The Quantum Thomist

Musings about quantum physics, classical philosophy, and the connection between the two.
Is God a failed Hypothesis? Part 3: Models

Intellectual conservatism interview.
Last modified on Sun Aug 9 16:54:57 2020

Last weekend I had an interview wih Suan Sonna of Intellectual conservatism. We Our discussion covered a range of topics including the relationship between physics and metaphysics, divine simplicity and timelessness, and how Aristotle fits into the picture.

Is God a failed Hypothesis? Part 4: Philosophical Objections

Reader Comments:

1. Benedict
Posted at 00:14:57 Friday August 21 2020

Hello Mr. Cundy,

Off topic but I have seen some claim that virtual particles can come from nothing, and was wondering what your thoughts are on this matter.



2. Frank M.
Posted at 04:36:22 Friday August 21 2020

Virtual particles do not come from nothing


You ask "I have seen some claim that virtual particles can come from nothing."

The claim is simply false. Virtual particles exist presupposing that *fields* exist. They are best understood as fluctuations of these fields due to the quantum mechanical properties nature (and thus fields) have.

So from a Thomistic P.O.V. perhaps virtual particles have no "efficient" cause, but do have what I would call a material cause (the field itself) and a formal cause (which we deduce from the laws of quantum mechanics).

Even not taking a Thomistic view, there is still a need for something to exist in order to bring these virtual particles about. What virtual particles shatter is really the "Newtonian View" of (deterministic) causality.

If you pardon me a funny analogy, imagine I slap someone in the face suddenly with no provocation.

That person (or bystanders) might say "That came out of nothing!", meaning that my slap had no rational motivation (in their eyes). However it did not come "come out of nothing", since I had to exist in the first place to slap someone, whether did I do it for some reason or it was just an involuntary spasm.

3. Nigel Cundy
Posted at 21:15:22 Saturday August 22 2020

Virtual particles

My thoughts on virtual particles are even stronger than Frank's. We agree that they certainly do not come from nothing. I would, however, go further than just saying that they are fluctuations or excitations of the fields (which they are, but no less or no more than the non-virtual or observed particles).

Firstly, we need to ask ourselves what a virtual particle is. We first encounter them in perturbative calculations in quantum field theory. Perturbation theory is a way of making a calculation through a series of systematically improved approximations. So you start by calculating an approximate answer to your problem. You then want to find the correction to that answer which gives you the exact solution. But you can't do that because it is too difficult, so you find an approximation of the correction. Then you approximate the correction to that, and so on ad infinitum. At each step, you gradually move closer to the real answer. And (just as importantly) at each step you can calculate a bound for the size of the remaining difference from the exact answer, so you can express how precise your approximation is.

In quantum field theory, the standard way of doing perturbation theory is using the Feynman diagram, or Feynman perturbative series. I have a few examples in this post here:

Some explanation is needed. Each straight line represents an electron or photon. Each wiggly line represents a photon. The left hand side of the diagram represents the initial state. The right hand side represents the final state. The axis from left to right represents the direction of causality. The naive way of looking at the diagram is to say that each diagram represents one possible path from the initial state to the final state. So, taking the second diagram in the left column, you see that the initial electron goes along, and at some point emits a photon. That photon and the electron then go on their uneventful way and are observed by the detector in the final state. The bottom diagram on the right column is similar, except here the photon decays into an electron and positron, and at the end of the process we observe two electrons and one positron.

You will notice that in some diagrams, there are particles which are emitted and then absorbed in the same diagram. They are not part of the initial or final states, and so are never directly observed. These are known as virtual particles. The most important difference between virtual particles and the observed states is that observed states always have an energy and momentum that satisfies Einstein's equation -- the dispersion relation -- linking the two and the mass (E2 = (pc)2 + (mc2)2), while virtual particles don't necessarily satisfy this relation. (That might, however, just be an artefact of the measurement process, which forces an observed particle into an exact eigenstate of the energy operator; i.e. forces the particle to obey the dispersion relation.)

There are various rules to calculating a probability amplitude from the Feynman diagram (and actually using it to make predictions), which I don't need to go into here, except to say that the more decay/emission/absorption events there are the smaller the amplitude (at least in quantum electrodynamics and the weak interaction). So we calculate all the diagrams to a certain order to get an approximate answer, and if we want to improve the approximation we just calculate the next set of diagrams. Each successive correction is smaller, and since we know roughly how fast they decrease, we can estimate the error of the calculation.

It is tempting to take the Feynman diagram expansion as a literal picture of reality. Each diagram represents one possible route from A to B. We would say that in reality there is a chance that the electron really does emit a photon, which really does get reabsorbed back into the electron to give our observed final state (top right of my diagrams). We just don't know which of the routes it actually took (or is going to take), so if we want to calculate the final probability, we have to take into account all of the possibilities and add up their amplitudes.

In practice, we have to be more sophisticated than adopting this naive picture. There are three main reasons for this need for sophistication. 1) The particles in these diagrams are unrenormalised (that is to say the operators representing the particles are in the wrong basis; we can convert to the correct basis, but that is usually done as the last step of the calculation after we have calculated all the amplitudes and drawn the diagrams). 2) Particularly in the strong nuclear forces, there are effects from what we call the quantum vacuum (but mean by that the background gluonic field) which aren't picked up on in perturbation theory (which assumes a perfectly flat vacuum). This leads to certain important experimental observations not being accessible to perturbation theory. 3) Particularly for the strong interaction, the perturbative series doesn't converge in certain circumstances, i.e. each successive "correction" gets larger rather than smaller.

I personally believe, however, that we can in principle -- albeit probably not in any practical calculation -- build up a similar picture that avoids these disadvantages (for example, if we switch to the renormalised basis before rather than after we construct the diagrams, which avoids the first problem). However, whether you agree with me on this or not, any discussion of virtual particles needs to assume that something like this picture occurs in reality. Virtual particles only make sense in the context where an electron really does emit a photon which really does decay into a (virtual) electron and (virtual) positron which really do annihilate into a photon which is then absorbed back into another electron. Unless you have this picture of particle creation and annihilation in the back of your mind, it makes no sense to give virtual particles the ontological status they need in order for their purported emergence from nothing to cause a problem.

You will notice that in all the diagrams I drew in the post I referenced, no virtual particle emerged from nothing. They were all emitted either from an observed particle or another virtual particle. And this is a general rule for the Feynman perturbation series. Only those virtual particles which are connected to both the initial and final states contribute to the final amplitude. And this is true for all amplitudes, and all physical events.

There is therefore nothing in the physical construction which suggests that virtual particles come from the quantum vacuum, let alone from nothing. In the theoretical construct in which they play a role, they always emerge from another particle (which serves as the efficient cause). And if you say (which I don't think is reasonable, but some people might say this) that the theoretical construct is merely an instrumentalist human construction which doesn't represent reality, then the same is true for the concept of a virtual particle which only appears in this construction.

Indeed, there is strong evidence that they don't regularly pop into or out of the vacuum. If they did, they would generate a constant gravitational background energy which we would be able to detect.

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