I've only done an introduction into quantum mechanics but I've seen several videos (This seemed the most credible and confused me the most https://www.youtube.com/watch?v=IRcmqZkGOK4) describing the Casimir effect and most seem to draw on the fact that it's not possible for a particle to have 0 energy/momentum because that would violate the the HUP. My understanding is that the HUP is always obeyed but it is with regard to what we observe and our increased uncertainty in another measurement as we become more certain of one.
It seems to me as if the videos are saying that since we can't know two quantities with perfect certainty, it somehow follows that particles cannot have 0 energy/momentum. When I try to make sense of this (I can't but I try) I can't help but think why does this argument only apply to 0 then. Would it not also be impossible to have 1,2,3... any precise amount of energy/momentum?
** Further Clarifications The video listed gives the following argument. The HUP states you can't know when a particle arrived and its energy. So if you measure a particles energy, even if it has 0 energy in reality, you won't actually be able to measure that it has zero energy.
This seems reasonable to me, where he loses me is when then goes on to say.
So really there is no particle with 0 energy. So what can end up happening is you can have particles popping into existence for some period of time as long as the energy is small enough for them to be around for that long.
The reason I've linked this to the Casimir effect is because he then claims that this popping in and out of existence is the cause of the Casimir effect.
A fairly wild effect (which I understand has been empirically shown to be true) is based upon this HUP and I don't understand how HUP supports it.
