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“Nothing” doesn’t exist. Instead, there is “quantum foam”
(bigthink.com)
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Can quantum particles be blocked or contained or otherwise impeded from entering a vessel?
Are they truly just appearing and disappearing or do they just move so fast (like, faster than C) that it only appears that way?
Nope, they actually appear and disappear. The idea is that even in vacuum there's a certain amount of background energy and that energy can randomly turn into matter-antimatter pairs in what is basically the inverse of matter-antimatter annihilation.
To a certain degree, as they mentioned in the article regarding the casimir effect. While one cannot keep out the quantum foam entirely, it can be restricted to specific wavelengths by altering the volume of the space.
So with a sufficiently small volume of space, we would have an actual nothing again? Or the foam can go infinitely small?
Consider this fact, some light waves like radio are large enough that a lot of matter is essentially invisible to their propagation; the radio waves just pass right by without any interactions. This becomes a similar problem when we try and measure such small quantum phenomena like zero-point energy. The quantum energy could be so small that they're invisible to our detectors, but are in fact still there - the two scales simple cannot interact in a measurable way. So, there'd like still be some quantum energy, just less and less until our detectors could not interact with the incredibly small quanta for measurement.