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Chapter 19: Discrete Field Theory

DP is very different than conventional philosophies of physics.  The DM field is totally defined by six fundamental constants.  All of the other numerical constants of the model, all the laws, all the differential equations, the set of particles and their characteristic are all emergent properties of the field.  When Einstein said "…we must find a way to get rid of the continuum altogether…” we believe that he was referring to the difficulties in the concept of particles, and effective constants of length, being emergent properties of a continuum.  DP has neither the continuum nor the difficulties. [1]   With 2 additional constants, all of cosmology and cosmogony becomes implicit in the theory.  Given a correct DM model, a simpler and more accurate statement is the following:  “All of physics and cosmology are emergent properties of the DM field.”

Of the eight constants of our DM model, 4 are already known exactly.  The fifth must be a small integer such as 6.  The sixth constant is the Rule of the CA, which defines the process.  The first 6 constants determine all fundamental facts about physics; the 7th and 8th are the cosmological constants.  In any case all these constants can be represented exactly by eight integers.  What is somewhat amazing about DP is that the eight constants all by themselves, with nothing else added, implicitly define every fact about the entire universe; all the laws of physics and the exact entire history and complete future of the universe. [2]   The fact that these eight constants can, in principle, determine all these things exactly does not mean that we, living in this universe, would be able to calculate them all.

DP suggests that the Universe, with finite resources, is busy computing its future as fast as it can.  The success of QM gives us good reason to assume that the most fundamental laws of physics are neither computationally trivial nor computationally inscrutable.  What the Speed-Up Theorem suggests is that there is no way from within the DM Universe to, in general, predict exact future states sooner than the Universe will get to those states.  If we could step outside of our Universe into some larger place we can call “Other”, then even in Other, there could be no way to get an exact future state of our Universe (before the Universe gets to that state) without expending even more local resources than our Universe requires.  The speed up theorem is a mathematical theorem that in no way depends on the laws of physics.  If there is a question whose answer depends on the exact future evolution of part of the Universe, then there is no faster way, in general, to get to that exact answer other than by letting that part of the Universe continue its evolution.  This basically mathematical observation has some bearing on understanding the nature of DP.  While DP is absolutely deterministic, we choose to call it “unknowable determinism”.  The knowledge that it is deterministic cannot allow us, who live in the Universe, to make any exact prediction of the future.  In this sense DM is like QM.  However, in principal everything in the future or in the past could be calculated exactly from knowledge of the 8 constants and a suitable computing engine (in some other, bigger universe!).

"If we imagine an intellect which at any given moment knew all the forces that animate Nature and the mutual positions of the beings that comprise it -- if this intellect were vast enough to submit its data to analysis -- could condense into a single formula the movement of the greatest bodies of the universe and that of the lightest atom. For such an intellect nothing could be uncertain and the future just like the past would be present before its eyes"

Pierre-Simon Laplace (Philosophical Essays on Probability) [3]



 

[1] DM doesn’t have the difficulty Einstein was thinking of, but it still has the very important difficulty in that it is, at this point, a grossly incorrect model of physics.  We are jumping the gun, speaking as though it had already evolved into a correct model.

[2] The meanings of the seventh and eighth constants requires the one time definition of 2 simple canonical computers, as these two constants are each, in effect, a small program for a computer.

[3] This famous remark is a restatement of the same concept as given earlier by Boscovich.  Laplace was infamous for failing to give credit to those whose ideas found their way into his papers.  The kind of determinism inherent in LaPlace’s statement was alluded to by Omar Khayyam.

                                                                                                                 



  
  


  
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