What about the subjective interpretation of probabilities?

People with a preference for subjective interpretations would say

''probabilities depend on someone's knowledge'' instead of

''probabilities are a property of the ensemble under consideration''. They talk of ''arrival of new information'' or ''learning'' instead of the objective and unassailable formulation ''restricting the ensemble to a subset defined by the conditions'' when discussing conditional probabilities (the classical analogue of the statistical collapse of the wave packet in quantum mechanics).

But knowledge is an even more poorly defined concept than probability, which at least has an undisputed axiomatic basis. Thus explaining probability in terms of knowledge only makes the meaning of probability more foggy by putting it deep into the psychological realm. Moreover, the subjective interpretation based on the Bayesian paradigm of conditional probability has no formal way of coping with misinformation (the ensemble grows if one learns that some of the information one believed to know turns out to be false!) while, on the objective level, the latter is just another change of the ensemble.

Thus the subjective interpretation of probability is an inadequate foundation for the use of probabilities in physics.

Arnold Neumaier (Arnold.Neumaier@univie.ac.at)

A theoretical physics FAQ