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I have edited this question with its title. Virtual particles, as I understand, arise as intermediaries in the calculations describing interactions such as scattering between real particles and in drawing certain Feynman diagrams.

My question is not whether virtual particles have real physical existence by direct observation. My question is, whether the mathematical language of "virtual particle-antiparticle popping in and out of existence", is even mathematically meaningful whenever you take everything (all real quanta) out of space. By empty space, I understand, the vacuum of a free or an interacting quantum field theory. May be this video roughly explains my question. Can the vacuum loops be given such a meaning?

Edit-The maximum voted answer in this post talks about virtual particles in real scattering experiments. But it does not address whether this virtual particles have any mathematical meaning, when there are no real quanta or particles present in the picture.

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marked as duplicate by AccidentalFourierTransform, user108787, Gert, Qmechanic Nov 13 '16 at 8:50

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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whether this virtual particles have any meaning (real or mathematical) when there are no real quanta of particles present in the picture.

Virtual particles have existence as internal lines in Feynman diagrams, used to calculate and predict real numbers like crossections and lifetimes. They carry the quantum numbers of their name but not the mass, the four vector describing them is within an integral and the mass is variable.

They are not real and are non existent if there are no real particles around. In addition they can also affect real interactions by their mathematical existence in vacuum loops:

If there are no external lines entering the Feynman diagram, there is no meaning to a closed loop in space, because it cannot be calculated. So the answer is that closed loops in the vacuum have no physical or mathematical meaning. Closed loops in vacuum acquire a mathematical meaning when a real particle with energy and momentum traverses space.

For real particles these vacuum loops which temporarily, within the uncertainty principle, appear and disappear as mathematical entities, (draining four momentum and giving it back ) are a mathematical problem, as the sum of these loops is divergent and introduces infinities in the calculations. These are taken care of by the renormalization program of Quantum field theory. Once the renormalization program has been carried out, the loop corrections do modify the output of the calculations, the real numbers in the problem. See for example the Lamb shift. Thus in some sense they have a portion of reality.

What one should keep in mind is that real energy and momentum should be present for the virtual loops (not individual particles) to acquire a real meaning/influence.

I have often seen physicists explaining vacuum as not nothing using analogy of particle-antiparticle pairs coming in and out of existence.

It is a handwaving description of how a "real" particle sees the vacuum, anthropomorphizing it. A "real particle" does swim through a vacuum playing ball with creation and annihilation loops within the heisenberg uncertainty. Real energy has to be supplied for this picture by the particle's four vector.

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Interactions such as scattering between real particles and in drawing certain Feynman diagrams. Do virtual particles have any real existence in vacuum when there are no real quanta of the fields present?

No, because they are not real under any circumstances.

I think, inexperienced though I am, that somebody needs to attempt to answer this valid question. I used to think VP's were real on Tuesdays, Thursdays and Saturday and not real on the other days of the week.

Virtual particles are not real, they are book keeping mathematical entities, that allow calculations to be made for say, scattering amplitudes between two electrons, as one example.

Another way to describe them, and I apologize if this not news to you, is to use the term on and off shell, instead of virtual particles.

Wikipedia On and Off Shell

In physics, particularly in quantum field theory, configurations of a physical system that satisfy classical equations of motion are called on shell, and those that do not are called off shell.

In quantum field theory, virtual particles are termed off shell (mass-shell in this case) because they don't satisfy the Einstein energy-momentum relationship; real exchange particles do satisfy this relation and are termed on shell (mass-shell). In classical mechanics for instance, in the action formulation, extremal solutions to the variational principle are on shell and the Euler–Lagrange equations give the on shell equations. Noether's theorem is also another on shell theorem.

Off shell particles are invoked to deal with calculations in somewhat the same way as electrical engineers use the square root of minus one, when calculations involving their work are needed. $\sqrt -1$ is used as an intermediate math step, but as long as they end up with real current and voltage values, the electrical guys are OK with that.

A real photon exists when you shine a light on a metal plate to eject some electrons, every aspect of that experiment is measurable and the photon will last until it's absorbed by an atom.

This last paragraph is my own personal view, and different people have different interpretations on what reality is. If you start chopping up a stick of wood, as you know, you eventually will not end up with tiny, tiny pieces of wood, you will end up with elementary particles, which can only be described by math.

Rembering that if it walks like a duck, and it quacks like a duck.....if an elementary particle, say an electron, even if you call it an excitation of a field, as in QED, follows mathematical rules and is explainable only in math terms, then it is, in my totally naive worldview, a mathematical object, similar to a virtual particle but different in that we take it as real because it follows on shell, not off shell rules.

Please read Matt Strassler's blog on this virtual particle idea, the silly notions in the above paragraph are a personal viewpoint, that are certainly not original to me. I think we can go back to Plato for the same general idea, but he couldn't prove his hypothesis and neither can I.

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