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 Syādvāda
has the properties described by the observables A and B at the same time will be described by the expression (α, Va2 V αz.... a) A (ẞ, Vẞ2 Vẞ, V... VB) according to the meaning given to the connective 'A'. If A and B are compatible observables, the expression (α, V α2 V.... V α) A (ẞ1 V ß2 V...... B) where we have put m = n, is an always true statement. If P and Q are incompatible observables with the corresponding EP's denoted by and then the statements (0, V 2 V ........ „) and (v, V V2 V....V are always true, but the statement (0, V 2 V....V 9) A (V1 VW2 V.....) where, in general m #n, signifying that the system has the properties P an Qat the same time, is an always false statement. It is often implied that a quantum mechanical system S simultaneously possess properties described by the compatible observables P and Q at all times and that it is the measurement process that introduces the uncertainty. This is evidently false as the above results shows.
4. The Distributive Law: In the classical logic, we have two different forms of the distributive law. We shall state each forms for the two cases below. The generalization is obvious. One form is
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(1) α V (BAY) = (a V B) A (a Vy) and
(1) (α A B) V (YA 8)
(α Vy) A (α V 8) A (a V 8) A (BV) A (BVS)
The other form is
(II) α A (ẞ V y) = (α A ẞ) V (α ▲ y)
=
(II) (α V B) A (Y V 8):
(α Ay) V (α A 8) V (ẞAp) V (BV 8)
First, let us consider the form (I). We apply it to two observables A and B with a complete spectrum of only one eigenvalue and two eigenvalues respectively. Then (I) can be written as a V (B, A ẞ2) = (α V B.) A (α V ẞ2). In this expression we note, on the right hand side, there occur expression of the