We propose a distinction between two different concepts of time that play a role in physics: geometric time and creative time. The former is the time of deterministic physics and merely parametrizes a given evolution. The latter is instead characterized by real change, i.e. novel information that gets created when a non-necessary event becomes determined in a fundamentally indeterministic physics. This allows us to give a naturalistic characterization of the present as the moment that separates the potential future from the determined past. We discuss how these two concepts find natural applications in classical and intuitionistic mathematics, respectively, and in classical and multivalued tensed logic, as well as how they relate to the well-known A- and B-theories in the philosophy of time.
10 Except for integrable classical dynamical systems. V. RELATION TO THE PHILOSOPHY OF TIME Before discussing in detail how our proposal of creative and geometric times relates to some positions in the philosophy of time, we would like to stress that, as most physicists, we are not taking a Humean position. On the contrary, we believe that laws of nature are real causal connections (they have an ontological status) and that they guide the evolution of things of the world at different times. Note that these laws may not connects states at different times by necessity (determinism), but only state a propensity . In either case, this puts an emphasis on the role of time in physical laws.
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In the vast literature devoted to the philosophy of time (see, e.g., [31, 32] and references therein), one finds a main separation into two camps, following the seminal works of J. M. E. McTaggart . The two camps are customarily referred to as A-theory and B-theory of time. While we acknowledge that the distinction in Aand Btheories presents a variety of modification and it may not even encapsulate the most striking features of time in physics (e.g., directionality, openness of the future, objective becoming, etc.), we cannot avoid drawing some parallel with our distinction between creative and geometric time, respectively.
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In fact, starting in reversed order, B-theorists regard positioning in time in dyadic relational terms: given two events E1 and E2, it is either the case that E1 is before E2, or simultaneous to E2, or after E2 . Clearly, these relations are somehow static, i.e., they are not tensed and hold unchanged since ever and forever. For example, according to the B-theory, the extinction of the dinosaurs has always been, is and will always remain before the French revolution. Note however, that this relation seems to us to necessarily presume determinism, otherwise, in an indeterministic world, it would have not been true at a time earlier than the dinosaurs extinction itself actualized, because that extinction was not necessary in the first place (nor was the French revolution). At the remote past time in which both events dinosaurs extinction and French revolution were only potential events, their relation of before-after was also indeterminate. After the actualization of dinosa
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Hence, B-theorists who take the beforeafter relation as fixed dont derive determinism but assume it from the outset.
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