Why do physicists argue that virtual particles aren't real because they aren't observable, when quantum superpositions are also not observable?

The most important thing to realize here is that this is a philosophical question, not a physical one.  As with the interpretation of the quantum wavefunction, the interpretation of virtual particles is going to vary wildly from one physicist to another--there simply is no consensus on the matter, and it's not even clear that "do virtual particles really truly exist?" is a meaningful question. I've given my thoughts on the matter here: Personally I don't think the idea that there's a sharp distinction between real and virtual particles is defensible, given that which they are is frame dependent.  Virtual particles such as quarks have real effects such as the angular distribution that comes out of a hadron scattering experiment... it shows that there is some composite structure there, even if a quark can never actually go into a detector.  Hawking radiation and Unruh radiation are also real physical effects that result from virtual particles. I think part of the confusion is that many people think of virtual particles as being simply intermediate states in Feynman diagrams.  If that's your definition of a virtual particle, then you can give a good argument (as Barak Shoshany has) as to why they shouldn't be regarded as having the same ontological status as real particles.  But my definition of a virtual particle would be more general.  I would say a virtual particle is any particle which doesn't satisfy the classical equations of motion for a particle (ie, one that is "off shell").  By this definition (which I would argue is more general and more sensible), it seems to me that real particles are if anything more of a mathematical approximation to virtual particles.  They are the classical limit of what you get when you sum a whole lot of virtual particles together and the phases add up in just such a way as to almost exactly cancel.  But exact cancellation of these phases only happens in an artificial mathematical limit. You can make an argument that breaking up a "physical state" like a real particle into a superposition which is a sum of virtual particles is just a mathematical trick, and in some cases... like when negative-norm states get involved, I'd agree that it is.  In other cases, such as expressing a proton as a composite of quarks, I'd disagree. In some ways, all particles are an artifact of perturbation theory.  At strong enough coupling, there is no interpretation in terms of interacting particles.  This goes for real particles just as well as virtual.  At weak coupling, it makes sense to me to think in terms of particles (both real and virtual).

I think is on the right track, but it may sound confusing to a layperson reading his answer. Let's clarify slightly. He is right, these "things" aren't really related in the way you think they are, which effectively finishes the argument. 1) Virtual particles are not detected because they are the intermediary pieces of a reaction. This isn't really like chemistry where you are (as far as I'm aware) able to observe each piece of a chemical reaction as well as observe the intermediary, if there is one. The problem tends to be something such as the time-scale of the reaction in a particle collision that the intermediary only exists for such a small fraction of a second, that our current detection methods just can't "see" it. 2) All superpositions are, literally by definition, observable. An observable is the outcome of a measurement on a quantum state. If a quantum state is a superposition of A, B, C -- then measuring it means that the outcome is either A, B, C. They're not observable beforehand because they are all equally likely -- we only know which one it is AFTER we make a measurement. Talking about the absolute physicality of a quantum state before a measurement is not something that makes sense.

They are not really the same. 1) You can never observe/detect the virtual particles, If you are looking at some other case like spin of a photon, each of the components of the superposed states is observable. 2) Virtual particles are off shell (kind of same as 1) I guess).

The crucial point is---contrary to popular belief---there is simply no clear-cut line separating "physically real" and "mathematically useful/convenient", the two concepts are only separable when they are on the two extremes of the "reality" spectrum. I've seen previous nice answers alluding to this point,  but I feel some fine points have not been clarified, so I'll put my two cents here. To better organize the answer I'll unfold it in three layers: (1)Virtual particles are mere mathematical tools, they are not real. Is it really so? (2)What's the meaning of the word "real"(to physicists)? (3)Virtual particles are more unreal than real. (1)Virtually particles are mere mathematical tools, they are not real. Is it really so? Common arguments for this include but are not limited to: virtual particles are nothing but internal lines of Feynman diagrams, they are only parts of perturbation series, their momenta are off-shell while in/out states of S-matrix must be on-shell, only cross-sections given by the S-matrix is observable etc. However, we also have a pretty (at least superficially) strong counter argument for this, briefly summarizing : which physical particle is ever truly on-shell? True on-shellness only happens at the asymptotic infinity, while no true detector can ever be put at a strict asymptotic infinity, so by the same spirit must we draw the conclusion that in/out states aren't "physically real" either? To further elaborate(still more or less repeating Kevin Grizzard), how do we know some process, say the annihilation of an electron-positron pair,  actually produces a real photon? We must have a photon detector and have the produced real photon interact with the particles constituting the detector, but then if we include the measurement process in our Feynman graph, isn't the real photon now an internal line of the graph, i.e. becomes a virtual photon? Does this suggest virtual particles are more "real" than real particles? (2)What's the meaning of the word "real"(to physicists)? By now a careful reader might have noticed that the line of reasoning of the last section can be easily developed to a rather slippery slope: Are electrons real? After all, all we've been observing are bright spots on a fluorescent screen, or resonance peaks of some graphs. Now, what does it truly mean by "real"? I don't claim myself to be a philosophically mature physicist, but here's what I consider as "real" which should be agreeable(?) to most physicists who have thought about the issue: "real (existence)" refers to, in the most accurate, natural and explanatory physical theory, not sacrificing its accuracy and naturalness, the indispensable concepts that cannot be further reduced or simplified. A bit dry isn't it? Let me elaborate: why do we say heliocentric model is real/true, and geocentric model is unreal/fictional? If one is to evaluate a theory merely by how good it fits the observed data, then by no means geocentric model should be disadvantaged, because within geocentric model there's unlimited accuracy fitting the observed data provided unlimited number of epicycles are allowed to be added. So in what sense do we declare geocentric model as unreal? Here is the place where I can invoke the definition of "real" (bold paragraph above): to calculate the trajectory of a planet in the geocentric model to the same accuracy than can be done in heliocentric model, the complexity of the task is so immensely higher that anyone who claims that geocentric model is "not really false" is just playing with semantics. Hence, not sacrificing accuracy and naturalness, "sun is at the center the our planetary system" is a conception that can neither be dispensed with nor reduced, and hence real. Please don't get me wrong, I'm no nominalist/conventionalist, all I'm saying is, in a rough sense, "extreme convenience +elegance+accuracy+irreducible"="real", I can't resist borrowing Henri Poincare's eloquence to close this section: It is true that it is convenient, it is true that it is so not only for me, but for all men; it is true that it will remain convenient for our decendants; it is true finally that it cannot be by chance. (The Foundations of Science). (3)Virtual particles are more unreal than real. After the deconstruction of semantics in section (2), to some extent it may no longer be an interesting question to ask "Are virtual particles real?" Rather, it probably makes more sense to ask "How real are virtual particles?" However, if I'm forced to take a stand in the (false) dichotomy of "real" and "unreal(but useful)", I'd prefer to consider virtual particles unreal: they seem to play a much more important role in QFT than geocentric model plays in astrophysics, but I don't believe they are important to the extent of being indispensable. We now know there are nonperturbative effects that are out of reach of arbitrarily high order perturbation theory, and lattice QFT suggests there can be a systematic nonperturbative formulation of QFT in which virtual particles only play an auxiliary role, etc.(For more points undermining the strength of virtual particles see 's answer.) On the contrary, concepts like in/out states, S-matrix are not quite dispensable/reducible in any conceivable way, therefore it's very much legitimate to call them real. Finally, the concept of superposition to QM is very very very much more indispensable even than S-matrix stuff to QFT, therefore real.

Bottom line, this is a messy question.  If one defines virtual particles to be internal lines on Feynman diagrams, with no referent or symbolic value, than fine, it is trivially true to say that they are just artifacts of formal calculations - we have literally just defined them that way.  But if one ascribes any physical meaning to Feynman diagrams at all - even only to the "in" and "out" external legs - then it's not clear to me how we can draw a sharp distinction between "real" and "virtual" particles.  That is to say, the only particle that is NOT an internal line on a Feynman diagram is a free particle that propagates forever, ie, a propagator that in at least one direction never connects to a vertex.  But then it never interacts with anything after being created, including our eye or our measurement apparatus.  So now the only completely "real" particle is one that by definition we can literally never observe.  Wait, what?  How'd that happen??  Virtual particles were supposed to be the ones we don't observe!  My interpretation is that we need to be comfortable with ambiguity, imprecision, and shades of grey in our language and concepts.  When we consider something an external line of a Feynman diagram, we are "zooming  in" in space and time so that only this little bit matters; the external line that represents this "external" particle would, if extended, eventually encounter another vertex, which would be part of a larger diagram.  I know we shouldn't take the "space" in which Feynman diagrams are written too literally, but I only mean that at some other point in spacetime, this particle will interact at some other vertex (or else it disappears into the distance, necessarily never to be seen or heard from by anyone or anything ever again).  However, the time and space scales on which the collision or scattering process represented by the Feynman diagram takes place, compared to the scales on which the "external" "real" particle propagates before another interaction, can easily be infinitesimal.  In that case, the particle propagating forever and the particle propagating for 5 seconds are the same thing to a high enough accuracy for our purposes. Another argument for the quantitative rather than qualitative difference between real and virtual particles is the energy-time uncertainty relation.  One of the (many roughly equivalent) definitions of virtual particles frequently used is that they are off the mass shell (as someone already mentioned here).  Well, but particles never have a precisely defined mass anymore than they do a precisely defined location or momentum.  The particle would have to be eternal for it to have a delta function mass profile - once again meaning that it would never interact with us or anything else.  Particles are only asymptotically real in that sense, just as they are every only asymptotically well-localized. As for the superpositions business, I think the OP may have been thinking of something different than some seem to take it to be.  Summing over superpositions would be... I don't even know, ridiculous.  But just as we don't know what happens in between "incoming" and "outgoing" particle scattering and have to take the path integral or perturbative series over all possible events consistent with the initial and final conditions, so too if we begin with some quantum state, perform some series of operations such as Stern-Gerlach or polarization experiments, and only then see what we get out at the end, we have to again include all possible intermediate states consistent with the initial and final conditions (really eigenstates - there's only one possible state after each operation we perform if we don't make any observations until the end).  Just consider starting with a spin-up state, send it through a magnetic field along a different axis, do it again along another axis, and then make an observation.  At each step, there is only one state - it's just that that state might be a superposition of eigenstates of some operator you're interested in. Like after the first polarization, instead of a spin-up eigenstate, now you'll have a superposition of two s_x eigenstates (or whatever axis you picked).  And the point is that at each step you have to keep all the terms in the superposition, ie, all eigenstates in the sum, so that when act with another polarizer, we have to express each of the s_x eigenstates in terms of the eigenstates of the new direction, and so on. You can imagine doing polarizations of this sort along all kinds of various angles, so that the magnitude of the coefficients of each term in the superposition is not just 1/2, and then it is more plain why you have to keep track of each term at each step.  This is not really different than a description of the path integral: we have to sum up the contribution from each possible "path" the particle might have taken, where here "path" refers to the sequence of spin polarizations - perhaps up -> left -> down, or perhaps up -> right -> up, etc., etc.  This is the same as all of the possible "paths" a particle in a Feynman diagram might have taken - maybe some photon turned into an electron-positron pair which then annihilated back into a photon; or maybe the photon just propagated along without incident; OR maybe it spawned a pair, the pair annihilated, then the photon did it again, spawning a pair that annihilated back into a photon, etc.  I mean, this is just the renormalization of the photon propagator, which does indeed involve an infinite sum over all number of 1-particle-irreducible insertions.  Feynman said something like "If it is not forbidden, it is mandatory."  They all happen.  In some sense.  Now of course, in some sense that is complete nonsense, also.  Just like it is nonsense to say the particle went through both slits of a double-slit experiment, and yet it may also convey the right idea to one who knows how to take it.  Like the Buddhists say, you can't help if people keep fixating on your finger when you try to point to the moon.

You are correct to be puzzled by physicists' choice of language about "real" versus "virtual" particles.  Virtual particles are as real as "real" particles.  A real particle is one that is restricted to obey the Einstein energy, momentum & mass relationship [math]E^2 = P^2C^2 + M^2C^4 [/math] - "on shell" -, whereas a virtual particle is less restricted - "off shell" - but it is better to view them all as one species, existing on a continuous scale according to how much they violate the Einstein relation.  Particles in in and out states are modeled as if they are exactly on shell, but this is a fiction, and a convenience adopted to make calculations easy.  In reality, all particles are virtual particles, since nothing is ever exactly on shell - the reverse of what you are usually told - and reality is just some enormous patchwork or web of interlocking Feynman diagrams of virtual particles. More generally anyone who describes a piece of mathematics in physics as "just a tool" doesn't really understand what they're are talking about, IMO, since everything could then be regarded as "just a tool".  Does that mean they believe nothing exists?  Sadly many of them do swallow and regurgitate - and presumably believe - this positivistic s**t.  But that's no reason why you have to. There are also ghost particles.  Again we told they don't exist - and this time there is some truth in this description, since ghost particles (with a suitable choice of gauge) manifest themselves as the absence of some Feynman diagrams we would otherwise expect to exist. https://en.wikipedia.org/wiki/Faddeev%E2%80%93Popov_ghost?wprov=sfla1

You are asking a question that is really about semantics. Specifically, about somewhat sloppy terminology. Particles that transfer energy and momentum, not to mention other quantum numbers, but are not directly observed and therefore do not need to satisfy the dispersion relation [math]E^2-p^2=m^2[/math] (in other words, they are "off the mass shell") are called "virtual". Particles that are emitted or detected by a classical instrument and therefore must satisfy the dispersion relation (i.e., they are "on shell") are called "real". They are both very real in the sense that they both carry energy, momentum, spin, charge, etc. But one type is observed directly (with classical instruments), the other one is not. Except that the lines get somewhat blurred even here, because depending on its lifetime and the method used to observe it, even a "real" particle may be slightly off-shell, and certainly nothing prevents a "virtual" particle from being on-shell. And then there is the not exactly unimportant point that "particles" (real or virtual) themselves are mathematical artifacts; the only physical reality, if our best theory to date (quantum field theory) can be believed, would be quantized fields, and it is these fields' excitation quanta (especially if they are spatially localized), that we recognize as ("real") particles, and that in a nonperturbative regime (e.g., strong interaction, possibly quantum gravity) the very concept of a "particle" may not even make sense.

I personally believe that virtual particles must be in some sense as real as on-shell particles because I don't think that the perturbation-theory argument is true.That argument goes that perturbation theory introduces Feynman diagrams with loops but the full non-perturbative result doesn't so therefore it doesn't involve virtual particles.But let’s take a typical non-tree level calculation like https://en.wikipedia.org/wiki/B%E2%80%93Bbar_oscillation. The presumably fairly accurate perturbative result is proportional to the top quark mass squared and the KM couplings of the top quark to down-type quarks. If the top quark isn’t involved in the B-meson mixing then why is the probability of the process proportional to the (virtual) top quark’s properties including its mass and couplings to the down-type quarks that ARE observed? Somehow there has to be a reality to the virtual particles that are contributing to the process since the process DEPENDS on their properties!How can we say that there isn’t a reality to the top quark in this process? And more than that, in some sense the B0 and B0 bar must REALLY interchange by the b and q quarks CHANGING into t quarks since the process is UNDOUBTEDLY and experimentally proportional to those couplings b->t and q->t (where q = d or s)!Remember that the full non-perturbative result will be similar to the perturbative result in this case.How can we be so sure that the processes are EXPERIMENTALLY proportional to these couplings (to unobserved particles)? Because we can look at SISTER processes like Bd0-Bd0 bar vs Bs0-Bs0 bar and divide out the other affects. We are left with the ratio of those processes being PURELY the ratio of the couplings (to unobserved particles!):rate (Bd0-Bd0 bar) / rate (Bs0-Bs0 bar) = (Vdt)^2 /(Vst)^2It’s uncanny. Remember we ALREADY know the Vdt and Vst couplings from observing REAL decays of t->d and t->s and the ratio matches! The couplings of the top quark that make appearance in the calculation of the virtual process are the SAME values these couplings have when the couplings are measured in processes with observed t quarks.The very fact we can say all this is evidence of the reality of virtual particles.I believe this is all related to other strangenesses of QM, but refer you to other answers above for that.So I guess that means I am saying the reality of the quantum superpositions is as great as that of virtual particles which MUST have some reality as discussed above.