# I Are virtual particles real or just math filler

#### J-eastwood

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?

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#### DrChinese

Gold Member
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.

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#### 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

Gold Member
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?

#### jlcd

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

Gold Member
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 doesnt use the concept of virtual photons?

#### bhobba

Mentor
so what is the lattice gauge theory of electric field that doesnt 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 lets 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

Mentor
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 modelled with a coupling constant in the Lagrangian.

Thanks
Bill

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#### vanhees71

Gold Member
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?

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#### 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

Mentor
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.

"Are virtual particles real or just math filler"

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