What, specifically is meant by "particles are popping in and out of existence all the time?"

Question

When I see that wording utilized, I have some confusion about what that means. Are the particle/anti-particle pairs each themselves popping in and out of existence, meaning the exact same particle exists for a time, but then that same exact particle ceases to exist, but then that same exact particle exists again, over and over again? Does that same particle continue on a cycle of existence to non-existence, back around to existence? I am not asking on a philosophical basis, as I think understanding the answer to this question will help me over a very large hurdle in my understanding of anything in this field of interest. I must emohasis what I do not understand, is if "popping in and out of existence" a valid, scientific way to say what is actually happening in nature? I think there might be something about this field that is just beyond my grasp, and my intuition is telling me it is because I need to know the answer to this question, in order to understand a whole lot more. I know I ask my questions in strange ways; I think it is a form of social hurdles as well. So I understand if I get booted or whatever. I do appreciate the warnings before cutting my account, as was warned. Because I do appreciate how patient everyone has tried to be with me. I will understand if you decide that this is not the medium in which I should continue my fascination with nature. It has been very helpful in many ways, though. So thank you. Peace, my fellow actual-monkeys.

Seriously though, don't forget... We are ACTUAL monkeys. It's ok. It's gonna be ok. We are some of the coolest monkeys, you and me.

But if anymonkey here wants to answer this monkey's question without pointing out how many social understandings I do not even understand I am making... that IS what I'm here to learn about... Ooh-ooh-ah-ah!

Answer 1

Thank you for this question. I've been waiting for an opportunity to address this issue. It is an important valid question.

The short answer is: there are no particles popping in and out of existence. This idea comes from some confusions that are (among others) relating to misconceptions about the relationship between the Fock basis and the quadrature bases.

For a longer answer: remember that the Fock basis is the particle number basis. Each Fock state is an eigenstate of the number operators and the eigenvalue is the occupation number telling us how many particles there are in the state. The uncertainties in the occupation number of these eigenstates are zero. For example, the vacuum state is an eigenstate of the number operator with an eigenvalue of zero and with zero uncertainty in the number of particles in the state.

The quadrature bases are also associated with the particle number degrees of freedom, but the elements of these quadrature bases are not eigenstates of the number operator and do not have a fixed number of particles associated with them. These bases are formed from the eigenstates of the quadrature operators. The associated eigenvalues of these quadrature eigenstates are often used as independent variables to represent quantum states on a phase space. One way to represent quantum states on such a phase space is in terms of Wigner functions.

When we consider the Wigner function of a vacuum state, we see that it is given by a Gaussian function which has a minimum width located at the origin of phase space. In other words, although the vacuum state has zero particles in it, it is nonzero at nonzero values of the quadrature variables. The width of this Gaussian is related to the minimum uncertainty that comes from the fact that the two quadrature operators do not commute.

If one does not think carefully about this, one may get the impression that this function shows that there is a fluctuation of particles in the vacuum state. However, this is not the case. The nonzero width of the Wigner function of a vacuum state does not indicate any fluctuations in the particle number degrees of freedom. Instead, the Gaussian function is an artifact of the relationship between the quadrature bases and the Fock basis. It comes form the fact that you need a Gaussian function as coefficient function for the quadrature basis to reproduce the Fock state of a vacuum state.

To clear up some other possible misconceptions: it is an experimental fact that one observe fluctuations in particle number when you measure for example the intensity in a weak laser beam. This fluctuation is called shot noise and it represents the discrete photons that are observed by the detector following a Poisson distribution. However, this fluctuation does not mean that particles are popping in and out of existence. The laser beam, however weak, does not represent a vacuum state.

Hope this clears up the confusion.

Answer 2

For a less technical answer, things like vacuum fluctuations and virtual particles and so on are purely artefacts of a mathematical trick we use to simplify the problem.

When we want to know what happens to a wave that is in some complicated, messy shape (like a square pulse), the maths gets too complicated. So what we do is we find a whole load of simple shapes (like sine waves) that we know how to handle, that add up to the complicated shape. Then we solve the problem for each simple shape, and then add the solutions together. If the equations are linear, then any sum of solutions is also a solution. So if the sine waves we started with add up to a square pulse, then the solutions to each sine-wave problem must add up to tell us what the square pulse does.

The sine waves are not real. There is only a square pulse, doing something complicated we can't follow. But mathematically a square pulse is a sum of sine waves, so we can imagine that they exist invisibly in the background like some cloud of possibilities that interfere and cancel out. We break down the problem into a sum over simple possibilities, trace what happens to each, then add them all back up.

When something happens in a narrow window of space or time, the intermediate state during the interaction is like a square pulse. Zero outside the interval. We can't solve this directly. But we can represent it as an infinite sum of sinusoidal waves. A sinusoidal wave in space is a pure momentum state, and a sinusoidal wave in time is a pure energy state, which are thus easy to handle. For any sufficiently spiky function, there are contributors of arbitrarily high energy and momentum. The narrower the space/time window, the more high energy contributors you get. These high energy contributors can then do things like cross potential energy barriers and make new super-heavy particles. Then we add them all up again and find out what our original square window interaction did.

Similarly, we can represent the vacuum with no particles as a sum of many states, each of which do have particles, but where the possibility of finding any when we add them back up cancels out. The vacuum state unambiguously has no particles and never changes. It does not fluctuate. Nothing "pops".

Breaking a wavefunction down into components like this doesn't mean the intermediate steps of the calculation really exist. It's just a useful way of thinking about it. But this being mathematics, it's not entirely clear what is meant by "exist" in the first place. If we calculate $7\times 6789$ $=7\times(6000+700+80+9)$ $=42000+4900+560+63$ $=47523$, do the values in the intermediate stages of the calculation "not exist"? Or are they just another equally valid way of representing the same thing?