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When this ambiguity is resolved at one point because phase shifts can propagate faster than the velocity of light and even with infinite velocity (an easily and demonstrable truth not often talked about) the state of the other particle is simultaneously resolved.
What you ask seems to be what rules there is to QM, and if they will make the same sense as our macroscopic?
That one speaks about a electron as a form of 'standing wave' around a atom, able to have a defined quantized 'energy'. This site is one of the nicest I've seen, defining QM concepts.
And when it comes to the duality we see in QM we have a new way, called weak measurements, that some see as 'the way' forward. The problem with such an idea being that as it assume that the possibility and probability of inferring something exists as a real thing, it also leads us to a presumption stating that because we can, it also must be. Quantum mechanics rule 'bent' in classic experiment. (particle/wave duality)
SR doesn't break down. It is defined from a constant, being 'c' and that one holds. I guess you're thinking of entanglements there? What they do is to beget a value 'instantaneously' as you measure one of them, the distance between particles notwithstanding, as far as we know that is, the furthest we have tested this was in optic fibers, some kilometers? As far as I remember.
If you could assume that there would be a applicable communication, making sense, then the idea of 'c' defining a limit for the 'speed' of communication would be wrong, but 'c' would still be a constant.
david (and others) when I say the probability in the wave function is a multiple locations with a particular probability it is only like that until you measure this and find it at one of the three locations and then it is clearly 100% at that location. However if you perform exactly the same experiment a large number of times the locations found would display the probabilities indicated. As with the original numbers I suggested 50%, 40%, 10%, within the normal probabilities of deviation of statistical experiments based on the total number of times the experiment was carried out.This is the way particle physicists measure the results of their experiments.
If the particle wave is on both ends of the scale, you can rightly say that the particle is in two places at once, and you won't know where it is until you measure it.
Letís start with the wave/particle duality. My understanding is that QM is consistent with the idea that particles may not actually exist as physical entities. The more precisely one can locate a wave, the more it resembles a particle. (See JPís post with the wave diagrams, above). This might lead to the conclusion that a particle is nothing more than a precisely located wave.
we treat the particle as a single infinitely small point
Quote from: JPwe treat the particle as a single infinitely small pointThis may seem like nit-picking, but it isn't intended as such, I just have this "thing" about infinity. (I bet that surprised you! ). Would I be right in thinking that "infinitely small" must refer to a mathematical infinity? Otherwise, how would you distinguish between "infinitely small" and "non-existent"?
It's zero dimensional - dunno if that helps or causes more confusion
They have position but no extension
"Experimental results have demonstrated that effects due to entanglement travel at least thousands of times faster than the speed of light. In another experiment, the measurements of the entangled particles were made in moving, relativistic reference frames in which each respective measurement occurred before the other, and the measurement results remained correlated." From Quantum_entanglement
Try this for a nice Signal Travels Farther and Faster Than Light. introduction, one thing though, Einstein didn't 'sneer' at all, as I know? Entanglements was actually his creation, as I understands it, although he expected the idea to prove the opposite to what it actually did. EPR paradox.
From a mathematics standpoint, a point with no extension is easy to imagine
Quote from: JPFrom a mathematics standpoint, a point with no extension is easy to imagineMathematically, I agree; but then I try to apply this to the "real" world and say something like: if I put 100 of these points side by side, would they still occupy no space, because 0 x 100 = 0.