Perhaps I’m being too simplistic, but I see a decent explanation that doesn’t get as far into the weeds as some of the others. It’s proportional to the square because both the event being observed and the observer need to be in the same universe. If the particle can be in A or B, the odds are:
P(A)&O(A) = A^2
P(B)&O(B) = B^2
P(A)&O(B) = Would be AB, but this is physically impossible.
P(B)&O(A) = Would be AB, but this is physically impossible.
There are a number of reasons this solution does not work. Here is one problem with the solution that does not require any discussion of the formalism or interpretation of quantum theory:
According to you, the location of the particle and the location of the observer are correlated (this follows from the fact that some combinations are physically impossible). If that’s the case, you can’t calculate the probability of the conjunction by multiplying the probabilities of the conjuncts. That only works if the conjuncts are uncorrelated.
More broadly, based on what you propose here I don’t think you have sufficient understanding of quantum mechanics to fully appreciate the nature of the problem or the kind of solution that would be required. Your comment suggests several fairly fundamental misunderstandings about the theory. I hope this doesn’t come off as impolite or condescending. It’s the kind of thing I’d want someone to say to me if they genuinely believed it (although that in itself doesn’t entail that it isn’t impolite or condescending).
I didn’t expect something that simple had escaped everyone’s notice(though I suppose I should have said that more explicitly in my post) - I threw it out there because it made sense at first glance and had no immediately obvious problems, not because I figured I had definitely cracked the problem. Easier to see if there’s a known response than to try to figure it out myself. So no, I’m not annoyed by your response.
And I do think I see what you’re getting at. Oh well, it was worth a shot.
Perhaps I’m being too simplistic, but I see a decent explanation that doesn’t get as far into the weeds as some of the others. It’s proportional to the square because both the event being observed and the observer need to be in the same universe. If the particle can be in A or B, the odds are:
P(A)&O(A) = A^2
P(B)&O(B) = B^2
P(A)&O(B) = Would be AB, but this is physically impossible.
P(B)&O(A) = Would be AB, but this is physically impossible.
Squares fall out naturally.
There are a number of reasons this solution does not work. Here is one problem with the solution that does not require any discussion of the formalism or interpretation of quantum theory:
According to you, the location of the particle and the location of the observer are correlated (this follows from the fact that some combinations are physically impossible). If that’s the case, you can’t calculate the probability of the conjunction by multiplying the probabilities of the conjuncts. That only works if the conjuncts are uncorrelated.
More broadly, based on what you propose here I don’t think you have sufficient understanding of quantum mechanics to fully appreciate the nature of the problem or the kind of solution that would be required. Your comment suggests several fairly fundamental misunderstandings about the theory. I hope this doesn’t come off as impolite or condescending. It’s the kind of thing I’d want someone to say to me if they genuinely believed it (although that in itself doesn’t entail that it isn’t impolite or condescending).
I didn’t expect something that simple had escaped everyone’s notice(though I suppose I should have said that more explicitly in my post) - I threw it out there because it made sense at first glance and had no immediately obvious problems, not because I figured I had definitely cracked the problem. Easier to see if there’s a known response than to try to figure it out myself. So no, I’m not annoyed by your response.
And I do think I see what you’re getting at. Oh well, it was worth a shot.