I've been able to construct an equation in propositional logic that
can be translated into mathematical terms that produce the Feynman
path integral. I start with the assumption that reality consists of
the universal set of statements that all exist in conjunction with
each other. This universal conjunction can be manipulated into a
conjunction of implications. Each implication can be equated to every
possible "path" of implications through every possible state. I show
that material implication can be represented by the Dirac delta
function in the form of a complex gaussian. The exponents in the
gaussian can be added up in the paths to form the Feyman path
integral. This gives the first quantization of quantum mechanics.
This procedure can be easily iterated to get the second quantization
of quantum field theory. And nothing prevents further iterations to
get third or even forth quantization. The first quantization procedure
is shown to require complex numbers. The second quantization seems to
require quaternions; the third quantization seems to require
octonions. Complex numbers form the U(1) symmetry, quaternions from
the SU(2) symmetry, and octonions form the SU(3) symmetry. All of
these form the U(1)SU(2)SU(3) symmetry of the Standard Model. This all
indicates that physics can be derived from logic.
news:83a83c99-f8cd-454e-8e5b-9fba4ffd6823@i16g2000yql.googlegroups.com...
| Can physics be derived from pure logic?
|
| I've been able to construct an equation in propositional logic that
| can be translated into mathematical terms that produce the Feynman
| path integral. I start with the assumption that reality consists of
| the universal set of statements that all exist in conjunction with
| each other. This universal conjunction can be manipulated into a
| conjunction of implications. Each implication can be equated to every
| possible "path" of implications through every possible state. I show
| that material implication can be represented by the Dirac delta
| function in the form of a complex gaussian. The exponents in the
| gaussian can be added up in the paths to form the Feyman path
| integral. This gives the first quantization of quantum mechanics.
|
| This procedure can be easily iterated to get the second quantization
| of quantum field theory. And nothing prevents further iterations to
| get third or even forth quantization. The first quantization procedure
| is shown to require complex numbers. The second quantization seems to
| require quaternions; the third quantization seems to require
| octonions. Complex numbers form the U(1) symmetry, quaternions from
| the SU(2) symmetry, and octonions form the SU(3) symmetry. All of
| these form the U(1)SU(2)SU(3) symmetry of the Standard Model. This all
| indicates that physics can be derived from logic.
|
| See more details at:
|
| http://webpages.charter.net/majik1/QMlogic.htm |
| Comments welcome.
|
According to Boyle's and Charles' laws, a fixed pressure of
a gas at 20 kelvin will have a volume that is twice that at 10
kelvin. If you heat the air in a balloon the pressure goes up
and the balloon expands according to the law P1.V1/T1 = P2.V2/T2
Using your "physics from logic", what is the volume of gas at zero kelvin?
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 concepts
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. This may
be of interest for its own sake. 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 think. Thank you.
On Mar 8, 11:55 am, Mike <maj...@charter.net> wrote:
> Can physics be derived from pure logic?
> I've been able to construct an equation in propositional logic that
> can be translated into mathematical terms that produce the Feynman
> path integral.
> .....
> See more details at:
This represents a major breakthrough in natural philosophy. It takes
all the guess-work out of theoretical physics. It's the only way to
derive a Theory of Everything (TOE). So I think it deserves a serious
review.
It seems traditionally theoretical physics is advanced by first
guessing at some kind of mathematics based on intuition, then making
predictions based on that math, and seeing if experiment confirms
those predictions. When many observation confirm the predictions and
none contradict them, then we develop confidence that the theory is
correct. But we can never really say that the theory is unquestionably
true since it might be possible that future observations may falsify
the theory.
But if theory is derived from logic alone, then physical laws become a
tautology and are true by construction. What would we do if logic
itself made a prediction that was contradicted by observation? Would
we say that reality was illogical? Or would we say that the experiment
was flawed? It would certainly be a difficult position to be in to
question reason itself. It's nice to see that my derivation so far
seems to be confirming the math we have been using in physics.
We could always questions the accuracy and meaning of experimental
results. And when we don't know the reason for the math we are using,
there is always room to wonder if there isn't something more basic
behind the math that might explain more things. So the question won't
stop until the answers come from reason itself. For once we have a
theory derived from reason itself (logic), then there is no recourse
but to question your sanity if you don't like the answers.
Mike wrote:
> But if theory is derived from logic alone, then physical laws become a
> tautology and are true by construction. What would we do if logic
> itself made a prediction that was contradicted by observation? Would
> we say that reality was illogical? Or would we say that the experiment
> was flawed? It would certainly be a difficult position to be in to
> question reason itself. It's nice to see that my derivation so far
> seems to be confirming the math we have been using in physics.
An alternative logic has been proposed for quantum theory. It was
invented by Birkhoff and von Neumann, see their 'The Logic of Quantum
Mechanics', Annals of Mathematics, 37.
-- When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting
> On Mar 8, 11:55 am, Mike <maj...@charter.net> wrote:
> > Can physics be derived from pure logic?
> > I've been able to construct an equation in propositional logic that
> > can be translated into mathematical terms that produce the Feynman
> > path integral.
> > .....
> > See more details at:
> This represents a major breakthrough in natural philosophy. It takes
> all the guess-work out of theoretical physics. It's the only way to
> derive a Theory of Everything (TOE). So I think it deserves a serious
> review.
> It seems traditionally theoretical physics is advanced by first
> guessing at some kind of mathematics based on intuition, then making
> predictions based on that math, and seeing if experiment confirms
> those predictions. When many observation confirm the predictions and
> none contradict them, then we develop confidence that the theory is
> correct. But we can never really say that the theory is unquestionably
> true since it might be possible that future observations may falsify
> the theory.
> But if theory is derived from logic alone, then physical laws become a
> tautology and are true by construction. What would we do if logic
> itself made a prediction that was contradicted by observation? Would
> we say that reality was illogical? Or would we say that the experiment
> was flawed? It would certainly be a difficult position to be in to
> question reason itself. It's nice to see that my derivation so far
> seems to be confirming the math we have been using in physics.
> We could always questions the accuracy and meaning of experimental
> results. And when we don't know the reason for the math we are using,
> there is always room to wonder if there isn't something more basic
> behind the math that might explain more things. So the question won't
> stop until the answers come from reason itself. For once we have a
> theory derived from reason itself (logic), then there is no recourse
> but to question your sanity if you don't like the answers.
The question is can you derive fundamental constants, the hallmark of
a TOE?
Or are you just building up any formula in a constructive step by step
system?
> I've been able to construct an equation in propositional logic that
> can be translated into mathematical terms that produce the Feynman
> path integral.
> .....
> See more details at:
This represents a major breakthrough in natural philosophy. It takes
all the guess-work out of theoretical physics. It's the only way to
derive a Theory of Everything (TOE). So I think it deserves a serious
review.
It seems traditionally theoretical physics is advanced by first
guessing at some kind of mathematics based on intuition, then making
predictions based on that math, and seeing if experiment confirms
those predictions. When many observation confirm the predictions and
none contradict them, then we develop confidence that the theory is
correct. But we can never really say that the theory is unquestionably
true since it might be possible that future observations may falsify
the theory.
But if theory is derived from logic alone, then physical laws become a
tautology and are true by construction. What would we do if logic
itself made a prediction that was contradicted by observation? Would
we say that reality was illogical? Or would we say that the experiment
was flawed? It would certainly be a difficult position to be in to
question reason itself. It's nice to see that my derivation so far
seems to be confirming the math we have been using in physics.
We could always questions the accuracy and meaning of experimental
results. And when we don't know the reason for the math we are using,
there is always room to wonder if there isn't something more basic
behind the math that might explain more things. So the question won't
stop until the answers come from reason itself. For once we have a
theory derived from reason itself (logic), then there is no recourse
but to question your sanity if you don't like the answers.
============================================
Start questioning.
On Apr 5, 5:17 pm, Frederick Williams <freddywilli...@btinternet.com>
wrote:
> An alternative logic has been proposed for quantum theory. It was
> invented by Birkhoff and von Neumann, see their 'The Logic of Quantum
> Mechanics', Annals of Mathematics, 37.
I have an objection to this "new" quantum logic. As I understand it,
this quantum logic denies the distributive law so that
p^(q v r) does not equal
(p^q)v(p^r)
as it does in classical logic.
My objection is that you can express any formula in logic by using one
connective, negation, and parenthesis. For example
(p^q)=~(p->~q), and
(p v r)= ~p->q = ~q->p
where ~ is negation and -> is material implication.
Given that, the distributive law can be expressed by this set of
negation, a connective, and parenthesis. So it would seem that denial
of the distributive law is the same as denying the definition of this
connective in this one case. That would be a case of special pleading,
which is a logic fallacy. We can't assert the validity of the
connective in one case and turn around and deny it another.
What I've shown is that there is no need to invent a new logic. QM can
be easily derived from classical logic.
On Apr 5, 5:28 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> The question is can you derive fundamental constants, the hallmark of
> a TOE?
> Or are you just building up any formula in a constructive step by step
> system?
I'm not actually claiming to have derived all of physics, yet. But I
do claim to have derive quantum theory and most likely the Standard
Model symmetry groups. When I iterate the process, the complex numbers
become quaternions that further iterate to octonions, which are
subsets of the more general Clifford algebra used to represent
differential geometry. So even there, there might be an in to help
derive GR. I cover all this on my website at:
logic is just the simplest of the three Rs,
which are nothing but language acquisition,
which is more-or-lsee organic, viz Chomsky. but,
if your symmetries are able to hold,
that is something.
> We could always questions the accuracy and meaning of experimental
> results. And when we don't know the reason for the math we are using,
> there is always room to wonder if there isn't something more basic
> behind the math that might explain more things.
On Apr 5, 8:49 pm, 1treePetrifiedForestLane <Space...@hotmail.com>
wrote:
> logic is just the simplest of the three Rs,
> which are nothing but language acquisition,
> which is more-or-lsee organic, viz Chomsky. but,
> if your symmetries are able to hold,
> that is something.
I think there is more to logic than language. It seems to be
describing something about the nature of reality. We wouldn't use it
if it did not.
> On Apr 5, 8:49 pm, 1treePetrifiedForestLane <Space...@hotmail.com>
> wrote:
>> logic is just the simplest of the three Rs,
There is nothing simple in every single particle as complex as the entire universe.
>> which are nothing but language acquisition,
>> which is more-or-lsee organic, viz Chomsky. but,
>> if your symmetries are able to hold,
>> that is something.
> I think there is more to logic than language. It seems to be
> describing something about the nature of reality.
That is wrong, upside down: logic *is* language. In fact, now yours rather is the onus of explaining how it is that there is (or there is not) a "reality" (what is it??) at all...
> We wouldn't use it if it did not.
Mind you, that is a basic logic fallacy.
There is nothing simple or "self-evident" in logic, and you should pay it *at least* the same respect as you pay to mathematics or physics.
On Apr 5, 11:40 pm, "LudovicoVan" <ju...@diegidio.name> wrote:
> "Mike" <maj...@charter.net> wrote in message
> > I think there is more to logic than language. It seems to be
> > describing something about the nature of reality.
> That is wrong, upside down: logic *is* language.
Then there is a great mystery to solve as to why nature is logical. Or
do you think otherwise?
> In fact, now yours rather
> is the onus of explaining how it is that there is (or there is not) a
> "reality" (what is it??) at all...
What do you mean? Do you mean I need to explain why there is something
rather than nothing? Isn't it enough to say that once there is
something, then there must be consequences too? Or isn't it enough to
say that once there is a set of facts called reality, then all those
facts must not contradict each other?
> On Apr 5, 8:49 pm, 1treePetrifiedForestLane <Space...@hotmail.com>
> wrote:
> > logic is just the simplest of the three Rs,
> > which are nothing but language acquisition,
> > which is more-or-lsee organic, viz Chomsky. but,
> > if your symmetries are able to hold,
> > that is something.
> I think there is more to logic than language.
Agreed. At the very least it is language with a consequence relation
defined on it. Maybe a partial consequence relation R, by which I mean
If R(x,y) is true then y is a consequence of x,
if R(x,y) is false then y is not a consequence of x,
for some x,y R(x,y) may be neither true nor false
(or, at least, it isn't known which).
> It seems to be
> describing something about the nature of reality.
An old fashioned view is that logic describes the laws of thought. It
is not a claim that you will find in any current text, but it is worth
considering:
Did Brouwer's brain (or the brain of any apologist for non-classical
logic) obey different laws from ours? And, since a brain is a physical
thing, did it obey different physical laws?
> We wouldn't use it
> if it did not.
Some will claim that logic _doesn't_ say anything about reality: that p
v ~p, for example, is true in virtue of the meanings of v and ~, and
that those meanings are just a matter of convention.
That physics might be derived from logic alone is an interesting thought
(I think I raised it myself years ago), but _which_ logic?
-- When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting
> On Apr 5, 5:17 pm, Frederick Williams <freddywilli...@btinternet.com>
> wrote:
> > An alternative logic has been proposed for quantum theory. It was
> > invented by Birkhoff and von Neumann, see their 'The Logic of Quantum
> > Mechanics', Annals of Mathematics, 37.
> I have an objection to this "new" quantum logic. As I understand it,
> this quantum logic denies the distributive law so that
> p^(q v r) does not equal
> (p^q)v(p^r)
> as it does in classical logic.
> My objection is that you can express any formula in logic by using one
> connective, negation, and parenthesis. For example
> (p^q)=~(p->~q), and
> (p v r)= ~p->q = ~q->p
> where ~ is negation and -> is material implication.
> Given that, the distributive law can be expressed by this set of
> negation, a connective, and parenthesis. So it would seem that denial
> of the distributive law is the same as denying the definition of this
> connective in this one case.
Are the connectives interdefinable in quantum logic as they are in
classical logic? If so (I doubt it) then one or both of ~ and -> will
behave non-classically as well.
-- When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting
Frederick Williams <freddywilli...@btinternet.com> writes:
> Mike wrote:
>> On Apr 5, 5:17 pm, Frederick Williams <freddywilli...@btinternet.com>
>> wrote:
>> > An alternative logic has been proposed for quantum theory. It was
>> > invented by Birkhoff and von Neumann, see their 'The Logic of Quantum
>> > Mechanics', Annals of Mathematics, 37.
>> I have an objection to this "new" quantum logic. As I understand it,
>> this quantum logic denies the distributive law so that
>> p^(q v r) does not equal
>> (p^q)v(p^r)
>> as it does in classical logic.
>> My objection is that you can express any formula in logic by using one
>> connective, negation, and parenthesis. For example
>> (p^q)=~(p->~q), and
>> (p v r)= ~p->q = ~q->p
>> where ~ is negation and -> is material implication.
>> Given that, the distributive law can be expressed by this set of
>> negation, a connective, and parenthesis. So it would seem that denial
>> of the distributive law is the same as denying the definition of this
>> connective in this one case.
> Are the connectives interdefinable in quantum logic as they are in
> classical logic? If so (I doubt it) then one or both of ~ and -> will
> behave non-classically as well.
The Bikhoff/von Neumann proposal doesn't have an implication operation
(it does have a notion of logical consequence). Negation on
its own is as usual ( ~~ p and p are interderivable). So Mike's
argument does not apply as it stands.
On Apr 6, 1:20 pm, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
> The Bikhoff/von Neumann proposal doesn't have an implication operation
> (it does have a notion of logical consequence). Negation on
> its own is as usual ( ~~ p and p are interderivable). So Mike's
> argument does not apply as it stands.
Actually, my argument does not rely on implication, only that the
distributive law can be expressed with one connective (be it
implicaiton, ORs or ANDs), parenthesis, and negation. Then the
argument is that it is not correct to consider the connective valid in
one formula but not in another.
And now that I think about it, I'm not sure my derivation makes use of
the distributive law.
> On Apr 6, 1:20 pm, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
> > The Bikhoff/von Neumann proposal doesn't have an implication operation
> > (it does have a notion of logical consequence). Negation on
> > its own is as usual ( ~~ p and p are interderivable). So Mike's
> > argument does not apply as it stands.
> Actually, my argument does not rely on implication, only that the
> distributive law can be expressed with one connective (be it
> implicaiton, ORs or ANDs), parenthesis, and negation.
Using de Morgan's laws? And does the Birkhoff/von Neumann logic satisfy
de Morgan's laws? It's a genuine question, I know nothing about it.
> Then the
> argument is that it is not correct to consider the connective valid in
> one formula but not in another.
> And now that I think about it, I'm not sure my derivation makes use of
> the distributive law.
-- When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting
Mike <maj...@charter.net> writes:
> On Apr 6, 1:20 pm, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
>> The Bikhoff/von Neumann proposal doesn't have an implication operation
>> (it does have a notion of logical consequence). Negation on
>> its own is as usual ( ~~ p and p are interderivable). So Mike's
>> argument does not apply as it stands.
> Actually, my argument does not rely on implication, only that the
> distributive law can be expressed with one connective (be it
> implicaiton, ORs or ANDs), parenthesis, and negation. Then the
> argument is that it is not correct to consider the connective valid in
> one formula but not in another.
It's clear that the quantum logic proposed does not
coincide with classical propositional logic; it's a strictly
weaker logic, in that if P1 entails P2 (P1, P2 just using
and, or, not) in quantum logic, it does in classical logic also,
but not vice versa.
So the usual truth tables do not apply --
but that makes sense if our judgements are about
QM properties, I think.
> And now that I think about it, I'm not sure my derivation makes use of
> the distributive law.
-- When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting
Frederick Williams <freddywilli...@btinternet.com> writes:
> Mike wrote:
>> On Apr 6, 1:20 pm, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
>> > The Bikhoff/von Neumann proposal doesn't have an implication operation
>> > (it does have a notion of logical consequence). Negation on
>> > its own is as usual ( ~~ p and p are interderivable). So Mike's
>> > argument does not apply as it stands.
>> Actually, my argument does not rely on implication, only that the
>> distributive law can be expressed with one connective (be it
>> implicaiton, ORs or ANDs), parenthesis, and negation.
> Using de Morgan's laws? And does the Birkhoff/von Neumann logic satisfy
> de Morgan's laws? It's a genuine question, I know nothing about it.
Yes, de Morgan's laws hold.
That's not enough to derive distributivity from the lattice
properties, though;
you get the laws corresponding to an orthocomplemented lattice
(plus an extra condition):
On Apr 6, 4:08 pm, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
> It's clear that the quantum logic proposed does not
> coincide with classical propositional logic; it's a strictly
> weaker logic, in that if P1 entails P2 (P1, P2 just using
> and, or, not) in quantum logic, it does in classical logic also,
> but not vice versa.
This seems to prove that quantum logic cannot be used in my efforts.
For I use a conjunction of implications to describe a "path". These
implication are really more entailment, since they derive from a
conjunction implying one of it operands. So if classical entailment
does not have a quantum logic equivalent, then quantum logic is
probably of no use in my efforts.
> So the usual truth tables do not apply --
> but that makes sense if our judgements are about
> QM properties, I think.
So I'm hoping we no longer have to consider quantum logic to fully
explain QM.
That's a good question. I have only a limited knowledge about
mathematics and mathematical logic and my physics is even
worse; so I could only speculate here.
I was probably not the only one but years ago I harbored a naive desire,
a dream, that one day all the physics laws would be just consequences
of mathematics and mathematical reasoning; and all the known properties
of the universe such as the speed of light, Planck constant would be
just values derivable from some mathematical relationships. In the
effort to see that dream though I tried to learn and discern some
"deep" properties of real numbers, of geometry, groups, rings, fields,
etc...
In the end I gave up: there are so many difficult things to learn
and yet nowhere have I found even a slightest hint in mathematics or
in logical reasoning that would explain the mystery as to why the speed
of light is 300,000.00 km/sec, instead of 299,299.99 km/sec! Or why I'm
here and now, instead of being there and then!
One day though, it just dawned on me that the answer to the mystery
above is quite simple and lies within a branch of mathematics that
we're all familiar with: Combinatorial Analysis, which involves
a concept known as permutation! You see, a coin has 2 sides: head or
tail; and you might not know the next time you encounter a coin
strolling on a beach whether it's a head or tail facing up, but
it got be either head or tail only: there's no 3rd side!
The long and short of the story is that I think the entire physical
universe is just a permutation out of however many possible combination,
permutations of possible point-wise states. And so we don't need to ask
why the speed of light is such and such: it just happens to be _that_
permutation. And if it's not that permutation, it would still be just
a different permutation, different value!
Iow, the entire physical universe is just a Choice function, out of
collection of however many choices there exist.
Something like that, imho. And so, to your question:
> Can physics be derived from pure logic?
I'd think the answer would be a yes, albeit trivially so: physics
would be just a mathematical permutation, a mathematical choice
function: things are just the way things are!
Incidentally, with just a minor twist, physics would be just
an autonomous axiomatic formal system! The twist is that rules
of inference are still applicable to some formulas, but there are
no (starting formulas known as) axioms!
(Think of the difference between the natural numbers that there's
a starting point, and the integer numbers that there's no starting one)
> I've been able to construct an equation in propositional logic that
> can be translated into mathematical terms that produce the Feynman
> path integral. I start with the assumption that reality consists of
> the universal set of statements that all exist in conjunction with
> each other. This universal conjunction can be manipulated into a
> conjunction of implications. Each implication can be equated to every
> possible "path" of implications through every possible state. I show
> that material implication can be represented by the Dirac delta
> function in the form of a complex gaussian. The exponents in the
> gaussian can be added up in the paths to form the Feyman path
> integral. This gives the first quantization of quantum mechanics.
> This procedure can be easily iterated to get the second quantization
> of quantum field theory. And nothing prevents further iterations to
> get third or even forth quantization. The first quantization procedure
> is shown to require complex numbers. The second quantization seems to
> require quaternions; the third quantization seems to require
> octonions. Complex numbers form the U(1) symmetry, quaternions from
> the SU(2) symmetry, and octonions form the SU(3) symmetry. All of
> these form the U(1)SU(2)SU(3) symmetry of the Standard Model. This all
> indicates that physics can be derived from logic.
