Time of Nature and the Nature of Time by Christophe Bouton & Philippe Huneman

Author:Christophe Bouton & Philippe Huneman
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

9.3.5 Conclusion of Section 9.3

Our aim in this section has been to answer the question: What does it imply to use a discrete representation of time in physics? We have examined two answers that we found implausible. First, we have shown that adopting a discrete representation of time does not imply having to use equations that are not as fundamental as continuous equations. In DM, the use of a discrete representation of time does not imply that discrete equations are model-specific and inevitably derived from fundamental, differential equations . In DM, the fundamental equations of motion are themselves discrete. Second, we have shown that the use of a discrete representation of time does not entail dispensing with the real numbers. For us, it is an important consequence. As far as we know, the distinction between representing time as continuous and using real numbers to represent time has not been introduced yet in the literature. We have made clear that in DM, time is represented as discrete even if instants are defined on real numbers.

We have then argued that an actual implication of the use of a discrete representation of time in physics is that physics can accordingly dispense with the continuous representation of time. In order to make explicit the meaning of this claim, we have first introduced the notion of a usable physical theory. It is a theory which enables one to actually describe, predict, and explain physical phenomena. Second, we have distinguished our dispensabilist implications from more ancient, similar claims, namely Carnap’s and Newton-Smith ’s. In our view, the question of the (continuous or discrete) structure of time cannot be legitimately asked when investigating how time is represented in (continuous and discrete) physical theories. We have suggested that the statement “time is continuous”, besides being judged true, false, or undecidable , can also be judged irrelevant.

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