# Are virtual particles real or just math filler

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anorlunda
Staff Emeritus
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.

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.

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anorlunda
Staff Emeritus
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.

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
Staff Emeritus
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
2019 Award
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!!

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bhobba
vanhees71
Gold Member
2019 Award
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
Gold Member
2019 Award
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 occuring 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).

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
Mentor
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
Gold Member
2019 Award
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 ;-)).

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?

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.

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

fresh_42
Mentor
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.

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
Gold Member
2019 Award
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.

bhobba
bob012345
Gold Member
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
Staff Emeritus
Homework Helper
Gold Member
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 and vanhees71
bhobba
Mentor
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&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&tag=pfamazon01-20

Thanks
Bill

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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!

Jilang, vanhees71 and bhobba
vanhees71
Gold Member
2019 Award
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 [Broken]
http://arxiv.org/abs/1208.6565

for an example.

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bhobba
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
2019 Award
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.

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vanhees71
Gold Member
2019 Award
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.

bhobba