Role of Space Time in Jainas Syadavada and Quantum Theory

Author(s): Filita Bharucha
Publisher: Shri Satguru Publications

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Role of Space-Time in Jaina's Syadvȧda
or bis occurring singly at a time. Such measurement results can be put into the logical language as a, VB, with 'V' again in the exclusive sense where the EP B, is M (SB1x>) = b,. The results of successive measurements of one or more observables on identical copies of a quantum mechanical system, all prepared to be in a given state, are expressible in terms of an exclusive disjunction given by the truth-table 1.
Truth-Table I
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Having given the experimental meaning to disjunction, we now turn to the connective 'L' symbolizing conjunction. Let L and M be Hermitian operators corresponding to two observables.
Let the discrete eigenvectors of these operators be denoted by li> and m1 and the corresponding eigenvalues to which they belong be 1, and m,. The indices i and j run through discrete integral values. Obviously li> and | mi> form a complete set of eigenvectors. We want to give meaning to the problem of simultaneous measurement of two observables. Suppose an experiment to measure simultaneously the values of L and M is performed on a system S in an arbitrary state 1 x>, we shall consider the result as read on two guages L-guage and M-guage-simultaneously. We imagine this as some kind of coincidence measurement technique used with L-guage and M-guage expected to respond at the same time. If we denote the EPM (SL) x>)=1, as λ, and M (SM1 | x>) = m, as μ, then the L-guage reading li and Mguage reading mi gives the experimental proposition the results of the simultaneous measurement of L and M on S in the state 1 x> are the real numbers 1, and m,. This EP can be translated into the logical language as λi ▲ μj. Hence the measurement of two observables furnishes us with the EP which is conjunction of two EP's.
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