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I understand the $\Delta t \cdot \Delta E \geq \hbar / 2$ relationship and the idea behind them. However, I don't understand why do we need them at all. I'm a physics undergraduate. As far as I know, all the physics equations I'm dealing with doesn't involve virtual particles at all. So why do we need them if we can get to the correct answers without them anyway?

I have read around some related questions to this (not exactly the same questions though). I believe it was pointed out that we need virtual particles for some mathematical model, but why do we call it "virtual particle"? I think we should call it force or field (a new type of force or field; something like that for example). Another point is why do we need that model in the first place if the model without virtual model works just as well? Thank you!

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    $\begingroup$ 1. If you think the "energy-time uncertainty relation" has anything to do with virtual particles, you understand neither, and have fallen prey to a popular, but false, interpretation. See this question for what the energy-time uncertainty actually means. 2. What do you mean by "what do we need them for"? We don't, as you say you can get every result without ever talking about them, since they are just fancy names for lines in a diagram. $\endgroup$
    – ACuriousMind
    Commented Nov 30, 2015 at 23:22
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    $\begingroup$ Well, virtual particles are allowed exist is exactly due to that inequality as far as I know. Anyway, you're saying we don't need them? What I don't understand is if we don't need them then why did anyone bother to come up with the entire new concept of "virtual particle" plus new "fancy" math behind it? $\endgroup$
    – Phu Nguyen
    Commented Nov 30, 2015 at 23:42
  • $\begingroup$ A short introduction to a different view about electric field excange I give here academia.edu/11805855/Are_photons_composed_particles, the longer one ist availible only in German academia.edu/12172263/…. $\endgroup$ Commented Dec 2, 2015 at 5:21
  • $\begingroup$ The English version "Complex one-dimensional structures of space" is now available academia.edu/19657550/… $\endgroup$ Commented Jan 17, 2016 at 18:45
  • $\begingroup$ Your question is answered in my answer to another thread at physics.stackexchange.com/a/261010/7924 $\endgroup$ Commented Jun 6, 2016 at 10:09

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One of the main reasons the virtual particles are used is that in many contexts we do not have a non-perturbative formulation of quantum field theory. What we can do is compute some amplitudes perturbatively (e.g. for outcomes of particle collisions) using Feynman diagrams. These diagrams have input/output lines in them, usually identified with colliding particles and collision products, but also intermediate lines that start at one vertex and end at another, staying entirely within the diagram. By extension, these came to be interpreted as virtual particles. One can also imagine diagrams without input/output lines at all, which would correspond to creation/annihilation of virtual particles in the vacuum.

So virtual particles are at least useful in the way pictures of chemical bonds are useful in chemical calculations, although from quantum-mechanical point of view these "bonds" are ephemeral. One place where virtual particles had heuristic value, for right reasons or not, is the prediction of Hawking radiation based on semi-classical mixing of QFT and general relativity near the horizon of a black hole. Out of a created virtual pair one particle falls below the horizon, and the other acquires escape velocity producing the radiation. This picture is suggestive, Hawking himself suggested it in Breakdown of Predictability in Gravitational Collapse (1976), and perhaps it served as his motivation, even if now there are ways to derive it without virtual particles. Here is Parentani's 2010 paper From Vacuum Fluctuations across an Event Horizon to Long Distance Correlations that utilizes Hawking's picture. The same heuristic value attaches to other "appearances" of virtual particles.

Are the virtual particles "real"? At this point we are not even 100% sure that there is something non-perturbative that QFT approximations approximate, let alone if a computational tool for these approximations can be projected onto reality. Some of those who believe that non-perturbative QFT exists expect that it will not be interpretable in terms of particles at all, or fields for that matter, but that undermines far more than virtual particles, see Baker's Against Field Interpretations of Quantum Field Theory. Even interpretations of quantum mechanics, where we do have a mathematically impeccable non-perturbative formulation, are still controversial. However, ideas about atoms and electrons in the 19th century were mostly wrong from modern point of view, but nonetheless provided valuable heuristics for developing modern theories. Ideas about ether helped Maxwell formulate his equations, even if later its existence was rejected. Virtual particles may end up in the same basket.

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  • $\begingroup$ This is a quite good answer. Okay, let me get this straight. The way I see it is that we don't really need virtual particles to explain physics phenomenon. We still can explain things without it, right? Netherless virtual particles become useful in explaining theories that are not known to be correct yet? Last question is what if virtual particles are real, and we just haven't been able to detect it yet? Or it could be an entire new phenomenon that is not a particle? The comparison to Ether is a good one! I feel like virtual particle is another of imaginary ether which is not even there. $\endgroup$
    – Phu Nguyen
    Commented Dec 1, 2015 at 0:59
  • $\begingroup$ I think to say that we don't have a non-perturbative formulation of quantum field theory is too broad a statement. Abstractly, we can axiomatize a non-perturbative QFT. We don't have a non-perturbative formulation of 4D YM theory coupled to all sorts of matter that's needed for the standard model, but, for lower dimensional scalar and fermionic field theories as well as some supersymmetric models, non-perturbative results are known (see e.g. the work of Glimm and Jaffe for the 2D and 3D scalar case). $\endgroup$
    – ACuriousMind
    Commented Dec 1, 2015 at 1:07
  • $\begingroup$ @Phu Nguyen For example, we can explain why light slows down in a medium using quantum theory, it is a monster of an explanation physics.stackexchange.com/questions/153904/…, or we can use wave optics even though we know it is a simplification, we may even use analogy with sound waves, implying a non-existent medium. Virtual particles may retain this role even after they are discarded like ether, if they are. As for reality even the status of collapse in QM is unsettled, so its anybody's guess. $\endgroup$
    – Conifold
    Commented Dec 1, 2015 at 1:10
  • $\begingroup$ @ACuriousMind, "We don't have a non-perturbative formulation of 4D YM theory coupled to all sorts of matter" we lack something even more basic than non-perturbative Yang-Mills: we lack a non-perturbative QED formulation. $\endgroup$
    – lurscher
    Commented Dec 1, 2015 at 1:19
  • $\begingroup$ @lurscher: It's not true that a non-perturbative QED formulation would be "more basic" - the presence of the Landau pole may indicate (but only indicate, since its presence itself is only known perturbatively or numerically) there is no such formulation. Conversely, the absence of such a pole in QCD/the Standard Model nurses hope such a formulation exists for the full theory. $\endgroup$
    – ACuriousMind
    Commented Dec 1, 2015 at 1:27

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