## Why don't virtual particles cause decoherence?

I was recently told virtual particles don't cause decoherence. Why not? Do they just never interact with their environment (apart from transferring energy/force) so they can never collapse a wavefunction?

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 Recognitions: Homework Help Science Advisor Interaction with real particles can be mediated via virtual particles, and cause decoherence. I think it is misleading to distinguish between real and virtual particles here.
 Recognitions: Science Advisor Decohence is due to factorizing the full Hilbert space H in Hsystem, Hpointer and Henvironment and then "tracing out" the environment degrees of freedom. The remaining "subsystem" can be described by an "effective density matrix" which is nearly diagonal in the pointer basis, so it seems as if it collapsed to the a pointer state with some classical probability. Virtual particles are artifacts of perturbation theory, i.e they are not present in the full theory w/o using this approximation. Using virtual particles does not introduce the above mentioned factorization of H. And last but not least virtual particles are not states in any Hilbert space Hsystem, Hpointer or Henvironment , but they are "integrals over propagators". It' like apples and oranges.

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## Why don't virtual particles cause decoherence?

 Quote by tom.stoer Decohence is due to factorizing the full Hilbert space H in Hsystem, Hpointer and Henvironment and then "tracing out" the environment degrees of freedom. The remaining "subsystem" can be described by an "effective density matrix" which is nearly diagonal in the pointer basis, so it seems as if it collapsed to the a pointer state with some classical probability. Virtual particles are artifacts of perturbation theory, i.e they are not present in the full theory w/o using this approximation. Using virtual particles does not introduce the above mentioned factorization of H. And last but not least virtual particles are not states in any Hilbert space Hsystem, Hpointer or Henvironment , but they are "integrals over propagators". It' like apples and oranges.
Or in slightly oversimplified terms, virtual particles don't cause decoherence simply because virtual particles don't exist.

 they are not existing in the physical (space time) sense !.

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 Quote by tom.stoer It' like apples and oranges.
I have a better analogy. If you have one apple, then in the equation
1 apple = (2 apples) + (-1 apple)
1 apple is a real apple, while 2 apples and -1 apple are virtual apples.

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 Quote by Demystifier Or in slightly oversimplified terms, virtual particles don't cause decoherence simply because virtual particles don't exist.
If they do not exist, please provide a more appropriate way to describe all particles ever detected. They are all virtual, see Bill_K's post (or this one from me) for an explanation.

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 Quote by mfb If they do not exist, please provide a more appropriate way to describe all particles ever detected. They are all virtual, see Bill_K's post (or this one from me) for an explanation.
See my post
http://www.physicsforums.com/showpos...8&postcount=12

The confusion stems from the unfortunate fact that physicists use two different DEFINITIONS of the word "virtual particle". According to one, it as any off-shell particle. According to another (more meaningful, in my opinion), it is any internal line in a Feynman diagram. The two definitions are not equivalent.

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 Quote by Demystifier According to another (more meaningful, in my opinion), it is any internal line in a Feynman diagram. The two definitions are not equivalent.
Where is the difference? An internal line in a Feynman diagram is not exactly on-shell, and particles not exactly on-shell are internal lines in Feynman diagrams.
Some particles are just more off-shell than others.

 Recognitions: Science Advisor Please have a look at the formal definition: an internal line is not a state but a propagator; and it's therefore not a particle
 Recognitions: Homework Help Science Advisor In that case, our universe has no particles. There are no particles (!) which will not interact with anything else in the future.
 Recognitions: Science Advisor No, the only problem is that you try to interpret a mathematical artifact
 Recognitions: Homework Help Science Advisor A mathematical artifact like our world? In the QFT sense of real particles, do you see* any real particles in the world? *actually, you must not be able to see it, as it must not interact with anything

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 Quote by mfb A mathematical artifact like our world? In the QFT sense of real particles, do you see* any real particles in the world? *actually, you must not be able to see it, as it must not interact with anything
Are you aware of the fact that you can formulate QFT non-perturbatively w/o Feynman diagrams? Do you see any relevance for propagators in non-rel. QM and density operators?

Mukilab asked why virtual particles do not cause decoherence.

The answers is simple: usually there is no need to introduce perturbation theory and propagators when studying density operators. The formalism is different. So there are no propagators in this context, and therefore they cannot cause anything.

 Quote by mfb A mathematical artifact like our world? In the QFT sense of real particles, do you see* any real particles in the world? *actually, you must not be able to see it, as it must not interact with anything
But isn't that the essence of the difficulty here? Namely:

Our world is a physical entity, including the ability to measure things. One of the things that can be measured is the state of incoming/outgoing particles in a scattering experiment. In the model, this corresponds to the in/out state containing noninteracting particles. Yes, in reality, they may be slightly off-shell. They must be since they haven't been around for an infinite time. In this sense the model is an idealization.

What happens whilst the particles are interacting, however, cannot be measured. In a model based on perturbation theory, this interaction includes the exchange of what we're calling virtual particles. If we could solve QED (say) exactly, presumably we wouldn't even need to chop up the interaction into these virtual particle contributions.

As soon as we wish to talk of an in state particle as something whose properties we can prepare or an out-state particle as something whose properties we can measure, it's no longer appropriate to model that particle by a propagator (and hence by our definition no longer appropriate to call it a virtual particle). For example, for a photon, I'd like to be able to prepare/measure its momentum/polarization, but the photon propagator $-i\frac{g^{\mu\nu}}{k^2+i\epsilon}$ doesn't have the right ingredients to allow me to do this.

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 Quote by sheaf )... For example, for a photon, I'd like to be able to prepare/measure its momentum/polarization, but the photon propagator $-i\frac{g^{\mu\nu}}{k^2+i\epsilon}$ doesn't have the right ingredients to allow me to do this.
Very good point, the photon propagator does not carry momentum in the sense we measure it.

In addition gauge boson propagators are gauge-dependent objects and are therefore unphysical. So virtual particles DO depend on the specific gauge fixing. Temporal gauge, Lorentz gauge, Coulomb gauge, ... result in different propagators and 'potentials', so you can't interpret these entities directly. The difference becomes visible in QCD, where you have ghost propagators only in some gauges!

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