Role of Space Time in Jainas Syadavada and Quantum Theory

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

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Role of Quantum Theory in Deviant Logic
For the purpose of extending the analysis to more than two EP's conjoined by the disjunction 'V', let us consider a Hermitian operator A corresponding to some observable. An EP of the form M (SA1x) = a, is denoted by i, i = 1, 2, 3 .... n(<co). We know from quantum mechanics that the system can be only in one state at a time. Hence at some time ifa, (ISisn) is true than all the other Q's with K+i are false at that time. We write Q, Va, V a..... a to mean that the system S has the property described by the observable A. Similarly from another Hermitian operator B with the spectrum of eigenvalues B, B...... B (in general m an EP of the form M (S81x)=b> will be denoted by B. Using the same argument, we consider B, VB, VB,.... B as an always true statement to mean that the system S has the property described by the observable B. Clearly in the above expressions, we see that the disjunction is true if only one disjunct is false if two ore more of the disjuncts are true at a time. This is the requirement of an exclusive disjunction we have introduced in our quantum logic.
Regarding the connective ‘A’signifying conjunction, we cannot extend its meanings to a statement of the form a AB YA.... of more than two EP's as this statement cannot be given a meaning, particularly for incompatible observables, since it refers to the result of simultaneous measurement of more than two observables. Even thee quantum mechanics such measurements are hardly required and discussed. As the connective il'conjoins two EP's which express the result of simultaneous measurement of two observable on a system S in an arbitrary state, we consider a statement of the form a, A a, as always false, where a, and a are the EP's corresponding to the same observables. This is due to the fact that if a, is true, a is false and that an observable is compatible with itself which follows the truth-table 2. Flowever, the statement the system