Space, time and probabilities not only form the arena of many physical theories, but also the arena of our everyday life. Therefore the problem of their ontological status becomes even more interesting. It seems that this problem cannot be solved before we have the final physical theory ('theory of everything'). However, various methods of looking for such a theory lead to converging results, and are able to elucidate the problem in question. We analyze noncommutative algebraic methods, and show that, when applied to model the fundamental level, they suggest a nonlocal regime in which there is no space and no time, in their usual sense, and which is essentially probabilistic (in a generalized sense). In the noncommutative approach there are many probabilistic measures (not just one 'probability' as in macroscopic physics), and none of them seems to be distinguished in any way. The tentative conclusion is that space, time and probability are not 'absolute categories', but rather aspects of the world structure emergent from the fundamental level. One should expect that the ultimate theory will be well off our traditional philosophical categories. This shows that our mind has a peculiar property allowing it to reach far beyond its usual limitations.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.