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 Syädväda
register anything, we shall assign the truth value T to a., F to B, and F to a AB. The reason is that by the very nature of the coincidence technique, this may be considered as the apparatus malfunction and the corresponding reading is rejected. So also if we assign F to Q,, T to B, then Q, AB has the truth value F. Lastly, if both guages fail to respond, we assign F to a Fto B, and F to a, A B, leading to the truth table 2.
Truth-Table 2 We see that the above truth table coincides with that classical logic.
Case (2): Let the two non-commuting Hermitian operators be noted by P and Q. These correspond to two incompatible observables. Let P and Q satisfy [P, Q1 = iR, where R is also a Hermitian operator corresponding to an observable. We denote the EP “the result of the measurement of Pon S in the state 1 x> is P, (a real eigenvalue) as 0, and the EP “the result of the measurement of Q on S in the state 1x > is a, (a real eigenvalue) as y,". In these EP's the results of measurements of P and Q are supposed to have the sharp values p, and qı with standard deviations Ap and Aq equal to zero. According to the uncertainty principle, if P and Q are measured simultaneously, Ap Aq 2 12 where r is the expectation value of R in state 1 x>. From this we see that 0, is true if Ap = 0 and y, is true if A = 0, but q, is false if Ap #0 and y, is false if Aq #0*. From the uncertainty principle, it is clear that 040, is false only in the case when both o, and y, are true, but it is true otherwise, resulting in the truth-table 3.
Truth Table 3 In fact for clarity, one may say that o, is true if Ap < 1o and V, is true if Aq< zip; but , is false if Ap> 2, and y, is false
if Aq? 2ap