Virtual particles do not exist
And there are no infinite particle-antiparticle pairs in a vacuum
Introduction
We often hear the word ‘virtual particle’ in physics and pop-sci explanations of quantum field theory. But, in reality, there are no such things as virtual particles. Today we will explore why (and how) virtual particles are needed, and also why they don’t exist.
QFT
Our story begins begins with QFT, i.e. Quantum Field Theory.
The above picture shows the graph of the Higgs field. Think about it like this: at very point in space and time, we assign a random property. This could be a number, a vector, a tensor, anything you want. Then we try to figure out how that property behaves as time passes and other things interact with it. This is field theory in a nutshell.
In quantum field theory, the first thing you do is assign a field to every point in space. This field could be described by simple numbers called scalars or even more complicated things like vectors.
Now, in QFT, when you add some energy to the field, the field changes: it oscillates between some particular values. This oscillation resembles a particle.
If all of this was too heavy, its okay, because we won’t need much details. All you need to keep in mind is that fields exist and oscillation in those fields are particles.
Feynman Diagrams and Interactions
Now, the image you see above is called a Feynman diagram. It describes the interactions between two or more particles.
For example, the above diagram describes how two electrons repel each other. We all know that like charges repel due to the electromagnetic force, but its actually a bit more subtle. When two electrons get too close to each other, they exchange a photon: a particle of light.
A completely optional but slightly more rigorous way of putting this is (you can skip this if you weren’t comfy with fields): two oscillations in the electron field come too close to each other that they overlap a bit.
This creates an oscillation in another field; the electromagnetic one. The electromagnetic oscillation makes the other two oscillations go away from each other.
The slight caveat, as you can see in my messy diagram above, is that there are many possible ways by which the two electrons can repel each other. We won’t go deep into the exact specifics of all the possible Feynman diagrams, but maybe I will follow up in the future.
Now, this point requires a bit more attention. We will flesh out some details.
Perturbation theory
Imagine you want to solve an algebra problem. You know the formula (x +a)² = x² + 2ax + a². But the problem is a more harder version than that. What would you do? You would try to solve the problem using the formula you know. If that does not work, then you would try fiddle around by adding or subtracting something, and then apply the formula.
This was a crude analogy of what perturbation theory is. Sometimes we have to solve problems that are too hard, like the interaction we saw above.
Two repelling electrons may not seem like much, but it it involves a lot of complicated (and a rather messy) range of calculations. So, to make it easier, we take a very simple case (which is far far far away from what is actually happening; like the first Feynman diagram we saw) and do the calculations.
Then, we take a little harder case (harder, but still way away from reality) and do the calculation for it. We take the results of our two approximate solutions and add them up, to get another good approximation.
It may seem we add diagrams in the above pic, but we do not. We add the integral equations they represent.
Each of these approximations contains different configurations of the electromagnetic field (the one which produces the photon). These configurations correspond to different oscillations in the field, which when added, pretty much replicate what really goes on, in reality.
Virtual particles
Keep in mind that the different oscillations which approximate reality, are just creations of us fiddling around to make our simpler equations fit the problem. These oscillation do not really exist. These are just dummy oscillations, or if you prefer, a mathematical sleight of hand.
Now, we have caught on an habit of calling them virtual particles. We think these particles “come in and out of existence” for “very miniscule periods of time”, or that they are “not real”.
Yes, oscillating fields correspond to particles, but these oscillations (and thus the corresponding particles) don’t exist. They are an invention to simplify a rather complex (and real) oscillation. They do not “exist” at all, even for very short intervals of time.
Heisenberg’s Uncertainty Principle
You may have heard or seen this somewhere:
This is the famous Heisenberg Uncertainty Principle: that both the energy and time of the field cannot be known at any instant.
This is taken to be the primary existence of the virtual particles: since for arbitrarily small time scales, we cannot know the energy, the field is bustling with particles.
While I do not deny the validity of this principle, there is no way that this is conclusive of virtual particles. What this says that in empty space, there is a small uncertainty for the amount of energy a field can have. That’s all.
If I were to sum this up: we cannot know for sure how much energy the field has for small values of time. This energy may be fluctuating from picosecond to picosecond, and there is no way we can accurately measure and predict the energy of any field.
These are the only particles that can and do exist:
Of course, maybe we will find more than these, but as of now, both theoretically and experimentally, these are the only particles that can exist. Unreal particles from the void? Only sci-fi or math.
Why the fuss?
This may seem like thinking about virtual particles is the wrong thing to do: NO.
Virtual particles are useful: they help make our math easier, they provide an intuitive way to imagine perturbation theory, they can be used to make new predictions and discover new physics. Yes, they are convenient and they are a lot of help, no doubt on that.
But, it is important to know what is math and what is real. Take Hawking radiation.
Hawking radiation is usually explained as the result when one pair of virtual particles are formed, and one of them enter the black hole, and the other escapes. Very intuitive and simple to understand right.
Technically speaking, Hawking radiation has nothing to do with virtual particles. It has do with the oscillations we talked about earlier, and how they appear differently to different people near and far from the black hole. I have been hoping to write an article on this too, but for now lets keep it at this level.
Just because virtual particles gave us a more intuitive understanding does not mean that is the whole picture. Hawking radiation is one of the cases in which a piece of math is taken too literally to simplify things.
What’s the harm in that? As long as I haven’t got it wrong, and I get the same result, I can think about it the simple way, right?
Yes, you can. As long as you know the distinction between reality and convenient math, and have a fair understanding of the big picture. That is what is this article aims to do.
I will let Feynman put this in a better way:
