Nick @internic@social.cleverlibre.org

@MichaelPorter Now this bit I've honestly never thought much about how to explain to a non-physicist, so...bear with me. In a field theory we generally start with a theory of, say, matter by itself and light by itself and then we introduce a "coupling" term that describes how they interact*. But once you've coupled them, that changes the set of energy states that the new coupled field theory can have.

Ideally when we want to calculate interactions in the coupled theory, we'd like to work in terms of the new energy states, however we generally don't know those states exactly. But in many cases we can use the trick of perturbation theory, which basically says we can compute things in terms of our original energy states with an infinite series of smaller and smaller corrections as long as the coupling term is small enough (small compared to 1 in dimensionless units). The individual terms in this expansion can appear to violate conservation of energy/momentum, but we know from Noether's theorem that the full summation must balance out to exactly conserve energy and momentum.

Many of the terms in such a perturbative summation can be thought of as corresponding to these short-lived virtual particles popping into existence (often in violation of energy/momentum conversation) to interact and then disappearing again. Physicists often talk about these as physically extant things, but I guess I would say that they are useful conceptual tools but nothing more than an artifact of this approximation technique; I don't view them as a real physical thing. I'm certainly not alone in this position, but I'm not sure it's the consensus among physicists.

In any case, the bottom line is that we know the full theory always exactly obeys conservation and these supposedly conservation-violating things involving virtual particles always have to be arranged just so in order that they cannot actually be observed. (2/2)

*Actually there's a totally different way to go about things using a notion called gauge theory, but that's too much of a detour.

@fraser

@MichaelPorter @fraser Yeah, I don't know much about the OMG particle specifically or even cosmic rays generally (although I know some experts), but @mcnees had what I thought was an illuminating thread on the OMG particle somewhat recently.

https://mastodon.social/@mcnees/111239708775364189

To answer your more general question about QFT, let me make what I said before a little more precise: Lagrangian field theories (of which QFT and most classical field theories I'm aware of are examples) obey a result called Noether's theorem, which tells us that for every continuous symmetry there is a conserved quantity (often called a "conserved current"). This is, in my opinion, one of the most beautiful and profound results in theoretical/mathematical physics.

A "continuous symmetry" would be some family of transformations you could make to the field that is scaled by some "knob" that's a continuous number, and it's a symmetry in the sense that it leaves the basic laws of the field theory (represented mathematically by the Lagrangian) unchanged. One example would rotational symmetry, i.e. if you can rotate your coordinates by any angle, and the laws of the theory are still the same. In that case the conserved quantity is angular momentum. Another example is time-translation invariance, where the laws of the field theory are the same a second, or a day, or a year from now. The corresponding conserved quantity is energy. And one more example would be space-translation invariance, where the laws of the theory look the same if you take a step to the right, or move a mile, or a light year. In that case, the corresponding conserved quantity is linear momentum.

Anyway, a field theory that has one of these symmetries must exactly obey conservation of the corresponding quantity. All of our fundamental theories of particle physics are invariant under translation in spacetime, so energy and momentum must always be exactly conserved at all times under those theories.

Now, you're not wrong that physicists do speak of the uncertainty principle allowing energy conservation being broken for a short enough period of time (i.e. as long as ΔE*Δt <= ħ ), but to my way of thinking this is a useful shorthand that is not, strictly speaking, correct (and leads to your well-justified confusion). (1/n)

@fraser

@MichaelPorter While many popular science pieces make it sound like particles can just pop out of the vacuum due to the uncertainty principle, quantum field theory doesn't quite work that way. Quantum field theory still obeys conservation of energy and momentum, so particles can't pop out of the vacuum, because it would violate conservation of energy. What makes virtual particles "virtual" is that they only feature within the interaction of other particles but are not actually observable in and of themselves. While they're often talked about as real physical things, they can be regarded as nothing more than a creative way of interpreting the terms summed up in the approximation method (perturbation theory) that we use to compute the observable results in quantum field theory.
@fraser