THE PUZZLE CONCERNING THE CONCEPT OF PROBABILITY IN SM

Throughout the book we have been preoccupied with a single simple scenario. We consider now an n-particle system M that is in a state st at t. We want to know whether st has a certain property A. The question that we are asking has a perfectly clear physical meaning. Nevertheless, the information that the answer requires may not always be available to us. It may be the case that the experiment needed to answer the question is too expensive or difficult to perform. It is also possible that there are theoretical reasons why we cannot perform the experiment, or, simply, the experiment has not been performed yet. In all of these cases the need for probabilities arises. We need to calculate the probability P(st ∈ A) and use our results to derive predictions concerning M. But, even if there is little doubt that we constantly use probabilities, there is a basic problem concerning the interpretation of the probabilities. It is difficult to define probabilities as observable parameters that depend only on the physical properties of M. This difficulty gives rise to a philosophical puzzle: If probabilities are not physical parameters that we discover by methods of observation and measurement only, how can we justify our willingness to be guided by them? How can we explain the utility of probabilities? In the previous chapters, we reviewed several attempts to solve this problem.