Why don't virtual particles cause decoherence?

tom.stoer

Could you solve he following puzzles: let's say virtual particles (internal lines in Feynman diagrams) are 'real'; then
1) why are there gauge bosons propagators with unphysical polarizations whereas in observations only two physical polarizations are present?
2) why is it not possible to attribute polarization and 4-momentum to gauge boson propagators whereas in observations we always have a certain polarization and 4-momentum?
3) why are there Fadeev-Popov ghost particles in certain gauges whereas they do appear in any observation? and why are they absent in other gauges? is reality gauge-dependent?

To answer your question: real particles do appear in observations. External lines in Feynman diagrams as representations of asymptotic states are an idealization for real particles. But what we observe in reality is rather close to these idealized asymptotic states, so it's OK to try to interpret them as a mathematical model of reality.

In contrast, internal lines in Feynman diagrams do not have attributes like 4-momentum, spin or polarization as we observe them. In addition the attributes of internal lines are gauge dependent whereas our observations aren't. So we can neither relate our observation of reality to these 'virtual particles', nor can we relate all 'virtual particles' we use in our calculations to our observation of reality. So the fundamental difference between internal and external lines is not only that internal lines are 'off-shell'. And b/c there is no working relation between attributes of observations of reality and attributes of internal lines, it is NOT OK to construct an interpretation of reality in terms of these virtual particles.

mfb

1-3: Your observations are too slow. You observe just long-living particles, which act like long-living particles.
But "rather close" is the main point. There is no fundamental line separating particles we observe from the virtual W in a weak decay.

If you try to "catch" a photon in the near field of an emitter, you get polarizations of the field which are impossible for real photons. If you go away, the radiative part gets more and more dominant, but there is no line after which you observe just radiation and nothing else.

tom.stoer

You ignore most of what I am saying.

mfb

No, I reduce it to the main point, and adress that.
Anyway, I don't think further discussion will produce anything new here.

tom.stoer

No, the main point are unphysical properties of virtual particles; ignoring these facts does not solve any problem. There are not even short-lived ghosts in reality; and reality is not gauge dependent. So focussing on livetime and off-shell is not the main point. It misses nearly everything which characterizes virtual particles.

JK423

Can i ask both of you a question?
The interaction time between two particles is finite. If we could make measurements during this finite period while interactions are still on, what would we see? What are the observables? Is, for example, the number operator of virtual particles (if such thing exists) an observable? Any idea?

tom.stoer

I don't think that the question regarding interaction time makes sense.

Regarding the number operator it's trivial: this operator acts on Hilbert space stars. But virtual particles (internal lines in Feynman diagrams) are propagators, not Hilbert space states. Therefore there is not operator 'counting' virtual particles.

JK423

I haven't seen anywhere a discussion of what happens during an interaction (not just in/out states). Why doesn't it make sense (theoreticaly at least)?

mfb

How would those measurements look like? They would be interactions with the particles, and not separable from the process you consider.

If you call everything "unphysical" which cannot be "observed" in non-interacting particles, sure. That is just playing with words. The near field of an antenna would be unphysical then, as electric and magnetic fields do not follow the rules for radiation (=light particles).

sheaf

Arnold Neumaier mentions this issue on his FAQ. Some results are known in <3 spatial dimensions, but it's a hard problem, and much of the formalism he discusses is beyond my knowledge.

tom.stoer

It seems that you are not familiar with the meaning of "unphysical" in the context of gauge theories. The 0-component of the gauge field A is an unphysical d.o.f. b/c it has no associated canonical momentum; states in the kinematical Hilbert space are unphysical if they are not annihilated by the Gauß constraint (= if they are not in the kernel of the Gauß Law operator = if they are not gauge singulets); Fadeev-Popov ghosts are unphysical d.o.f. b/c they are artificial d.o.f. Introduced to eliminate other unphysical d.o.f. (polarizations) of the gauge fied.

All these entities are unphysical simply b/c strictly speaking they are not required; you can find formulations avoiding them, so there is no fundamental reason to introduce them into the formalism (they are artifacts of the formalism) and therefore there is no reason to interpret them as physical entities.

Maui

I was under the impression that "physical" means exchange and interaction of virtual particles(at least according to qft) between....er... objects/real particles or whatever you want to label it. If they are not real(don't exist), is anything real? How would physicalness arise?

mattt

Imagine I develop a new mathematical formalism, that is a good enough mathematical approximation to, say, Newtonian Mechanics, based on a given mathematical Serie.

Imagine I call each element of the Serie, "a little green dwarf", because I like it.

Would you say that those "little green dwarfs" are "real" or "physical"?

Would you say that gravity exists because of the actions of those "little green dwarfs"?

Maui

If i see a multitude of little green dwarfs all around me for a life time, i might be inclined to believe they are real and exist. The mathematics wouldn't work if it had no resemblance to reality. Why would it work otherwise? Just a happy coincidence?


If little green dwarfs are the curvature of spacetime, yes.

tom.stoer

I guess we should come back to the question

My first answer was

The discussion over the last couple of days did not change anything; the first answer is still correct.

Let me summarize some additional ideas

But all this is not directly relevant for the original question b/c virtual particles are completely irrelevant in the context of decoherence: they are not present in the full theory; they do neither introduce the above mentioned factorization of H nor the partial trace; and they are not states in any Hilbert space H_system, H_pointer or H_environment .

Last but not least: nobody would assume that any approximation like a Taylor series (or green dwarfs) do introduce additional effects which are not already present in the full theory w/o the approximation (w/o green dwarfs). So if the theory w/o virtual partices green dwarfs) already contains decoherence (gravity) it would be silly to say that decoherence (gravity) is due to virtual particles (green dwarfs). This changes if the theory cannot be formulated w/o virtual particles (w/o green dwarfs), or if the formulation is conceptally simpler (in the sense of Ockham's razor) using virtual particles (green dwarfs).

I am not an expert regarding green dwarfs, but I know that perturbation theory is incomplete and misses relevant non-perturbative effects. So I can't see any reason to rely on the interpretation of partially unphysical artifacts due to an incomplete approximation instead of using the full theory.

Demystifier

There are internal lines which are exactly on-shell.
There are external lines which are slightly off-shell (see e.g. http://en.wikipedia.org/wiki/Scharnhorst_effect ).

TrickyDicky

Hi Tom, I tend to sympathize with the way you present the answer to this FAQ, but I have a doubt about the "virtual particles are just artifacts of perturbation theory" issue, you often use the example of QCD where this methodology is not necessary, but if we consider only QED ("the jewel of the physics crown") for a moment it does seem that perturbation is needed to obtain reasonable results, so in that sense at least for QED VP seem like something you can't get rid of so easily.