The Flavors Of Nothing

I have a problem with this:

I think Krauss makes a logical error when he gets to the second example of nothing (no space).  He says that space itself becomes a quantum mechanical variable that can fluctuate in and out of existence and therefore space and time can be created (notice he didn't say space-time originally, but he did later (pun intended)).

But fluctuations require time, and since space and time are part of the same continuum, fluctuations wouldn't occur.

Consider that there is an uncertainty in knowing a particles location (q) and momentum (p).  Called the Heisenberg Uncertainty Principle:

(dq)(dp) > h

where d is the uncertainty and h is a positive constant and > means greater than or about equal to.

Most people have heard of that, but there is a similar expression for the uncertainty in knowing energy (E) and time (t).

In other words, t can't be known precisely, otherwise its uncertainty would equal zero which would make the left hand side of the equation equal zero which is no longer > a postive constant.

There CAN'T BE a physical state where we know (with certainty) time doesn't exist!

So rather than saying space-time fluctuate (implying over time), Krauss should just say that that state of nothing isn't physically allowed based on our understanding of quantum mechanics.

It is the energy-time equation which leads to the virtual particles of the first nothing Krauss mentions. Quantum mechanics doesn't allow the uncertainty in measuring energy to be zero, which means energy can't be known to be exactly zero.

So empty space (free of observable radiation and matter, both of which are energy via E=mc^2) can exist, but there's always an underlying energy or virtual particles.