Time is a major topic in philosophy. I wonder if there are philosophical works that have digged into the possibilities and impacts of discrete time instants.

Present theories in physics suggest that matter, energy, is apparently made of quanta. Combining universal constants, one can come up with a universal length, mass and duration. Planck time is sometimes considered as a fundamental limit.

So what if we were living over grains of time, flickering like in a 1/24 movie, possibly interleaved? What would be the impacts on causality, free will, moral, for instance.

  • Side note: It has been demonstrated that spacetime cannot be discrete at the Planck scale, i.e. if it is discrete then the irreducible units must be considerably smaller than the Planck length. – Era Apr 25 '16 at 21:08
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    I don't blame you since this misconception is repeated too many times in too many places to count. But what modern theories suggest the matter, energy, etc., are "made of" has little to do with partitioning into discrete pieces that most people imagine when they hear the word "quanta". In particular, even if time is quantized what that means has nothing to do with "discrete time", which is a purely classical contrivance favored by "universe is a simulation" enthusiasts. See Butterfield-Isham on possible quantization of time in quantum gravity arxiv.org/abs/gr-qc/9901024 – Conifold Apr 26 '16 at 0:43

The concepts of causality, free will, and morality will be unaffected for the most part. Most of the discussion on those topics assume that there is something more than the continuous physical world, so a shift to a discretized physical world would not cause much of a shift in discussion. Obviously the discussion which does focus on the continuous physical world would shift... in particular the discussion of free will if one assumes there is no metaphysics will get interesting, but it's interesting already!

One thing that would change is any discussion of chaotic systems. Right now, it is believed by the majority that we exist in a 3-dimensional Euclidean space, with one dimension of time. In this continuous environment, chaotic systems can form from a finite number of linear components. If it were discretized, one is obliged to either have nonlinear components, an infinite number of components, or chaotic systems cannot form. Given that most of the rules of physics we are familiar with are defined in linear systems, this would be a big deal.

How much would this affect the greater discussion on those topics? Probably not all that much. It is a hot point for me because I have seen reasons to argue that one of the challenges of identifying a metaphysical "consciousness" is that we cannot define it in a way which excludes all purely-physical chaotic systems. Phrased another way, it appears possible to construct a P-zombie using chaotic systems. If it was possible that the rules of the universe prohibit true chaotic behavior, it would be possible to define a test to separate the purely physical from any metaphysical consciousness, answering once and for all whether we, ourselves, are concious. However, that is not a widely held opinion, so it should not be thought of as a statement about the wider discussions on freewill.

  • "it is believed by the majority that we exist in a 3-dimensional Euclidean space, with one dimension of time" - Perhaps too nitpicking, but this isn't the current scientific understanding of spacetime. The currently best-supported model is a 4D manifold (Minkowski space) which has close to zero curvature globally, but is noneuclidean. At first glance the two seem similar, but their properties are quite different. – Era Apr 26 '16 at 15:16
  • @Era You have a point. Let me think about the best way to word it without diving too deep into non-Euclidean geometry! For this topic, I don't think the difference matters, but you are correct when you point out that I oversimplified the majority opinion. – Cort Ammon Apr 26 '16 at 15:18
  • "chaotic systems can form from a finite number of linear components" -- I though chaos required non-linearity in the eqn's of motion. – Dave Apr 26 '16 at 15:35
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    @Dave In a differentiable system, a linear system of equations is sufficient for chaotic behavior. One classic example is the population model dP/dt = r(P)(1-P), which is chaotic for some values of r – Cort Ammon Apr 26 '16 at 16:06
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    @LaurentDuval Oh, that's a much easier question to answer, because its a well known one. I thought you were going after a more complication question involving the mathematics of physics. Look up perdurantism and endurantism, and the famous question of the Ship of Theseus. The question of persistence is a well known one since the time of the Greeks, with many answers through the years. – Cort Ammon May 1 '16 at 15:37

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