Can energy be taken out of the QFT vacuum?

Question

There have been recent questions about the vacuum. In my simplified knowledge the vacuum is like a ground state energy level, and also that there might even exist other lower energy levels than the vacuum we find ourselves in. The sea is a soup of created and annihilated pairs of virtual particles with virtual energies and momenta.

In a normal sea on earth, which also represents a ground state of water, energy can be taken out of random waves by the clever construction of valves that allow only one way motion of water. Is it conceivable that a gadget of similar function could be found for the vacuum sea, or is it forbidden by conservation laws?

My intuition tells me that it might be possible if GR is taken into account, but my physics knowledge does not stretch to support this.

Edit : An explanation of why I am asking this question:

Let me expand on the example of the sea. The energy from the waves comes from either tides, i.e. gravitational forces, or wind (temperature differentials). If these were missing the oceans would be like glass representing a unique ground state of the gravitational well of the earth.

In an analogy, a gravitational wave going through the vacuum would be supplying energy to the vacuum sea.

I have been thinking of this analogy ever since cold fusion surfaced and refuses to die out, the most recent one being discussed here too. Approached from nuclear physics orders of magnitude the claims seem preposterous. There are people though who believe they have results of extra energy over input energy, much more than chemical reactions could supply.

This set me thinking on vacuum energy and the analogy with getting energy from the sea. A crystal is a prime candidate for any exploration of such concepts and in all cold fusion "successful" results crystals have been used. Now if the effect depended on the vacuum and how much distorted it was by a passage of a gravitational wave at the time of the experiment, or the exact orientation of the crystal, or the type of impurities in the crystal ( F centers etc) one would expect to get haphazard results, and non repeatable by other experimenters.

Of course this would be the first experimental evidence of gravitational waves :).

Edit 20/7/12

Maybe I should clarify that an acceptable answer in the negative would be one based on conservation laws. I believe that data trumps theory, and next in line are conservation laws,because they are the distillation of an enormous amount of data. Some people seem to think that theoretical definitions can substitute for proof in physics, but physical theories change, solid data do not, and this is physics, not axiomatic mathematics.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user anna v

Comments

@Marek The question is not about pumping energy from different vacua, although it might be related, if, for example, vacua had an "uncertainty principle" type of existence. The question relates to the marrying of QFT and gravity. Whether a gravitational wave would change the vacuum energy level as it is propagating in time so that energy might be captured of its passage, as in the sea wave analogy.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user anna v

---

@MBN: it is not unique. It is related e.g. to spontaneous symmetry braking: after the breaking the system may choose from many vacua (all of which are equally good but differ by some vacuum expectation value). Moreover, in the context of quantum gravity there is a whole lot of additional problems as there are no global coordinates, etc... @anna: I see, that is indeed interesting but I have no idea, I am afraid :)

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user Marek

---

if one takes GR into account, what should be the vacuum?

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user Marcel

---

@Marek, ok, I trust you, it is not unique, but that doesn't remove my confusion. I can understand what a non-unique minimum is, or that it depends on choice or another, but what bugs me is the lower than the minimum part. Anyway, may be, when someone gives an answer it will be clearer to me.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user MBN

---

There's also the possibility that we live in a quasi-vacuum (local minimum) - see, e.g. metastable supersymmetry breaking. But then extracting energy from the vacuum might cause the system to move to the real minimum state, kick starting a new inflationary period that wipes out everything as we know it. Wind farms sound like the safer option :)

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user Simon

---

@MBN Think of different potential wells ( representing maybe nuclei). The lowest energy state of each potential well can be different. It is called the ground state for that potential. If so, there can be tunnelling from a higher energy one to the different lower energy one ( though that is not what my question is about). The hypothesis is that the vacuum we sit in is not unique and there might be more, with a lower ground state energy around.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user anna v

---

@MBN: in QFT the vacuum is not unique and neither are annihilation operators. There exist unitarily non-equivalent representations (corresponding to different vacuum expectation values). I suppose this might be what @anna's question is about; but I am also a bit confused by it.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user Marek

Answer 1

Well, let us be honest here. This question was not supposed to be answered from the very beggining. First of all we don't know how to mix quantum mechanics and gravity. There is no good consistent theory for that. Another thing is that today "the Dirac sea" analogy is not considered to be a very good thing. It is a pre-QFT naiive picture. Finally we are supposed to talk about "waves" in this "sea"... While the "sea" itself is an obsolete analogy... And all that is in a context of non-existing theory... Come on...

Now. There is actually a formal way to answer the question, because the question is about the "QFT vaccuum". And the QFT vacuum have a precise definition. Which basically says that it is "something you cannot take energy from". Actually, we start from that definition to build QFT. So the answer is: "you cannot take energy out of the QFT vacuum by definition".

Maybe we are wrong to start from this definition. Maybe for quantum gravity we need another starting point. But then it wouldn't be a QFT -- it would be a new theory which will have QFT as a limiting case. And in the range of validity of QFT that "formal" answer will hold.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user Kostya

Comments

See my comment to @ChrisGerig . There are theories mooted which do have several vacua, QFT would be working on one of those, at the moment the one we find ourselves in. I believe my simplistic analogy of the tides should give an intuition.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user anna v

---

"it would be a new theory which will have QFT as a limiting case." This is what I am exploring with this question. "And in the range of validity of QFT that "formal" answer will hold." Do you have a strong argument that you know how that limiting case is approached? For example, superconductivity , quantum mechanics on kilometer scales, shows that it is not dimension that defines absolutely the limit between QM and classical.There is the added ingredient of complexity of bulk matter and its different responses.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user anna v

---

@Kostya , if you expand a bit your last paragraph I would accept your answer. I am in disagreement with the answer chosen by the bounty setter. It is not the answer of a physicist, but of a mathematician. A theory can be beautiful and fully consistent in its definitions. The results may agree with data to the available limit of measurements, but that does not mean that the definitions define nature, as progress in physics has shown us again and again. It is at the limits of the validity of a theory that it may be tested against nature with surprising results, for the theory.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user anna v

---

@annav I've tried to expand my last paragraph. But I can't. I just really have nothing else to say on the point: whatever I try, I either already said that or don't know what I'm talking about. I should note that I'm a bit formal here as well -- I'm answering the question. I'm not participating in any discussion or "exploration" or whatever. Let me finally stress that I'm against this distinction you draw between "mathematicians" and "physicists". Intuition is great. But if rationality tells that intuition is wrong -- have courage to leave it.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user Kostya

---

Well, by "mathematicians" I mean people who are satisfied with an axiomatic/self_contained theory and assume, because it fits a certain range of data, it will dictate ab initio what will happen in all ranges. A physicist is a person who appreciates that ( as an example) the Standard Model works very well (btw congratulations for the Higgs ) but is open to beyond the standard model possibilities . I will choose your answer because it is close enough . We only disagree on whether there is a window of possibility at the limit between possible new theories and QFT.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user anna v

Answer 2

No you cannot take energy out of the vacuum, BY DEFINITION.

Using this analogy with a "sea" is nonsense, because the statement "vacuum is a sea of virtual particles" is also an ambiguous statement not to be taken literally.

The definition of vacuum is ground-state energy, and so if you could take energy away from it, then the energy of the vacuum would be lowered, contradicting the fact that it's already in the lowest possible state.

This is also the reason why spontaneous absorption does not occur with electrons/atoms (whereas spontaneous emission can occur).

---

I want to point out why this question is not closed yet:
Anna's train of thought is "The answer does not satisfy me because it is dependent on definitions which change as theories change."
BUT, the question itself is dependent on definitions... you can't ask about apples and then say 'well maybe they can be oranges'. If you can pose a question about 'energy' and 'vacuum' then they have to be defined.
I now vote to close!

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user Chris Gerig

Comments

The ground state energy is the energy of the quantum mechanical system whose potentials one knows and has solved. It is different for different initial set ups. I am talking of something like the Theory of Everything, which in some speculative theories does have several ground states.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user anna v

---

p.s. BTW, nature does not follow definitions, it is observers who make them, and new definitions can supersede or embed old ones.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user anna v

---

...the fact remains, you cannot take energy out of the vacuum. And what you're trying to say doesn't make sense: If I have a bag of apples which are my objects, you can't say well here's an orange, because it has nothing to do with my apples... the energies are part of the system that defines the vacuum as the lowest possible energy. Nothing else is left to say.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user Chris Gerig

---

Please try to think out of the box. I have in my college studies been taught a field theory, creation and annihilation operators, for nuclear physics. The vacuum was the ground state . Does that mean there are no other ground states than this nuclear one? The ground state is defined by the accepted potentials. For this nuclear physics field theoretical model the potential would not change by the QED ground state except maybe in neutron stars. But a theory that distorts space, if strongly enough, should be adding something to the calculations of specific potentials.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user anna v

---

What you are calling "thinking outside the box" completely sounds like meta-physics. I am appealing to nothing but definitions.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user Chris Gerig

---

Well, usually the physics of tomorrow hides in the metaphysics of today, though I do not think of this as metaphysics. Rather at the frontier of physics. Your answer does not satisfy me, because it says: these are the definitions, do not bother me with facts. We would have never gotten quantum mechanics if questioning were stop by current definitions.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user anna v

---

The answer does not satisfy me because it is dependent on definitions which change as theories change. Are you saying that gravitational waves do not carry energy by "definition" and it is futile to try and discover them?

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user anna v

---

For you to even begin talking to anyone, you have to specify what a vacuum is and what energy is, otherwise your question doesn't even make sense, and no logical statements can be made! Therefore, once you bring in the words "energy" and "vacuum", then a priori they have a definition which your question must adhere to. And this question has an answer... the end.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user Chris Gerig

---

But it could be that one can take energy out of the vacuum locally, i.e. there could be a state which has lower energy density than the vacuum in some region but a total energy higher than the vacuum. At least this doesn't contradict the definition of the vacuum.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user jjcale

Answer 3

Peter Milonni has devoted a lot of work to this area, i will recommend this book: The Quantum Vacuum, it basically gives a overview on lot of physical systems where vacuum field effects are dominant, and how certain boundary conditions can effect them to produce unexpected effects

the expansion of fields around the vacuum in harmonic modes with quantized particle population of the modes is only valid when the physics can be fairly approximated in terms of the vacuum eigenmodes (which are the regular field wave functions). Of course, when there are special boundary conditions, this doesn't change too much since we still have eigenmodes (which correspond to the boundary geometry) but still can talk about particle populations

when the system (meaning, the boundary conditions) are dynamic (moving mirrors, or superconductor walls moving over the superconductivity phase) i don't think there is an authoritative answer about the validity of these approximations. So in short, there could be interesting things to say about the vacuum dynamics when a more friendly framework exists to make computations in highly dynamical regimes

I made a somewhat relevant question a while ago about casimir walls that melted and froze back with an oscillatory transversal magnetic field.

i'm sorry, i'm not addressing your larger question, as to what relevant things change when taking GR in consideration. Hopefully someone more knowledgeable on the matter will.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user lurscher

Comments

-1: This is nonsense. You can't take energy out of the vacuum, and this is conservation laws.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user Ron Maimon

---

you aren't doing GR.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user Ron Maimon

---

GR effects do not manifest locally--- the lack of conservation in GR can be attributed to new material entering a region on cosmological scales, or leaving it. The conservation of energy in QFT vacuum is a fact, and it is impossible to pump energy out unless the vacuum is unstable and you then wreck the whole universe by tunneling to a lower energy state.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user Ron Maimon

---

Wrong. What experimental evidence? Casimir force? This is attractive, and seeks to make the energy more negative.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user Ron Maimon

---

Lurscher Thanks, you remind how much we depend on the harmonic oscillator and no law says that all potentials are harmonic oscillators. The reason it is ubiquitous is a mathematical one: the harmonic oscillator potential is the first term in the expansion of any symmetric potential.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user anna v

---

@Ron, there is no such thing as an energy conservation law in GR.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user lurscher

---

GR effects should manifest locally as out-of-equilibrium boundary conditions, which is why my answer tried to make those points.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user lurscher

Answer 4

In theory, QFT vacuum state is isotropic and invariant for all observers, as the base of all ladder operator algebras. It does not have any features other than the fluctuations. Hence, you cannot extract any more energy from it.

In practice, extracting energy out of the vacuum is not only possible, but it has been already achieved in laboratory using optical parametric amplifiers (NOPA); they are used for squeezing input light, but when there is nothing in the input, the output is a field that has lower average standard deviation of the energy than the normal vacuum in the range of frequencies where the amplifier is active. If we assign to the normal vacuum zero energy, then this "squeezed vacuum" field must have negative energy.

Of course, let's make perfectly clear that this mechanism cannot be used to extract useful energy, since the energy spent pumping the amplifiers greatly exceed anything that you could extract.

“In theory, theory and practice are the same. In practice, they are not.” ― Albert Einstein

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user diffeomorphism

Comments

The concept of squeezing does NOT truly beat the "standard quantum limit", because although it squeezes one variable, the other canonical-variable increases.

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user Chris Gerig

---

@ChrisGerig, "it squeezes one variable, the other canonical-variable increases" that is correct. But do not forget you can choose what canonical variables you use. In most experimental setups, the variables chosen are amplitude versus phase. In this case, amplitude-squeezed vacuum has smaller amplitude fluctuations, which implies smaller average energy

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user diffeomorphism

---

@ChrisGerig, there is however, a valid critisism, if we accept that some form of quantum inequalities must hold, then the negative energy regions need to be overcompensed by regions with extra positive energy, so even the time-averaged energy density is nonnegative or the space-averaged energy density is nonnegative, but not both

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user diffeomorphism

Answer 5

There has been a proposal to use Casimir force and meta materials to build a vacuum energy extractor. Casimir force applied on parallel plates made of "normal" material pushes the plates outwardly and inwardly for metamaterials. I do not know if the idea has yet been tested.

http://physicsworld.com/cws/article/news/2007/may/02/casimir-force-could-drive-tiny-ratchets

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user Shaktyai

Answer 6

The vacuum state has a property named passivity, which means that any local operation onto the vacuum state does not extract but inject energy to the system. This implies that energy cannot be taken out of the vacuum only by local operations. However, if we adopt local operations and classical communication (LOCC), a part of zero-point energy of the vacuum state can be extracted. The scheme is called quantum energy teleportation. More information is available in wikipedia and a review article by Hotta, who first proposed the concept: http://www.tuhep.phys.tohoku.ac.jp/~hotta/extended-version-qet-review.pdf .

This post imported from StackExchange Physics at 2014-04-01 13:27 (UCT), posted by SE-user Peacefull World