The Physics of Virtual Particles - Comments

[A. Neumaier]

A. Neumaier submitted a new PF Insights post

The Physics of Virtual Particles

Continue reading the Original PF Insights Post.

 

[naima]

If an accelerated observer tells you that she is in a hot bath of particles that you do not feel, will you call them virtual?

 

[A. Neumaier]

If an accelerated observer tells you that she is in a hot bath of particles that you do not feel, will you call them virtual?

Particles generated by the Unruh effect are indeed virtual only - of the same kind as the virtual photons in the Coulomb interaction. Since the bath is hot, one needs a quasiparticle picture to get something resembling actual particles.

 

[anorlunda]

Help please, "another 3-vector describing infinitesimal boosts"

I tried searching for a definition of "infinitesimal boosts" but all I can find are citations of its use, no definition

 

[A. Neumaier]

Help please, "another 3-vector describing infinitesimal boosts"

It is the $K_i$ in the standard notation for the generators. https://en.wikipedia.org/wiki/Poincaré_group
The boost itself is the corresponding exponential, given here: https://en.wikipedia.org/wiki/Lorentz_boost

 

[dextercioby]

Hi Arnold, nice and thorough writing, bravo! Now, there's a tiny, but relevant, addendum. The fundamental observables of the quantum harmonic oscillator are coordinates, momenta and the Hamiltonian. There's no way you can leave out the Hamiltonian from the algebra: if you do, there's no way to tell a system from another and there's no dynamics.

 

[A. Neumaier]

Hi Arnold, nice and thorough writing, bravo! Now, there's a tiny, but relevant, addendum. The fundamental observables of the quantum harmonic oscillator are coordinates, momenta and the Hamiltonian. There's no way you can leave out the Hamiltonian from the algebra: if you do, there's no way to tell a system from another and there's no dynamics.

I was careful in my language, not talking about a harmonic oscillator but about an oscillator in general. The Hamiltonian tells which kind of oscillator one has - harmonic or anharmonic. The form of the Hamiltonian depends on the way the system is embedded into its surrounding.

The Hamiltonian of interest for virtual particles is part of the representation of the Poincare group, $H=cp_0$. Note that this article is about what is necessary to talk about virtual particles - not about giving a complete discussion of what it means to have a general quantum system. For the latter see another thread, in particular the link in the first post.

 

[naima]

You say that virtual particles "are" internal lines in Feynman diagrams. Is it the case with the virtual particles of the Unruh effect?

 

[A. Neumaier]

You say that virtual particles "are" internal lines in Feynman diagrams. Is it the case with the virtual particles of the Unruh effect?

In technical terms, the Unruh effect produces from the vacuum state (in the rest frame) a coherent state (in the accelerated frame), more specifically a so-called Hadamard state. When phrased in finite terms, the accelerated observer sees no physical particles but a heat bath modeled by the coherent state. The virtual particles are an artifact of forcing upon the coherent state (in a non-Fock space) a particle picture (that makes sense only in a Fock space).

However, in an approximation with UV and IR cutoffs, this Hadamard coherent state can be described perturbatively by Feynman diagrams (hence by virtual particles) in a similar way as the coherent states for the soft photons making up the dressing of a physical charged electron. For the latter, cf. the discussion in Section 13.2 of Weinberg's book on quantum field theory and the corresponding coherent state version in http://dx.doi.org/10.1016/0370-1573(76)90003-X .

Note that all this talk about soft virtual photons in coherent states (or virtual particles in an accelerated vacuum state) is valid only with the cutoff and becomes completely meaningless in the physical limit, as all terms except for the final results become infinite.

This is due to the fact that the charged representation in QED belongs to a different Hilbert space (superselection sector) than the Fock space from which the virtual stuff is built. Similarly, the accelerated representation in the accelerated frame and the vacuum representation in the rest frame belong to different superselection sectors.

 

[Ben Wilson]

"Physical system. A physical system is characterized abstractly by the collection of observables that are meaningfully assignable to the system, the defining commutation relations specifying a Lie algebra, and its representation on a Hilbert space. The spectral analysis of this representation determines the possible values the observables can take. The most well-known example is an oscillator, whose observables are scalar position and momentum variables satisfying the canonical commutation rules and can take arbitrary real values."

If your audience can understand this definition, then you are preaching to the converted.

 

[bhobba]

"If your audience can understand this definition, then you are preaching to the converted.

Even people who understand QM at the level inherent in statements like that can, and do, get confused about virtual particles.

Even if you don't its not hard to get the gist.

Thanks
Bill

 

[Demystifier]

Particles generated by the Unruh effect are indeed virtual only - of the same kind as the virtual photons in the Coulomb interaction. Since the bath is hot, one needs a quasiparticle picture to get something resembling actual particles.

To avoid confusion, it would be useful to give a precise difference between virtual particle and quasiparticle, and also between quasiparticle and real particle. It is probably only a matter of definition, but from your statement above it seems that my definition differs from yours.

 

[naima]

We have a hot bath in a microwave oven. do we need quasiparticles or virtual particles to cook the food?

 

[vanhees71]

In a microwave oven we have coherent states that cook the food :-).

 

[A. Neumaier]

it would be useful to give a precise difference between virtual particle and quasiparticle, and also between quasiparticle and real particle.

do we need quasiparticles or virtual particles to cook the food?

In a microwave oven we have coherent states that cook the food :-).

Real particles are the elementary excitations of the vacuum state.

Quasiparticles are the elementary excitations of a coherent state or a squeezed state (or their fermionic analogues), treated as if it were a vacuum state. But the space-time symmetry is broken.

Virtual particles are stateless and live in cartoons only, including cartoons that try to paint a complicated particle picture of the simple non-particle notion of a coherent state.

Ordinary particles in the rest frame of an observer would look to a uniformly accelerated observer like quasiparticles over the Unruh coherent state - if the accelerated observer were able to observe such a particle. But the latter is possible only if the accelerated observer passes the observer at rest very, very slowly - in which case the Unruh coherent state is physically indistinguishable from the vacuum state.

 

[naima]

I think that you are talking about that.
You and Vanhees use coherent states here. How do they appear in the context of an accelerated observer?

 

[A. Neumaier]

coherent states here. How do they appear in the context of an accelerated observer?

See post #9.

 

[A. Neumaier]

To avoid confusion, it would be useful to give a precise difference between virtual particle and quasiparticle, and also between quasiparticle and real particle. It is probably only a matter of definition, but from your statement above it seems that my definition differs from yours.

I added the following paragraph to the Insight text:

Quasiparticles. The particles described by the S-matrix are the elementary excitations of the vacuum state. At finite temperature and in general relativity, the asymptotic particle concept in quantum field theory must be modified to take account of a nontrivial background. Typically, the background (which takes the place of the vacuum state) is modeled as a coherent state or a squeezed state, or their fermionic analogue. Quasiparticles are the elementary excitations of the background, treated as if it were a vacuum state; the background also deforms the mass shell, leading to a dispersion law different from $p^2=m^2$. Moreover, the space-time symmetry is broken. Typical examples of quasiparticles are phonons in solid state physics and Cooper pairs in superconductivity. Quasiparticles are associated with states and creation and annihilation operators, hence are as real as ordinary particles.

 

[naima]

I found here a link between accelerated observer and coherent states thru Bogoliubov transformation.

 

[A. Neumaier]

I found here a link between accelerated observer and coherent states thru Bogoliubov transformation.

The Bogoliubov transformation is the unitary transformation that turns the vacuum state (in an approximation with cutoff) into a coherent or squeezed state, or their fermionic analogue. In the physically relevant cases, it becomes, however, ill-defined in the limit where the cutoff is removed, reflecting the fact that quasiparticles states belong to a different representation (superselection sector) of the observable algebra than the vacuum state and ordinary particle states.

 

[naima]

is virtual synonymous to unmeasured?

 

[vanhees71]

I'd say, virtuality implies unobservability.

 

[naima]

So you think that there are not registered things which are not virtual. such as external lines in the diagrams?
diagrams

 

[vanhees71]

The external lines in Feynman diagrams for $S$-matrix elements stand for asymptotic free states, which are observable.

 

[naima]

So give me something that is not virtual and not observed.
(if virtuality is strictly included in non observability)

 

[vanhees71]

I don't know what you mean. You cannot observe off-shell particles. Tell me where you think virtual particles are observed.

 

[Demystifier]

So give me something that is not virtual and not observed.
(if virtuality is strictly included in non observability)

Free particles.

 

[naima]

@VanHees,
You say "Tell me where you think virtual particles are observed." I say the opposite

you say that asymptotic free states are observable.
@Demystifier, you give me free particles as an example for a not observed thing.

I think that
measured <=> not virtual
not measured <=> virtual
and as we have partial measurements that
partially measured <=> partially not virtual.

 

[naima]

I recommend Neumaier insights post on virtual particles.
I would like to add that they only appear in processes where one need to add the amplitudes of the different possibilities and to square them to get the probability.
This is the case with Feynman diagrams, the path integral or with Young slits.
If in the Young experiment (and in all cases) the possibilities are measured, we do not need virtual particles with amplitudes (the result would be false) it is enough to add the probabilities.
One advantage is that intermediate situations (partial measurements) can be considered using a fringe visibility parameter.

 

[A. Neumaier]

If your audience can understand this definition, then you are preaching to the converted.

The present insight article is intended to be preaching to the converters.

I am preaching to the unconverted in the followup article[/PLAIN] Misconceptions about virtual particles.

 

[A. Neumaier]

I updated my Insight article by adding at the end a lot of factual information on vacuum fluctuations and related topics, based on the fairly precise definition of vacuum fluctuations on p.119 in the quantum field theory book by Itzykson and Zuber 1980.

 

[vanhees71]

To be pedantic: You write

According to the Born rule, the distribution of a quantum observable gives the probabilities for measuring values for the observable in independent, identical preparations of the system in identical states. Thus the presence of a Gaussian distribution means that the attempt to measure the electromagnetic field in the vacuum state cannot be done with arbitrary precision but has an inherent uncertainty.

I would write

According to the Born rule, the distribution of a quantum observable gives the probabilities for measuring values for the observable in independent, identical preparations of the system in identical states. Thus the presence of a Gaussian distribution means that the value of the electromagnetic field in the vacuum state is not determined with arbitrary precision but has an inherent uncertainty.

The fluctuations of observables are not due to the limitations of measurement accuracy but due to the state the system is prepared in. This is also often discussed in a misleading way in context of the usual uncertainty relation. Also in this case the uncertainty/fluctuations of observables are due to the impossibility to prepare the system in such a way that both incompatible observables have a determined value; it's not a limitation to the accuracy you can measure the one or the other observable.

 

[A. Neumaier]

According to the Born rule, the distribution of a quantum observable gives the probabilities for measuring values for the observable in independent, identical preparations of the system in identical states. Thus the presence of a Gaussian distribution means that the value of the electromagnetic field in the vacuum state is not determined with arbitrary precision but has an inherent uncertainty.

Yes, that's an improvement. I updated the page.