Can physics be derived from logic?

[Majik]

ABSTRACT

Starting from the premise that all facts are logically consistent with each other, reality can be defined as the logical conjunction of all facts,

R =

This conjunction implies that each fact proves every other, since



,where is conjunction, or the logical AND function,and is the material implication of propositional logic, and the qi are propositions which are true or false.

The conjunction of all these implications between states can be arranged into a disjunction of every possible "paths" from one state to another, where each path consists of steps from start to finish. For example, one path might be



It is possible to view a set of propositions as elements in set theory. The disjunction of paths can be viewed as a union of paths through a sample space. And measure theory prescribes that the measure of a union of sets is the addition of the measures of the individual subsets. And a measure for implication can be derived from set theory to be the Dirac delta function. So the disjunction of paths can be replaces with an infinite number of integrations of an infinite number of delta functions.

When the measure for implication is taken to be



this can be substituted for the . And this can be manipulated into the Feynman path integral formulation of a free particle. And it is interesting to note that the path integral can be derived from nothing more then the definition of the Dirac delta function.

The full details are at: (a 250KB download)

Physics derived from logic alone

This is not a long article. It might take 15 minutes to read. It is written with sophomores in mind who have taken introductory calculus. If you take my word for the Feynman path integral, you might appreciate the fact that it can be derived from logic.

[Majik]

Would anyone be interested in my posting this derivation in sections so we can discuss the validity of the reasoning used? Thanks.

[ughaibu]

I'll have a look at your article over the weekend. My initial impression is that you have demonstrated the logical validity of the Feynman path integral, not that you have demonstrated that one can derive the whole of physics.

[Majik]

Originally Posted by ughaibu

I'll have a look at your article over the weekend. My initial impression is that you have demonstrated the logical validity of the Feynman path integral, not that you have demonstrated that one can derive the whole of physics.

You are correct. I've not yet actually shown how all of physics can be derived from the path integral. One problem I'm sure will be tough is the number of dimensions. But having gotten the path integral, I feel encouraged that the rest can be obtained, and there seems to be some hints and clues that it can be done. See the "Document History" page for further areas of interest toward completion. I'd like to see if there are any issues so far before I move on, however. Thanks.

[Overdog]

Have you seen Doctordick's post?

http://hypography.com/forums/philoso...-variable.html

His starting point strikes me as similar to yours...it's a long thread but worth the read.

[modest]

Not everything that is logically consistent must (or indeed does) exist in reality. I can describe some truly outrageous things using math that are logically airtight but have no place in our reality.

Observation is necessary to determine what logically consistent ideas are real in our universe.

Take the gravitational constant or the speed of light - can they be derived from pure logic alone? Don't they need to be measured at some point? I think so.

I'd suggest Kant's critique of pure reason.

-modest