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I read here that particles/antiparticles appear and annihilate each other spontaneously in empty space.

Since particles appear and disappear in empty space, it would seem that empty space has some form of energy. Otherwise these particles' fluctuations appear to be completely uncaused events, which defies reason.

Does space have some form of energy, or is this phenomenon completely uncaused?

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For bosonic fields, the idea is the same as for the quantum harmonic oscillator, that is, the ground state energy is positive, . (Bosonic fields $\phi(\vec k,t) $could be considered as standard quantum harmonic oscillators) However, for fermionic fields, the ground state energy is negative. –  Trimok Jun 10 '13 at 8:38
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Possible duplicate physics.stackexchange.com/q/67582/2751 –  Dilaton Jun 10 '13 at 11:52

2 Answers 2

It's not quite right to say that "particles/antiparticles appear and annihilate spontaneously" for the following reason:

Particles and antiparticles are modelled as excitations of quantum fields. The things that are being described as appearing and annihilating in the vacuum are disturbances to these quantum fields, which are sometimes called "virtual particles". Virtual particles are not particles. A particle (or antiparticle) is a special type of excitation or "wiggle" which has a life of its own - it can travel off quite happily. (Think of wiggling a slinky toy and watching the wiggle travel off). The virtual particle is more of a twitch that didn't quite make it to being a fully fledged wiggle.

Now no analogy is perfect, and this one certainly isn't either.

1 A quantum field might have an excitation which is more analogous to a wave all along the slinky, rather than a small wiggle travelling off. This is also a like a particle/antiparticle.

2 You might get the impression that the field is changing with time and these virtual particles are twitches that you could "see happening". However it's more subtle than that - actually these quantum fields are subject to the uncertainty principle, and the "twitch" that is a quantum vacuum fluctuation is merely a potential field configuration arising from the uncertainty principle.

these particles appear to be a completely uncaused event which defies reason

The vacuum fluctuations do not have any cause (other than that their existence is mandated by the laws of physics). However, it's not correct to say that they're "events", for the reason I mentioned - they're uncertainties rather than things happening as a function of time.

To address your point about energy, you are right, if you apply general relativity these vacuum fluctuations contribute an energy which will gravitate. This causes a discrepancy which has been called the vacuum catastrophe

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but how can an "uncertainty" in our ability to measure things be enough to cause even virtual particles. it still seems to be a completely uncaused phenomena –  good_ole_ray Jun 10 '13 at 9:21
    
An uncertainty (in the sense of the Heisenberg principle) isn't just an uncertainty in our ability to measure - it's an inherent uncertainty in the physical system. In quantum mechanics this means that you can't squeeze a particle so that it's in a given location and not moving, i.e. perfectly still. This same inherent uncertainty applies to the field too, so in the vacuum, the field doesn't "have a definite -no wiggles- value" (using sloppy language here to try to convey the idea) - this is where the fluctuations come from. –  twistor59 Jun 10 '13 at 9:27
    
does this mean there is an uncertainty whether there is any energy there, therefore the uncertainty of energy causes the phenomena through E=mc2? –  good_ole_ray Jun 10 '13 at 9:30
    
Given that there's uncertainty in the field configuration, there is an infinite number of potential configurations, and each one will have an energy. What I can do is take the average of the energy over all these configurations. If I do I get a huge number. This is the vacuum catastrophe. People can't really agree on how to fix it, but without having supersymmetry in your toolbox, it's going to be tricky! –  twistor59 Jun 10 '13 at 9:38

What is really being said is that it is not an uncaused event in the vacuum, but in simplistic terms, it could be said to be more a property of the vacuum. No event is taking place as such. Describing it as an event is trying to put it in simplistic terms, which while it may help in understanding to some degree, is not an exact description. You could equally well (and again not with accuracy, but as another way of trying to describe it in a word) call it the texture of a vacuum rather than an 'event' – looking at it like that means you don't need a cause.

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very helpful. thanks. –  good_ole_ray Mar 10 at 8:17

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