:

1. a manifold equipped with a metric = spacetime

2. some matter/energy

The manifold and metric are what we think of as spacetime, and the matter is (obviously) the stuff that makes up you and I. Matter curves spacetime, and the curvature controls how matter moves.

We get the geometry of spacetime from general relativity, and in particular we get the geometry of the universe by solving a simplified model of the universe to get the FLRW metric. This metric predicts there was a Big Bang 13.7 billion years ago, and it predicts that the geometry of the universe becomes singular at the Big Bang, so the metric cannot describe the universe at the moment of the Big Bang or before it. This is why it's commonly said that the universe came into existance at the Big Bang and nothing existed before it.

And, assuming I understand you correctly, this is where you come in. Because if nothing existed before the Big Bang how could there have been a quantum fluctuation to create the universe?

The resolution for this is to point out that the FLRW metric ignores quantum effects, and we expect quantum effects to becme critically important at the very high densities near the Big Bang. We have no theory of quantum gravity, so we simply don't know what happened at the Big Bang. However we expect that spacetime will not become singular, so there is no sense in which the universe was created at the Big Bang. We expect that the universe existed at, and before, the Big Bang, but the geometry of spacetime may well have been very strange indeed - in the absence of a theory of quantum gravity we simply don't know.

So the point is that spacetime (in some form) did exist before the universe we know and love evolved. So there was a spacetime in which quantum fluctuations could happen.

The question is where all the matter came from, and this is where suggestions of quantum fluctuations come in. If a quantum fluctuation occurred it would have produced some energy from nowhere. This energy could have curved the spacetime, and the curvature created a negative energy that exactly balanced out the newly created energy making the total energy zero. More energy could be created and the spacetime curved a bit more to keep the total energy zero, and the system could have ballooned into the spacetime and matter we see around us today.

But your bullshirt detectors should be twitching by now. The reason the previous paragraph is so vague and woolly is that there is no theory that describes such phenomena, just lots of speculative ideas. There is no agreement that the total energy of the universe is zero (as required by the fluctuation idea) or indeed that the total energy of the universe is actually a meaningful concept.

Answer 2

"So the point is that spacetime (in some form) did exist before the universe we know and love evolved. So there was a spacetime in which quantum fluctuations could happen."

If spacetime existed before the big bang something would have to bring it into existence.

It couldnt be eternal because an infinite amount of time would have had to pass in order to reach the big bang.

Imagine it like this: I am at the end of a infinitely long trail of dominoes. Lets say that you are at the other end. You push your first dominoe over. The question is, when will my dominoe fall over? The answer is never because an infinite amount od dominoes would have to topple before my dominoe does.