I only skimmed this post, but I want to point out that most computational physics (and engineering) uses discretized space and time much as you’ve described. This is not new, just how things are often computed in practice.
Whether or not reality is discrete in this sense is beyond my knowledge as an engineer, but I have had conversations with physicists about this. (As I recall, it’s possible, but the spatial and temporal resolution would be very small.)
Also, there are some exact solutions for discretized physics like this, but in general it’s harder to do. Plus, because physical laws tend to be written in continuous form, very few people look for exact solutions like this.
makes all the contradictions go away
Not really. In computational fluid dynamics, converting to discrete equations can introduce major problems. One important problem is conservation. Depending on how you formulate your discrete equations, mass, energy, etc., may be no longer conserved and might not even be approximately conserved. “Equivalent” continuous equations would not have the same problem. And I would not say solving this problem is trivial by any means, though I know at least one way to do it.
I only skimmed this post, but I want to point out that most computational physics (and engineering) uses discretized space and time much as you’ve described. This is not new, just how things are often computed in practice.
Whether or not reality is discrete in this sense is beyond my knowledge as an engineer, but I have had conversations with physicists about this. (As I recall, it’s possible, but the spatial and temporal resolution would be very small.)
Also, there are some exact solutions for discretized physics like this, but in general it’s harder to do. Plus, because physical laws tend to be written in continuous form, very few people look for exact solutions like this.
Not really. In computational fluid dynamics, converting to discrete equations can introduce major problems. One important problem is conservation. Depending on how you formulate your discrete equations, mass, energy, etc., may be no longer conserved and might not even be approximately conserved. “Equivalent” continuous equations would not have the same problem. And I would not say solving this problem is trivial by any means, though I know at least one way to do it.