# What are virtual particles? **URL:** https://boards.straightdope.com/t/what-are-virtual-particles/601242 **Category:** Factual Questions **Created:** [October 30, 2011, 12:13am UTC](https://boards.straightdope.com/t/what-are-virtual-particles/601242 "2011-10-30T00:13:17Z") **Posts on this page:** 20 **Page:** 1
### Author: ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom) #### Post date: [October 30, 2011, 12:13am UTC](https://boards.straightdope.com/t/what-are-virtual-particles/601242/1 "2011-10-30T00:13:17Z")
I’ve tried to perform due diligence on this, basically the Wik and the longer, semi-okay description in the [Usenet physics FAQ on virtual particles](http://www.desy.de/user/projects/Physics/Quantum/virtual_particles.html). But, of course, I need to ask the Dopers for their clearer, if less detailed explanation for the benefit of my pea brain. ---
### Author: ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos) #### Post date: [October 30, 2011, 3:14am UTC](https://boards.straightdope.com/t/what-are-virtual-particles/601242/2 "2011-10-30T03:14:58Z")
They’re a can of worms, and you just opened it. What we can say for sure about virtual particles is that they’re a mathematical bookkeeping device, part of the framework of the Feynman calculus which can be used to calculate many particle interactions. You’ve got some bits and pieces of the calculation which correspond directly to the particle(s) you have going in or coming out (the real particles), and then you’ve got some other bits and pieces of the calculation which look a lot like those real particle bits, but don’t correspond to any real particles, and we invent the concept of virtual particles and say that that’s what those bits are describing. So far, everyone agrees on that. Some folks will say that that’s _all_ they are, and that we shouldn’t think of them as having any actual physical existence, because they can’t be directly detected. But that’s complicated, too, because the line between virtual and real particles isn’t actually all that clear, and if you try to make it a sharp distinction, then there’s some sense in which you can argue that _only_ virtual particles can be detected, and real particles never can be. See, a real particle is defined as one that propagates in from infinity, or propagates out to infinity, but you’re not an infinite distance away from whatever process you’re observing. The particles that you observe _don’t_ propagate all the way out to infinity, because they interact with particles in your eye (or whatever detector you’re using) before they get there. So really, it’s just a virtual particle that behaves _almost_ exactly like a real one. ---
### Author: ![JWT\_Kottekoe](https://avatars.discourse-cdn.com/v4/letter/j/3ec8ea/32.png) [@JWT\_Kottekoe](https://boards.straightdope.com/u/JWT_Kottekoe) #### Post date: [October 30, 2011, 3:37am UTC](https://boards.straightdope.com/t/what-are-virtual-particles/601242/3 "2011-10-30T03:37:37Z")
The age old question: “Are all particles really virtual, or are virtually all particles real?” ---
### Author: ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus) #### Post date: [October 30, 2011, 5:54am UTC](https://boards.straightdope.com/t/what-are-virtual-particles/601242/4 "2011-10-30T05:54:59Z")
Unless this has been superseded…or I’m getting it wrong entirely…virtual particle decay – akin to Hawking radiation – has been observed, not near black holes, but simply near very heavy atomic nuclei. Article in Scientific American humpty-um years ago, entitled “Breakdown of Empty Space.” Essentially, a virtual particle pair tries to materialize/dematerialize – y’know, virtually, i.e., too fast to be observed – but one of the two particles gets pulled (by gravity, if I understand it correctly) into a heavy nucleus (say, a convenient Uranium atom) and so the other is forced to “become real” and wanders off – thus providing a kind of radiation near heavy nuclei. If valid, nifty, and an indirect observation of virtual particles. If invalid, I take full blame… Trinopus ---
### Author: ![BigT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bigt/32/12044_2.png) [@BigT](https://boards.straightdope.com/u/BigT) #### Post date: [October 30, 2011, 8:36am UTC](https://boards.straightdope.com/t/what-are-virtual-particles/601242/5 "2011-10-30T08:36:58Z")
The way you are describing it here, it just sounds like particles that don’t exist for very long. Or, to put it less simply, it’s like a wave theory of space where particles are just standing waves, and virtual particles are perturbations of the waves. That a particle is only real because it isn’t canceled out quickly. Does this work? Virtual particles are just the waves between two standing waves interacting? The particles only exist in the sense of there being something traveling through space between the particles? It makes more sense in my head than the way I’m describing it. I hope you can understand why a short lived wave would also be a short lived particle. ---
### Author: ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit) #### Post date: [October 30, 2011, 9:31am UTC](https://boards.straightdope.com/t/what-are-virtual-particles/601242/6 "2011-10-30T09:31:26Z")
> [@Trinopus](#): > > Essentially, a virtual particle pair tries to materialize/dematerialize – y’know, virtually, i.e., too fast to be observed – but one of the two particles gets pulled (by gravity, if I understand it correctly) into a heavy nucleus (say, a convenient Uranium atom) and so the other is forced to “become real” and wanders off – thus providing a kind of radiation near heavy nuclei. Gravity is far too weak to create such an effect in the vicinity of atomic nuclei; it’s actually the (immense!) electric field of a “superheavy” nucleus (which doesn’t really exist; you need a number of protons greater than 140 for the effect to occur, which can only be achieved temporarily by mashing two nuclei together very closely) that leads to particle creation in this case. ---
### Author: ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat) #### Post date: [October 30, 2011, 11:17am UTC](https://boards.straightdope.com/t/what-are-virtual-particles/601242/7 "2011-10-30T11:17:53Z")
One of the clearest viewpoints on what virtual particles ‘are’ comes from the below passage (which rtaher than paraphrasing I will just quote. Also note in the article itself he details some of the ontological problems of viewing virtual particles as real, phsycial artifacts): > [@Hrvoje Nikolic](#): > > The calculational tool represented by Feynman diagrams suggests an often abused picture according to which “real particles interact by exchanging virtual particles”. Many physicists, especially nonexperts, take this picture literally, as something that really and objectively happens in nature. In fact, I have never seen a popular text on particle physics in which this picture was not presented as something that really happens. Therefore, thispicture of quantum interactions as processes in which virtual particles exchange is one of the most abused myths, not only in quantum physics, but in physics in general. Indeed, there is a consensus among experts for foundations of QFT that such a picture should not be taken literally. The fundamental principles of quantum theory do not even contain a notion of a “virtual” state. The notion of a “virtual particle” originates only from a specific mathematical method of calculation, called perturbative expansion. In fact, perturbative expansion represented by Feynman diagrams can be introduced even in classical physics, but nobody attempts to verbalize these classical Feynman diagrams in terms of classical “virtual” processes. So why such a verbalization is tolerated in quantum physics? The main reason is the fact that the standard interpretation of quantum theory does not offer a clear “canonical” ontological picture of the actual processes in nature, but only provides the probabilities for the final results of measurement outcomes. In the absence of such a “canonical” picture, physicists take the liberty to introduce various auxiliary intuitive pictures that sometimes help them think about otherwise abstract quantum formalism. Such auxiliary pictures, by themselves, are not a sin. However, a potential problem occurs when one forgets why such a picture has been introduced in the first place and starts to think on it too literally. [Quantum Mechanics Myths and Facts](http://arxiv.org/abs/quant-ph/0609163) ---
### Author: ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos) #### Post date: [October 30, 2011, 5:41pm UTC](https://boards.straightdope.com/t/what-are-virtual-particles/601242/8 "2011-10-30T17:41:18Z")
Well, you do certainly have to be careful about taking virtual particles too literally, since even in the most literal interpretation (where the virtual particles “really exist”), it’s always ambiguous as to just _which_ virtual particles exist. No process is described by a single Feynman diagram; ever process is described by a superposition of multiple (in fact, an infinite number of) Feynman diagrams, each with its own set of virtual particles. ---
### Author: ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta) #### Post date: [October 30, 2011, 6:25pm UTC](https://boards.straightdope.com/t/what-are-virtual-particles/601242/9 "2011-10-30T18:25:07Z")
First, note that all real particles are real. The electrons in your body and the photons hitting your eyes are the real deal. To be sure, these objects have the usual quantum mechanical features like wave-particle duality and uncertainty about their true locations and/or momenta, but in everyday language we call these things “particles”, and they are real. We also have a mathematical framework for calculating interaction rates for particles. If we are interested in what happens when an electron and a positron approach each other, we can write down a big mathematical expression that tells us the answer, but just because you can write down some math doesn’t mean you can easily extract a number from it. So, you can play some tricks. In case you aren’t familiar with Taylor expansions, here is a brief aside that you should work through. **Taylor series (or Taylor expansions)** Consider the function _e[sup]x[/sup]_, that is [2.718…](http://en.wikipedia.org/wiki/E_(mathematical_constant)) raised to the power of _x_. This expression is simple to define, but just because you can write \*e[sup]\*0.17[/sup] doesn’t mean you can easily calculate its numerical value. So, you wait for the insight of Brook Taylor, who in the 1700s used calculus to prove that the following equation is true: _e[sup]x[/sup]_ = 1 + _x_ + _x_[sup]2[/sup]/2! + _x_[sup]3[/sup]/3! + _x_[sup]4[/sup]/4! + (etc.) , where the “!” notation means [factorial](http://en.wikipedia.org/wiki/Factorial), with 4! = 4_3_2\*1 = 24. The infinite series of terms on the right hand side of that equation is called the “Taylor expansion” or “Taylor series” for the function _e[sup]x[/sup]_. It may not seem like we’ve made much headway, since we’ve given ourselves the impossible task of adding up an infinite number of terms to calculate _e[sup]x[/sup]_, but it turns out that for certain values of _x_, the terms get smaller and smaller so quickly that we can ignore all but the first few. Taking only the first few terms means we will actually only have an approximation of the answer, but we can get as good an approximation as we require by adding up the right number of terms. So, try it for _e[sup]0.17[/sup]_. The true value is 1.18530485… Take your calculator and add up, term by term, 1 + 0.17 + 0.17[sup]2[/sup]/2 + 0.17[sup]3[/sup]/6 + … After only the first three terms, you will be within 0.07% of the true value. After four terms, 0.003%. That’s very useful! So, the not-at-all-straightforward task of calculating _e[sup]x[/sup]_ has been reduced to adding up a handful of simple terms. For larger values of _x_, the convergence isn’t as fast. (For _x_=2, for instance, four terms gets you only within 5%. But as long as you know how good the approximation is (and there are ways to determine this), then you know how far out you need to go.) **Back to particle physics** When we write down the math for calculating the interaction probability for two particles coming towards each other, we have a similar situation: we can _write it_, but we can’t calculate it, at least not practically. In particular, the math looks like this: probability = A \* S \* B where A is a cumbersome mathematical object that represents the incoming particles, B is the same for the outgoing particles, and S is a different cumbersome mathematical object that says what happens in between. What Feynman showed was that the S part could be broken out into an infinite number of terms, much like a Taylor series. Further, as long as the “_x_” in the series expansion is small, you only need to use the first handul of terms to get a good approximation. Very conveniently, this is true for electrical forces (quantum electrodynamics), where _x_ turns out to be the [fine structure constant](http://en.wikipedia.org/wiki/Fine-structure_constant), equal to 0.007297… So each term in the series is a lot smaller (and more negligible) than the last. So now the calculation looks like: probability = A\*S[sub]0[/sub]_B + A_S[sub]1[/sub]_B + A_S[sub]2[/sub]\*B + … . Just as there is an obvious pattern in the terms of the _e[sup]x[/sup]_ expansion, there is a pattern in the terms here. Feynman noticed this pattern and also noticed that it could be cast into a pictorial form. The resulting pictures are called [, and they help you remember what terms you need to be considering for the interaction in question. Consider the left part of this [url=[http://timlshort.files.wordpress.com/2011/03/f11.jpg](http://timlshort.files.wordpress.com/2011/03/f11.jpg)]image from the web](]“Feynman diagrams”[/url). It shows an electron and positron coming in from the left, an electron and positron leaving to the right, and a squiggle connecting the two particles. In the math, this is the A\*S[sub]0[/sub]\*B term, which says “particles come in (represented by A), something happens (S[sub]0[/sub]), and particles leave (B)”. The S[sub]0[/sub] part has a mathematical structure remarkably akin to that of a particle (in this case, a photon, drawn traditionally as a sqiggly line), so the bookkeeping trick is to represent it as a particle in the picture. Hence: there is a photon drawn connecting the two interacting particles. Now consider the other half of the image, which shows a loop in the middle of the squiggle. This represents, say, A\*S[sub]1[/sub]\*B. The mathematical structure of this term looks remarkably akin to a photon turning into two quarks which then annihilate and produce a photon again. So, the bookkeeping trick is to represent this term pictorially as such. By following a few simple rules, you can draw all the diagrams needed to represent all the terms in the series expansion. The ones with fewer things going represent larger values, so you can “calculate” those first. By “calculate a diagram”, I mean: look at the lines in the diagram and work out what the actual mathematical expression for the term must have been, and then calculate the value of that expression. The diagrams are just to help you figure out which terms are present and which terms are the dominant ones. **Virtual particles** So, the lines in these diagrams that look like particles and are representing parts of the S expansion (_i.e._, the “stuff happens” part of A_S_B) are called “virtual particles”. The real particles are the A and B parts – the particles that are coming in and going out. Linguistically, we say that these real particles “exchange virtual particles” when they interact. These virtual particles are just mathematical bookkeeping devices, though, and one must take care not to let the language elevate them further. (To be sure, tremendous physical insight can be gained by thinking in terms of virtual particles. But, that’s just because they really do diagrammatically represent the real math.) ---
### Author: ![KarlGauss](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/karlgauss/32/3713_2.png) [@KarlGauss](https://boards.straightdope.com/u/KarlGauss) #### Post date: [October 30, 2011, 6:37pm UTC](https://boards.straightdope.com/t/what-are-virtual-particles/601242/10 "2011-10-30T18:37:01Z")
> [@Pasta](#): > > \ . . .These virtual particles are just mathematical bookkeeping devices . . . \ You can see by the time of my post that I haven’t spent anything close to the required time (for an idiot like me) to digest what you’ve said. Still, I will ask: _If_ Hawking radiation is ever obseved, does that not mean that either virtual particles can “pop into” existence (thereby becoming more than bookkeeping devices), or at least cause ‘real-world’ measurable effects (indicating that they must have at least some properties typically associated with real particles, i.e. they cause measurable effects), again indicating that they’re something more than just bookkeeping devices? Thanks! ---
### Author: ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos) #### Post date: [October 30, 2011, 6:43pm UTC](https://boards.straightdope.com/t/what-are-virtual-particles/601242/11 "2011-10-30T18:43:13Z")
The Hawking radiation that is observed (if it ever is) is real particles (or at least, really, really close to real). The process by which that radiation came into existence is fuzzy, and may well involve virtual particles, but even if it does, we can’t say which virtual particles. And Hawking radiation isn’t special at all in this way: The same can be said of any particle, produced in any sort of interaction. ---
### Author: ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom) #### Post date: [October 31, 2011, 3:52am UTC](https://boards.straightdope.com/t/what-are-virtual-particles/601242/12 "2011-10-31T03:52:52Z")
First, thanks **Pasta**. Fantastic. I’ll give it my best. Second, from **Chronos** : > [@Chronos](#): > > …The same can be said of any particle, produced in any sort of interaction. My reply: :eek: ---
### Author: ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom) #### Post date: [October 31, 2011, 4:06am UTC](https://boards.straightdope.com/t/what-are-virtual-particles/601242/13 "2011-10-31T04:06:29Z")
You know, regarding my “:eek:” of a few minutes ago, I see that this point was raised right off the bat by **Chronos** , and then explored more strongly by **Pants** (whose cite I did “read”, with expected results). Apologies. But I guess I need to hear these points put to me as science and as philosophy (damn my lack of physics training!) as many times as possible, each time w/ more insight. _Later on,_ I’ll ask if you smartiepants are saying nothing is real, after all? Physicists have been on the receiving end of this for millennia. But that’s for another thead. ---
### Author: ![iamnotbatman](https://avatars.discourse-cdn.com/v4/letter/i/858c86/32.png) [@iamnotbatman](https://boards.straightdope.com/u/iamnotbatman) #### Post date: [October 31, 2011, 5:39am UTC](https://boards.straightdope.com/t/what-are-virtual-particles/601242/14 "2011-10-31T05:39:47Z")
> [@Chronos](#): > > But that’s complicated, too, because the line between virtual and real particles isn’t actually all that clear, and if you try to make it a sharp distinction, then there’s some sense in which you can argue that _only_ virtual particles can be detected, and real particles never can be. See, a real particle is defined as one that propagates in from infinity, or propagates out to infinity, but you’re not an infinite distance away from whatever process you’re observing. The particles that you observe _don’t_ propagate all the way out to infinity, because they interact with particles in your eye (or whatever detector you’re using) before they get there. So really, it’s just a virtual particle that behaves _almost_ exactly like a real one. Since some of the responses here have lingered over this point, I think I’ll jump-in with a nitpick. First of all, a real particle is not defined as one that propagates in/out from infinity (for the experts in the room, a real particle is simply a particle that is on mass shell, and it can be on mass shell without coming from infinity). As a general statement it is incorrect to say that all particles are virtual, and it happens that there is in fact a clear distinction between real and virtual particles after all. This is a misconception owing to the fact that the external legs of feynman diagrams are (purely out of calculational convenience when studying scattering processes) generally taken to represent particles coming in/out from infinity. But this is by no means a requirement – particles can scatter many times, and still be “real” the entire time. Despite the seductive allure of taking the external legs of one feynman diagram and attaching it to another feynman diagram so that one of the previously external legs is now internal and calling ‘virtual’ what was previously ‘real’, doing it is misguided. Real particles are not themselves the internal legs for some larger feynman diagram, because that larger feynman diagram would involve summing over a whole lot of different internal virtual states; it would NOT involve a ‘slightly virtual’ internal leg, which in this context I hope should now be clear to you is a pretty silly concept. Feynman diagrams are for calculating probabilities about real particles. They are a mathematical tool for when you have two particles aimed at each other and you want a statistical prediction about the outcome, and it involves purely mathematical figments called ‘virtual particles.’ But in the real world there are no virtual particles, only real particles. That said, quantum field theory is not fully understood, and everything we know about it is through various approximate calculational tools. In reality interactions between particles involve messy vibrations of fields, and ‘virtual particles’ probably do have some real physical meaning in that they are one way of looking at those messy vibrations and describing them in terms of things that we are more familiar with. But that’s really no different than looking at a particle and calling it a rocket ship. Sure, particles and rocket ships have a bit in common, and you can try to describe a particle in terms of rocket ships (it gets complicated ;)) but that doesn’t mean a particle actually _is_ a rocket ship. ---
### Author: ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos) #### Post date: [October 31, 2011, 4:48pm UTC](https://boards.straightdope.com/t/what-are-virtual-particles/601242/15 "2011-10-31T16:48:31Z")
But a particle propagating from one interaction to another isn’t necessarily on its mass shell. It’s very close to its mass shell, if the propagation distance is long compared to its Compton wavelength, but it can still be slightly off of it. And in fact the set of states where it’s _exactly_ on its mass shell is of measure zero, so it’s not only _possible_ that it’s slightly off; it’s overwhelmingly likely. ---
### Author: ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta) #### Post date: [October 31, 2011, 5:29pm UTC](https://boards.straightdope.com/t/what-are-virtual-particles/601242/16 "2011-10-31T17:29:23Z")
I would propose to the OP that he ignore for now all the (IMHO) pedagogically distracting semantic arguments about whether there are any real particles, especially as I expect this side discussion will continue. Just take it as a given for now that there are _real_ real particles, as your intuition suggests there are. Our methods for calculating the interaction probabilities for these real particles involve steps that introduce the notion of virtual particles, as described upthread. These virtual particles share some characteristics with real particles, and vice versa – otherwise, the term “virtual particle” wouldn’t have been a very good term to choose – but real and virtual particles are quite distinct. ---
### Author: ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat) #### Post date: [October 31, 2011, 7:43pm UTC](https://boards.straightdope.com/t/what-are-virtual-particles/601242/17 "2011-10-31T19:43:51Z")
In that paper I quote earlier the author makes the interesting point that real particles don’t actually have that firm a theoretical existance in quantum field theory. However what he does say (or at least imply) is that as the existance of real particles is an empirical fact and that their problematic status in QFT is actually a problem for QFT not for the existance of real particles. ---
### Author: ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos) #### Post date: [October 31, 2011, 7:47pm UTC](https://boards.straightdope.com/t/what-are-virtual-particles/601242/18 "2011-10-31T19:47:39Z")
Then again, _most_ things that we take for granted in the macroscopic world turn out to be on rather shaky ground when you get down to the quantum underpinnings. ---
### Author: ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit) #### Post date: [October 31, 2011, 7:49pm UTC](https://boards.straightdope.com/t/what-are-virtual-particles/601242/19 "2011-10-31T19:49:58Z")
> [@These are my own pants](#): > > In that paper I quote earlier the author makes the interesting point that real particles don’t actually have that firm a theoretical existance in quantum field theory. However what he does say (or at least imply) is that as the existance of real particles is an empirical fact and that their problematic status in QFT is actually a problem for QFT not for the existance of real particles. But QFT predicts the observations that make the existence of real particles an empirical fact, so how can that be a problem for QFT? ---
### Author: ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat) #### Post date: [October 31, 2011, 8:10pm UTC](https://boards.straightdope.com/t/what-are-virtual-particles/601242/20 "2011-10-31T20:10:55Z")
> [@Half\_Man\_Half\_Wit](#): > > But QFT predicts the observations that make the existence of real particles an empirical fact, so how can that be a problem for QFT? I don’t know enough about QFT to do more than merely echo what Nikolic says in section 9, but he seems to suggest that the main problems that in QFT their isn’t necessarily any such observable that corresponds to the number of real particles in a system. So that’s not just that the number of partcles is subject to quantum uncertianity, but that it’s not a basic property of the system i.e. that the relationship between the quantum state and the number of particles is non-trivial. [Next page](https://boards.straightdope.com/t/what-are-virtual-particles/601242.md?page=2)