Quantum Theory derived from logic

[Majik1]

At the link below, I derived quantum Theory from logic alone.

 

 

http://webpages.charter.net/majik1/QMlogic.htm

 

 

The Feynman path integral of quantum mechanics is seen as the

mathematical representation of a similar construction in logic. Paths

in logic are constructed as the conjunction of many implications,

where the consequence of one implication is the premise of the next

implication, forming steps through what appears to be paths. Any

implication can be equated to the disjunction of every alternative

path from the original premise to the original consequence. Then I

show how implication is represented by the Dirac delta function. This

then requires that disjunction (OR) be mapped to addition and

conjunction (AND) be mapped to multiplication. And the Sum and Product

rule for probabilities easily falls out of this formulation. When the

complex gaussian distribution is used for the Dirac delta functions,

the multiplications required by the conjunction allows the

exponentials in the gaussian to be added and form what appears to be

an Action integral. The disjunction of all of these paths gets mapped

to integration as the number of possibilities goes to infinity. These

integrations of the Actions in the exponential form the Feynman path

integral.

The above process give the 1st quantization of quantum mechanics. And

the process can be iterated to give the 2nd quantization procedure of

quantum field theory. It is also interesting to consider that the

iteration process requires the complex numbers to become quaternion

that then iterate to octonions. And it is believed that the complex

numbers, quaternions, and octonions specify the U(1)SU(2)SU(3)

symmetry of the Standard Model.

 

 

I should also mention that there is a very brief intro to logic for

the un-initiated, in order to establish language and notation. And I

try to keep the math to a sophomore college level. It should only take

about an hour to read the article. I've been developing this theory

for about 5 years now. And no one is showing me any errors yet, though

there have been some who have had questions. These questions gave rise

to revisions so that I think the article should be easier to read.

Edited April 4, 2012 by Majik1

[questionposter]

At the link below, I derived quantum Theory from logic alone.

 

 

http://webpages.char...ik1/QMlogic.htm

 

 

The Feynman path integral of quantum mechanics is seen as the

mathematical representation of a similar construction in logic. Paths

in logic are constructed as the conjunction of many implications,

where the consequence of one implication is the premise of the next

implication, forming steps through what appears to be paths. Any

implication can be equated to the disjunction of every alternative

path from the original premise to the original consequence. Then I

show how implication is represented by the Dirac delta function. This

then requires that disjunction (OR) be mapped to addition and

conjunction (AND) be mapped to multiplication. And the Sum and Product

rule for probabilities easily falls out of this formulation. When the

complex gaussian distribution is used for the Dirac delta functions,

the multiplications required by the conjunction allows the

exponentials in the gaussian to be added and form what appears to be

an Action integral. The disjunction of all of these paths gets mapped

to integration as the number of possibilities goes to infinity. These

integrations of the Actions in the exponential form the Feynman path

integral.

The above process give the 1st quantization of quantum mechanics. And

the process can be iterated to give the 2nd quantization procedure of

quantum field theory. It is also interesting to consider that the

iteration process requires the complex numbers to become quaternion

that then iterate to octonions. And it is believed that the complex

numbers, quaternions, and octonions specify the U(1)SU(2)SU(3)

symmetry of the Standard Model.

 

 

I should also mention that there is a very brief intro to logic for

the un-initiated, in order to establish language and notation. And I

try to keep the math to a sophomore college level. It should only take

about an hour to read the article. I've been developing this theory

for about 5 years now. And no one is showing me any errors yet, though

there have been some who have had questions. These questions gave rise

to revisions so that I think the article should be easier to read.

 

Why would anyone think quantum mechanics isn't derived from logic? Granted, the actual paths of particles themselves don't follow conjunctions, they just "appear".

[Majik1]

Why would anyone think quantum mechanics isn't derived from logic? Granted, the actual paths of particles themselves don't follow conjunctions, they just "appear".

 

 

When you consider that in quantum mechanics particles take every possible path, then each position is no longer unique to any one trajectory, and each position seems to be an entity all to itself, which sometimes acts as the destination of some other point and sometimes acts as the starting point to some other destination. So none of the points can negate the existence of any other point, since they all appear in many different paths. And if no point can negate another, they all exist in conjunction, and the logic I developed applies.

[qsa]

Hi majik,

 

you are "friend" from another forum. If you are around I like to talk to you.

I also found something that might interest you.

 

 

 

http://carlbrannen.w...uantum-numbers/

 

http://geocalc.clas.asu.edu/pdf/UGA.pdf

 

 

http://www.montgomerycollege.edu/Departments/planet/planet/Numerical_Relativity/bookGA.pdf

Edited May 2, 2012 by qsa

[Ronald Hyde]

You're very close to getting it right. Unitarity and Boolean logic go together, and should be part of every ones thinking about physics.

Unitarity can be derived from Boolean logic in a very straightforward manner. If an occurrence is allowed by logic it has a probability of

one of happening, if it's not allowed it has a probability of zero, if its allowed under some conditions and not others, it may have a probability

between zero and one in general.

[studiot]

Unitarity can be derived from Boolean logic in a very straightforward manner. If an occurrence is allowed by logic it has a probability of

one of happening, if it's not allowed it has a probability of zero, if its allowed under some conditions and not others, it may have a probability

between zero and one in general.

 

 

The square root of -1 is excluded from the graph of y = x squared, yet we talk of i