2=i(tn-tn-1)
Record of Document Changes
for Main
Article
The article, Quantum Theory Derived from Logic, attempts to derive all of physics from the principles of logic alone. I expect this will be an ongoing effort, and changes will be made to this Document with further insight and developments.
DOCUMENT CHANGES:
4/17/07 - First mention of this effort was posted . I will keep this page intact as part of the record. It tries to make use of the square root as an expression of implication. But this was mostly based on intuition and a more rigorous derivation was desired.
2/5/08 - This effort is more rigorously developed. Implication is represented instead by the Dirac delta function, and reasons for this are developed from first principles.
2/13/08 - Used clearer language to explain the arbitrary use of m and h-bar in the delta of the gaussian in equation [18] so that it does not appear to be covertly introducing physics. Thanks for discussion on alt.sci.physics.
6/2/08 - Simplified notation of infinite multiple integral to single integral sign. Added remarks to show that the gaussian form of the Dirac delta with complex exponent was no special choice in order to force the formulation to conform to physics. Renumbered formulas.
12/5/11 - Posted 3rd revision. Use references to give more complete explanation for the Dirac delta functions being a complex gaussian and the manner in which propositional logic is mapped to the math of probability theory. Also give some explanation as to the origins of the the potential energy term in the lagrangian, the Born rule, and quantum field theory. I also toned down my initial enthusiasm to recognize that I have not actually derived physics from logic; I only derive some (perhaps all) of quantum theory from logic for whatever subject it might be used.
2/8/12 - Added paragraph on bottom of THE LARGER IMPLICATIONS section to consider whether similar efforts on 2nd or 3rd quantization might be used to derive the quaternions and octonions used to establish the SU(2) and SU(3) groups of particle physics.
4/1/12 - Posted 4th revision. Removed reference to Scaled Boolean Algebra. I could not parse it, and it took too long to read. I replace it with short discussion of how algebraic concerns need to be preserved across the map from logic to math. This also seems to provide an easy justification of the Sum and Product rule for probabilities. I briefly introduce basic definitions of logic and use this notation more explicitly and consistently throughout. This also allows me to remove many of the pictures I had to explain the set theory concepts. I give better reasons why the Dirac delta should be the gaussian version and why it should be complex based on algebraic concerns.
5/19/12 - Posted 5th revision. Improved notation, propositions
are in lower-case italic bold font, numerical variables are in lower-case italic
not bold font. I explained more about how the logic continues to work after
going from the discrete Kronecker delta to the continuous Dirac delta function.
I removed reference to the paper "Origin of Complex
Quantum Amplitudes and Feynman's Rules", since I never really proved how
the Dirac delta is a vector such that the paper would be relevant. However, I
now try to explain the use 2=i(tn-tn-1)
3/21/16 - Added a couple of paragraphs at the end of Section 7 to explain that the Chapman-Kolmogorov equation could have been used to get a wider gaussian and not just a Dirac delta which is of little use as a path integral.
11/11/18 - Posted 6 revision. Removed some of the more difficult passages. Corrected some grammar. Used clearer language in some places. Revised a bit section 8. Created mouseover tooltips, on references to equations so you don't have to scroll back to find them. And made text versions of logic equations with a link to a truth-table generator so you can cut and paste them into the generator and see that they are always true. I believe this revision will be much easier to follow.