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Duhoc
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is equal to the amplitude squared in quantum mechanics.
Why?
Why?
... not quite, but a fair summary.is equal to the amplitude squared in quantum mechanics.
Because thems the rules.Why?
Duhoc said:is equal to the amplitude squared in quantum mechanics.
Why?
Duhoc said:Why?
Simon Bridge said:That's the way Nature works.
Nugatory said:Because we developed quantum mechanics to match the way the world works.
Duhoc said:is equal to the amplitude squared in quantum mechanics. Why?
Duhoc said:The probability of something happening is equal to the amplitude squared in quantum mechanics.
Why?
tom.stoer said:Bill, I don't think that Gleason's theorem answers this question completely. Gleason's theorem explains that if there's a probabilistic theory to be formulated on Hilbert spaces, then the probability is given by Born's rule. But the theorem doesn't answer the if.
agreedbhobba said:?.. its no longer pulled out of the air so to speak - you can see what goes into it - the most important being non-contextuality ...
Duhoc said:is equal to the amplitude squared in quantum mechanics.
Why?
Of course. Given a quantum system prepared in state |f> we can calculate the probability to find it in a state |g>.naima said:So it is a theory of conditional probabilities.
naima said:QM theory does not give a probability value to events.
We only have amplitude for couples <f|g>
So it is a theory of conditional probabilities. Who knows Luders Rule?
Theorem 1. Existence and Uniqueness.
Let Q be any projector in the lattice L(H) of projectors of a Hilbert space
H, dim(H) > 2. Let p(·) be any probability measure on L(H), with correspond-
ing density operator W , such that pW (Q) > 0. For any P in L(Q) define
mpW (P ) = pW (P ) / pW (Q) , where pW (P ) = Tr(W P ), as fixed by Gleason’s theorem.
Then,
1. mpW (·) is a probability measure on L(Q)
2. there is an extension pW (·|Q) of mpW (·) to all L(H)
3. the extended probability measure pW (·|Q) is unique and, for all P in L(H),
is given by the density operator WQ = QW Q / Tr(QW Q) so that
pW (P |Q) = ##\frac{Tr(QWQP)}{Tr(QWQ)}##
(2)
Expression (2) is referred to as the Lüders rule.
Probability is a measure of the likelihood of an event occurring. It is usually expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.
To calculate the probability of an event, divide the number of favorable outcomes by the total number of possible outcomes. This can be expressed as a fraction, decimal, or percentage.
Theoretical probability is based on mathematical calculations and assumes all outcomes are equally likely. Experimental probability is based on actual observations and may differ from theoretical probability due to chance or other factors.
No, probability cannot be greater than 1. This would indicate that an event is more certain to occur than certain.
Probability and odds are two different ways of expressing the likelihood of an event. Probability is the ratio of favorable outcomes to total outcomes, while odds are the ratio of favorable outcomes to unfavorable outcomes. Odds can be converted to probability by dividing the number of favorable outcomes by the total number of outcomes plus the number of unfavorable outcomes.