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I've been told that a vacuum isn't actually empty space, rather that it consists of antiparticle pairs spontaneously materialising then quickly annihilating, which leads me to a few questions.

Firstly, is this true? And secondly, if so, where do these particles come from?... (do the particles even have to come from anywhere?)

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I don't think the particle-anti-particle picture is a very good one to grasp what's going on. Essentially, it's a consequence of zero-point energy. In classical physics, the lowest energy state of a system, it's ground state, is zero. In quantum mechanics, its a non-zero (but very small) value. The easiest way to see how this zero point energy arises is through an elementary problem is quantum mechanics, the quantum harmonic oscillator. The classical harmonic oscillator is a system in which there is a restorative force proportional to the displacement. For example, a spring - the further you pull the end of a spring, the more force the spring resists your pull. Modeling this system in classical physics is very easy. Things are a bit different in quantum mechanics - the state of a particle is specified by its wavefunction, which encodes the probabilities of finding the particle in certain positions. Another property of quantum systems is that their energies come in discrete energy levels. If you're interested in how it is worked out, you can see here. You can derive the following result for the energy levels of the particle $$E=\hbar \omega( n+\frac {1}{2})$$ Since n specifies the energy level, setting n to zero will give us the ground state. However, we can see this isn't zero - so the lowest possible state of a quantum system still contains some energy.

In a practical example, liquid helium does not freeze under atmospheric pressure at any temperature because of its zero-point energy. One very important thing to note is the following - zero-point energy does not violate the conservation of energy. A common explanation is that the uncertainty principle allows particles to violate it 'if they're quick enough!'. This simply isn't true. From the Wiki page on conservation of energy:

In quantum mechanics, energy of a quantum system is described by a self-adjoint (Hermite) operator called Hamiltonian, which acts on the Hilbert space (or a space of wave functions ) of the system. If the Hamiltonian is a time independent operator, emergence probability of the measurement result does not change in time over the evolution of the system. Thus the expectation value of energy is also time independent. The local energy conservation in quantum field theory is ensured by the quantum Noether's theorem for energy-momentum tensor operator. Note that due to the lack of the (universal) time operator in quantum theory, the uncertainty relations for time and energy are not fundamental in contrast to the position momentum uncertainty principle, and merely holds in specific cases (See Uncertainty principle). Energy at each fixed time can be precisely measured in principle without any problem caused by the time energy uncertainty relations. Thus the conservation of energy in time is a well defined concept even in quantum mechanics.

Now, on to your question - in quantum field theory, all particle are modeled as excitations of fields. That is, every particle has an associated field. For the particles that carry forces, these are the familiar force fields - such as the electromagnetic field. Fields take a value everywhere in space. Now, in classical mechanics, this value would be zero in most places. However, as we saw above, the ground state of a quantum field is non-zero. So, even in empty space (or 'free space') these fields have a a very small value. So, empty space has vacuum energy.

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Nice answer: however, there has recently been good evidence that the explanation that He does not solidify at ambient pressure due to the zero-point motion is wrong, see physics.aps.org/articles/v5/75. –  Fabian Aug 13 '12 at 14:21
Oh, okay. Thanks for the link, I wasn't aware of that. –  Mark M Aug 13 '12 at 14:31
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Nothing goes on; the vacuum is completely inert. Virtual particles don't exist in time, except in a (literally) figurative sense. They don't have associated states, hence no expectations, probabilities, uncertainties.

See http://physics.stackexchange.com/a/22064/7924 and Chapter A8 ''Virtual particles and vacuum fluctuations'' of my theoretical physics FAQ at http://www.mat.univie.ac.at/~neum/physfaq/physics-faq.html

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+1 For you unpopular and correct (in my opinion) answer. By the way, is it possible to get your excellent theoretical physics FAQ questions in pdf format? –  drake Aug 13 '12 at 19:14
@drake: pdf/ No. I have the FAQ as a collection of ascii files and html files, and don't know how to easily convert it into pdf. If you'd point me to open domain software for doing this, I'd be happy to create a pdf version for you. –  Arnold Neumaier Aug 14 '12 at 7:05
Thank you! If I figure out how convert them, I will tell you. –  drake Aug 14 '12 at 16:10
The QCD vacuum has a complicated structure, at least, if this article ist true : en.wikipedia.org/wiki/QCD_vacuum. –  jjcale Aug 14 '12 at 19:27
@jjcale from a quick glance, I believe it is correct. –  David Z Aug 14 '12 at 21:57
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Your question has been addressed in two physics.stackexchange articles: are-elementary-particles-actually-more-elementary-than-quasiparticles and what-is-the-relationship-between-string-net-theory-and-string-m-theory

In short, vacuum is not inert but a dynamical medium. Casimir effect has experiemntally demonstarted that vacuum is indeed a dynamical medium. As a dynamical medium, vacuum can have motions which is the wave in the vacuum. Those waves are colloective excitations which correspond the elementary particles in the vacuum. The order in such vacumm-medium determine the nature of the elementary particles. For example, if vacuum-medium is a quantum string liquid (with topological order), its wave will satisfy Maxwell equation which correspond to photons. The ends of strings will correspond to electrons/quarks.

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Are those links truly addressing the OP question? –  drake Aug 14 '12 at 18:05
The more important issue is whether the content of the answer addresses the question (which I believe it does). Answers should be answers without their links, remember. –  David Z Aug 14 '12 at 22:00
If the vacuum were truly dynamical, you should be able to give a reference to a nontrivial equation of motion for the vacuum state! -- The Casimir effect doesn't make the vacuum a dynamical medium, see mat.univie.ac.at/~neum/physfaq/topics/casimir –  Arnold Neumaier Aug 15 '12 at 16:11
I have always wondered why most physicists ignore Jaffe's work. –  drake Aug 15 '12 at 23:23
(a) We may assume the vacuum-medium is form by a collection of qubits, whose dynamics is governed by a quantum Hamiltonian. There are many Hamiltonians to make the qubit ground state to have a string-liquid order (or string-net condensation). The collective excitations above the string-net condensed state can be gauge bosons and fermions. (b) If vacuum is truely empty, then there is no Casimir effect. So Casimir effect imply that vacuum is not empty (ie has dynamical effects). (c) Coulomb interaction is indeed, just like the Casimir effect, an effect of dynamical vacuum. –  Xiao-Gang Wen Aug 15 '12 at 23:48
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protected by Qmechanic May 5 at 15:48

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