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 Syadvāda
n
1x>= a, >< a, x>
i=1
If a, denote the eigenvalues of A for the states la>, then A laaa. The process of measurement in quantum mechanics consists of three successive stages; (1) A preparatory stage when the quantum mechanical system S is 'prepared' to be in an arbitrary state 1x>, considered as the initial state; (2) a working stage in which the 'prepared' system S interacts with the measuring apparatus (a macroscopic body), we shall call the analyzer and goes over to the superposition state
n
1x= |a><a1 | x>
i = 1
and (3) a registering stage in which the system S is registered in one of the eigenstates forming the superposition in the above expression (reduction of the wavepacket). Hence the process of measurement can be described as
n
(1) 1x> = (2) |a, >< a, | x> (3) |a, >
i=1
Experimental Proposition (EP) is a statement of the form: "The result of a measurement on a system S in the state 1x> and for the observable A is" The completion of the sentence can be made in two ways, (1) "a real number ai giving the value of the real dynamical A at time" and (2) "... that the system, after the measurement is complete, is described by the state vector lai>", If the statement is completed in the manner (1), we shall call that statement as the experimental proposition of the first kind (EP I) and denote by, say, a, if the statement is completed in the manner (2), we shall call that statement as the experimental proposition of the second kind (EP II) and