Particle ontology and quantum fluctuations

[TheHeraclitus]

TL;DR

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How does Particle ontology account for quantum fluctuations and virtual particles?

I have been reading about ontologies in quantum physics recently and I came across Bohmian mechanics. If I understood it correctly BM endorses Particle ontology. Particle ontology claims that point-like particles that move continuously in time are the fundamental building blocks.
I know some people are trying to use field ontology for BM but I will ignore it here.

My question is, how does Particle ontology account for quantum fluctuations and virtual particles? It seems to me these concepts require field ontology.

Thank you!

 

[Demystifier]

First, quantum fluctuations appear also in the context of nonrelativistic QM, which has nothing to do with fields. In field theory there are vacuum fluctuations, which are just a special case of quantum fluctuations.

Second, quantum fluctuations and virtual particles are not ontological. Hence, whatever your choice of ontology is (particles or fields), it has not much to do with quantum fluctuations and virtual particles.

For more details about possible particle ontology in QFT see my https://arxiv.org/abs/0904.2287 Fig. 2 may be particularly interesting to you.

 

[vanhees71]

Nonrelativistic QM can very well be described as a quantum field theory and as such it also has to do with fields. A classical point-particle ontology (I understand under ontology as being related to observable phenomena) is very difficult to make consistent given the well-established existence of spin, while within a (quantum) field picture it's a very natural property.

 

[TheHeraclitus]

First, quantum fluctuations appear also in the context of nonrelativistic QM, which has nothing to do with fields. In field theory there are vacuum fluctuations, which are just a special case of quantum fluctuations.

Second, quantum fluctuations and virtual particles are not ontological. Hence, whatever your choice of ontology is (particles or fields), it has not much to do with quantum fluctuations and virtual particles.

For more details about possible particle ontology in QFT see my https://arxiv.org/abs/0904.2287 Fig. 2 may be particularly interesting to you.

What do you mean they are not ontological? I thought Quantum fluctuations are particle-antiparticle pairs, Wikipedia even says they violate the conservation of energy.

 

[vanhees71]

It's hard to get rid of bad popular-science writer's flawed pictures. Even the Wikipedia uses them, and obviously nobody was successful to erase them. We have some Insights articles on the subject:

https://www.physicsforums.com/insights/what-are-virtual-particles-intro/
https://www.physicsforums.com/insights/misconceptions-virtual-particles/
https://www.physicsforums.com/insights/vacuum-fluctuations-experimental-practice/
https://www.physicsforums.com/insights/vacuum-fluctuation-myth/

Particularly energy and momentum are conserved in each scattering process. There were early ideas to the contrary (Bohr and Kramers theory just before the correct quantum theory has been discovered) but as early been refuted by experiment (Bothe's coincidence measurement of Compton scattering).

 

[PeroK]

What do you mean they are not ontological? I thought Quantum fluctuations are particle-antiparticle pairs, Wikipedia even says they violate the conservation of energy.

There is a significant difference between physics as presented in popular science and physics as taught at university level as an academic subject. The nature of virtual particles is a case in point. It's important, therefore, if you want to philosophise about physics that you philosophise about the real thing and not some artificially simplified version that may indeed not stand up to close scrutiny.

 

[Demystifier]

I thought Quantum fluctuations are particle-antiparticle pairs, Wikipedia even says they violate the conservation of energy.

That's wrong, we have a lot of threads here explaining it.

 

[TheHeraclitus]

That's wrong, we have a lot of threads here explaining it.

I have read some of the threads and I think I understand virtual particles. But I am still confused on how should I visualize Quantum fluctuations

 

[PeroK]

I have read some of the threads and I think I understand virtual particles. But I am still confused on how should I visualize Quantum fluctuations

Look at Feynman diagrams!

 

[TheHeraclitus]

Look at Feynman diagrams!

I think Feynman diagrams describe virtual particle exchange between real particles like 2 electrons.
I am more interested in Vacuum fluctuation. When there are no particles but because of Uncertainty principle particle-antiparticle pairs are created from "nothing".

 

[PeroK]

I am more interested in Vacuum fluctuation. When there are no particles but because of Uncertainty principle particle-antiparticle pairs are created from "nothing".

The quantum vacuum has a non-zero expectation value for a measurement of energy. The way to calculate that energy is to use perturbation theory, which generates a series of terms that must be calculated. Each of these terms can be represented by a Feynman diagram, essentially with virtual antiparticles being created in pairs and subsequently annihilating. In that sense, the virtual particles are an aid to calculation. You don't have to imagine the virtual particles: you can simple calculate the perturbation series using whatever mathematical tools you have at your disposal.

The popular-science explanation that you quote implies there is a zero-energy vacuum; then, particle anti-particle pairs are created "from nothing"; the vacuum briefly violates conservation of energy before returning to its zero-energy state.

That's not true: the vacuum simply has a non-zero expected energy, and the virtual particles are a heuristic used in the calculation of the vacuum expectaion value.

This is why I cautioned against analysing a popular, designed for lay-people who don't like mathematics, watered-down version of QFT. If you want to tackle QFT, you have to tackle the real thing.

 

[Imager]

We have some Insights articles on the subject:

@vanhees71 Thank you for the references. I hadn't seen the first one and it was very helpful!

 

[Demystifier]

But I am still confused on how should I visualize Quantum fluctuations

Do you know how to visualize fluctuations in classical statistical mechanics? If you don't, that's what you should study first.

 

[vanhees71]

I think Feynman diagrams describe virtual particle exchange between real particles like 2 electrons.
I am more interested in Vacuum fluctuation. When there are no particles but because of Uncertainty principle particle-antiparticle pairs are created from "nothing".

Feynman diagrams are utmost clever and condensed notations for certain quantities called Green's functions, which are needed to calculate S-matrix (scattering-matrix) elements which encode the probability transition rates for reactions in particle collisions using perturbation theory.

The particle ontology (I hate this philosophical gibberish anyway; I'd rather speak about particle interpretation) is also to be taken with great care. The only states that have such a particle interpretation are the asymptotic free states, depicted by the external lines of a Feynman diagram. There is no particle interpretation for transient states, i.e., for times where the interaction itself takes place. If there's any interpretation of the internal lines other than their mathematical meaning as mathematical functions called time-ordered Green's functions, it's a field picture.

 

[Peter Morgan]

I suppose a different start, instead of introducing virtual particles right away, is to understand the nature of quantum and thermal fluctuations in the mathematics a free quantum field theory. For a quantum field $\hat\phi(x)$, which we might think to use as a model for measurements, the variance of measurement results is infinite because it is an operator-valued distribution.
If we consider an average, however, weighted by a function $f(x)$, $\hat\phi_f=\int\hat\phi(x)f(x)\mathrm{d}^4x$, then $\hat\phi_f$ is an operator instead of being an operator-valued distribution, so we can use it as a model for (very idealized) measurements, for which we find that there is a finite variance. In particular, the variance is proportional to Planck's constant, but it's also a quadratic functional of a real function $f(x)$, $\mathrm{Var}_{\mathrm{Vacuum}}[\hat\phi_f]=\hbar\int f(x) G(x-y)f(y)\mathrm{d}^4x\mathrm{d}^4y$, where $G(x-y)$ is a Lorentz invariant function of the distance between $x$ and $y$.
If we introduce thermal fluctuations into a free quantum field theory as well, then $G(x-y)$ is no longer Lorentz invariant, and kT makes an appearance, but the structure is in broad terms the same, so quantum fluctuations and thermal fluctuations for the free field can be thought of as quite similar, but different in a very specific way.
When we introduce interactions as well, the point there is to modify $G(x-y)$ in various ways, but also to add higher-order correlations between different measurements. Things get complicated because of renormalization, but we can say it's always just statistics of a noisy field. The virtual-particles talk is just a way to talk about that noise in terms of particles, but we can also talk in terms of a noisy field theory (really, that it's noisy is crucial!)
Everything above is in terms of mathematics. As always for mathematics, any given model may or may not be a good model for a given experiment. Indeed, a free quantum field theory is not a good model for experiments, but we can deform it in various ways to give some pretty good models. Keep in mind that some global measurements are not noisy, but local measurements in general are (indeed there are theorems proving that no local measurement of the vacuum state can be noise-free, for some choices of axioms.)