It now seems possible to derive physics from nothing more than logic. See
the website at:
http://hook.sirus.com/users/mjake/QMfromlogic.htm
I posted this on sci.physics.foundaitons, but I mostly got philosophical
concerns being raised. I'm hoping here to get more constructive criticism
on the mathematics. The derivation starts with propositions and then moves
on to set theory and then to measure theory. It could be that I'm not
using
these concepts in a completely critical way. I could use some expert
opinion
in these areas to identify possible flaws in my argument. It's a 250KB
download because of the figures. But it should only be a 15 minute read
for
those skilled in the art. I would appreciate your constructive criticism.
Thank you.
ABSTRACT:
Starting from the premise that all facts are consistent with each other,
the
Feynman path integral formulation of quantum mechanics can be derived.
It is assumed that all facts or events in reality will be consistent with
each other. This means that no fact will contradict any other fact. In
symbols this means that for any two facts in reality, q1 and q2,
~(q1>~q2),
meaning it is not true that fact q1 will prove false q2, since they both
exist. But this is also equivalent to a conjunction, ~(q1>~q2)=q1^q2,
where
~ symbolizes negation, > symbolizes material implication, and ^ symbolizes
conjunction, and q1 and q2 symbolize propositions of deductive logic.
So all facts being consistent is equivalent to a conjunction of all facts,
q1^q2^q3^q4^... But we can prove by truth table that
(q1^q2)>[(q1>q2)^(q2>q1)] This means that the conjunction of facts implies
a
conjunction of every implication between all facts. And since
(qi>qj)=(qi>qj)^(qi>qj)^..., the conjunction of every implication can be
manipulated into a conjunction of paths from a starting point to an ending
point, where one path would be
(q1>q3)^(q3>q9)^(q9>q7)^(q7>q4)^(q4>q25)^(q25>qn)
where q1 is the starting point of the path, and qn is the ending point.
And
here the conclusion of the previous implication is the premise of the next
implication. This series of implications can be stepped through using some
parameter, t.
But since it is also true that (A^B^C)>(AvBvC), where v symbolized
disjunction, the conjunction of paths implies a disjunction of paths.
In set theory implication is represented by subsets , a set always implies
its subsets. And a subset should be counted as part of a set only if it is
a
subset of that set. When these ideas are shrunk down to individual
elements,
it can be seen that a natural measure for implication is the Dirac delta
function. With the gaussian distribution substituted for the Dirac delta
function in the disjunction of paths, the Feynman path integral results.
This is a new effort. And I would appreciate your review. I look forward
to
some interesting conversation. I'd like to keep this thread focused on the
math in my proof. Thanks.
Mike.
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