# Vacuum in Quantum Field theory is not empty

1. Aug 1, 2007

### emanaly

I know that the vacuum in Quantum Field theory is not empty, but sometimes I find some people say that the particles are created from nothing because they are created from the vacuum , are those people expression a misleading?

Last edited by a moderator: Mar 7, 2013
2. Aug 1, 2007

### bel

When we say vacuum, we mean that it is space, emptied of matter. The particles created in a vacuumn are created by pair production when two beams of energetic (in both sense of the word) electromagnetic radiation collide to form a particle- anti-particle pair in accordance with Einstein's energy mass equivalence. In effect, the particles are created out of energy, not exactly nothing.

3. Aug 1, 2007

### Norman

I think the original poster was wondering about pair production in the vacuum with respect to fluctuations due to the Heisenberg Uncertainty Principle. This does not need a reaction to create particles. See for instance the Casimir Effect.

So, the real question is "Can you call the QFT vacuum 'nothing'?"

I don't know. Personally I don't think of it as nothing since I see it as a dynamic system in which these pairs are being created. So in my mind the QFT vacuum is not "nothing."

I think this question may be borderline philosophy however.

4. Aug 1, 2007

### emanaly

Yes Norman, you expressed rightly what I mean

5. Aug 1, 2007

### humanino

There are philosophical questions you might ponder about in those matters, somewhere else.
However, in QFT the vacuum is well-defined, if not well-known.
The vacuum in QFT is the state of lowest energy possible.

You can work the mathematics out, and see for yourself that indeed, it is not "empty".
It fluctuates and has non-vanishing average values for some observables.

6. Aug 1, 2007

### meopemuk

In quantum field theory, the ideas of "vacuum" and "particle" become rather complicated. In the beginning, we define vacuum $|0 \rangle$ as a no-particle state and we define creation operators $a^{\dag}$ which produce 1-particle states by acting on the vacuum

$$|1 \rangle = a^{\dag} |0 \rangle$$

So far, everything is nice and easy. Next, we define the Hamiltonian of our theory, which is an operator expressed as a function of creation and annihilation operators $H(a^{\dag}, a)$.

Now, according to physical intuition, we would expect that our vacuum $|0 \rangle$ is an eigenstate of the Hamiltonian with lowest (zero?) energy. We would also expect one-particle states $|1 \rangle$ to be eigenstates of the Hamiltonian. But this is not true in QFT! It appears that (almost) all Hamiltonians used in QFT do not have $|0 \rangle$ and $|1 \rangle$ as their eigenvectors.

The usual answer to this puzzle is to say that vacuum $|0 \rangle$ is not the real physical vacuum state, and $|1 \rangle$ are not states of real physical particles. It is said that $|0 \rangle$ is a so-called "bare" vacuum, and $|1 \rangle$ are states of "bare" particles. The vacuum and particles we see in reality are called "physical". These physical vacuum $|vac \rangle$ and one-particle $|one \rangle$ states are true eigenvectors of the Hamiltonian, and they are expressed as some complex linear combinations of "bare" particle states. This is the reason why one often hears that vacuum if full of (bare and virtual) particles, and that physical particles are "dressed" by the cloud of (virtual bare) particles.

This situation is a bit paradoxical. In QFT nobody cares about properties of bare particles and states. We want to study physical particles and states. However, our Hamiltonian $H(a^{\dag}, a)$ is expressed through bare particle operators. This makes all calculations and their interpretation very cumbersome.

A great new idea arrived in 1958:

O. W. Greenberg, S. S. Schweber, "Clothed particle operators in simple models of quantum field theory", Nuovo Cim., 8 (1958) 378.

They said (rephrased): "since we don't care about bare particles, there is no reason to keep their creation and annihilation operators in the theory. Let's express our Hamiltonian directly in terms of creation and annihilation operators of "physical " or "dressed" particles. Let's work directly with the full physical vacuum state $|vac \rangle$." Greenberg and Schweber were able to show that "bare" particles can be eliminated and quantum field theories can be reformulated in this "dressed particle" picture without losing anything of importance. In this picture, vacuum $|vac \rangle$ is a no-particle state (there are no "physical" particles in vacuum). One-particle states $|one \rangle$ have just one (physical) particle in them. So, our physical intuition should not be offended.

So, in answering you question about vacuum filled with virtual particles, I should say that this (unfortunately widespread) idea is an artefact of using unphysical (bare) states as our basis in QFT. In fact, there are no "physical" particles in the "physical" vacuum.

Eugene.

Last edited: Aug 1, 2007
7. Aug 2, 2007

### Barmecides

Thanks a lot meopemuk for this great answer very clear !
By the way, when we are talking about vacuum in electroweak symmetry breaking for example, are we talking about |0> or |vac> ?

8. Aug 2, 2007

### meopemuk

Unfortunately, gauge field theory (including spontaneous symmetry breaking and confinement) is formulated in a language that is quite different from what I presented. I am still struggling to understand its exact meaning. So, I'll let others to answer your question.

Eugene.

Last edited: Aug 2, 2007
9. Aug 2, 2007

### Nick666

Cant it be that the fabric of space-time continuum or space is transforming into the virtual particle and vice-versa?

10. Aug 2, 2007

### meopemuk

As I tried to explain, virtual (and bare) particles should be understood as mathematical fictions that are characteristic for one particular (perturbative) formulation of quantum field theory. Virtual particles can be met at certain intermediate steps of calculations (e.g., Feynman diagrams), however, they cannot be directly observed in real life.

I don't know what definition of "the fabric of space-time continuum" you have in mind, but I suspect, it is something as fictitious as virtual particles. Can two unreal things transform into each other? Sure. But this is not question about physics, in my opinion.

Physics is about things that we can observe in experiments: energies of atomic transitions, scattering cross-sections, positions and momenta of real particles, etc. If you want to get a satisfactory answer, you should try to formulate your question in this language.

Eugene.

11. Aug 2, 2007

### Nick666

Do virtual particles have size? Comparable to planck size. (length)

I heard that when the latest mega particle accelerator will function, they will discover new and exciting things, and new particles, and they might discover that space-time is fabricated of planck size particles.

Last edited: Aug 2, 2007
12. Aug 2, 2007

### olgranpappy

Embarrassingly non-vanishing in some cases...

E.g., RMS electric field in the vacuum:

$$<0|\vec E|0>=0$$
Great!

$$<0|E^2|0>=\infty$$
Uh oh!

13. Aug 2, 2007

### meopemuk

No.

Most certainly, yes.

Possible

No way.
Eugene.

14. Aug 2, 2007

### lightarrow

Sorry, in which region of space such average values are computed?

15. Aug 2, 2007

### olgranpappy

I'm not averaging with respect to space, I'm evaluating the expectation value of the electric field with respect to the ground state.

If you are asking me what is the spacial argument of the electric field... it doesn't matter, all points of empty space are equivalent.

16. Aug 2, 2007

### meopemuk

Hi olgranpappy,

I wouldn't worry about this infinity at all. First, in QED the "electric field" $\vec E$ is a certain combination of photon quantum fields, or equivalently, a certain function of photon creation and annihilation operators. It is questionable whether this combination has anything to do with real macroscopic observable electric fields. At least, I haven't seen reliable (and comparable with experiment) calculations of macroscopic electric fields within QED. The main purpose of QED is to calculate the scattering matrix (S-matrix) for physical particles and some other properties (e.g., energies of bound states) that are directly related to the S-matrix. And QED does that brilliantly.

Second, it is even questionable whether electric fields are truly observable physical objects. When we "measure" the electric field at point x we, actually, place a test charge at point x and measure its acceleration. The acceleration is created, of course, by interactions of this test charge with other charges around it. It can be debated whether this interaction is transmitted by some independent agent (also known as "field", which, presumably, has energy and momentum of its own) or that we are dealing with "action-at-a-distance". Since fields are not measurable directly, it is, at least, conceivable to think that a theory can be formulated in such a form that electric fields (just as virtual and bare particles discussed in my previous posts) can be eliminated from the theory without any adverse effect. The "dressed particle" theory achieves exactly that.

Of course, I am not talking here about free transverse electromagnetic fields associated with propagating light. They are known to be directly measurable and possess their own momentum and energy. However, within QED these transverse "fields" are better described as collections of large numbers of discrete physical particles - photons. The same description is valid within the "dressed particle" version of QED. And the energy contained in this "field" is just the sum of energies of all photons, so it cannot be infinite. So, there is no contradiction.

Eugene.

17. Aug 2, 2007

### olgranpappy

Oh yes, I agree with you. I just find the example I gave amusing.

18. Aug 3, 2007

### Nick666

Why dont virtual particles have size(length)?

Is their size (length) zero ?

Why cant they discover that space is composed of particles of planck size (length) or much smaller. or whatever particles of whatever size?

19. Aug 3, 2007

### olgranpappy

I hate to say it, but as usual, it gets down to what exactly do you mean by "size(length)?"

But regardless, you can't just go up with a ruler and measure a virtual particle because they only exist as "intermediate states" and not as what actually comes out of, say, a scattering experiment.

no.

Look. That just doesn't make sense. And besides, it's seems to be just a random statement that you plucked out of thin air.

20. Aug 4, 2007

### Nick666

Then why do I see physicist saying all the time "the fabric of space-time continuum......bla bla" , "space expands..........bla bla" ?

What exactly is expanding?

What is the fabric of space-time ?

What is it composed of?

Is it composed of nothing?

Is it composed of something?

Do I define it as the quantum vacuum (field), the lowest energy state ?

If so, what could that energy transform into ? (from what I know energy and matter can change into one another.....d`oh)

Last edited: Aug 4, 2007
21. Aug 4, 2007

### meopemuk

These are very deep questions, and I don't think there exists a consensus opinion among practicing scientists. If you decided to learn general relativity, you would have definitely noticed that space-time there plays a role of a physical object, which has its own energy-momentum and can "interact" with matter. Some modern attempts to quantize gravity also treat space-time as a kind of "fabric", whose physical properties (e.g., dimension, Planck-scale structure) emerge from something even more fundamental (?).

In my personal opinion (which, I should warn you, is not the "mainstream"), all this "space-time continuum" stuff is not relevant to physics. All we need to know is that there exists an observable called "position", and that each measurement can be labeled by the parameter "time", which is simply the reading of the laboratory clock at the instant of the measurement.

No "fabric", no "field", no "energy", no "structure", no bla-bla...

Eugene.

22. Aug 6, 2007

### Nick666

You mean space is ... nothing ?

23. Aug 6, 2007

### meopemuk

Yes, that's what I mean.

In quantum mechanics there is one place where we meet the "position space" with coordinates (x,y,z). This is the 3-dimensional "space" of common eigenvalues of 3 commuting components of the position operator. Wavefunctions in the position representation are defined on this "space". In quantum mechanics we are free to choose any other set of mutually commuting operators and define our wavefunctions on their common eigenvalues. For example, we can choose 3 components of the momentum operator to define wavefunctions in the momentum space.

There is no any fundamental difference between position-space and momentum-space wavefunctions in quantum mechanics. However, we still have this intuitive belief that the position space is somehow more important and more fundamental. Indeed our organs of sensation (e.g., vision) tell us that we are "embedded" in the 3D position space, not in the 3D momentum space. Why it is so? I think the reason is that by natural selection nature found that it is preferable for our survival to have this "position space" feeling. One can imagine that in other conditions living creatures could develop a primary sensation of the momentum space, and keep the idea of the position space as an afterthought, if it would be benefitial for their survival.

On the other hand, if we assume that the position space is some fundamental "continuum" with its "structure", "curvature", "energy", etc. then we need to explain how this vision corresponds to the QM position space described as common eigenvalues of the position operator, which I mentioned above. I believe that we cannot have two different notions for the same thing (space).

Anyway, these are my ideas about space. I understand that they are controversial, crazy, and perhaps not worth your attention, but that's what I've got.

Eugene.

Last edited: Aug 6, 2007
24. Aug 7, 2007

### Nick666

But how is it that matter can move through space? Or in fact, space "is created" by motion ?

Last edited: Aug 7, 2007
25. Aug 7, 2007

### olgranpappy

First of all, this question is ridiculous. Second of all, here is an experiement that you can try at home to convince yourself that matter *does*, in fact, move throught space: