By Andrei Khrennikov

ISBN-10: 9814411736

ISBN-13: 9789814411738

The current wave of curiosity in quantum foundations is brought on by the great improvement of quantum details technological know-how and its purposes to quantum computing and quantum verbal exchange. It has turn into transparent that a number of the problems encountered in realizations of quantum info processing have roots on the very primary point. to unravel such difficulties, quantum thought needs to be reconsidered. This e-book is dedicated to the research of the probabilistic constitution of quantum conception, probing the bounds of classical probabilistic illustration of quantum phenomena.

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5. b For simplicity, we can consider a ﬁnite-dimensional Hilbert space instead of L (R3 ) 2 (as people often do in quantum information theory). In this case, PCSFT considers Beyond-Quantum 33 February 12, 2014 16:5 PSP Book - 9in x 6in 34 Introduction By using the Riemann–Silberstein representation the electromagnetic random ﬁeld can be represented in the complex form φ(x, ω) = E (x, ω) + i B(x, ω). 5 and Chapter 9). , in radiophysics [265]; these are electromagnetic ﬁelds depending of a random parameter.

4) D = ⊗ , , u ∈ H . , D u = u| | . 5) a It seems that there are no problems (neither physical nor mathematical) to develop a relativistic variant of PCSFT. I plan to do this in future. Beyond-Quantum 35 February 12, 2014 16:5 PSP Book - 9in x 6in Beyond-Quantum 36 Introduction where E denotes the classical mathematical expectation (average, mean value). By applying a linear functional y to the random vector φ we obtain the scalar random variable. In the L2 -case we get a family of scalar random variables: ω → ξ y (ω) ≡ R3 φ(x, ω)y(x)dx, y ∈ L2 .

44, 249]). The presence of this ﬁeld plays the crucial role in SEDs description of quantum eﬀects. We recall that already in 1911 Planck introduced the hypothesis of the zero point electromagnetic ﬁeld in an eﬀort to avoid Einstein’s ideas about discontinuity in the emission and absorption processes. It is important for our further considerations that neither the semiclassical approach nor SED resolve the wave–particle dualism. Neither was it resolved by Bohmian mechanics, the modern version of de Broglie’s double solution approach.

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