We know that , Bell’s inequality lead critical decision about locality of the quantum physics and it’s experimental results !. But, if it is the case that classical probability theory(present day probability theory) is incomplete and fail to predict the nature of observation of quantum mechanical experiments ?. What’s your idea about kind of a most general probability theory can be call as complex probability , in complex number plain ? (Note-there is a paper BELL'S INEQUALITY AND COMPLEX INTERPRETATION OF PROBABILITY)
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Should we extend the probabilistic calculus? What about a more general probability theory, e.g. with COMPLEX probabilities? Could it succeed to predict the quantum results?
See details in my article :
Bell's inequality isn't ``weak'' and classical probability theory isn't ``incomplete''-indeed the term ``classical'' is wrong, because it isn't probability theory that changes-just the space of states. The space of a quantum system contains more states than the space of its classical limit. And only certain combinations of states of the former can be identified as states in the latter, that's all. Bell's inequality expresses the fact that there do exist states in the former that do not belong to the latter. So it's an experimental question, whether such states have physical consequences-and it turns out that they do.
Dear Stam,
Try to be a teacher, not only a critic. The terminology used by Manoj is not the best, but he has a couple of legitimate questions. Please be kind and try to understand what he asks, from his post to this question, in which he explains his doubts. Please take into account that he speaks English quite badly.
With best regards,
Sofia
Dear Manoj,
The terminology "classical" for the probability theory is not good, people don't understand what you say. The probability theory is neither classical, not otherwise. There is only one probability theory. Your statement,
==>"But, if it is the case that classical probability theory is incomplete and fail to predict the nature of observation of quantum mechanical experiments ?"
should be improved as follows:
Could it be that the probabilistic calculus is unfit for describing the nature of the observation in quantum mechanics experiments?
I suggest you to use the Edit option and improve your text.
Good luck!
If somebody say that QM is nonlocal , because it violate Bell's inequality !.following conclusions are correct !
*In the other hand 2+2>10 is a wrong mathematical interpretation (Or incomplete logical statement) and 2+2>=< 10 have some meaning ! (complete Statement in logics)
In short: Good luck.
You may not realize it, but the ordering of (real) numbers is crucial if you want to use random variables, i.e., study non-toy problems. Even with simple set theory, you are probably hard pressed to find a satisfying set of intuitive axioms that gets you anywhere.
While the nature of probability can be debated at length, "everyone" intuitively "understands" the meaning of "the probability of a certain number of eyes on a dice is 1/6" . With complex probabilities, you add a complex phase with no obvious real world counterpart (and little practical use: mathematicians never bothered with complex probabilities for a reason).
Finally, if you argue that there is a real world counterpart, namely all the quantum mechanics stuff, what would your complex probability theory achieve except reformulating quantum mechanics with other words? Yes, the complex phases appearing there are unpleasant from a classical point of view. So what makes you think that they become any better if you label probabilities as complex?
Note- The complex probability theory can be reduce all the cases in classical probability theory (present day probability theory ). Also there is an example ,(in paper : Minkowskian -QM ) describe an practical example how to explain faith of Games (compere performance of two teams) using complex probability. Therefor theory can be adopted as kind of a game theory or statistical tool.
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