Symmetry of physical laws. Part III: prediction and retrodiction
Abstract
An attempt is made within the framework of the accepted quantum physics to achieve the maximum
paralllism between prediction (inference of the future observational data from the present ones)
and retrodiction (inference of the past observational data from the present ones). To implement this
program, it is shown that the retrodictive state function (extrapolation of the present data to the
past) can be just as useful as the ordinary "predictive state function" (extrapolation of the present
data to the future). This leads to a formalism in which time-reversal becomes a linear
transformation and double time-reversal becomes a c-number. In spite of this formal symmetry, it
can be shown that the actual success of a retrodiction depends on the satisfaction of an additional
condition which is not required in prediction, and which is not always fulfilled. From the same point
of view, a logical loophole is pointed out in the indiscriminate application of the H-theorem
to the past. The so-called irreversibility of observation is interpreted in terms of the decrease of
"information" in the process of inference.
Rights
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