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[Edit June 2, 2016: A significantly updated version of the material below can be found in the two articles https://www.physicsforums.com/insights/misconceptions-virtual-particles/ and https://www.physicsforums.com/insights/physics-virtual-particles/ ] Let me give a second, more technical answer. Observable particles. In QFT, observable (hence real) ...

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$$\sin(x) = x-\frac{x^3}{3!} + \text{trigonometric fluctuations}$$ Above you can see why I don't like the language of "quantum fluctuations" -- what people mean by them is just "terms in perturbation series we can't make classical sense of". Similarly the phrase ... particles pop in and out of existence... is a yet another naive attempt of describing ...

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The short answer to your question is that the statements that "virtual particles need not conserve energy" and "intermediate components of Feynman diagrams need not be on the mass shell" are equivalent statements, but from two different historical perspectives. The concept of a virtual particle was introduced into physics in the mid-1920s while the ...

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Ever since Newton and the use of mathematics in physics, physics can be defined as a discipline where nature is modeled by mathematics. One should have clear in mind what nature means and what mathematics is. Nature we know by measurements and observations. Mathematics is a self consistent discipline with axioms, theorems and statements having absolute ...

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The classical Coulomb potential can be recovered in the non-relativistic limit of the tree-level Feynman diagram between two charged particles. Applying the Born approximation to QM scattering, we find that the scattering amplitude for a process with interaction potential $V(x)$ is \mathcal{A}(\lvert p \rangle \to \lvert p'\rangle) - 1 = 2\pi \delta(E_p -...

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I'm neither an expert on QFT, nor do I have a very deep knowledge of how the ideas developed - so this is at best a partial answer. I always thought that your first guess is what they actually meant: A virtual particle is an "off-shell"-particle, which means that it does not obey the usual energy-momentum equation. Now people tend to interpret this as the ...

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The reason for many contradictory statements regarding the nature of virtual particles is that they are often invoked for heuristical explanations of phenomena that arise within the framework of quantum field theory. One then tries to justify those explanations by attributing certain properties to virtual particles they do not actually possess. What ...

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The paths of the Feynman path integral are not actually taken. The phrase "takes every possible path" is a mangled statement of the mathematical instruction to take the integral of $\exp(-\mathrm{i}S)$ over all possible paths for the action $S$ to get the probability amplitude of something happening. It is a fact of quantum mechanics that this integral ...

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This is the table of particles on which the standard model of elementary particle physics is founded: These particles are completely and uniquely characterized by their mass and quantum numbers, like spin, flavour, charge... The standard model is a mathematical model based on a Lagrangian which contains the interactions of all these particles, and it is ...

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Virtual particles refer to actual, nonzero features in the quantum fields of real objects, but they are features that are not particles in many ways so you should not expect anything from their being named "particle". Basically, the idea of virtual particles was invented as a device for when you want to hold on to the particle picture while doing quantum ...

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When thinking about fundamental entities, it's quite easy to ask a question that, upon reflection, is contradictory. The questions of this kind take the form: What is [some fundamental thing] made of? The contradiction here is that there can only be an answer if the fundamental thing isn't fundamental! The electromagnetic field is one such fundamental ...

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In Physics "nothing" is generally taken to be the lowest energy state of a theory. We wouldn't normally use the word "nothing" but instead describe the lowest energy state as the "vacuum". I can't think of an intuitive way to describe the QM vacuum because all the obvious analogies have "something" instead of nothing "nothing", so I'll do my best but you may ...

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Here are from wikipedia drawings of the field lines of two magnets in two orientations, like-like, like-unlike . North pole to north pole North pole to south pole. The lines distort but do not intersect. These field lines are solutions of the formal Maxwell differential equations. Differential equations do not give discontinuous solutions, as would be ...

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The answer is no. And to be clear about this: the set of quantum fields in their least energy state, which we call the vacuum, when left to its own devices, in the absence of stuff (including gravitating stuff) does not fluctuate at all. In this context the term 'fluctuation' was introduced by well-meaning physicists in an attempt to draw an analogy ...

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There is only one kind of photon. Indeed, when we describe elementary interactions between two electrons for example, we call the photon "virtual" as opposed to a physical photon that might exist outside of this process. Still, these are the same particles, i.e. excitations of the same fundamental field, as the photons that make up light for example. ...

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Photons do not exhibit the property of virtual particles, but it is not your reasoning that is faulty, you have simply fallen prey to an imprecise use of terminology. Let me start with my view of the wave/particle duality. Most of the images of "particles" and "waves" comes from a time when we really didn't understand the quantum world, and some ...

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This answer is basically an argument about why you should treat the terms of a perturbation series as interesting objects under the right circumstances. It doesn't really change the fact that these are just mathematical terms, but it shows that they have explanatory value in addition to simply being part of the sum because each term can be the leading term ...

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(I henceforth assume $c= \hbar=1$.) It is forbidden by the four-momentum conservation law. Put yourself in the centre of mass reference frame of the couple of massive particles (electron and positron). There $P_{e\overline{e}} = (2E,\vec{0})$ with $E\geq m_e>0$. Just because four momentum is conserved, this four-momentum must be the same as the one of the ...

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This is an excellent question, which clearly demonstrated the lie perpetuated by a lot of people, that the Energy time uncertainty relationship has the same meaning as the momentum and position uncertainty relationship. First of all, there is no energy and time uncertainty. Recall that the uncertainty principle for operators $\hat A$ and $\hat B$ have the ...

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No, the virtual photon is not a particle, since a virtual particle is what one calls the internal lines in a Feynman diagram, and there are no asymptotic particle states associated to these lines, so a virtual particle is not a particle in the usual (or any other rigorous) sense. Therefore, the question is non-sensical because it is not clear what an ...

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I will use the expressions "virtual particles" and "internal lines in a Feynman diagram" interchangably in this answer. This interpretation fails because you can draw Feynman diagrams in both position and momentum space. When you draw them in momentum space and squint really hard, you might be able to convince yourself they have something to do with "...

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This has been asked before at least twice: Does incidence of appearance of quantum fluctuation particles being lowered due to space expansion? Does the density of virtual particles decrease when space expands due to dark energy? And in both cases the question was closed because it isn't very meaningful. The problem is that the popular science description ...

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I don't think the particle-anti-particle picture is a very good one to grasp what's going on. Essentially, it's a consequence of zero-point energy. In classical physics, the lowest energy state of a system, its ground state, is zero. In quantum mechanics, it's a non-zero (but very small) value. The easiest way to see how this zero point energy arises is ...

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Here's an answer from a non-particle physicist to complement what (former) professional particle physicist Anna V has written. "Real particles" enter and leave Feynman diagrams. Therefore, in principle, they can be detected in an experiment - they are the "terminals" of a Feynman diagram: ports through which we can "see" the system within. In contrast, ...

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Short answer: A virtual particle is not the opposite of a classical particle. While the other answer captures some aspects correctly, there are still a few flaws and inaccuracies which in the following, I will try to set straight. Wave-particle duality Strictly speaking, quantum objects are neither waves or particles. They are entities behaving like ...

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Virtual particles are not real. They come, as I've said in many answers on this site, from a naive interpretation of Feynman diagrams which should not be taken as an actual, exact description of how the physics works. The actual description of an interaction in the quantum field theory is more complicated than "photons are exchanged". In particular, "...

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There is no virtual photon as a physical entity here. Not only is it neither absorbed nor emitted, it doesn't exist as anything physical. It is literally just a line in the Feynman diagram. It represents a "fictitious" intermediate state that is distinct from the actual state of the system at any time, as I argue in this answer on the relation between ...

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The short answer is "no", the total mass-energy is zero so there's nothing to create when the meet again. The longer answer is that it is vital to understand that virtual particles are not "real". It's just a name we give to lines on a diagram. Literally. We have those lines, and a name for them, because it makes certain aspects of QFT easier to understand. ...

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Yes there are "virtual" Higgs bosons. A virtual particle isn't really a particle but a ripple / disturbance in a field. So a virtual electron is a ripple in the electron field. A virtual higgs is a ripple in the higgs field. Virtual particles are just a convenient conceptual model for describing field disturbances in terms of particles. Matt Strassler ...

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