Abstract
A new approach to probability theory is presented with reference to statistics and statistical physics. At the outset, it is recognized that the “average man” of a population and the “average particle” of a gas are only objects of thought, and not real entities which exist in nature. The concept of average (man) is generalized as a new concept of represental (man) whose epistemological status is intermediate between those of the particular (the man) and the universal (a man). This new concept has become necessary as a result of emergence of statistics as a new branch of human knowledge at the beginning of the nineteenth century. Probability is defined with reference to the represental. The concept of probability is the same in probability theory and in physics. But whereas in statistics the probabilities are estimated using random sequences, in statistical physics they are determined either by the laws of physics alone or by making use of the laws of probability also. Thus in physics we deal with probability at a more basic level than in statistics. This approach is free from most of the controversies we face at present in interpreting probability theory and quantum mechanics.
Highlights
The theory of probability and the theory of quantum mechanics are well developed disciplines
The relations between the derived probabilities and the primary probabilities are mathematically exact. These relations are governed by the laws of probability theory. These laws should be consistent with the relations the relative frequencies approximately satisfy by definition; otherwise the probability theory would have no relevance to random sequences
We deal with probability in both probability theory and in statistical physics
Summary
The theory of probability and the theory of quantum mechanics are well developed disciplines. In quantum mechanics the main issue has been whether the state function, the basic concept of the theory, is relevant to a single system or to a large number of systems [6]-[13]. Mr Jones is a particular man (an object of perception) with whom we can associate a well defined space-time region and well defined properties like height, weight, number of children, etc.; in contrast, a man is a universal (an object of thought) with whom we cannot associate any space-time region and any well defined values of height, weight, number of children, etc It is only from the beginning of the nineteenth century have scientists been dealing with large amounts of quantitative data relevant to agricultural yield, industrial products, and human population, etc. For the sake of completeness (and the benefit of students of probability theory) the limitations of subjective application of probability to a particular (entity or an event) [19] [20] and differences between the present approach and von Mises’ approach [21] [22] are mentioned
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