Misconceptions about Virtual Particles - Comments

[A. Neumaier]

It makes absolutely no sense to argue about "existence" of either "real" or "virtual" particles, it is subjective and context-dependent

With such an attitude it makes no sense to argue about anything since language and its use is always subjective and context-dependent.

But science consists in restricting the language to a precise enough usage so that things can be discussed objectively, independent of the little subjectivity and context dependence left, which is now confined to agreeing to a common set of conventions. My article ”The Physics of Virtual Particles” collected these common conventions as they are written in the standard books on the subject.

Of course one can ignore conventions - but then one loses the common cultural basis that enables objectivity.

 

[Collin237]

But if real particles go in, and real particles come out, and if it's valid to say the real particles have position and momentum, then how can it not be valid to say there are incoming and outgoing rays in spacetime, and a region where they meet?

The distinction between physics and philosophy exists only in college floor-plans. Everyone who studies physical equations speculates on what they mean -- even you -- and deserve respect as fellow thinkers. They may be wrong, but they're not worse than wrong.

 

[RockyMarciano]

With such an attitude it makes no sense to argue about anything since language and its use is always subjective and context-dependent.

This has nothing to do with attitude, it is about the physics. What I'm saying is that your approach is as misleading as the naive talk about virtual particles. In short, you have interactions to describe and in order to do it there are certain mathematical abstractions and calculational devices that you have to use. In order to have some visual intuition on these mathematical abstractions you can view them in terms of particles, real and virtual, since the math that they both are substituting graphycally is necessary for the current state of the theory.

So it strikes as quite odd to give any of those parts of the graphic description of the mathematics any ontological sense or existence in detriment of the other. In fact none of them exist to the extent that they are just graphical support for the mathematical abstractions needed to obtain the predicitions, but if for whatever reasons one were to give them some ontological meaning it would have to include both external and internal lines as both are needed to describe a Feynman diagram.

The calculated predictions of the interaction description include both, and what is really naive is identifying the detections with the external lines only just because in the diagrams they appear as the inputs and outputs, that is really mistaking a graphical illustrationof a perturbative calculational device with the actual physics.

 

[RockyMarciano]

But if real particles go in, and real particles come out, and if it's valid to say the real particles have position and momentum, then how can it not be valid to say there are incoming and outgoing rays in spacetime, and a region where they meet?

The validity of this description is already hard to impose to simple non-relaticvistic quantum mechanics although it sort of work for simplified semiclassical description with one particle. It completely breaks when you get to interacting quantum field theory.

The distinction between physics and philosophy exists only in college floor-plans.

You'll see that it exists in PF forums too ;)

 

[A. Neumaier]

how can it not be valid to say there are incoming and outgoing rays in spacetime, and a region where they meet?

It is valid to say that they travel on incoming and outgoing rays in spacetime while they are far apart, since this is a good semiclassical description of the free particles in a paraxial approximation.

But when they come close, the semiclassical description breaks down and one needs full quantum field theory to describe what happens. The state of the system is now a complicated state in a Hilbert space that no one so far was able to characterize; it is only known (Haag's theorem) that it cannot be the asymptotic Fock space describing the noninteracting particles. Since it is not a Fock space, talking about particles during the interaction makes no longer sense - the quantum fields of which the particles are elementary excitations become very non-particle like.

After the collision products separated well enough, the semiclassical description becomes feasible again, and one can talk again about particles traveling along beams.

Thus the field picture is always valid, and the particle picture is appropriate except in the region where they would meet. The behavior in the latter is effectively described by the S-matrix, which is a reasonable approximation if the collision speed is high enough, so that one can take the in- and outgoing particles as being at time $-\infty$ and $+\infty$, and ignores what happens at finite times during the encounter.

Untangling the S-matrix using bare perturbation theory replaces the real-time dynamics of the quantum fields by an non-temporal infinite sum of contributions of multivariate integrals depicted in shorthand by Feynman diagrams showing a web of virtual particles. Most of these contributions are also infinite and physically meaningless. The renormalization process turns the sum of all diagrams with a fixed number of loops into finite numbers whose sum over not too high orders (the series is asymptotic only) has again an (approximate) physical meaning, but the connection to the intuitive pictures with the lines (the alleged world lines of virtual particles, in the popular myth) gets completely lost in the renormalization process.

Nothing here resembles anything like a process in time - described by the theory and the computations is only a probabilistic model of the black box in-out behavior.

 

[A. Neumaier]

to give them some ontological meaning

requires to be able to assign to them a state, since only that gives the conceptual basis for assigning probabilities to events in space and time. It is impossible to assign states to virtual particles (internal lines), while states are always assigned to real particles (external lines).
This is the physics. It has nothing to do with physical intuition or subjective or context-dependent side issues that you try to bring to bear on the problem.

 

[RockyMarciano]

requires to be able to assign to them a state, since only that gives the conceptual basis for assigning probabilities to events in space and time. It is impossible to assign states to virtual particles (internal lines), while states are always assigned to real particles (external lines).

You are again relying on the superficial appearance of a graphic diagram. The key here is that to obtain any kind of precise prediction of what is to be measured, and that is what we do with those diagrams in physics, you are using renormalization that allows you to keep assigning probabilities to the different interactions and this uses the math as much of what is represented as internal lines(the perturbation in the perturbative process), as the math that represents the external lines(the perturbed part). You shouldn't go back to the states assigning of nrqm because as you said in a previous state you no longer have a Fock space as in the free theory. So the events in spacetime are mathematically relegated to fixed-points describing the interaction at some order.

It has nothing to do with physical intuition or subjective or context-dependent side issues that you try to bring to bear on the problem.

Certainly, when you are ready to let go of a false virtual/real dilemma.

 

[mfb]

After the collision products separated well enough, the semiclassical description becomes feasible again, and one can talk again about particles traveling along beams.

What is "well enough"? That is exactly the arbitrary cutoff discussed.

Also, "can" is exactly the right word: We can use the description. We don't have to.

 

[A. Neumaier]

What is "well enough"? That is exactly the arbitrary cutoff discussed.

It depends on the accuracy with which you want to rely on the semiclassical description.

Mathematically speaking, it means close enough to infinity, so that the error in working with the S-matrix is less than the error in the semiclassical approximation. In a reaction rate calculation, the intermediate states can be treated as real when the total reaction rate factors to the intended accuracy into an integral over the product of the reaction rates for the partial processes to and from the intermediate states. Sometimes one can make both calculations and then sees whether or not the intermediate particles can be treated as real.

But there remain always these qualitative and somewhat ambiguous statements when it comes to deciding when to use which approximation. That's why we have these terms in the language to express fuzzy concepts.

 

[mfb]

Well, that was my point earlier, and I think also what Collin and nikkkom mentioned. There is no sharp line between things we call virtual particles and things we call real particles.
Technically you can treat a muon produced in cosmic rays or a proton produced in an LHC collision as virtual particle (which means: not treating it as particle). It doesn't make sense, but you can, and it leads to the same predictions if you do it correctly.

 

[nikkkom]

But when they come close, the semiclassical description breaks down and one needs full quantum field theory to describe what happens.

Define "close".
Two electrons repelling each other (in term of Feynman diagrams, "by exchanging virtual photons") over a separation of, say, one kilometer, still involves virtual photons.

There is no cutoff. It would be illogical to declare that unstable particles up to particular short lifetime are virtual, but above it they can be either real or virtual.

Maybe "virtualness" should not be seen as a boolean quantity, "yes or no". It can be more useful to explain it this way: with increasingly smaller scales and higher energies, the notion of a "particle" with definite energy, position, momentum, etc is increasingly inaccurate. The short-lived particles are "increasingly virtual".

 

[Collin237]

the notion of a "particle" with definite energy, position, momentum, etc

What do you mean by "definite"? Obviously a particle's position and momentum are fuzzy just by dint of being wave operators (by the wave interpretation of the HUP). Do you mean this as opposed to also having another kind of fuzz?

 

[A. Neumaier]

Two electrons repelling each other (in term of Feynman diagrams, "by exchanging virtual photons") over a separation of, say, one kilometer, still involves virtual photons.

This doesn't change the status of the electrons from real to virtual.

 

[A. Neumaier]

"virtualness" should not be seen as a boolean quantity, "yes or no". It can be more useful to explain it this way: with increasingly smaller scales and higher energies, the notion of a "particle" with definite energy, position, momentum, etc is increasingly inaccurate. The short-lived particles are "increasingly virtual".

No, definitely not. Virtualness is a matter of where something appears in a Feynman diagram, hence none-or-all. It is meaningless to say that a particle is described to 90% by an external line and to 10% by an internal line. Virtual particles are by definition (in any textbook where they are defined) terminology for internal lines of a diagram.

 

[A. Neumaier]

as virtual particle (which means: not treating it as particle). It doesn't make sense, but you can, and it leads to the same predictions if you do it correctly.

You can as well treat any physical system as a black box, even classically. This doesn't make the content of the black box less real. It just means that one is modeling at a lower resolution.

Thus, making my account precise, whenever the factorization is possible, the particle is real, even when you choose to take the black box road.

However, one cannot go the other way with virtual particles - you cannot make them real by going to a higher resolution, since the calculations then lead to different predictions.

 

[Collin237]

So on the one hand you claim that the theory doesn't work unless you define virtual particles this way. But on the other hand you claim that most of the community that studies the theory and performs the experiments that confirm it has been led astray from this definition. You can't have it both ways.

 

[A. Neumaier]

So on the one hand you claim that the theory doesn't work unless you define virtual particles this way. But on the other hand you claim that most of the community that studies the theory and performs the experiments that confirm it has been led astray from this definition. You can't have it both ways.

No. I only claim that the community is sloppy in their use of the terminology, and that there is a higher standard (defined in the textbooks) worth paying attention to, since it reduces ambiguity and hence improves the communication quality. Sloppy usage of terms is very common in many branches of science; so this is not a criticism specific to experimental particle physics.

 

[Collin237]

Sloppy usage of terms is very common in many branches of science

So are books that resolve the ambiguities. But those books are not meta-studies of textbook usage; they are the textbooks themselves.

The higher standard is commitment to honestly understanding the theory as established by experimental verification. The textbooks don't define the standard. They follow it, or else get roundfiled.

 

[vanhees71]

It's not that difficult. Any textbook about QFT starts with analyzing free fields, and for these free fields everything can be solved analytically. It turns out that for free fields there is a particle interpretation in the sense of a complete set of states with definite particle number, where the particle number can take any integer (including 0) value. Given a one-particle basis (for massive particles usually defined by the Lorentz boosts of a particle at rest with definite spin-$z$ component or for massless particles by the Lorentz boosts of the quantum with momentum in $z$ direction and definite helicity $\pm s$), the complete Hilbert space is spanned by the occupation number eigenstates for these single-particle states, and depending on the integer or half-integer spin you necessarily must quantize the fields as bosons or fermions, respectively (spin-statistics theorem following from microcausality and boundedness of the Hamiltonian). In this way you get a definite particle (or massless quantum) interpretation of QFT. This is all pretty straight forward and just a bit of more or less complicated math of the representation theory of the proper orthochronous Lorentz group and some thought about the discrete factors of the rest of the Lorentz group (parity, time reversal, and charge conjugation).

Now the trouble starts when you switch on interactions. Here, the particle interpretation breaks generally down, and (except in some academic toy cases in low space-time dimensions) you can't solve the problem to construct the Hilbert space out of the Lagrangian/Hamiltonian and symmetries as in the free case. Usually, what's done is to restrict oneself to the socalled S-matrix that describes the transition probabilities from an asymptotically free initial to another asymptotically free final state, i.e., you start usually with two free particles and ask what's the probability (per unit time and unit volume) that these particles scatter to some final state with again asymptotic free particles, and you use perturbation theory to evaluate these transition probabilities. This evaluation is tremendously simplified by introducing the ingenious notation in terms of Feynman diagrams, which even suggest to interpret them as the "microscopic mechanism" of this scattering process. The important point is that one cannot take this intuition too far. The internal lines of Feynman diagrams, which are just a clever notation for the expressions of perturbation theory to get the S-matrix elements, are called "virtual particles", but that's a misnomer since even in the sense of perturbation theory, there's no way to interpret these mathematical expressions, the socalled free time-ordered propagator (which in vacuum QFT is identical with the Feynman propgator), as particles in any way. A more close to physics interpretation is indeed as in classical field theory (i.e., electrodynamics) to see it as a solution of the field equations describing the interactions leading to the scattering process whose S-matrix element you want to calculate. A proper physical interpretation in terms of particles are only given by the asymptotic free Fock states of the free theory, and these are represented exclusively by the external legs of S-matrix Feynman diagrams, and stand mathematically for certain coefficients in the plane-wave solutions of the corresponding free field equations.

Another complication is that as soon as you have massless quanta in the theory (e.g., photons in QED), the above given picture of asymptotic free particles is too naive, and one usually has to resum an infinite number of Feynman diagrams to get useful results (e.g., for bremsstrahlung in QED even at the tree level), i.e., you have to dress the "naive" plane-wave solutions of the free particles to describe the long-range interactions described by the massless fields/quanta. In other words the true "asymptotic free electron" in QED with it's own electromagnetic field around it is not fully described by the free solutions of the Dirac field, but in this picture is always surrounded by a "cloud of soft photons" or better said "coherent em. fields".

In short: The "particle interpretation" of relativistic QFT is much more involved than in non-relativistic QT or even suggested by the apparently "intuitive pictures" of Feynman diagrams.

 

[Collin237]

these mathematical expressions, the socalled free time-ordered propagator

Ah, now we're finally getting somewhere! Would you be willing to write a series of Insights about these expressions?

 

[vanhees71]

It's much easier to write manuscripts. Here's one:

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

 

[A. Neumaier]

So are books that resolve the ambiguities. But those books are not meta-studies of textbook usage; they are the textbooks themselves.

All textbooks on QFT define virtual particles via internal lines of Feynman diagram. There is no other definition. Sticking to this definition there is no ambiguity at all. Thus nothing is resolved. The sloppy usage happens outside of any sensible definitional framework!

 

[Collin237]

Why do you have what you call a "Thermodynamic Interpretation"? If there's no ambiguity, why don't you have a textbook like the one vanhees71 wrote, and gave me in a pdf just for the asking?

 

[A. Neumaier]

If there's no ambiguity, why don't you have a textbook like the one vanhees71 wrote, and gave me in a pdf just for the asking?

There are enough textbooks on quantum field theory, so I don't need to write my own. They all agree on the meaning of the notion of a virtual particle.

Why do you have what you call a "Thermodynamic Interpretation"?

My ''thermal interpretation'' is an interpretation of quantum mechanics in general, and the measurement problem in particular. I developed this since none of the present interpretations gives an interpretation fully compatible with the actual practice of using quantum mechanics - where many things - such as spectral lines, Z-boson masses, or electric fields) are measured that are impossible to capture with the Born interpretation underlying all previous interpretations.

But the thermal interpretation is completely independent of virtual particles. Most of quantum mechanics does not use the notion of virtual particles at all. Even in quantum field theory, this notion can be completely avoided - see the book Diagrammatica by Veltman (and my partial review of it in my insight article “Misconceptions about Virtual Particles“)

 

[Collin237]

Even in quantum field theory, this notion can be completely avoided

Lots of things can be avoided. I've read that the Beatles didn't use sheet music drafts to develop their songs.

But having found a way to get by without a formal technique doesn't justify calling it misconception that others who do use it are being sloppy about!

 

[vanhees71]

Well, all these quantities are measured with the corresponding measurement devices like spectrometers, particle detectors (for the Z-boson mass and width you measure dilepton spectra in various ways), etc. you find in the physics labs around the world. In physics in fact quantities are defined by giving appropriate (equivalence classes of) measurement protocols to quantitatively observe them. That's why they are called observables after all. Also there is nothing more needed concerning the application of the quantum-theoretical formalism (e.g., formulated as the representation of an observable algebra on Hilbert space, based on various symmetry principles which themselves are discovered by observation of conservation laws) than Born's rule, i.e., the minimal interpretation.

Where you need something like a "thermal interpretation" is when it comes to understand the overwhelming success of classical physics (including classical relativistic and non-relativistic mechanics, electrodynamics, and thermodynamics) to describe macroscopic systems. Here you need some coarse graining to describe macroscopic effective (relevant) degrees of freedom as (spatio-temporal) averages over many microscopic degrees of freedom.

 

[A. Neumaier]

Well, all these quantities are measured [...] as (spatio-temporal) averages over many microscopic degrees of freedom.

To avoid that this thread (about virtual particles) is polluted by a discussion of measurement issues I created a new thread answering this.

 

[Collin237]

However, one cannot go the other way with virtual particles - you cannot make them real by going to a higher resolution, since the calculations then lead to different predictions.

So? External lines become internal if the diagram is extended to show more interactions "surrounding" the scattering, but internal lines don't become external unless the diagram is changed by breaking a line. That's just basic topology. What does it have to do with "existence" vs "myth" or anything?

 

[A. Neumaier]

External lines become internal if the diagram is extended to show more interactions "surrounding" the scattering, but internal lines don't become external unless the diagram is changed by breaking a line.

In both case you get diagrams describing different situations, corresponding to calculations of different collision processes, compared to the original diagram.

 

[Collin237]

In both case you get diagrams describing different situations, corresponding to calculations of different collision processes, compared to the original diagram.

There are collision processes happening everywhere all the time. The vast majority of them occur without anyone situating or calculating them.

 

[A. Neumaier]

There are collision processes happening everywhere all the time. The vast majority of them occur without anyone situating or calculating them.

This doesn't change what I said. One can always ignore or coarse-grain things (unobserved things being very coarse-grained) without changing what happens. It is a big conceptual mistake to think of a sequence of collisions with particle worldlines in between as being a particular Feynman diagram, so that the worldlines would become internal lines of a diagram. Most paths in a complex Feynman diagram have a very different topology from those you'd get by a sequence of collisions, and their mathematics is completely different!

 

[Collin237]

What? The theory is non-extensible? Can someone corroborate this?

 

[A. Neumaier]

What? The theory is non-extensible? Can someone corroborate this?

My assertion was that the theory of properties of virtual particles (aka internal lines of Feynman diagrams aka integration variables of multivariate integrals) has very different properties from the theory of properties of systems of multiply colliding particles (aka systems with states changing upon collisions according to computable scattering statistics). Thus there is no way to mix them up.

 

[Collin237]

(aka systems with states changing upon collisions according to computable scattering statistics).

But wouldn't that be a collapse, i.e., an interpretational issue? Which, as I've seen oft repeated here, doesn't change the basic math?

I'm still waiting for someone else to corroborate.

 

[A. Neumaier]

But wouldn't that be a collapse, i.e., an interpretational issue? Which, as I've seen oft repeated here, doesn't change the basic math?

No. The Boltzmann equation is based on such a collision picture, and nothing ever collapses there. Collapse is related to the change of state of a few-particle system upon acknowledging a measurement as definite. But as you correctly observed, most collisions in nature are never observed. But they still happen, or the Boltzmann equation would not work.

Better learn the math rather than complaining about formal issues without understanding them!