|Now Standard Model from Pure Logic||Mike||3/2/12 6:55 PM|
Previously, I derived quantum mechanics from logic alone. It turned
out to be an easy matter to iterate the process to get the 2nd
quantization of QFT. When the procedure used to justify complex
numbers in first quantization is iterated in 2nd quantization, it
appears that this calls for the creation of quaternions. And when
iterated to get 3rd quantization it calls for octonions. Now, I'm
informed that the complex numbers specify the U(1) symmetry, the
quaternions specify the SU(2) symmetry, and the octonions specify the
SU(3) symmetry. And when these are put together, you get the
U(1)SU(2)SU(3) symmetry of the Standard Model. References supplied at
I recently discovered this iteration process. So I'm not well versed
in the hypercomplex numbers, nor in group theory. So maybe some who
are well versed in these subjects would like to take a look at my work
and give comment or advice.
The whole webpage might take an hour to read, and I know some are
busy. So below is a bookmark to the last few pages where the
iterations process begins. If this seems interesting, please scroll to
the top and review the whole thing. Thank you.
|Re: Now Standard Model from Pure Logic||Raphael S. A. Alexis||3/3/12 9:47 AM|
Just recently I read a paper on arXiv about how one could deduce quantum theory from algebraic probability by adding but one axiom that allowed for vector spaces to have other vector spaces as their components, it really impressed me and your deductions look pretty much the same to me, keep up that work, pal!
|Re: Now Standard Model from Pure Logic||Mike||3/8/12 6:47 PM|
On Mar 3, 12:47 pm, Raphael Alexis <nervtoeter.n...@yahoo.de> wrote:
> > The whole webpage might take an hour to read, and I know some arePlease try to take this more seriously. I've been developing it for
years, and now I think I've essentially correct. It has the potential
of being a Theory of Everything.
|Re: Now Standard Model from Pure Logic||Mike||3/10/12 2:18 PM|
On Mar 2, 9:55 pm, Mike <maj...@charter.net> wrote:...
Perhaps some here could help with a problem I'm having.
In the derivation I go from ANDs and ORs to multiplication and
addition in a rather quick fashion by quoting the paper, Scaled
Boolean Algebra. I don't spend much time on it because it seems this
is the usual procedure to go from unions and intersections to the
addition and multiplication of probabilities. However, I'm trying to
find a more complete and obvious proof that one can map ANDs and ORs
to multiplication and addition.
So what I'm thinking is that there might be some sort of proof in the
fact that there is a strong similarity between expansion for
implication in terms of other implication and the expansion of the
Dirac delta in terms of other Dirac deltas. Is this a type of
isomorphism or homomorphism that exists only for implication if
disjunction is mapped to addition and conjunction is mapped to
multiplication? The math for this question can be seen at:
Any help would be appreciated.
|Re: Now Standard Model from Pure Logic||Mike||3/13/12 1:01 PM|
On Mar 10, 6:18 pm, Mike <maj...@charter.net> wrote:So what do we know for sure about any map from logic to math? Well, we
would have to map binary operations in logic to binary operation in
math, right? We would have to map the operands of binary logic to the
operands of math, proposition in logic would have to map to numbers in
math, right? The question is whether there is something in the algebra
of ANDs and ORs that requires them to be mapped to multiplication and
addition. Perhaps the map from logic to math must preserve the
commutative or associative properties of the binary operations.
And I'm still not sure why False should be mapped to the number zero
and True to non-zero. Is there something inherently necessary about
only counting objects if they are in a certain region - we don't
count objects outside our scope of interest, right? That would suggest
the Dirac measure as being fundamental.
If anyone has any ideas about all this, please let me know. Thanks.
|Re: Now Standard Model from Pure Logic||Raphael S. A. Alexis||3/13/12 7:59 PM|
Very interesting question. Natively AND and OR would have to be represented by functions (switches), possibly with limitations.
Think of a term - some term - where there is two variables, one being "true" state, thus incorporating everything that is true if the EITHER is true, and then the other variable being the OR variable. Now have them be MULTIPLIED with 0 OR 1 to mark which one is currently "true". That is why we use 1 and 0.
Now, to decide how this EITHER or OR is to be combined in an AND we need to look at what they represent, it can practically be any operator known to man as long as it makes sense - such is the power of logic.
However, if the EITHER states something that needs to be applied with some operator and the OR needs another operator we'd have to decide whether to sum up the outcomes and then devise them by the number of ORs and EITHERs (or ANDs) or handle it otherwise.
In any case, 1-0 would be EITHER; 0-1 would be OR; 1-1 would be AND; 0-0 would be NEITHER you can even go as far as to map MAYBE to 0.5 and basically every possible word for probabilities and quantities as well - no matter how vague they may be in actual speech, they need to be to the point in maths.
Hope this may have helped you on the philosophical part, I have to admit I didn't find the time to go through your maths again yet... maybe I will do so later, maybe not.
======================================= MODERATOR'S COMMENT:
You should please figure out why your lines are not wrapping properly when posting via googlegroups. -fd
|Re: Now Standard Model from Pure Logic||Ross A. Finlayson||3/14/12 4:57 PM|
> You should please figure out why your lines are not wrapping properly when posting via googlegroups. -fd- Hide quoted text -
> - Show quoted text -
Well you could just scale addition and arithmetic up into
multiplication space like that (into area) and they would be constant
rate in area but why bother when it's simple to derive from first or
common principles. Still so wide.... Basically still is memoryless.
Model power electonics through generally there inert crystalline media
(with built in flow gradient).
You want a hybrid of binary logic and basically speciated lines.
Would seem to be holographic projection on the reset so then would
benefit crystal doping or along lines of sample reconstruction.
"I extended that analogy to reconstruct Feynman's Path Integral from
simple logic. The conversion is achieved by representing the material
implication of logic with the Dirac delta function and then using the
complex gaussian form of the Dirac delta. However, at this point my
derivation has not been reviewed by reputable sources. It has yet to
pass the standards of rigor required by mathematical logicians. Until
that time, this effort should be considered preliminary."
Yeah, me neither, haven't yet all explained Feynmann integrals (path
integrals). How I explain Path integrals' difference from 1.000...
in measurement is simply vanishing constant on measurement power and
configuration. Yeah sure they work out to 1.000... but spin it up
and it's relative. I work that up from first principles on the
polydimensional. Still working on: electron or photon.
I think the quote describes a framework for discussing representations
of the phasics of concern quite generally, which I just invented that
word, from the real out through the hypercomplex and that's plain in
phase and transport, then see from the first and universal principles
that the add-up would have those values and why. I don't know what
all those are, ..., just these things I notice, from basically
hammering on foundations for, some time.
So for the Path integral, it is famous where Feynmann shows us how the
particle transmits through space and that while the distance is 1,
that it adds up to 1.00000018.... or 1.00000000018... or smaller in a
reducing constant along measurement, just like in the standard
experiment that higher energy experiments increase instead of bound.
Yet, the constant matters even as it vanishes in the resolution so for
the effect. This must somehow transfer up to the general bond media.
Then maybe it would do so along variously organizing normal lines.
Physics from first principles: none.
|Re: Now Standard Model from Pure Logic||Mike||3/30/12 9:49 PM|
So I think I got it. I reworked the derivation. I made it more
straight and obvious from logic. I removed some of the pictures and
replaced the concepts with more reliable math. So I include a a very
light, brief introduction of logic to introduce language and notation.
And I use these concept throughout.
I removed the reference to Scaled Boolean Algebra since I could not
parse it, and it took too long to read. I replace it with a 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. And I
give better reasons why the Dirac delta should be the gaussian version
and why it should be complex based on algebraic concerns. Hopefully,
this will stand up to mathematical inspection. Let me know what you
Look for it tommorow 4/4/12.
|Re: Now Standard Model from Pure Logic||Ross A. Finlayson||4/1/12 12:18 PM|
On Mar 30, 9:49 pm, Mike <maj...@charter.net> wrote:It is one thing but shouldn't be what it's not, delta the gaussian
version, you might consider for example a square version for uniform
It still adds up, as it were, but sometimes the error terms are
smaller to evaluate it over the course. (Then in the infinitesimals,
infinities: sums and products aren't necessarily having all their
properties as in the classical algebra, each still consistent, no
longer interchangeable, in a general framework where the product is
the collected sums.)
About probability - that is very interesting if you are explaining the
parastatistics constructively from first principles.
Sure, good luck with that.
|Re: Now Standard Model from Pure Logic||Mike||4/1/12 5:04 PM|
On Apr 1, 3:18 pm, "Ross A. Finlayson" <ross.finlay...@gmail.com>
I'm finding it increasing difficult to parse even one of your
sentences. And I'm beginning to think that your responses are a
deliberate attempt at deflection or obfuscations. For your sentences
only seem remotely relevant because you mention a few familiar terms.
But they don't seem to be focused enough to even be considered a
comment or a question. You don't seem to be adding to the
conversation, and my preference would be that you stop responding to
my posts, at least until you are able to express enough interest
worthy of a response. Thank you.
======================================= MODERATOR'S COMMENT:
Yes, I had a hard time parsing what Ross said also but let it pass in case you understood it somehow. -fd
|Re: Now Standard Model from Pure Logic||Mike||4/2/12 7:43 PM|
On Mar 31, 12:49 am, Mike <maj...@charter.net> wrote:Revision 4, now on-line at:
The rather simple way to get the Sum and Product rule for probablities
may be of interest for its own sake. The argument that a gaussian
distribution is needed for a fundamental theory may be of interest as
well. And I think the reasons for the Dirac delta to mathematically
represent material implication are now stronger and easier to
understand from the math. I no longer rely on graphs to explain how to
impose a coordinate system. Instead, I just let the discrete variable
become continuous. This is a serious effort, and I would appreciate a
critical reading. It should only take about an hour to read. Thank you.