Does the nature of the assortment of virtual particles depend upon the warping of spacetime in a direct manner ?
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1$\begingroup$ See also "Hawking Radiation" for one interesting limit. $\endgroup$– dmckee --- ex-moderator kittenCommented May 6, 2011 at 23:00
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$\begingroup$ Its a bit of a bad question too and depends what formalism you are working in. First you have to describe what you mean by a virtual 'particle'. This is all really subtle in qft on curved space. In particular there is no obvious notion or even existence of what a good local observable is (much less what a particle is here, even less so a virtual particle). So you will have to be more precise $\endgroup$– ColumbiaCommented May 7, 2011 at 7:31
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$\begingroup$ I'll try Colombia: "Do heavier virtual matter particles generally manifest themselves more often when spacetime is warped?" - I'm not comfortable this leaves you satisfied regarding clarification though. $\endgroup$– Andersi2Commented May 7, 2011 at 9:03
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2 Answers
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I will undertake a hand waving answer and maybe since the question will come to the top somebody knowledgeable will give a full answer.
Virtual particles are the province of quantum mechanics and led to the development of quantum field theory with creation and annihilation operators.
This led to the realization that the vacuum, in the QFT description is not "empty" but is like a sea where virtual particles continuously create and annihilate with no loss of energy. The vacuum is a "ground state".
Interestingly enough this field theoretic description with creation and annihilation operators does not correspond one to one with particle physics. Back in 1963 I sat through a field theoretical course for nuclear physics where creation and annihilation operators acted on nuclear levels. But I digress.
Now the curvature of space is a unique proposal of General Relativity. General relativity has not been quantized in an irrefutable manner. String theorists believe that they have managed to do that, but I leave it to them to describe what a sea of virtual particles in a string universe is like.
Trying to naively say: suppose gravity is quantized in the classic QFT manner and gravitons exist in the vacuum sea too,
the answer would be: the higher the curvature the more the distribution of the particle antiparticle sea would be weighted statistically towards heavier pairs, due to energy considerations with respect to flat space.
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$\begingroup$ In that very naive picture, would the inclination towards heavier virtual matter pair production bear any significance on the chances of local formation of complex molecules - see also this link physics.stackexchange.com/questions/9647/space-time-hospitality $\endgroup$– Andersi2Commented May 10, 2011 at 21:23
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$\begingroup$ Or just, has this particular issue been given attention? I do realize this is a rarther unreasonable additional question. $\endgroup$– Andersi2Commented May 10, 2011 at 21:36
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$\begingroup$ @Anders I just saw your comments. I do not think so, within the present gravitational framework. The gravitational interactions are orders of magnitude weaker than the electromagnetic ones. One cannot exclude at present that in a future theory of everything the unification will produce unexpected correlations, of course. At the moment it can only be envisaged in science fiction. $\endgroup$– anna vCommented Aug 15, 2011 at 4:30
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Unruh effect, coordinate dependence.
Creation and annihilation operators are coordinate-dependent.
A ground state in one is a squeezed state in another.
