Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2002-08-13
Int.J.Theor.Phys. 42 (2003) 1229-1256
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
30 pages. Invited contribution to Peyresq VII Conference, France, June 2002; a correction of a reference in this version
Scientific paper
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient implies that we need to accept non-additive probabilities. This has the desirable consequence of removing constraints of standard theorems about the possibility of describing quantum theory with commutative variables. Motivated by the formalism of consistent histories and keeping an analogy with the theory of stochastic processes, we develop a (statistical) theory of quantum processes. They are characterised by the introduction of a "density matrix" on phase space paths -thus including phase information- and fully reproduce quantum mechanical predictions. In this framework wecan write quantum differential equations, that could be interpreted as referring to a single system (in analogy to Langevin's equation). We describe a reconstruction theorem by which a quantum process can yield the standard Hilbert space structure if the Markov property is imposed. Finally, we discuss the relevance of our iresults for the interpretation of quantum theory (a sample space if possible if probabilities are non-additive) and quantum gravity (the Hilbert space arises after the consideration of a background causal structure).
Anastopoulos Charis
No associations
LandOfFree
Quantum vs stochastic processes and the role of complex numbers does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quantum vs stochastic processes and the role of complex numbers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum vs stochastic processes and the role of complex numbers will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-579701