18 research outputs found
Locality and Bell's inequality
We prove that the locality condition is irrelevant to Bell in equality. We
check that the real origin of the Bell's inequality is the assumption of
applicability of classical (Kolmogorovian) probability theory to quantum
mechanics. We describe the chameleon effect which allows to construct an
experiment realizing a local, realistic, classical, deterministic and
macroscopic violation of the Bell inequalities.Comment: 23 pages, Plain TeX, A talk given at Capri conference, July 2000,
Corrected and Extended versio
PROBABILITY MEASURES IN TERMS OF CREATION, ANNIHILATION, AND NEUTRAL OPERATORS
Let u be a probability measure on Rd with finite moments of all orders. Then we can define the creation operator a+(j), the annihilation operator a-(j), and the neutral operator a0(j) for each coordinate 1 < = j < = d. We use the neutral operators a0(i) and the commutators [a-(j), a+(k)] to characterize polynomially symmetric, polynomially factorizable, and moment-equal probability measures. We also present some results for probability measures on the real line with finite support, infinite support, and compact support. 1. Creation, annihilation, and neutral operators Let u be a probability measure on Rd with finite moments of all orders, namely, for any nonnegative integers i1, i2,..., id,Z Rd |x i11 xi22 * * * xid d | du(x) < 1, 1 April 20, 2004 10:2 Proceedings Trim Size: 9in x 6in acks-levico 2 where x = (x1, x2,..., xd) 2 Rd. Let F0 = R and for n> = 1 let Fn be the vector space of all polynomials in x1, x2,..., xd of degree < = n. Then we have the inclusion chai
PROBABILITY MEASURES IN TERMS OF CREATION, ANNIHILATION, AND NEUTRAL OPERATORS
Let µ be a probability measure on R d with finite moments of all orders. Then we can define the creation operator a + (j), the annihilation operator a − (j), and the neutral operator a 0 (j) for each coordinate 1 ≤ j ≤ d. We use the neutral operators a 0 (i) and the commutators [a − (j), a + (k)] to characterize polynomially symmetric, polynomially factorizable, and moment-equal probability measures. We also present some results for probability measures on the real line with finite support, infinite support, and compact support. 1. Creation, annihilation, and neutral operators Let µ be a probability measure on R d with finite moments of all orders, namely, for any nonnegative integers i1, i2,..., id, R d |x i1 1 xi2 2 · · · xid d | dµ(x) < ∞,