- #71
Pythagorean
Gold Member
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apeiron said:What is so hard to understand about any of this?
Because you're kind of making it up, or at least discussing a particular aspect of position and momentum that is unclear. The position and momentum of a particle aren't jointly exhaustive properties of the particle (and you haven't showed how they are in your responses to me; you've only given more vague implications).
Head and Tails are a textbook dichotomy. The coin can only land on heads or tails (in the probability model; not reality where it can, with some probability, land on it's edge) so they're jointly exhaustive; the coin can't be both heads and tails at the same time, so they're mutually exclusive.
A particle can have a momentum and a velocity at the same time (they're not mutually exclusive properties of the particle) and momentum and velocity aren't the only two properties a particle can have (they're not jointly exhaustive properties of the particle).
So you must be talking about something specific. The HUP isn't dichotomistic: there is some bit of mutually exclusive (if you want to talk about the "crispness" of position and momentum, as you would call it)... but still, you can sacrifice a little from each and have both a momentum and a position that are both equally vague/crisp. It's not fixed to where you must measure one with high accuracy and one with low accuracy. You can compromise... that seems to fail the test for mutual exclusivity.
I can see how HUP might be jointly exhaustive (the HUP, after all, only has two variables in it), but you're still talking about a false dichotomy if only 1/2 conditions are satisfied.