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A particle in a box exerts pressure on the walls of the box. This makes sense from a classical perspective. A particle that's bouncing back and forth in a box will exert an average force on the walls over time. But it also makes sense if we model the particle as a harmonic oscillator. If we increase the width of the box, the energy of the particle inside will decrease. The fact that there's a change in energy tied with a change in distance/position means there's a force at work. And it turns out that the bouncing particle model and the harmonic oscillator model give the exact same results mathematically.

The reason I think this might be similar to virtual particles is that the harmonic oscillator model represents what's happening with the particle more accurately, but the bouncing particle model might be easier to understand. This seems to be the case with virtual particles. Real particles aren't exchanging virtual particles one by one to exert force on each other as Feynman diagrams would suggest. But there is a change in energy associated with a change in distance, so there must be a force involved. But that can be really hard to conceptualize, so instead we act like they're exchanging individual particles so we can write simple equations and make simple Feynman diagrams.

I'm not suggesting that this is a perfect parallel. But is it on the right track?

zucculent
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    Kind of related: https://physics.stackexchange.com/q/230113/123208 – PM 2Ring Oct 11 '21 at 22:49
  • This helps a lot. It seems to be in line with what I was imagining. If I understand correctly, these disturbances have an energy associated with them, which changes with the distance between the particles, meaning there must be a force. Is this correct? – zucculent Oct 13 '21 at 23:47
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    Because of Heisenberg Uncertainty, classical notions like trajectories & forces don't work so well at the quantum scale. See (for example) https://physics.stackexchange.com/q/24068/123208 You might like to discuss these topics in The h Bar. – PM 2Ring Oct 14 '21 at 11:06

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First thing first: virtual particles can't be observed (by definition). That statement is very deep for your question. I don't know how familiar you are with QFT but Feynman diagrams are a way of representing terms of a very complicated system perturbatively. If you want to imagine in your head (like Feynman conceived) particles coming in and exchanging particles to mediate a force that's fine so long as it doesn't interfere with your calculations or reasoning.

As you already know, building an intuition behind quantum mechanics is hard. Sometimes thinking of virtual particles as particles coming in and out of existence or whatever can be counterproductive. For instance, people think of the Hawking effect as two virtual particles close to the event horizon where one falls and the other one scapes. In my opinion, it is much more fruitful to think of the process from the point of view of information theory (see Rindler wedges and the Unruh effect).

I guess my point is virtual particles aren't, in some sense, more real than the Hilbert space we work with as they can't be observed. If you are talking about something you cant observe you can be asking for trouble specially if you are just learning about QFT.

FriendlyLagrangian
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    I think the wording of my question may have given you the wrong idea. I was trying to ask whether my analogy of the particle in a box and the two ways to model it mathematically was a good first step to understanding what's actually going on when we talk about virtual particles. – zucculent Oct 11 '21 at 22:04