I Are virtual particles real or just math filler

[J-eastwood]

Hello,
My question on virtual particles is quite simple but I cannot find an answer. Are virtual particles just a filler for math or do they actually come into existence?

 

[Mentz114]

See here

https://www.physicsforums.com/threads/is-matter-created-continuously.850478/

 

[DrChinese]

Hello,
My question on virtual particles is quiet simple but i cannot find an answer. Are virtual particles just a filler for math or do they actually come into existence?

Welcome to PhysicsForums, J-eastwood!

The generally accepted answer is: Virtual particles are artifacts of the math of Quantum Field Theory. Many find them convenient for discussion purposes. Whether they are "real" or not is something of a matter of philosophy. There is no known physical test that would further answer this question.

 

[A. Neumaier]

I wrote here a thorough answer (see the subsection on virtual particles). Virtual particles are not more than a useful visual aid for displaying technical mathematical details without using complicated formulas. Popular claims about their alleged temporal behavior are completely unfounded.

 

[J-eastwood]

Ok thank you for the responses it helped a lot!

 

[jlcd]

Isn't it that electric field is an exchange of virtual particles. If virtual particles are just artifacts of mathematical procedure that is not there when you use other procedure. Then what is an electric field composed of? Maybe we need to go back to Faradays where electric field are really flux lines?

 

[Mentz114]

Isn't it that electric field is an exchange of virtual particles. If virtual particles are just artifacts of mathematical procedure that is not there when you use other procedure. Then what is an electric field composed of? Maybe we need to go back to Faradays where electric field are really flux lines?

This is covered in the link in post #4. Please read it.

 

[jlcd]

This is covered in the link in post #4. Please read it.

Arnold Neumaier answer in the link is very complicated. His answer is "Observable particles. In QFT, observable (hence real) particles of mass m'>m m are conventionally defined as being associated with poles of the S-matrix at energy E=mc2'>E=mc 2 E=mc2 in the rest frame of the system (Peskin/Schroeder, An introduction to QFT, p.236). If the pole is at a real energy, the mass is real and the particle is stable; if the pole is at a complex energy (in the analytic continuation of the S-matrix to the second sheet), the mass is complex and the particle is unstable."

I'm asking about the electric field. The link is about W and Z bosons of the electroweak field. I can't relate electric field to the S-Matrix or whatever.

So what are electric field specifically? just virtual photons? Note it has no mass so can't relate this to the link that has mass. Just need a direct answer to this question. Thanks.

 

[Mentz114]

Arnold Neumaier answer in the link is very complicated. His answer is
So what are electric field specifically? just virtual photons? Note it has no mass so can't relate this to the link that has mass. Just need a direct answer to this question. Thanks.

This is a quote from the linked document which does apply to the virtual particles you ask about

Virtual (or off-shell) particles. On the other hand, virtual particles are defined as internal lines in a Feynman diagram (Peskin/Schroeder, p.5, or Zeidler, QFT I Basics in mathematics and physiics, p.844). and this is their only mode of being. In diagram-free approaches to QFT such as lattice gauge theory, it is even impossible to make sense of the notion of a virtual particle. Even in orthodox QFT one can dispense completely with the notion of a virtual particle, as Vol. 1 of the QFT book of Weinberg demonstrates. He represents the full empirical content of QFT, carefully avoiding mentioning the notion of virtual particles.

As virtual particles have real mass but off-shell momenta, and multiparticle states are always composed of on-shell particles only, it is impossible to represent a virtual particle by means of states. States involving virtual particles cannot be created for lack of corresponding creation operators in the theory.

A description of decay requires an associated S-matrix, but the in- and out- states of the S-matrix formalism are composed of on-shell states only, not involving any virtual particle. (Indeed, this is the reason for the name ''virtual''.)

For lack of a state, virtual particles cannot have any of the usual physical characteristics such as dynamics, detection probabilities, or decay channels. How then can one talk about their probability of decay, their life-time, their creation, or their decay? One cannot, except figuratively!

 

[jlcd]

so what is the lattice gauge theory of electric field that doesn't use the concept of virtual photons?

 

[bhobba]

so what is the lattice gauge theory of electric field that doesn't use the concept of virtual photons?

QFT starts with a field, divides it into a lot of blobs, treats each blob using standard QM, then let's the blob size go to zero. Taking the blob size to zero means you are assuming the theory is valid for all scales - even below the Plank scale where we are pretty sure our current physics breaks down. Ok - so instead of taking the blob size to zero we can make it very small and solve the resulting theory on a computer - that's lattice theory. Wonder of wonders - when you do that no virtual particles. This suggests they are simply an artefact of the methods normally used by pushing them too far.

Thanks
Bill

 

[jlcd]

ok so what does an electric field detector detect? if its not virtual photons then what is the terms of it? lattice blob interchange?

 

[bhobba]

ok so what does an electric field detector detect? if its not virtual photons then what is the terms of it? lattice blob interchange?

The quantised EM field it couples to just like classical EM where the coupling is modeled with a coupling constant in the Lagrangian.

Thanks
Bill

 

[vanhees71]

ok so what does an electric field detector detect? if its not virtual photons then what is the terms of it? lattice blob interchange?

It depends on the electric-field detector. If it's something like a CCD, it detects photons. A classical electromagnetic (wave) field from the point of view of QFT is a coherent state, i.e., the superposition of all photon-number Fock states in a specific way that describes the details of this wave field. The probability to detect a photon is given as usual by Born's rule.

 

[A. Neumaier]

what does an electric field detector detect?

It detects the electric field. In quantum electrodynamics the basic entities are an electromagnetic field operator $A(x)$ and an electon/positron field operator $\psi(x)$. The expectation of $dA(x)$ (where $d$ denotes exterior differentiation) is the classically measurable field at any space-time point $x$, with three electric and three magnetic components. Similarly, the expectation of $e\psi(x)^*\psi(x)$ is the classically measurable charge density.

Conceptually, this is very simple, just as the quantum-classical correspondence in the Ehrenfest theorem of quantum mechanics.
Introducing virtual particles only obfuscates the picture.

 

[friend]

If virtual particles are ONLY a tool for visualizing math procedures, then why is it not fair to use them to develop math for subjects like the Casimir effect, Hawking and Unruh radiation, screening effect on a bare point charge, etc? I don't think anyone ever mentions them as being something measurable. They always seem to be used for visualization purposes. Why (or when) is that not a fair approach for development?

 

[A. Neumaier]

why is it not fair to use them

It is appropriate to use them as visual aids.
But they are treated in much of the world of nonphysicists (including many wikipedia articles) as something dynamical, which is pure science fiction.

 

[friend]

It is appropriate to use them as visual aids.
But they are treated in much of the world of nonphysicists (including many wikipedia articles) as something dynamical, which is pure science fiction.

Are there some guidelines for how to use virtual particles in theory development? For example, I'm thinking of how two charged particles might interact in terms of the screen of virtual particles that surround each. It is said that the virtual particles (vacuum fluctuations) are polarized by the presence of a bare charge. Can the theory describing the force between the particles be developed in terms of how the virtual particles are polarized by both charges together? Or would such a theory depend on some dynamics which you say does not exit for virtual particles? Yet, wouldn't polarizing the vacuum (virtual particles) be a type of dynamics? Or would polarizing the vacuum only be a way of taking into account some potential without relying on the dynamics of how each of the virtual particle pairs actually propagate through space? Is it fair to use virtual particle only in terms of the probable effect of a potential on the virtual pairs?

 

[A. Neumaier]

Are there some guidelines for how to use virtual particles in theory development?

You use them to illustrate whatever you do on the mathematical level. The decisions what to do there must come from your mathematical and physical understanding.

 

[anorlunda]

I wrote here a thorough answer (see the subsection on virtual particles). Virtual particles are not more than a useful visual aid for displaying technical mathematical details without using complicated formulas. Popular claims about their alleged temporal behavior are completely unfounded.

Wow. I just read your answer here . It was very educational, and not too difficult to read. Here is my suggestion. Add a couple of pictures and make it a PF insights article. I thinks it would be much appreciated. Also, a link to an article is presumably more permanent than a link to a post, and therefore can be cited when editing those many incorrect Wikipedia articles that you mentioned.

 

[A. Neumaier]

Add a couple of pictures and make it a PF insights article.

For me, making figures is quite time-consuming. But if you'd make figures for me, I'd convert the article (with a few changes) to an insight article.

 

[friend]

You use them to illustrate whatever you do on the mathematical level. The decisions what to do there must come from your mathematical and physical understanding.

As opposed to what? When has anyone ever used them otherwise?

 

[A. Neumaier]

As opposed to what? When has anyone ever used them otherwise?

No opposite needed. I was only saying the obvious.

 

[anorlunda]

For me, making figures is quite time-consuming. But if you'd make figures for me, I'd convert the article (with a few changes) to an insight article.

I would be honored to assist you with graphics for an article. But first step, I need you to change your PF settings to allow me to start a private conversation with you so that we can collaborate without publishing our emails on a public forum.

Edit: alternatively, you could start a private conversation with me.

 

[friend]

The decisions what to do there must come from your mathematical and physical understanding.

Does this mean virtual particles do indeed have properties that can be use to develop theory? What would those properties be? Do the virtual particles have all the properties of a real particle, except they only last an undetermined short period of time? I know of some physicists that are considering the entanglement of virtual particles (quantum fluctuations) to "stitch" spacetime together, Leonard Susskind, for example.

 

[anorlunda]

I know of some physicists that are considering the entanglement of virtual particles (quantum fluctuations) to "stitch" spacetime together, Leonard Susskind, for example

I saw the Susskind video where he talked about entanglement of real particles stiching spacetime together.

 

[friend]

I saw the Susskind video where he talked about entanglement of real particles stiching spacetime together.

See:
at: 1:10:15
He talks about the entanglement between virtual particles, which would seem to imply that virtual particles have all the wave function properties of real particles.

 

[anorlunda]

at: 1:10:15
He talks about the entanglement between virtual particles, which would seem to imply that virtual particles have all the wave function properties of real particles.

I stand corrected. I was thinking of another video where Susskind talked about spreading waves of entanglement with more and more particles, as an alternative to wave function collapse.

Thank you for linking that video. In the video, he does indeed seem to say what you said. Here's my transcript of what he said in that clip.

"How do you entangle vacuum? The vacuum is entangled. The entanglement happens because of these virtual particles. The virtual particles that are created and annihilated continuously have the pattern of a quantum state which is entangled. Ah, and it's a property of the lowest energy state that likes to be entangled. Um, I don't have much more to say on that. We don't make the vacuum entangled. The vacuum just is entangled."

Someone else interjects. Susskind replies,

"That's the word. It relaxes to the entangled state. Yeah. Very good. I said that it radiates away that energy and that's a form of relaxation"

But in the strictest sense, he did not say the virtual particles are entangled, he said that the vacuum is entangled because of those virtual particles. Does that distinction have meaning? I can't say.

 

[friend]

I stand corrected. I was thinking of another video where Susskind talked about spreading waves of entanglement with more and more particles, as an alternative to wave function collapse.

That's interesting. Is he saying that the wave function (which collapses) is made up of entanglement with virtual particles? That does make a kind of sense to me. I'd appreciate it if you could point me to that video and time reference. Thanks.

 

[anorlunda]

I'd appreciate it if you could point me to that video and time reference. Thanks.

I'll try, but I've seen so many of his videos, it's hard to remember which one. It was in the 2013 QM course. I think that his point was that spreading waves of entanglement are featured in one or more of the many interpretations of QM, and discussions of those interpretation is frowned upon here at PF.

 

[A. Neumaier]

What would those properties be? Do the virtual particles have all the properties of a real particle

They have precisely the properties of the Feynman integrals they represent; thus they have mass and spin. But no states; in particular no spin up/down, no polarization, no position; they lack all properties that would make contact with the real world. They are just a figure of speech; using them correctly means using the formal perturbation formalism correcly, for which they are an abbreviation.

Everything about them is virtual - unreal. They live in a different world from the world of real particles, namely in the platonic world of formulas. There they stitch together symbolic calculations that can be barely expressed in words, except by making gross simplifications that convey more magic than reality. But they sell well to the general public!

 

[vanhees71]

I stand corrected. I was thinking of another video where Susskind talked about spreading waves of entanglement with more and more particles, as an alternative to wave function collapse.

Thank you for linking that video. In the video, he does indeed seem to say what you said. Here's my transcript of what he said in that clip.
Someone else interjects. Susskind replies,

But in the strictest sense, he did not say the virtual particles are entangled, he said that the vacuum is entangled because of those virtual particles. Does that distinction have meaning? I can't say.

Hm, does he say what he really means? I mean, without a minimum of math and a clear definition of what is entangled these are just empty words.

 

[vanhees71]

Well, "virtual particles" are what's represented by internal lines of Feynman diagrams, and these stand for free propagators (in the most simple sort of Feynman diagrams used in calculations order by order in perturbation theory, and I'd keep the discussion to these most basic application). Each free propagator reflects the mathematical properties of the quantum field the particle describe. There is no other meaning to them than that. Feynman diagrams are very suggestive in making pictures on "what's going on in a collision", but that's misleading. The observables refer to counting "real particles", i.e., something that hits a detector that can write information to a storage device, and this information refers to observable "real particles", represented by the external legs of Feynman diagrams. These are defined in terms of free-particle states, and even this is problematic for electrically charged particles, because the usually used naive free-particle states are not the correct asymptotic free states due to the long-ranged nature of the electromagnetic interaction. The true asymptotic states in this case are characterized by a coherent state, which usually is taken into account by appropriate soft-photon resummation techniques as explained, e.g., in Weinberg, Quantum Theory of Fields, vol. 1, to cure the associated IR and collinear divergences.

The most simple example is tree-level bremsstrahlung in the scattering of a charged particle on a classical Coulomb field representing a very heavy charged particle (e.g., electron scattering on a heavy nucleus). There you need to take into account at least also the elastic scattering + the one-loop radiative correction a la Bloch and Nordsieck.

To make a long story short: Feynman diagrams only look simple and intuitive. In fact they are highly efficient symbols to express complicated mathematical manipulations of the Feynman diagrams occurring in perturbative evaluations of S-matrix elements in QFT (including the organization of renormalization of UV divergences and resummations to cure IR and collinear divergences).

 

[friend]

Can we say that virtual particles are only mathematical entities that have no reality? These "mathematical" artifacts (Feynman diagrams = virtual particles) are necessary in the calculation of physical events. They are just as "real" as the wave function itself. Consider an electron propagating through space. There are virtual particles (a.k.a. mathematical entities, Feynman diagrams) at various places around the bare particle that contribute to its overall properties. Now if another electron comes close to the first, then to which of the electrons does a virtual particle (Feynman diagram) at a particular point belong? Can you have two different virtual particles (Feynman diagrams), one for each real electron, at the exact same location at the exact same time? If not, then to which electron does the virtual particle belong? Is there some sense in which the virtual particle at a point belongs to both electrons? And if it contributes positively to the calculations of the properties of both electrons, is there an attractive force?

 

[jtbell]

These "mathematical" artifacts (Feynman diagrams = virtual particles) are necessary in the calculation of physical events.

No, they are not necessary. See the discussion of lattice field theory in this thread which has been going on parallel to this one. (in particular, post #6 onwards)

 

[vanhees71]

Well, you don't need to use Feynman diagrams but just the mathematical formalism. Famously Schwinger apparently never used Feynman diagrams but got the same results as Feynman. With Feynman diagrams it's of course tremendously more easy to get the calculations. I guess that the full understanding of perturbative renormalization theory (BPHZ) would have been also very much more complicated without the use of Feynman diagrams. Zimmermann's forest formula is even formulated in terms of Feynman diagrams. Ironically, the corresponding paper, where it's proven doesn't draw a single Feynman diagram ;-)).

 

[friend]

No, they are not necessary. See the discussion of lattice field theory in this thread which has been going on parallel to this one. (in particular, post #6 onwards)

Which particles are never used in a Feynman diagram? If they can possibly be used in virtual processes, then why should it be wrong to develop a theory using them?

 

[BertMorrien]

The name "virtual particle" suggests that there is something like "real particle", but we know that the name "particle" in quantum physics means something else than a classical particle. In this sense a virtual particle is as real as a 'real' particle, but it cannot be observed directly. However, their effect can be measured and this must be taken into account in theoretical models.
See also http://www.scientificamerican.com/article/are-virtual-particles-rea/

 

[friend]

See also http://www.scientificamerican.com/article/are-virtual-particles-rea/

There's something wrong with your link. The text only appears at the bottom and keep moving around.

 

[fresh_42]

There's something wrong with your link. The text only appears at the bottom and keep moving around.

Here it works fine. Plus I'm looking forward for another explanation of the Lamb effect.

 

[BertMorrien]

There's something wrong with your link. The text only appears at the bottom and keep moving around.

I don't have problems with the link, but the content may depend on your particular browser.
SA's way of advertising is a bit anoying. Try to get rid of ads by clicking on the X.

 

[vanhees71]

Here it works fine. Plus I'm looking forward for another explanation of the Lamb effect.

Well, I could read it too, and I'm shocked that someone like Kane could write it, who wrote a good textbook on introductory particle physics, including QFT.

 

[bob012345]

Welcome to PhysicsForums, J-eastwood!

The generally accepted answer is: Virtual particles are artifacts of the math of Quantum Field Theory. Many find them convenient for discussion purposes. Whether they are "real" or not is something of a matter of philosophy. There is no known physical test that would further answer this question.

I would only add that the entire QFT approach is unphysical or unreal if you like.

 

[Orodruin]

I would only add that the entire QFT approach is unphysical or unreal if you like.

Unphysical and unreal are not the same thing. QFTs are definitely physical theories. They have made several astonishing predictions which have later been verified, which is what a physical theory is all about. Something being "real" or not is more of a philosophy issue than a science one.

 

[bhobba]

Something being "real" or not is more of a philosophy issue than a science one.

Very true.

In this sense a virtual particle is as real as a 'real' particle, but it cannot be observed directly. However, their effect can be measured and this must be taken into account in theoretical models.

They do not appear in Lattice theory so obviously do not have to be taken into account.

They are simply the pictorial representation of terms that appear in a Dysen series, which is what a Feynman diagram is.

Real particles are responsible for things like clicks in a particle detector - virtual particles are not. That's pretty common-sense, but as Orodruin says its a philosophical minefield. Scientists generally don't worry about such things, the consequences of which can be seen by the progress each field has made.

There is thread after thread about this issue on this forum, and its all exactly the same - they get no-where because some simply do not want to accept the obvious. Anything said outside an actual QFT textbook is very suspect and must be taken with a grain of salt. Study the real deal and this semantic quibbling never comes up. Its a much better use of an enquiring minds time. Recently some very good books have started to appear that can, with effort, be studied after a first course, or the study of a good text, in QM:
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20

Having got that book and studied it myself I think, again with effort, it can be studied after reading Susskinds text:
https://www.amazon.com/dp/0465062903/?tag=pfamazon01-20

Thanks
Bill

 

[sheaf]

I've always taken the view:
In-State = physics
Stuff in between = mathematics to get the right transition amplitudes in<->out
Out-State = physics

Statements like
"Quantum theory predicts that every particle spends some time as a combination of other particles in all possible ways. These predictions are very well understood and tested"
strike me as misleading. If you've done a QFT course you know what he's alluding to, but to phrase it like this is a bit sloppy. But then he's a professional physicist and I'm just a guy on the internet!

 

[vanhees71]

I've always taken the view:
In-State = physics
Stuff in between = mathematics to get the right transition amplitudes in<->out
Out-State = physics

Yes! An the correct adiabatic switching a la Gell-Mann and Low is crucial. See

F. Michler, H. van Hees, D. D. Dietrich, S. Leupold, C. Greiner, Non-equilibrium photon production arising from the chiral mass shift
Ann. Phys. 336, 331 (2013)
http://dx.doi.org/10.1016/j.aop.2013.05.021
http://arxiv.org/abs/1208.6565

for an example.

 

[friend]

I'm a little surprised that I've not seen any math equations in this thread showing where virtual particles appear in the equations. Are virtual particles a part of QFT? Or do they exist in QM as well?

 

[A. Neumaier]

Are virtual particles a part of QFT? Or do they exist in QM as well?

One can find them in both, and even in classical field theory (as explained in the link given)!
But the corresponding Feynman diagrams are heavily used primarily in QFT.

Giving formulas is not really useful since their whole purpose is to substitute imagery for formulas. You can read the Feynman rules relating the diagrams to integrals in any QFT book.

 

[vanhees71]

I'm a little surprised that I've not seen any math equations in this thread showing where virtual particles appear in the equations. Are virtual particles a part of QFT? Or do they exist in QM as well?

Well, that's easy. What's called "virtual particle" in popular science books is symbolized by internal lines of Feynman diagrams, and they stand for free-particle Green's functions (in usual perturbation theory; sometimes they can have a different meaning, e.g., in the context of resummation schemes like the $\Phi$-derivable approximation or the functional RG methods), but that doesn't matter too much on the level of this discussion.

In the Standard Model you have only scalars, (Dirac-)spinors, and vectors (gauge fields). Thus the "virtual particles" stand for the corresponding propagators
$$\Delta(k)=\frac{1}{k^2-m^2+\mathrm{i} 0^+},$$
$$G(p)=\frac{p_{\mu} \gamma^{\mu}+m}{p^2-m^2+\mathrm{i} 0^+},$$
$$D_{\mu \nu}(k)=-\frac{g_{\mu \nu}}{k^2+\mathrm{i} 0^+},$$
the latter in the Feynman gauge.