Virtual particles and Heisenberg

[jcalises]

I registered yesterday in this forum with the intention of someone clarifying me how the Heisenberg uncertainty principle can explain the existence of virtual particles. More energy implies less lifetime is only possible if ΔE Δt = h/4Pi, but that's not Heisenberg's principle, the principle is ΔE Δt≥ h/4Pi, and it says nothing about a maximum value of Δt. Before asking, I searched the forum for similar threads and found that the general opinion was that virtual particles did not exist, that they were a mere mathematical artifice and that they did not even have lifetime.
Ok, I'm not asking for an explanation anymore, but I can't help but express my surprise that so many serious physics books state something that isn't true.
Sorry for the speech and thanks for the attention.

 

[PeterDonis]

Before asking, I searched the forum for similar threads and found that the general opinion was that virtual particles did not exist, that they were a mere mathematical artifice and that they did not even have lifetime.

That might be a little strong, but it is certainly the case that the actual physics that is pointed at by the term "virtual particles" is not what many people appear to think.

These Insights articles might help:

https://www.physicsforums.com/insights/physics-virtual-particles/

https://www.physicsforums.com/insights/misconceptions-virtual-particles/

https://www.physicsforums.com/insights/what-are-virtual-particles-intro/

I can't help but express my surprise that so many serious physics books state something that isn't true

That is too strong. First, you need to distinguish between pop science (I'm not sure what you mean by "serious physics books" but I suspect they are pop science books) and actual textbooks and peer-reviewed papers. The latter have to be much more careful about what they say.

Second, you need to distinguish between a description that is just intended to entertain (which, like it or not, is the primary purpose of pop science books, articles, videos, etc.), a description that is intended to teach a certain method without making assertions about "reality" (which is what most textbook presentations of "virtual particles" do), and a description which is intended to be a claim about "how things really are". Only in the last kind of description do statements about what "virtual particles" are not really come into play.

 

[jcalises]

Thanks for answering.
I don't want to give titles, but I'm referring to college textbooks, not popular science, that explain virtual particles using Heisenberg's uncertainty principle.

 

[Meir Achuz]

Virtual particles are artifacts of perturbation theory. In Feynman diagrams, they arise from Fourier transformations that eliminate the time variable. You can't talk about lifetime without a time variable.

 

[Nugatory]

Thanks for answering.
I don't want to give titles, but I'm referring to college textbooks, not popular science, that explain virtual particles using Heisenberg's uncertainty principle.

Even undergrad college textbooks will do that, especially ones not written for students on their way to a physics PhD. The E/t and p/x formulations of the uncertainty principle are useful heuristics in many problems, so it makes sense to teach them instead of instead of going all-in on quantum field theory for students who don’t need it.

 

[jcalises]

Thanks for the answers.

 

[Demystifier]

but I'm referring to college textbooks, not popular science, that explain virtual particles using Heisenberg's uncertainty principle.

Can you give an example of such textbook?

 

[vanhees71]

Thanks for answering.
I don't want to give titles, but I'm referring to college textbooks, not popular science, that explain virtual particles using Heisenberg's uncertainty principle.

The problem is that sometimes textbooks try to be pedagogical and use half-true "pictures". When it comes to relativsitic quantum theory one should first remember that the only successful description is in terms of quantum-field theory. That is, because it is the only way to describe interacting particles in a way that's consistent with the relativistic spacetime model, i.e., Minkowski space and particularly the notion of causality following from it.

That is because, if you try to localize particles, you have to confine them with some "force" and at some point, making this force stronger and stronger to better and better localize a particle, rather new particle-anti-particle pairs are created. E.g., if you try to confine an electron to smaller and smaller volumes due to the electromagnetic interaction new electron-postron pairs are created, and you cannot even specify which of the electrons was your original electron. That's why you cannot indefinitely localize this specific electron.

For such situations, where particle number is not conserved, the most natural way to describe these creation and annihilation processes is quantum field theory. Here the prime observables are fields like the electromagnetic field, and indeed there are commutation relations implying Heisenberg uncertainty principles saying that not all field components can have determined values at the same time, i.e., there are quantum fluctuations of these fields. The only exception is "the vacuum", i.e., the state of lowest energy, where there is really nothing. To observe the field fluctuations you need something to observe, e.g., an electron. According to relativsitic QFT (or more specifically quantum electrodynamics, QED, describing charged particles and the electromagnetic field) an electron is not simply a charged point particle but it's always accompanied by its own electromagnetic field, which fluctuates. Sometimes they call these fluctuations "virtual particles", but in fact they have nothing particle like. It's rather like the classical Coulomb field around a point charge, but in addition it fluctuates, and this makes quantum corrections to the classical field. One of the most accurate predictions of QED is the anomalous magnetic moment of the electron. Despite the electric field an electron is also a magnetic dipole with a corresponding magnetic moment, and at lowest order perturbation theory, corresponding to the "classical picture" an electron's magnetic moment is 2 Bohr magnetons, but due to the fluctuations of the electron's own electromagnetic field, there are higher-order corrections leading to small deviations from this value, and the corresponding predictions are accurate to about 12 or so significant digits.

Also one should be aware that the so-called energy-time uncertainty relation is very spacial. That's, because time is not an observable in the formalism of quantum theory, but must be inferred from observables. E.g., to measure time you can use a pendulum and count oscillations. The uncertainty in time is then inferred from the usual Heisenberg uncertainty relations corresponding to observables. Here both position and momentum have the usual uncertainty and to really know, when the pendulum has made one period is thus uncertain, which means that also the time measured by counting oscillations of the pendulum has some uncertainty. That doesn't imply that energy conservation were violated. All the conservation laws are strictly valid also in quantum theory.

 

[jcalises]

Thanks for the answers.
Demystifier, As I said before, I don't want to give titles, but I found an article on the web that deals with this topic, "Time-energy uncertainty does not create particles", and it gives some examples.
http://philsci-archive.pitt.edu/17443/1/TEUncertaintyVirtual.pdf

 

[vanhees71]

You can find a very elementary derivation of the energy-time uncertainty relation and its interpretation here in Appendix B:

https://arxiv.org/abs/2207.04898

 

[martinbn]

...
I don't want to give titles, but ...

Why not!!!

 

[Vanadium 50]

serious physics books

Like what? Textbooks?

 

[Vanadium 50]

sometimes textbooks

Do we know that?

I mean when the OP refuses to give references its kind of hard to go on, but most of what he complains about is found in popularizations.

 

[vanhees71]

True, but you find such narratives even in some (otherwise good) textbooks like, e.g., Peskin and Schroeder. I think it's just that many authors just copy from other textbooks, particularly introductory sections.

 

[PeterDonis]

Why not!!!

when the OP refuses to give references

The OP did reference an article that gives examples. That's sufficient for this discussion.

 

[Vanadium 50]

Adequate? Maybe. As helpful as it might be? Definitely not.

Are the texts wrong? Is it an oversimplification on the last page? Just a misunderstanding? Hard to go further in the dark.