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?

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?