# What is “Energy” of a vacuum in the context of quantum theory?

I'm not a physicist or cosmologist, so I hope I am asking the right question with the right words here.

My question regards the word "energy" as it pertains to quantum vacuum states, and to concepts such as Lawrence Krause's "something from nothing" theory.

When I hear the word "nothing" I envision a "void" that is an empty set. But Krause, Eva Silverstein and J. Richard Gott (2 hr YouTube video of debate on "nothing" hosted by Neil deGrasse Tyson - last url segment = watch?v=sNh-pY3hJnY) seem to be saying, if I understand correctly, that this void has a non-zero energy state, and that quantum fluctuations create "something" out of nothing because of this.

I have to say that this sounds a bit to me like hand waving and weasel words, but perhaps my ignorance is committing an injustice.

But if this is what is happening, is this "nothing" actually a void? Energy is something, and that would make "nothing" contain something. And I fail to see how this could be so.

The question: What, exactly, IS "energy." In usage in this context it sounds a lot like phlebotinum.

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Have a look at Wikipedia quantum harmonic oscillator. You will see that, because the position and the momentum operator do not commute, the lower energy is not zero. In quantum field theory, the behaviour of relativistic bosonic fields is just the same (a relativistic bosonic field is just a sum of independent quantum harmonic oscillators labelled by momentum and eventually spin) – Trimok Jul 21 '14 at 8:20
From a mathematical standpoint, the vacuum in quantum field theories is not the empty set. It is a precise vector of the (Hilbert) space of each particular theory. Thus has different properties from those of the empty set. – yuggib Jul 21 '14 at 10:36
See also Casimir effect for a realization of physical forces arising from the vacuum. – Trilarion Jul 21 '14 at 14:28
The problem with 'true nothing' is that it is unphysical: Take a volume of space and remove 'everything', and you won't end up with 'nothing', but with the vacuum, which, philosophically speaking, is a 'something'. Krauss goes a step beyond the vacuum and assumes that spacetime as well as the laws of physics as we know them emerge dynamically (eg via symmetry breaking) from the true groundstate of a theory of quantum gravity. This groundstate is what he calls 'nothing'. – Christoph Jul 21 '14 at 15:39

I think the key conceptual hurdle is that the vacuum state is not nothing.

Quantum field theory describes matter as excitations in quantum fields. These quantum fields are very strange things, and I don't know of any easy way to explain to a non-physicist what a quantum field is. The key thing is that the quantum fields fill all of spacetime. So a vacuum is not nothing, but rather it's the lowest energy state of the quantum fields. This lowest energy state is not zero energy, it's just the state from which it's impossible to extract any energy - that's what makes it lowest.

Viewed this way things (hopefully) look less mysterious. The fluctuations don't create something from nothing. The nothing actually contains quantum fields and the fluctuations are fluctuations in these quantum fields.

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John Rennie's answer is good already, but I want to add a single point: These fluctuations are very very short. In quantum mechanics you've got Heisenbergs uncertainty principle, which is often stated as $$\Delta x \cdot \Delta p \le \frac \hbar 2$$ and which means, that for any quantum object (think of an electron or a positron created in such a vacuum fluctuation) you will never know it's place and its momentum (which is mass times velocity) at the same time. This might not be that intuitive, but with some basic math, it's possible to show that you can state this principle equally as $$\Delta E \cdot \Delta t \le \frac \hbar 2$$ so energy times time (of existence!) of this particle is smaller as a very very small number. And as the energy of the particle is rather high (at least it has to have its mass, which is just another form of energy, remember Einstein's $E=mc^2$ ) it's life-time is extremely short.

And in fact, if you look at the vacuum for a longer time and take the average energy you've seen, it's actually zero (because as John said, it's defined as extracting energy is not possible), but from the average doesn't contain any information about the state at a single point in time.

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This info is useful, but I am not sure that it directly answers my question. This is probably my fault for being "all over the road" with mentions of the context I am referring to. You mention the "average energy" of the vacuum; so what IS this energy? What is it MADE of, or consist of? – Old Guy in Stanton Jul 21 '14 at 16:11
@OldGuyinStanton Energy is an abstract quantity. By physical definition, it's the capability of a system to do "work". In classical mechanics this is obvious and rather easy to comprehend. And these definitions got expanded and generalized with the development of modern physics... But energy is not "made of", it doesn't "exist" - it's just a number to describe the system/object/universe within the given axiomatic framework of physics... – Benedikt Jul 22 '14 at 7:22