Misconceptions about Virtual Particles - Comments

[A. Neumaier]

But if even you can't guess what Susskind actually meant, how are his students supposed to understand it?

I ask this myself about every lecture or paper about many worlds.

In the TASI lectures I have no difficulty guessing the intended meaning. It is clear that Susskind meant to say (and illustrate in a visually impressive way) that Hawking radiation implies that there is a complex ''interplay between gravity and quantum mechanics'' (p.14). The details didn't matter since they were not needed for what follows. (It is usually in such situations that inaccuracies creep into a description.) Thus intelligent students lose nothing by being mystified about his remarks on p.13.

Only the dumb ones that take for gospel everything uttered by a famous physicist have problems. Rightly so. It is the standard payoff of credulosity.

 

[Nugatory]

Closed for a bit of moderation

 

[Nugatory]

This thread has been reopened. However, I have to remind everyone that the point of this thread is to discuss the article by @A. Neumaier. Arguments and disagreements with its content should be based on experience with the computations that he describes, not non-specialist and popular presentations.

 

[A. Neumaier]

any misconceptions related to Hawking radiation and virtual particles? As I recall, it was in the 1970s when I attended a presentation at MIT by Hawking describing his concept of black hole radiation based on the creation of particle pairs [...]

I just learned from a discussion on http://chat.stackexchange.com/rooms/71/the-h-bar that [quoting ACuriousMind, bold is his]

Hawking's original article contains the "virtual particle analogy" with an explicit warning that that is not the reason! It says: "One might picture this negative energy flux in the following way. [virtual particles, blah, blah]. It should be emphasized that these pictures of the mechanism responsible for the thermal emission and area decrease are heuristic only and should not be taken too literally."

Indeed, Hawking's original article gives on p.4 the following version of the fairy tale, including the caveat at the end:

One might picture this negative energy flux in the following way. Just outside the event horizon there will be virtual pairs of particles, one with negative energy and one with positive energy. The negative particle is in a region which is classically forbidden but it can tunnel through the event horizon to the region inside the black hole where the Killing vector which represents time translations is spacelike. In this region the particle can exist as a real particle with a timelike momentum vector even though its energy relative to infinity as measured by the time translation Killing vector is negative. The other particle of the pair, having a positive energy, can escape to infinity where it constitutes a part of the thermal emission described above. The probability of the negative energy particle tunnelling through the horizon is governed by the surface gravity K since this quantity measures the gradient of the magnitude of the Killing vector or, in other words, how fast the Killing vector is becoming spacelike. Instead of thinking of negative energy particles tunnelling through the horizon in the positive sense of time one could regard them as positive energy particles crossing the horizon on pastdirected world-lines and then being scattered on to future-directed world-lines by the gravitational field. It should be emphasized that these pictures of the mechanism responsible for the thermal emission and area decrease are heuristic only and should not be taken too literally.

In the discussion mentioned above, yuggib also mentioned an (idealized, but within the idealization fully rigorous) derivation by Fredenhagen and Haag.

 

[Haelfix]

At the heart of this is a little bit of philosophy. Do you prefer an ontology based on the concept of states, or do you prefer an ontology based on Feynman diagrams.

The real answer is that neither quite works in QFT, the Feynman diagram ontology for all the reasons listed here, the state ontology b/c no Hilbert space has ever been constructed for interacting quantum fields in 3 + 1 dimensions (bound states and states in a confining phase are also mathematically difficult to deal with).

So I disagree a little with the thrust of this thread. I would say one uses the concept that is useful to solve problems with. Practicing physicists have absolutely no problem talking about the Dirac sea for instance, even though it's clear the concept has limited validity. In particle physics, it is often useful to visualize things with the Feynman diagram ontology, although again it depends the details of the circumstance. It works great for an Abelian theory like QED, less useful for something like QCD.

 

[A. Neumaier]

the state ontology b/c no Hilbert space has ever been constructed for interacting quantum fields in 3 + 1 dimensions

This doesn't mean that it doesn't exist, only that the mathematical tools to prove its existence with full rigor are not yet strong enough. The concept of an S-matrix would be completely meaningless if the Hilbert space wouldn't exist. Most physics is not mathematically rigorous, but nevertheless believed to be correct.

it is often useful to visualize things with the Feynman diagram ontology

I never disputed that. Diagrams are there to illustrate, not to provide causal agents (as virtual particles are considered in the view for lay people). In the insight article under discussion I had stated explicitly:

The only way the usual dynamical language for virtual particles is justified by the theory is as purely figurative analogy in ”virtual reality”, useful for informal talk about complicated formulas and for superficial summaries in lectures capturing the imagination of the audience. This has to be kept in mind when reading in professional scientific publications statements involving virtual particles. Otherwise many statements become completely misleading, inviting a magical view of microphysics and weird speculation, without the slightest support in theory or experiment.

 

[vanhees71]

At the heart of this is a little bit of philosophy. Do you prefer an ontology based on the concept of states, or do you prefer an ontology based on Feynman diagrams.

The real answer is that neither quite works in QFT, the Feynman diagram ontology for all the reasons listed here, the state ontology b/c no Hilbert space has ever been constructed for interacting quantum fields in 3 + 1 dimensions (bound states and states in a confining phase are also mathematically difficult to deal with).

So I disagree a little with the thrust of this thread. I would say one uses the concept that is useful to solve problems with. Practicing physicists have absolutely no problem talking about the Dirac sea for instance, even though it's clear the concept has limited validity. In particle physics, it is often useful to visualize things with the Feynman diagram ontology, although again it depends the details of the circumstance. It works great for an Abelian theory like QED, less useful for something like QCD.

What's the difference? Feynman diagrams are just a mathematical notation for the perturbation series for S-matrix elements (in the original version applied to "vacuum QFT", i.e., for treating the scattering of two particles (or decays of one particles) into a few other particles). Underlying is just the formalism of QFT, as has been demonstrated by Dyson in 1948ff.

As a practitioner of QFT, including equilibrium and non-equilibrium relativistic many-body QFT, I've never ever used nor had the desire to use the Dirac sea, which doesn't exist but is renormalized away at the very first steps in building up the formalism employing "normal ordering" to define local observables of (asymptotic) free fields.

I also don't know, what you mean by "Feynman diagram ontology". Is there in ontology implied by Leibniz's vs. Newton's notation of calculus or any other mathematical notation used in physics? Imho this is an example for philosophical mumbo-jambo that discredits philosophy in the opinion of many scientists!

 

[Haelfix]

Hi Vanhees,

I've never ever used nor had the desire to use the Dirac sea, which doesn't exist but is renormalized away at the very first steps in building up the formalism employing "normal ordering" to define local observables of (asymptotic) free fields!

What you say is true, nevertheless, the concept is still utilized all the time by colleagues in solid state physics as a sort of effective description. Indeed it is even utilized more broadly as a cursory google scholar search shows. The point is convenient fictions are ubiquitous in physics.

Feynman diagrams are just a mathematical notation for the perturbation series for S-matrix elements (in the original version applied to "vacuum QFT", i.e., for treating the scattering of two particles (or decays of one particles) into a few other particles). Underlying is just the formalism of QFT, as has been demonstrated by Dyson in 1948ff

I certainly never suggested the contrary.

I also don't know, what you mean by "Feynman diagram ontology". Is there in ontology implied by Leibniz's vs. Newton's notation of calculus or any other mathematical notation used in physics? Imho this is an example for philosophical mumbo-jambo that discredits philosophy in the opinion of many scientists!

Perhaps philosophy is a poor word choice and an example would make the point. When we talk about a background like Higgs to WW(star), what we might have in mind is a decay that first produces a W and a virtual W, and then is completed to a final state which might be something like l l v v. The intermediate state is just going to influence the final amplitude much like an extra slit does in the interpretation of the final result of a double slit experiment. However if you are completely dogmatic about the state interpretation, the first part of the sentence is nonsense as one of the W's is offshell and carries no interpretation as a particle state. Despite this, hundreds of papers analyzing backgrounds has been written about this exact thing. Ok?

So now if you follow this convenient fiction down the rabbit hole, you might ask, well what we measure is actually not even those final leptons (and missing energy). What we measure is a voltage drop after some long chain of indirect emissions, absorptions and inferences. So the curious student would then say.. Wait a second, since what we measure is not those leptons but they in fact have a finite lifetime within the detector, why couldn't I write the whole thing as a larger diagram where the leptons are in fact internal lines of a bigger diagram? What's the difference between doing something like this and talking about virtual W's?

That is the sort of chain of reasoning (and ontology) that Profesor Neumaier I think would reject, for reasons given in this thread and countless others, but my point was that it is sometimes useful to talk about decays like W Wstar.

At the end of the day, philosophy enters into this b/c things we measure don't exactly correspond mathematically to idealized Von Neuman measurements (with perfect response functions) of S Matrix elements in an infinitely large box off in the infinite future. The mathematics is unambigous, but how you apply the math to the physics does correspond to implicit choices.

 

[Haelfix]

This doesn't mean that it doesn't exist, only that the mathematical tools to prove its existence with full rigor are not yet strong enough. The concept of an S-matrix would be completely meaningless if the Hilbert space wouldn't exist. Most physics is not mathematically rigorous, but nevertheless believed to be correct.

Yes, I agree although I do prefer not to prejudice myself too much. The failure of things like AQFT likely means the tools we use are wrong, but it could also mean that the theory actually doesn't exist or even alternatively a qft in 3+1 might exist but doesn't correspond to anything physical (much like trying to make the Navier-Stokes equation is essentially an academic exercise, as atomic structure enters into the picture at a certain scale).

 

[A. Neumaier]

that it is sometimes useful to talk about decays like W Wstar.

If it is sometimes useful to talk about a decay like this in terms of virtual mythology, could you please be more specific about what its usefulness consists of?

Unstable particles (with complex mass) are very real - in the present case observable as a resonance. I cannot see what's the use of treating them as virtual particles (with real mass). One trades a clear physical picture with a clear mathematical representation (as complex pole of certain cross sections ) for a fuzzy picture in virtual reality without any substance .

After the trade, there is no longer a way of talking about half-life (an essential property an unstable particle) except in terms of a vague reference to an alleged uncertainty principle that would allow particles to pop in and out existence for a split fraction of a picosecond.

So where is the usefulness?

[Added May 2: Part of the subsequent discussion in posts #101-#152, partly based on a misunderstanding on my part, is resolved in post #153.]

 

[A. Neumaier]

W Wstar

The physical way of handling $W^*$ is not to represent it as a virtual particle but to treat it as a transition state.
This is a well-developed science in the case of chemical and nuclear reactions, and it applies in nprinciple down to the smallest scales. See, e,g,,
Hänggi, P., Talkner, P., & Borkovec, M. (1990). Reaction-rate theory: fifty years after Kramers. Reviews of modern physics, 62(2), 251.

There is no sound reason at all that would justify confusing transition states with virtual particles.

 

[vanhees71]

Hi Vanhees,

What you say is true, nevertheless, the concept is still utilized all the time by colleagues in solid state physics as a sort of effective description. Indeed it is even utilized more broadly as a cursory google scholar search shows. The point is convenient fictions are ubiquitous in physics.

In solid-state physics you usually have a Fermi sea, and the advantage of the Fermi's sea over Dirac's is that the former really exists ;-)).

 

[vanhees71]

Unstable particles (with complex mass) are very real - in the present case observable as a resonance. I cannot see what's the use of treating them as virtual particles (with real mass). One trades a clear physical picture with a clear mathematical representation (as complex pole of certain cross sections ) for a fuzzy picture in virtual reality without any substance .

Yes, but it is important to keep in mind that resonances are, strictly speaking, not asymptotic free states, and it is sometimes even important to tell, how you define there properties in terms of the cross sections, where they appear as "resonance peaks". An example is the $\rho$ meson, which in the particle data book is defined (!) as the resonance appearing in $\mathrm{e}^+ \mathrm{e}^{-} \rightarrow \pi \pi$ or in $\tau \rightarrow \pi\pi \nu$ in the invariant-mass region of the $\pi \pi$ around 770 MeV.

If you work in my field of relativistic heavy-ion collisions, the light vector mesons also occur in dilepton emission rates in terms of effective hadronic models, describing the electromagnetic transition form factors of hadrons (most importantly baryon resonances), the socalled vector-meson dominance model. In other words, here the $\rho$ appears as an intermediate state in the Dalitz decay of hadrons, and there its shape of course looks completely different. To take a not too narrow resonance as a kind of "particle" can lead to many misunderstandings and a lot of discussion. The $\rho$ meson, however, is not that narrow with a mass of around 770 MeV and a width of about 150 MeV. So one should keep the meaning of resonances as compared to "particles" in mind to avoid such misunderstandings! See, e.g., an informal presentation I've given some time ago for discussing right this:

http://th.physik.uni-frankfurt.de/~hees/publ/tud-dileps15.pdf

 

[A. Neumaier]

it is sometimes even important to tell, how you define there properties in terms of the cross sections, where they appear as "resonance peaks".

This is covered by the notion of a transition state - see post #101. They are asymptotic states in a complex deformation of the Hilbert space, e.g., by what is called complex scaling. I covered this in the companion Insight article to that under discussion. I updated the discussion there to include the references in posts #101 and #103.

 

[mfb]

The physical way of handling $W^*$ is not to represent it as a virtual particle but to treat it as a transition state.

So where is the border? Is the W in a pion decay still a transition state? What about the Ws in neutral meson mixing? What about gluons in a NLO Feynman diagram?

 

[A. Neumaier]

So where is the border? Is the W in a pion decay still a transition state? What about the Ws in neutral meson mixing? What about gluons in a NLO Feynman diagram?

An intermediate state in a reaction (happening in space and time) is a transition state as long as it can only be detected as a resonance (i.e., if it does not travel far enough for its trajectory to be reconstructible from its decay products.

An intermediate line in a Feynman diagram is always a virtual particle. There is no border between objects having short-living states (resonances) and objects having no state at all (virtual particles), since these kinds of objects occupy completely different worlds. It would be like asking for the border between real people and characters in a fiction movie.

 

[mfb]

An intermediate line in a Feynman diagram is always a virtual particle.

The W* in H->WW* -> ... appears as intermediate line in a Feynman diagram (unless we have different understandings of "intermediate line"), and does not appear as proper resonance in any mass plot, so why is this a transition state? Same for pion decays.
You are contradicting yourself here.

 

[DarMM]

Resonances are still states in the Hilbert Space though. In non-relativistic quantum mechanical models you can explicitly solve, or in QFTs which have been rigorously studied to the point of full analytic control of at least some of their multi-particle states, you can see that resonances are actual physically occurring states. They simple tend to "quickly" evolve into other states.

Virtual particles however don't correspond to anything in the Hilbert space, they're simply pictorial labels on terms appearing in perturbative integrals.

 

[A. Neumaier]

welcome back, DarMM; I was missing you!

 

[A. Neumaier]

The W* in H->WW* -> ... appears as intermediate line in a Feynman diagram (unless we have different understandings of "intermediate line"), and does not appear as proper resonance in any mass plot, so why is this a transition state? Same for pion decays.
You are contradicting yourself here.

Maybe I was irritated by the star, which typically denotes a transition state; I was talking in general, not about $W^*$ in particular. . Could you please give a reference to a paper where this particluar process is discussed? Then i can tell you more.

 

[mfb]

H -> WW* -> whatever? It is one of the standard Higgs decays. The experimental papers have nice collections of references: CMS, ATLAS 1, ATLAS 2

 

[samalkhaiat]

Maybe I was irritated by the star, which typically denotes a transition state; I was talking in general, not about $W^*$ in particular. . Could you please give a reference to a paper where this particluar process is discussed? Then i can tell you more.

I don’t know your purpose of creating this unnecessary hostile environment against necessary field theory concept.
QFT deals with on-shell states as well as off-shell states. Even though the off-shell states do not trigger our detectors, their existence must be accounted for in order to explain the stuff we see in the detectors. Furthermore, it is now an experimental fact that baryons contain (beside their valence quarks) a sea of virtual quarks and gluons. Even worse for you, enormous experiments confirmed that the sea quarks of the proton have more $\bar{d}$ than $\bar{u}$! Indeed, this flavour asymmetry has been measured [1-4] to be $\bar{d} - \bar{u} = 0.118 \pm 0.012$.

And, to throw more stones on your unnecessary use of language, the “meson cloud” model [5-6] is the best model we have that can explain the above mentioned proton sea quarks flavour asymmetry. The calculations can be done even with no reference to perturbation theory.


[1] Towell R. S. et al.(FNAL E866/NuSea Collaboration), Phys.Rev.D,(2001),64, 052002.
[2] Ackerstaff K. et al.(HERMES Collaboration), Phys.Rev.Lett.(1998), 81, 5519.
[3] Arneodo M. et all. (New Muon Collaboration), Phys. Rev. D,(1994), 50, R1.
[4] Baldit A. et al. (NA51 Collaboration), Phys. Rev. Lett. B,(1994), 332, 224.
[5] Garvey G.T, Peng J-C, Prog. Part. Nucl. Phys,(2001), 47, 203.
[6] Julia-Diaz B, Riska D. O, Nucl. Phys. A,(2006), 780, 175-186.

 

[DarMM]

Furthermore, it is now an experimental factthat baryons contain (beside their valence quarks) a sea of virtual quarks and gluons.

Where has this been proven? There are solvable 2D model field theories where perturbatively a certain state looks like the Lagrangian particles* plus a sea of virtual particles, but non-perturbatively is simply a state, not containing this "sea". I don't see how protons are different.

*By which I mean one-particle states of the Lagrangian fields.

 

[DarMM]

QFT deals with on-shell states as well as off-shell states. Even though the off-shell states do not trigger our detectors, their existence must be accounted for in order to explain the stuff we see in the detectors.

Yes, in the usual formalism they are necessary, but that doesn't mean they exist. For instance in the usual formalism of GR the Christoffel symbols are necessary, but that doesn't mean there are physical "Christoffel waves" or "Christoffel fields".

 

[samalkhaiat]

Where has this been proven? There are solvable 2D model field theories where perturbatively a certain state looks like the Lagrangian particles* plus a sea of virtual particles, but non-perturbatively is simply a state, not containing this "sea". I don't see how protons are different.

*By which I mean one-particle states of the Lagrangian fields.

What are you talking about? What proof has to do with experimentally confirmed fact? And, why did you need to bring nurealistic 2D models into the disscussion?
Read the paper I mentioned first, then you understand what i was talking about.

 

[DarMM]

What are you talking about? What proof has to do with experimentally confirmed fact?

I don't mean mathematically proven, I mean where has it been experimentally demonstrated, I just used "proven" colloquially.

And, why did you need to bring nurealistic 2D models into the disscussion?

To show that what a QFT looks like perturbatively does not indicate its true behaviour. If you don't like it though, why not take 4D QCD on a lattice. Here the proton emerges as simply a state, no sea of virtual gluons.

 

[samalkhaiat]

I don't mean mathematically proven, I mean where has it been experimentally demonstrated, I just used "proven" colloquially.

If you are not in the game, then just look at the following:
[1] Towell R. S. et al.(FNAL E866/NuSea Collaboration), Phys.Rev.D,(2001),64, 052002.
[2] Ackerstaff K. et al.(HERMES Collaboration), Phys.Rev.Lett.(1998), 81, 5519.
[3] Arneodo M. et all. (New Muon Collaboration), Phys. Rev. D,(1994), 50, R1.
[4] Baldit A. et al. (NA51 Collaboration), Phys. Rev. Lett. B,(1994), 332, 224.

To show that what a QFT looks like perturbatively does not indicate its true behaviour. If you don't like it though, why not take 4D QCD on a lattice. Here the proton emerges as simply a state, no sea of virtual gluons.

Lattice QCD could not account for many observed facts, because of the ambiguous treatment of fermions. Your computer can not work with Grassmann numbers.

 

[DarMM]

Lattice QCD could not account for many observed facts, because of the ambiguous treatment of fermions. Your computer can not work with Grassmann numbers.

Computers can work with Grassmann numbers, they're just slow at doing so due to how the Grassmann algebra functions.
Plus it's not relevant to the discussion, in lattice QCD the proton is just a state, it isn't composed of a sea of particles. In perturbative lattice QCD, just as in perturbative continuum QCD, the proton is valence quarks + sea of quarks. This suggests very strongly, as it remains true at arbitrary lattice spacing, that in nonperturbative continuum QCD the proton is just a state as well.

If you are not in the game, then just look at the following:
[1] Towell R. S. et al.(FNAL E866/NuSea Collaboration), Phys.Rev.D,(2001),64, 052002.
[2] Ackerstaff K. et al.(HERMES Collaboration), Phys.Rev.Lett.(1998), 81, 5519.
[3] Arneodo M. et all. (New Muon Collaboration), Phys. Rev. D,(1994), 50, R1.
[4] Baldit A. et al. (NA51 Collaboration), Phys. Rev. Lett. B,(1994), 332, 224.

I had a look at them, I don't see them confirming what you are saying. They just show that nucleons are heavier than simple quark models suggest. This doesn't mean QCD depicts the proton as a sea of virtual quarks, or that such a sea has been observed.

 

[DarMM]

welcome back, DarMM; I was missing you!

Thanks A. Neumaier, kind of you to say. I'm looking forward to getting back into the forum.

 

[samalkhaiat]

Computers can work with Grassmann numbers, they're just slow at doing so due to how the Grassmann algebra functions.

Really? I must be an illiterate then. For your information, when dealing with fermions there are 2 kinds of problem: (1) A straightforward discretization using a chiral invariant action always leads an action which when $a \to 0$ produses a spectrum with twice as many fermions as possessed by the original theory. Various lattice actions which avoid this problem have been suggested, the most popular are the Wilson and the Kogut-Susskind models. These give up explicit chiral invariance for non-zero lattice spacing, a rather worrying matter given that chiral invariance is an important approximate symmetry of nature. (2) In the path integral formulation, which underlies the whole lattice method, the “classical” fermion fields are not true commuting numbers. They are non-commuting numbers, so cannot be directly simulated on a computer. However, it is possible to formally integrate out the fermion fields and thereby transmute the problem into one of inverting Dirac operator. In practice, this means inverting a very large matrix, so that computer time becomes a serious issue. For this reason, most people replace the Dirac operator by the unit operator, which simply corresponds to eliminating all fermion-antifermion loop diagrams. This is, in the lattice-people language, referred to as the quenched approximation. So, you might as well claim that fermions don't exist because we can get rid of them in the quenched approximation! Give yourself a break for goodness sake.

I had a look at them, I don't see them confirming what you are saying.

Are you accusing me of making up a story?

They just show that nucleons are heavier than simple quark models suggest. This doesn't mean QCD depicts the proton as a sea of virtual quarks, or that such a sea has been observed.

Really, is that all? Look, I told you something and asked to READ at least one of the 4 paper.
The title of [1] : Improved measurement of the $\bar{d}/ \bar{u}$ asymmetry in the nucleon sea.
From the abstract of [1]:
From these data, the ratio of down antiquark $\bar{d}$ to up $\bar{u}$ antiquark distributions in the proton sea is determined over a wide range in Bjorken-x.These results confirm previous measurements by E866 and extend them to lower x. From these data, $\bar{d} - \bar{u}$ and $\int (\bar{d} - \bar{u}) dx$ are evaluated for 0.015< x < 0.35 .

Did you read this part? Did you ask yourself why should there be a $\bar{d}$ and a $\bar{u}$ in the proton?