Insights Misconceptions about Virtual Particles - Comments

[jtbell]

https://en.wikipedia.org/wiki/Force_carrier

It seems in one place it can be said that the field is a mathematical description of the particle and does not exist if an ACTUAL particle is not there.

Where exactly did you find what I put in bold face?

 

[A. Neumaier]

It seems physics is done which way is convenient at the time.

Talk about physics is indeed done in whatever way it seems convenient.

But the physics is not in the talk but in the formulas. The formulas are the same even when different people talk about them in different (more sloppy or more careful) ways. On the formal level you always have the fields, and sometimes you can interpret them as particles (with the same names as the fields) . But since particles are easier to visualize, one often prefers to use the particle language, knowing that it is not fully appropriate. This is deemed acceptable by many since anyway no talk can fully express the complexities studied in quantum mechanics.

Thus strictly speaking the gauge fields are the force carriers since manifestations of the fields cause the forces between particles (that are themselves field excitations). It is convenient to say that the gauge bosons mediate the forces. Here ''gauge bosons'' may still refer either to the gauge fields or the associated particles.

If one combines this with the virtual particle analogy, one can say without too much error that virtual gauge boson mediate the force (and hence serve as force carriers). The big mistake is made only when one takes the virtual particles as real objects moving in time rather than as graphical abbreviations of the formulas that allow one to calculate the forces.

 

[mfb]

It seems in one place it can be said that the field is a mathematical description of the particle and does not exist if an ACTUAL particle is not there.

That is certainly wrong.

Then again it seems that the field can exist EVEN if a particle does not show up, as in Higgs for example.

That is right.

It seems physics is done which way is convenient at the time.

Physics is not about "reality", it is about making good predictions, if different models can make the same good predictions then they are equally fine. In particular, the predictions are from quantum field theory, and QFT does not care about our words "particles" and "fields".

 

[ftr]

Where exactly did you find what I put in bold face?

That is certainly wrong.

How I understand QFT is that it is a generalization of QM wave function which itself has an unwieldy and controversial existence. Certain computations FROM the wavefunction can be interpreted as a physical outcome. And yet in QFT some of those are also become controversial like position. EVEN then the single particle state is only an approximation, DR A. Neumaier will tell you that. The uninterpretable "virtual particles" also point to the mathematical nature of fields.

I am not saying that it is wrong using them I just think there should be something that has a better picture.

 

[ftr]

More specificallyhttps://arxiv.org/ftp/arxiv/papers/1204/1204.4616.pdf

quote page 3
"Physics education is affected directly, and scientific literacy indirectly, by what textbooks say about wave-particle duality and related topics. To find out what textbooks say, I perused the 36 textbooks in my university's library having the words "quantum mechanics" in their title and published after 1989. 30 implied a universe made of particles that sometimes act like fields, 6 implied the fundamental constituents behaved sometimes like particles and sometimes like fields, and none viewed the universe as made of fields that sometimes appear to be particles. Yet the leading quantum field theorists argue explicitly for the latter view (Refs. 10-18). Something's amiss here."

 

[A. Neumaier]

It seems in one place it can be said that the field is a mathematical description of the particle and does not exist if an ACTUAL particle is not there. Then again it seems that the field can exist EVEN if a particle does not show up, as in Higgs for example.

The first sentence is nonsense. The field always exists (in the sense that one can in principle measure the field expectations anywhere). In the special case where the field primarily consists of one or more elementary excitations of the vacuum state it can be described approximately in terms of particles. For interacting fields, the particle interpretation is strictly valid (without approximation) only in an asymptotic sense - for times $t\to\pm\infty$.

Nevertheless, the particle terminology is frequently used in a pictorial way since it looks simpler and more intuitive than the field picture. The price to be paid for it is that the picture becomes highly misleading when taken literally.

 

[vanhees71]

How I understand QFT is that it is a generalization of QM wave function which itself has an unwieldy and controversial existence. Certain computations FROM the wavefunction can be interpreted as a physical outcome. And yet in QFT some of those are also become controversial like position. EVEN then the single particle state is only an approximation, DR A. Neumaier will tell you that. The uninterpretable "virtual particles" also point to the mathematical nature of fields.

I am not saying that it is wrong using them I just think there should be something that has a better picture.

If you refrain from too much speculation, aka "interpretation", the QM wave function (appropriate for a part of non-relativistic physics, where the particle numbers are strictly conserved) has a very clear meaning, providing the probabilities for the outcome of measurements via Born's Rule. From a physics point of view there's not more but also no less to it than that, and there's nothing controversial about it since this "minimal interpretation" is very well confirmed by all the very accurate experimental tests of QM we have available these days.

The same holds for relativistic QFT. Among physicists there's not much controversial about it. The perturbative evaluation of renormalized perturbation theory together with some resummation techniques and the use of renormalization-group methods as well as ab-initio calculations of the interacting theory on the lattice (for QCD) is also among the theories with the best confirmation by experiment ever (for some observables up to 12-16 significant digits!).

If you take out philosophical quibbles and stick to the physics part of QT (both non-relativistic and relativistic), it's a great success story without much controversies!

Of course there are open physical questions. Among them is a consistent description of gravity, applicable to observable effects (maybe even to find observables for quantum behavior related with gravity at all!), a perhaps related way to understand the observed values of the constants entering the standard model of elementary particle physics and standard cosmology, particularly the observed value for the cosmological constant/"dark energy" in the universe, a clear confirmation of the existence of "dark matter" and identification of corresponding "new particles" if they exist. So there's a lot to do in physics besides the philosophical muttering, too often discussed in this subforum, and I'm very sure that these open questions won't be solved by philosophical speculations but by the usual solid work of experimental and theoretical physicists, i.e., by model building based on solid observational input, as it has been in the last ~400 years of modern science since Galileo and Newton!

 

[ftr]

The first sentence is nonsense. The field always exists (in the sense that one can in principle measure the field expectations anywhere).

How do you do that.

Do each electron has its own field, or all the electrons in the universe share one field.

How can a specific point in space-time carry all the values of the fields of all known particles since these are suppose to be real and intrinsic and not effective like temperature or pressure.

 

[vanhees71]

There's one electron field (Dirac field) in the standard model of elementary particle physics. Why should there be more than one? There's a well-defined kind of quantum field for any particle species in the standard model (leptons, quarks, gauge bosons, and Higgs bosons).

Also, what's the problem to have several fields defined in space-time? In my room the air has a temperature, a velocity field, a density, a pressure field. This makes a lot of fields, which all can be measured at any point in space and at any time. Then there's also light in my room, i.e., an electromagnetic wave field, which I can measure at any point in space and time, if I wish. That's all. There's nothing mysterious in this.

Of course, quantum fields and observables expressed in terms of them are at a higher level of abstraction than these classical fields.

Perhaps I don't understand your questions right...

 

[ftr]

There's one electron field (Dirac field) in the standard model of elementary particle physics. Why should there be more than one? Perhaps I don't understand your question right...

Does this one electron field has a value at a specific space time representing all the electrons in the universe or has multiple values for each electron.

 

[vanhees71]

No, because it's a quantum field. Itself it is not observable in the sense that it has a classical limit, but only quantities like the four-current density, energy-momentum density, etc. define observables and have a classical limit.

That's different only for the electromagnetic field, which has a classical limit called classical electrodynamics.

 

[ftr]

No, because it's a quantum field. Itself it is not observable in the sense that it has a classical limit, but only quantities like the four-current density, energy-momentum density, etc. define observables and have a classical limit.

That's different only for the electromagnetic field, which has a classical limit called classical electrodynamics.

I am talking about that bold capital psi that we see in Lagrangian, can you measure those at specific space-time points directly.
when you solve for it for one problem and you go and measure it(assume you can) do you see that value. If another physicist solve's another problem does he measure his own value at that same point in space time. how does that work, they can't have different values if the one field is real.

 

[A. Neumaier]

he measure his own value at that same point in space time.

There cannoit be two physicists at the same point in space and time. All measuring physicists measure the fields they measure essentially at their position and time.

 

[vanhees71]

I am talking about that bold capital psi that we see in Lagrangian, can you measure those at specific space-time points directly.
when you solve for it for one problem and you go and measure it(assume you can) do you see that value. If another physicist solve's another problem does he measure his own value at that same point in space time. how does that work, they can't have different values if the one field is real.

No you can't. It's a fermionic quantum field and represented, in the path-integral approach, as a Grassmann-number valued quantity. In the operator formalism they are fermionic field operators. The measurable quantities are S-matrix elements, i.e., correlation functions, evaluated as averages over expressions built from the field operators or as functional derivatives of the generating functionals in the path-integral formalism.

The resulting S-matrix elements are transition-probability amplitudes, i.e., there modulus squared are the probabilities per unit time and volume for a specified collision to happen, given the incoming (asymptotic free) particles (usually you have two particles in the incoming state) and the outgoing (asymptotic free) particles after the collision.

 

[ftr]

There cannoit be two physicists at the same point in space and time. All measuring physicists measure the fields they measure essentially at their position and time.

No you can't. It's a fermionic quantum field and represented, in the path-integral approach, as a Grassmann-number valued quantity. In the operator formalism they are fermionic field operators. The measurable quantities are S-matrix elements, i.e., correlation functions, evaluated as averages over expressions built from the field operators or as functional derivatives of the generating functionals in the path-integral formalism.

The resulting S-matrix elements are transition-probability amplitudes, i.e., there modulus squared are the probabilities per unit time and volume for a specified collision to happen, given the incoming (asymptotic free) particles (usually you have two particles in the incoming state) and the outgoing (asymptotic free) particles after the collision.

But isn't Ψ defined over all space time. If so, the two would compute different values.

 

[A. Neumaier]

But isn't Ψ defined over all space time. If so, the two would compute different values.

What is measured is the expectation value $\langle \Psi(x)\rangle$ at the point $x$ in spacetime, for suitable operators $\Psi(x)$ (not necessarily the basic field).

 

[ftr]

What is measured is the expectation value $\langle \Psi(x)\rangle$ at the point $x$ in spacetime, for suitable operators $\Psi(x)$ (not necessarily the basic field).

Thank you Dr Neumaier, you have been most helpful. Can you please elaborate on how a conflict will not arise if Field is real in the case of the two experiments.

 

[A. Neumaier]

Thank you Dr Neumaier, you have been most helpful. Can you please elaborate on how a conflict will not arise if Field is real in the case of the two experiments.

Two different physicists will measure the expectation at different $x$, so why should they measure the same?

 

[ftr]

But doesn't the values of Ψ of A includes values at x for B experiment.

 

[A. Neumaier]

But doesn't the values of Ψ of A includes values at x for B experiment.

No, why should it? It include the value of exactly one property at $x$. Different properties correspond to different field operators constructed from the set of fundamental fields.

 

[vanhees71]

Well, the Dirac-field operator cannot be an observable, because it doesn't commute but anti-commute at space-like separated arguments, and indeed all observables are built from Dirac-field operators by local products of even numbers of dirac operators which commute at space-like distances of their arguments as it must be for observables.

 

[A. Neumaier]

Well, the Dirac-field operator cannot be an observable, because it doesn't commute but anti-commute at space-like separated arguments, and indeed all observables are built from Dirac-field operators by local products of even numbers of dirac operators which commute at space-like distances of their arguments as it must be for observables.

Yes. I had said that $\Psi(x)$ is a suitable operator made from the basic fields, not necessarily the basic field. The commutator at spacelike distances must vanish in order to be observable.It can e.g. be a component of the Dirac current.

 

[Jilang]

That is certainly wrong.That is right.Physics is not about "reality", it is about making good predictions, if different models can make the same good predictions then they are equally fine. In particular, the predictions are from quantum field theory, and QFT does not care about our words "particles" and "fields".

If physics is not concerned with reality then who is taking care of it? Please don't tell me it's the philosophers!

 

[mfb]

If physics is not concerned with reality then who is taking care of it? Please don't tell me it's the philosophers!

Let's say the philosophers think they do.
Physics cannot. Describing and predicting observations is the best we can do in hard science.

 

[jtbell]

Suppose that we were to discover the true nature of reality. How would we know that we have done it?

 

[mfb]

What does "true nature of reality" even mean?

 

[Jilang]

These questions strike me as the ones philosophers would ask.

 

[thephystudent]

 

[A. Neumaier]

If physics is not concerned with reality then who is taking care of it?

An interpretation of physics takes care of that.

There may be multiple interpretations to the same physics; in this sense, physics is agnostic to philosophy. But people are not, and have one or more philosophies abut what it all means. And they may switch from one to the other whichever is more convenient for what they do at the moment. That's why they have intuitive, figurative ways of thinking and speaking, and why they may use virtual imagery in places where it seems to help. But they all calculate by the same formulas, getting the same physics. The formulas are the essence, not the imagery.

 

[nikkkom]

What is different? After a long time, you get stable particles flying away. W* or muon are "just" our description how those particles got created.Someone in this thread argued that there was a difference between those categories I think.

Indeed. The author is in fact quite clear in defining them as different things, and he states that off-shell particles are unobservable. From "The Physics of Virtual Particles" text:

>> On-shell and off-shell particles. The mass shell of a particle of (real or complex) mass m is the 3-dimensional quadric p^2=m^2 in 4-dimensional momentum space. On-shell means that this equation holds, off-shell that this equation is violated. All observable particles are on-shell, though the mass shell is real only for stable particles. Therefore, off-shell particles (also called virtual particles; see below) are necessarily unobservable.

Either there is an actual disagreement, or you use different definitions of what phrase "off-shell" means.

 

[mfb]

I use the definition used in particle physics, which fits to the one you quoted.

If you take that literally, every particle involved in some measurement is off-shell, even if the deviation is extremely tiny. You cannot interact with on-shell particles because they have to exist forever to be guaranteed to be exactly on-shell. Typically we call particles on-shell if the deviations are so tiny that they don't matter, e. g. for muons or protons but also for other particles with a reasonable lifetime. The cutoff is completely arbitrary, however.

 

[A. Neumaier]

Typically we call particles on-shell if the deviations are so tiny that they don't matter, e. g. for muons or protons but also for other particles with a reasonable lifetime.

According to the terminology made precise in my insight article, unstable real particles are regarded as on-shell but with a complex mass (giving rise to a peak in the S-matrix elements), which is what one gets when defining them as usual as poles of the S-matrix in the second sheet. This implies an uncertainty in the measurement results. But this is of a completely different origin than what one has for virtual particles, which are off-shell with a completely unconstrained (and unmeasurable) momentum, which in reality is only an integration variable.

 

[nikkkom]

According to the terminology made precise in my insight article, unstable real particles are regarded as on-shell but with a complex mass (giving rise to a peak in the S-matrix elements), which is what one gets when defining them as usual as poles of the S-matrix in the second sheet. This implies an uncertainty in the measurement results. But this is of a completely different origin than what one has for virtual particles, which are off-shell with a completely unconstrained (and unmeasurable) momentum, which in reality is only an integration variable.

In your picture, very short-lived particles (say, top quarks), are they always virtual? Sometimes virtual, sometimes real? What is the difference, since they can never be practically directly observed in either case?

 

[A. Neumaier]

In your picture, very short-lived particles (say, top quarks), are they always virtual? Sometimes virtual, sometimes real? What is the difference, since they can never be practically directly observed in either case?

You should read the insight article itself, where I gave details.

As with any other particle, a particle is virtual if the process is represented by a Feynman diagram, and real if it is directly or indirectly observed.
Virtual particles have no life and no lifetime; they don't exist in any meaningful sense. The lifetime of a short-living particle is defined in terms of its complex mass (pole of the S-matrix) and corresponding complex momentum, while a virtual particle always has a real momentum.

 

[Jilang]

Complex mass seems..a bit complex. Isn't it just a different way of making something slightly virtual?

 

[A. Neumaier]

Complex mass seems..a bit complex. Isn't it just a different way of making something slightly virtual?

No. This has not the slightest touch of being virtual.

It is just the relativistic analogue of complex frequencies. Complex frequencies are extremely natural for describing decaying oscillations. It is used a lot in electrical engineering. http://www.cs.mun.ca/av/old/teaching/cs/notes/complexFreq_printout.pdf

 

[Jilang]

Sorry, where does relativity come into it?

 

[nikkkom]

As with any other particle, a particle is virtual if the process is represented by a Feynman diagram, and real if it is directly or indirectly observed.

What does "observed" mean, precisely?

We infer top quark existence by detecting collision products which indirectly tell us that the process they were produced in involves a top quark.

But in all cases, the diagram with that quark has it as an internal line, not an outgoing one. Thus, by your terminology (I did read your articles) that quark is always virtual: "Virtual particles. Virtual particles are defined as (intuitive imagery for) internal lines in a Feynman diagram".

So, top quarks are always virtual?

 

[A. Neumaier]

Sorry, where does relativity come into it?

Unstable particles, Feynman diagrams and hence virtual particles are all described in terms of relativistic quantum field theory.
Particles are in quantum field theory elementary oscillations of the quantum fields. Their mass is proportional to the oscillation frequency in their rest frame, according to the formula $\hbar\omega=E=mc^2$. Thus real mass is the relativistic analogue of real frequencies, corresponding to stable particles and stable oscillations, and complex mass is the relativistic analogue of complex frequencies, corresponding to decaying particles and decaying oscillations.

 

[A. Neumaier]

top quarks are always virtual?

They are virtual if you describe them in terms of internal lines of Feynman diagrams. They are real if you describe/predict them in terms of decays or resonance width (which requires a time frame that doesn't exist for virtual particles). This is technically different since a decay of a top quark is a scattering calculation with top quark in and products out, and hence has the top quark as an external line.

 

[nikkkom]

They are virtual if you describe them in terms of internal lines of Feynman diagrams. They are real if you describe/predict them in terms of decays or resonance width (which requires a time frame that doesn't exist for virtual particles). This is technically different since a decay of a top quark is a scattering calculation with top quark in and products out, and hence has the top quark as an external line.

Yes, technically you can draw a diagram where t is an external line.

My point is that this is physically irrelevant description. After their creation, top quarks created at LHC scale energies can barely travel about 1/10 of proton diameter before they decay. They are no more "real" than gluons inside protons.

 

[A. Neumaier]

Yes, technically you can draw a diagram where t is an external line.
My point is that this is physically irrelevant description.

If you are that much nit-picking, all quarks should be considered virtual only because of confinement, since nonperturbatively, they cannot exist as asymptotic states. But it is convenient to treat them as real because of jets.

 

[Collin237]

If the distinction between real and virtual particles depends on the context of observation, then your original claim that virtual particles don't exist is invalid. A proposition that depends on observation doesn't qualify as "existence" in the modern sense of the word.

 

[A. Neumaier]

If the distinction between real and virtual particles depends on the context of observation, then your original claim that virtual particles don't exist is invalid. A proposition that depends on observation doesn't qualify as "existence" in the modern sense of the word.

You misunderstand the usage of the words.

The word ''muon'', say, can both mean an existent, measurable real particle (in cosmic radiation, say) with physical properties such as position, momentum, and lifetime, and a nonexistent, nonmeasurable virtual particle (in a Feynman diagram describing part of a scattering process for other particles).

As a real particle, the muon exists in a very real sense, while as a virtual particle, it exists only on paper and other visual media. Thus context is needed to decide on the meaning of the word ''muon'' or ''particle''. But once a particle is qualified as virtual, it means (by definition) that the correspondence to quantum field theory is given via internal lines of Feynman diagrams. These virtual particles don't exist in any physically meaningful sense, since existence (the possibility of assigning probabilities in space and time) requires possession of a state.

 

[RockyMarciano]

It makes absolutely no sense to argue about "existence" of either "real" or "virtual" particles, it is subjective and context-dependent on both the notion of "existence" and "particle". At most one could try to speak about detections/interactions(without which there is no physics to talk about to begin with)and at the present point in the quantum theory that would be difficult and limiting, there is still quite a lot of mathematical abstract baggage that has to be included to describe the interactions.

So I'm sorry but this counterargument constructed to avoid certain mythical argument is as flawed and subjective as the image that it tries to denounce.

 

[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.