# Can we view quantum fluctuations as a type of quantum power?

(Note: I will let the question stand as is, it has generated a good answer, but the question is too "wishy washy" and needs to be tighter.)

We know that the uncertainty principle tells us that the product of the standard deviation of energy and the standard deviation in time must always be greater than h-bar. Since there is a unit element of action, is there a unit element of power as well? In other words, if action is always present, then must power always be positive?

Clarification: This is not intended to be a question related to people who think that there is "vacuum energy/zero point energy/free energy" that can be harvested. This is more along the lines of whether the universe can self-perpetuate.

Clarification 2: Self perpetuate I would define as the ability for the universe, through mechanisms of quantum fluctuations related to the uncertainty principle to produce another epoch similar to our own that would appear to be later in time, from our perspective, and after an apparent thermodynamic death of our current universe.

Question restatement: Is quantizing action analagous to there being a source of power at the quantum level?

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The existence of quantum fluctuations and the ability of a system to harness them are two very different things. And, what do you mean by "the universe can self-perpetuate"? –  user346 Jan 17 '11 at 0:25
@space_cadet: I think it would be a question of whether the universe can harness quantum fluctuations to self perpetuate. However, what I really want to know is whether that would be viewed as a type of power. –  Humble Jan 17 '11 at 1:02
"the universe can harness quantum fluctuations to self perpetuate" ... @Humble that sounds like mumbo-jumbo. Seriously. –  user346 Jan 17 '11 at 1:09
@humble you need to specify what you mean by that. Why does the universe need energy to self perpetuate? –  Bruce Connor Jan 17 '11 at 2:28
@bruce connor: It is often discussed that energy is not conserved in general relativity. So notions of energy summing to zero at cosmological scales seem contradictory. –  Humble Jan 17 '11 at 3:41

I don't fully understand what you're asking but let me try to answer, anyway.

1. The Universe is probably able to reproduce itself indefinitely. The most obvious physics mechanism that seems to coincide with your somewhat unusual terminology is known as "eternal inflation". During eternal inflation, bubbles - fluctuations - in the spacetime of our Universe may suddenly become seeds of another Universe that may grow and contain billions of new galaxies after some time. In the daughter Universe, the same process may get repeated many times. The "family tree" of these Universes that "self-perpetuate" is known as the multiverse. It's conceivable that such a multiverse exists.

2. In general relativity, the energy conservation law becomes either invalid or vacuous, see e.g. this question. GR allows spacetime to get curved and dynamical, so in general - and especially in cosmology - it doesn't have a time-translational symmetry. However, that symmetry is needed for Emmy Noether's theorem to be able to claim that a conserved energy exists.

3. Already today, the biggest portion of the energy in the Universe comes from the vacuum energy density, and this energy density is indeed receiving large (in fact, too large) contributions from the zero-point energy of quantum fields that exist - and are nonzero - exactly because of the vacuum fluctuations. These fluctuations contribute to the so-called cosmological constant - more generally known as "dark energy" - and this cosmological constant has a fixed energy density per unit volume. Because the volume can get (and is getting) larger in cosmology according to the general relativity and because the density is remaining constant, the total energy in the Universe is increasing, too.

4. At the beginning of the expansion of our Universe, when it was very small, there was probably a very similar period of accelerated expansion called the inflation that I already mentioned in point 1. The difference from the current expansion was that it was much faster and the energy density was greater than the current vacuum energy density by many dozens of orders of magnitude. In that era, the total energy of the Universe - carried by the "vacuum energy density" or, more precisely, the inflaton potential energy - increased exponentially, by a factor of $\exp(50)$ or more. When the era ended, this energy was largely converted (through the kinetic energy of the inflaton field) to mass that would become seeds of the galaxies - or "structure" - we inhabit today. Again, the cosmic inflation may also be partly blamed in the vacuum fluctuations which follow from quantum mechanics.

5. In the first point, I mentioned the eternal inflation in which a point in space suddenly goes crazy and decides to produce a whole new Universe. The process of "getting crazy" depends on quantum mechanics as well. The small region of space is getting crazy because of another kind of a quantum fluctuation. So it's a random quantum process - essentially quantum tunneling (analogous to the ability of an object to spontaneously penetrate the wall, something that wouldn't be possible in non-quantum physics) - that is responsible for the emergence of the self-perpetuating multiverse, too.

6. I don't understand why you think that your question about the "quantization of action" that creates a new "source of power" is equivalent to the original question. What has the action have to do with it - except that it is a tool to define the laws of physics and we're talking about physics? Nevertheless, if by "quantizing the action", you simply mean going to the quantum theory, it is surely true that the switching from classical physics to quantum physics - by quantizing the action, Hamiltonian, or anything we use to define physics - implies that the character of energy is changing. Energy of some systems may become discrete - that's why quantum mechanics was called quantum mechanics in the first place. Also, there are new terms contributing to energy that didn't exist in classical physics - such as the vacuum zero-point fluctuations. But the whole world is changing if one switches to a completely new - quantum - theory so it shouldn't be shocking that the allowed values and terms contributing to the energy change, too. Quantum mechanics is a completely new theory that changes our description of everything - and on the contrary, one has to use special arguments to show that something "hasn't changed much" (the classical limit of the quantum theory). Also, energy itself becomes an operator called the Hamiltonian whose value (the eigenvalues of the operator) can only be predicted probabilistically. The value measured in a particular copy of an experiment is random. A numerous repetition of the same measurement is needed to verify such predictions. Again, it's true for all predictions of quantum mechanics, not just energy.

All the best, LM

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@lumo: thanks, I plan on re-asking without discussion of fate of the universe. I think that came in out of fear of having a simple question being dismissed out of hand. However, my simpler question wasn't very clear, so I need to give it another shot. –  Humble Jan 17 '11 at 12:37
Let us consider an atom in its ground state with $E_0$. The energy is perfectly defined and conserved so there are no energy fluctuations in this state. In some books one can find statements like "there are coordinate and momentum fluctuations in such a state":
$\partial p /\partial t = [H,p]$ or so.