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Quantum Theory derive from logic
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Mike
May 19, 2012, 9:16:41 PM5/19/12
to
I've updated my website where I prove that quantum theory can be
derived from pure logic. I improved the notation a bit to make it
easier to read. And I explain how the map from logic to math is
consistent even in the continuous case. I also try to explain a bit
more why the exponent should be complex in the gaussian form of the
Dirac delta function that is used to represent logical implication.
For your inspection at:
http://webpages.charter.net/majik1/QMlogic.htm
derived from pure logic. I improved the notation a bit to make it
easier to read. And I explain how the map from logic to math is
consistent even in the continuous case. I also try to explain a bit
more why the exponent should be complex in the gaussian form of the
Dirac delta function that is used to represent logical implication.
For your inspection at:
http://webpages.charter.net/majik1/QMlogic.htm
adel sadeq
May 19, 2012, 10:39:04 PM5/19/12
to
I send you this message in another forum but you did not reply. I am
really interested to connect our theories, but you have to make some
effort to read mine. I know time is in short supply , but I have spent
at least 3 hours on yours. I cannot start a communication with you if
you don't know the basics of my theory, I am sure there is a link and
as you can see I have so many direct results. BTW, I liked those
probabilty graphs that you have removed. I think both our theories
imply logic based on probabilities.
I keep thinking that my theory has something to do with your's but
have not had the time to dig deep. Can you look at my theory and see
what you make of it in terms of your theory. Actually, My theory has a
totally probabilistic interpretation (and also information). I have
even computed the Fine structure constant since it is looked upon as
the probability of emitting photons. Thanks.
P.S. have you tried to publish anywhere like vixra?
http://www.qsa.netne.net.
Message has been deleted
Mike
May 20, 2012, 1:59:15 PM5/20/12
to
You're going to have to develop a concise abstract that summarizes
your efforts. No one should have to wade through your diary in order
to get the jist of your work.
Secondly, you're going to have to develop some mathematical equations
that others can understand where you got them. You have a computer
program, but there's probably some sort of equation that is being
implimented.
I'm sorry, but I don't feel I understand what your trying to do well
enough to comment. You mentioned something about random lines between
points, or was it random points on a line. That might be similar to my
gaussian distributions along paths, but I can't be sure.
In any event, I think logic takes precedence over math. If the
mathematics of the universe is logical, then there must be some way to
map logic to the math. I think I've accomplished that.
PS. I will need to convert my HTML pages into pdf format since I'm not
a PhD nor do I know any PhDs that would sponsor me.
qsa
May 20, 2012, 5:21:38 PM5/20/12
to
>
> First off my dear (for lack of a better name),
>
> You're going to have to develop a concise abstract that summarizes
> your efforts. No one should have to wade through your diary in order
> to get the jist of your work.
>
> Secondly, you're going to have to develop some mathematical equations
> that others can understand where you got them. You have a computer
> program, but there's probably some sort of equation that is being
> implimented.
>
> I'm sorry, but I don't feel I understand what your trying to do well
> enough to comment. You mentioned something about random lines between
> points, or was it random points on a line. That might be similar to my
> gaussian distributions along paths, but I can't be sure.
>
> In any event, I think logic takes precedence over math. If the
> mathematics of the universe is logical, then there must be some way to
> map logic to the math. I think I've accomplished that.
>
> PS. I will need to convert my HTML pages into pdf format since I'm not
> a PhD nor do I know any PhDs that would sponsor me.
Of course, my website is not detailed, but should be enough for a reasonably careful reader. In "how I arrived" I do describe( Although, more detail is needed to get a better grip) the derivation process in not unlike your method of step by step. To my mind I like to convert my theory to a mathematical form that matches current theories, but I think it is more important for your theory and mine to be converted into a new purely probabalistic theory which shows the true nature of nature. I hope I have to say a lot more about your theory, but I do need some time.I think I know of a better arqument for the use of sqrt(-1)in you equations.
Adel
Mike
May 20, 2012, 9:50:59 PM5/20/12
to
On May 20, 5:21 pm, qsa <sadeq.adel...@gmail.com> wrote:
> My name is Adel. If you import your file into a WORD document you can output it as pdf in 5 sec. I converted your file and it looks good except for these weired webbot commands, I will send it by email to you if you like. Are you sure you need a PHD to sponsor you for VIXRA ?
>
Thanks, Adel. I'll have to give that a try. No, you don't need a
> My name is Adel. If you import your file into a WORD document you can output it as pdf in 5 sec. I converted your file and it looks good except for these weired webbot commands, I will send it by email to you if you like. Are you sure you need a PHD to sponsor you for VIXRA ?
>
sponsor to Vixra. But it is my impression that accedamia does not take
it seriously. I might be discrediting myself to post there.
> I hope I have to say a lot more about your theory, but I do need some time.I think I know of a better arqument for the use of sqrt(-1)in your equations.
>
> Adel
Yes, my modification to complex numbers is probably not motivated very
well. I'm not absolutely sure it is even necessary. After all,
sometime physicists use what is called a Wick rotation where they use
complex time. It result is no complex numbers in the path integral and
is called the euclidean path integral. But it would be nice if I could
prove it necessary. For then, the iteration to quaternions and
octonions would be justified too.
Phillip Helbig---undress to reply
May 21, 2012, 9:03:51 AM5/21/12
to
In article
<d77fd197-52d4-40b4...@pr3g2000pbb.googlegroups.com>,
A: I will need to convert my HTML pages into pdf format
B: since I'm not a PhD nor do I know any PhDs that would sponsor me
Why should A logically follow from B?
<d77fd197-52d4-40b4...@pr3g2000pbb.googlegroups.com>,
Mike <maj...@charter.net> writes:
> PS. I will need to convert my HTML pages into pdf format since I'm not
> a PhD nor do I know any PhDs that would sponsor me.
This post was about logic. Let's see:
> PS. I will need to convert my HTML pages into pdf format since I'm not
> a PhD nor do I know any PhDs that would sponsor me.
A: I will need to convert my HTML pages into pdf format
B: since I'm not a PhD nor do I know any PhDs that would sponsor me
Why should A logically follow from B?
Mike
May 21, 2012, 12:38:11 PM5/21/12
to
On May 21, 9:03 am, hel...@astro.multiCLOTHESvax.de (Phillip Helbig---
undress to reply) wrote:
> In article
> <d77fd197-52d4-40b4-9ce2-09e237280...@pr3g2000pbb.googlegroups.com>,
Sorry, I was watching TV at the time. I thought I had started the last
sentence before I finished it. I must have thought I actually typed
out what I was thinking in my head when I returned to the keyboard to
finish the sentence started in my head. What I really meant (now that
the TV is on mute) is that 1) I will need to convert my HTML pages
into pdf format, and 2) I don't know if I can publish on arXiv.org
undress to reply) wrote:
> In article
> <d77fd197-52d4-40b4-9ce2-09e237280...@pr3g2000pbb.googlegroups.com>,
sentence before I finished it. I must have thought I actually typed
out what I was thinking in my head when I returned to the keyboard to
finish the sentence started in my head. What I really meant (now that
the TV is on mute) is that 1) I will need to convert my HTML pages
into pdf format, and 2) I don't know if I can publish on arXiv.org
Mike
May 21, 2012, 7:10:31 PM5/21/12
to
complex exponential in the gaussian Dirac delta. One thing that the
complex exponential does is to introduce a cyclic nature as x
continuously changes. So I ask myself is there a cyclic nature
necessary in the Dirac delta function when it represents logical
implication?
Let D(x1-x0) stand for the Dirac delta function in the special case
where it is suppose to represent implication of q1=>q0. Here, x1 is
the position in the coordinate space where the proposition q1 resides,
and x0 is the position where the proposition q0 resides. Then we
already know that q1=>q1 is inherently true and is mapped to 1. So is
it correct to ask if it is also necessarily true that
(q1=>q2)(q2=>q3)(q3=>q4)(q4=>q1)=T?
This would seem to require a cyclic nature to implication. But I'll
have to think about it some more unless someone here already knows the
answer.
qsa
May 21, 2012, 9:24:52 PM5/21/12
to
> > Yes, my modification to complex numbers is probably not motivated very
> > well. I'm not absolutely sure it is even necessary. After all,
> > sometime physicists use what is called a Wick rotation where they use
> > complex time. It result is no complex numbers in the path integral and
> > is called the euclidean path integral. But it would be nice if I could
> > prove it necessary. For then, the iteration to quaternions and
> > octonions would be justified too.
>
> So I'm still thinking about a better justification for the use of the
> complex exponential in the gaussian Dirac delta. One thing that the
> complex exponential does is to introduce a cyclic nature as x
> continuously changes. So I ask myself is there a cyclic nature
> necessary in the Dirac delta function when it represents logical
> implication?
>
> Let D(x1-x0) stand for the Dirac delta function in the special case
> where it is suppose to represent implication of q1=>q0. Here, x1 is
> the position in the coordinate space where the proposition q1 resides,
> and x0 is the position where the proposition q0 resides. Then we
> already know that q1=>q1 is inherently true and is mapped to 1. So is
> it correct to ask if it is also necessarily true that
> (q1=>q2)(q2=>q3)(q3=>q4)(q4=>q1)=T?
> This would seem to require a cyclic nature to implication. But I'll
> have to think about it some more unless someone here already knows the
> answer.
http://arxiv.org/pdf/hep-th/9307019
Mike
May 22, 2012, 10:03:53 AM5/22/12
to
elements I'm working with. I especially like how he links
"implication" with complex probablity. I'll have to read it in more
depth in order to comment further.
Mike
May 22, 2012, 2:43:20 PM5/22/12
to
glosses over too much to be useful to me. In the paper, he doesn't
seem to define his terms well enough to even follow the discussion.
And he leaves out critical derivations without any reference.
As far as "frequency" is concerned, he does seem to be talking about
periodicity with time. But his proof of frequency depends on some
"Prob" function on page 5 that is given without motivation out of thin
air. I didn't see a reference for that either. At this point, I'm not
convinced he knows what he's talking about. Or perhaps he's talking to
a very narrow audience; perhaps it's just a note to himself.
qsa
May 22, 2012, 11:52:07 PM5/22/12
to
Mike
May 23, 2012, 1:53:58 PM5/23/12
to
On May 21, 7:10 pm, Mike <maj...@charter.net> wrote:
> Let D(x1-x0) stand for the Dirac delta function in the special case
> where it is suppose to represent implication of q1=>q0. Here, x1 is
> the position in the coordinate space where the proposition q1 resides,
> and x0 is the position where the proposition q0 resides. Then we
> already know that q1=>q1 is inherently true and is mapped to 1. So is
> it correct to ask if it is also necessarily true that
> (q1=>q2)(q2=>q3)(q3=>q4)(q4=>q1)=T?
> This would seem to require a cyclic nature to implication. But I'll
> have to think about it some more unless someone here already knows the
> answer.
Let x1, x2, x3 be propostions with values of true or false. Let =>
> Let D(x1-x0) stand for the Dirac delta function in the special case
> where it is suppose to represent implication of q1=>q0. Here, x1 is
> the position in the coordinate space where the proposition q1 resides,
> and x0 is the position where the proposition q0 resides. Then we
> already know that q1=>q1 is inherently true and is mapped to 1. So is
> it correct to ask if it is also necessarily true that
> (q1=>q2)(q2=>q3)(q3=>q4)(q4=>q1)=T?
> This would seem to require a cyclic nature to implication. But I'll
> have to think about it some more unless someone here already knows the
> answer.
sybolize the relationship of material implication between
propositions. And let juxtaposition represent conjunction. Then
(x1=>x2)(x2=>x3)(x3=>x1) is equal to
(x1=>x2)(x2=>x3)(x3=>x1)(x1=>x2)(x2=>x3)(x3=>x1)
since x = x AND x
Imagine that these three propostions form a triangle, and the next
factor in a conjunction indicates the next move along a path. Then the
top equation is a single trip around a triangle and the bottom
equation is two trips around the same triangle. Since the two
equations are equal, this reveals a cyclic nature to this definition
of terms. If each step in the conjunction is parameterized by an
increased value of t, then the equality indicates a periodic function
with increasing time. Any thoughts?
Mike
May 23, 2012, 7:57:05 PM5/23/12
to
PDF file now available at:
http://webpages.charter.net/majik1/QM_Logic.pdf
I would appreciate it if some could proof read it for any kind of
mistakes at all. Thank you.
Mike
http://webpages.charter.net/majik1/QM_Logic.pdf
I would appreciate it if some could proof read it for any kind of
mistakes at all. Thank you.
Mike
Phillip Helbig---undress to reply
May 23, 2012, 7:56:52 PM5/23/12
to
In article
<4d0bdd70-50c1-4a36...@ri8g2000pbc.googlegroups.com>,
> I don't know if I can publish on arXiv.org
> since I'm not a PhD nor do I know any PhDs that would sponsor me.
One does need a sponsorship, but a PhD (or any other degree) is not a
requirement, nor does having such a degree automatically allow one to
sponsor.
<4d0bdd70-50c1-4a36...@ri8g2000pbc.googlegroups.com>,
Mike <maj...@charter.net> writes:
> I thought I had started the last
> sentence before I finished it.
I should hope so! :-)
> I thought I had started the last
> sentence before I finished it.
> I don't know if I can publish on arXiv.org
> since I'm not a PhD nor do I know any PhDs that would sponsor me.
requirement, nor does having such a degree automatically allow one to
sponsor.
Mike
May 26, 2012, 6:19:14 PM5/26/12
to
OK, still working to better justify complex numbers in QM. How does
this sound...
Equation [6] on my webpage at:
http://webpages.charter.net/majik1/QMlogic.htm
is a logical equation
(qs=>qf) = OR_from i=1 to n, of (qs=>qi)(qi=>qf)
where (qs=>qf) is the propositional logic statement that qs implies
qf, with similar difinitions for (qs=>qi) and (qi=>qf). And OR_from
i=1 to n means the logical disjunction of n statements, where for
example if n=1, we'd have
(qs=>qf) = (qs=>q1)(q1=>qf)
and if n=2, we'd have
(qs=>qf) = (qs=>q1)(q1=>qf) OR (qs=>q2)(q2=>qf).
But what if for the n=1 equation we had qf=qs? This would represent a
path from qs to q1 and then immediately reverse course and go back
from q1 to qs. This would be written
(qs=>qs) = (qs=>q1)(q1=>qs).
As explained on my website for the discrete case, implication can be
represented by a Dirac delta function D_ij, where D_ij = 1 if i=j and
0 otherwise. Then the n=1 case is mapped to
D_sf = D_s1 * D_1f
where * is numerical multiplication.
Now, consider the case there f=s. Then we'd have
D_ss = D_s1 * D_1s = 1
since D_ss = 1 by definition. Obviously, this is trivially true if
s=1, for you'd have 1=1*1. But what about the case where s is not 1,
where s is outside the range of 1 to n? How do we reconcile that D_ss
= 1 for any s inside or outside the range of 1 to n, with the fact
that D_s1 and D_1s should normally be 0?
Can we make D_s1 be 1 with a phase angle, a complex number with
absolute value of 1, and D_1s be the complex conjugae of D_s1? I'm not
seeing anything in the logic that disallows s from being outside the
range of 1 to n. Any comments? Thanks.
this sound...
Equation [6] on my webpage at:
http://webpages.charter.net/majik1/QMlogic.htm
is a logical equation
(qs=>qf) = OR_from i=1 to n, of (qs=>qi)(qi=>qf)
where (qs=>qf) is the propositional logic statement that qs implies
qf, with similar difinitions for (qs=>qi) and (qi=>qf). And OR_from
i=1 to n means the logical disjunction of n statements, where for
example if n=1, we'd have
(qs=>qf) = (qs=>q1)(q1=>qf)
and if n=2, we'd have
(qs=>qf) = (qs=>q1)(q1=>qf) OR (qs=>q2)(q2=>qf).
But what if for the n=1 equation we had qf=qs? This would represent a
path from qs to q1 and then immediately reverse course and go back
from q1 to qs. This would be written
(qs=>qs) = (qs=>q1)(q1=>qs).
As explained on my website for the discrete case, implication can be
represented by a Dirac delta function D_ij, where D_ij = 1 if i=j and
0 otherwise. Then the n=1 case is mapped to
D_sf = D_s1 * D_1f
where * is numerical multiplication.
Now, consider the case there f=s. Then we'd have
D_ss = D_s1 * D_1s = 1
since D_ss = 1 by definition. Obviously, this is trivially true if
s=1, for you'd have 1=1*1. But what about the case where s is not 1,
where s is outside the range of 1 to n? How do we reconcile that D_ss
= 1 for any s inside or outside the range of 1 to n, with the fact
that D_s1 and D_1s should normally be 0?
Can we make D_s1 be 1 with a phase angle, a complex number with
absolute value of 1, and D_1s be the complex conjugae of D_s1? I'm not
seeing anything in the logic that disallows s from being outside the
range of 1 to n. Any comments? Thanks.
Mike
May 29, 2012, 2:19:55 PM5/29/12
to
On May 26, 6:19 pm, Mike <maj...@charter.net> wrote:
> D_ss = D_s1 * D_1s = 1
>
> since D_ss = 1 by definition. Obviously, this is trivially true if
> s=1, for you'd have 1=1*1. But what about the case where s is not 1,
> where s is outside the range of 1 to n? How do we reconcile that D_ss
> = 1 for any s inside or outside the range of 1 to n, with the fact
> that D_s1 and D_1s should normally be 0?
>
> Can we make D_s1 be 1 with a phase angle, a complex number with
> absolute value of 1, and D_1s be the complex conjugae of D_s1? I'm not
> seeing anything in the logic that disallows s from being outside the
> range of 1 to n. Any comments? Thanks.
This seems to work for conjunction when mapped to multiplication. But
> D_ss = D_s1 * D_1s = 1
>
> since D_ss = 1 by definition. Obviously, this is trivially true if
> s=1, for you'd have 1=1*1. But what about the case where s is not 1,
> where s is outside the range of 1 to n? How do we reconcile that D_ss
> = 1 for any s inside or outside the range of 1 to n, with the fact
> that D_s1 and D_1s should normally be 0?
>
> Can we make D_s1 be 1 with a phase angle, a complex number with
> absolute value of 1, and D_1s be the complex conjugae of D_s1? I'm not
> seeing anything in the logic that disallows s from being outside the
> range of 1 to n. Any comments? Thanks.
it breaks down with addition. How do you add two complex numbers
together where each has an absolute value of 1 and get a sum also with
an absolute value of 1? I suppose you could define addition to include
the division by the number of states being added. But then the
addition of 3 states would not equal the addition of two of those
states that is then added to the third state.
Mike
May 30, 2012, 9:06:19 PM5/30/12
to
OK, let's try this...
Looking at equation [23] at:
http://webpages.charter.net/majik1/QMlogic.htm
a delta is equated to an infinite number of integrals of an infinite
product of deltas. But any one of the deltas could be expressed in
terms of the rest of them. So any equation that represents a delta
would have to have the same form for any delta.
Also, each delta in the infinite product is a function of two
variables D(x1-x2). And each of the variables x1 and x2 varies
independently within the range of R in the integration process. This
means for each argument where x1-x2 is positive, there will also be an
argument where x1-x2 is negative as each of x1 and x2 independently
take on all values in the integration range of R.
So the two paragraphs above require that D(x1-x2) must have the same
form as D(x2-x1). Therefore, the exponent of equation [24] with the
requirement that del^2=t_n-t_n-1 cannot be negative for x1-x2 and
positive for x2-x1. That would make the two cases of a different form
and too much of a discontinuity between the two cases.
But we also need D(x1-x2) to be not equal to D(x2-x2) since they
mathematically represent the logic of q1=>q2 which is not equal to
q2=>q1. So my contention is that the only way to get the delta of one
argument to be not equal to the delta of the negative argument and yet
be of the same form is to have the exponent to be complex. Then the
only difference is a phase angle to an absolute magnitude of 1 for
every delta. The real part of the complex exponential is a cos(x)
which is the same for a negative argument. But the complex part is
sin(x) which changes sign for a negative argument.
Having a complex exponential with an absolute value of 1 also seems to
be consistent with a value of 1 or 0 for the discrete version of the
Kronecker delta for every implication. But I'm not sure this is a
necessary or sufficient argument for a complex exponential for the
deltas in the continuous case. Any thoughts would be welcomed.
Looking at equation [23] at:
http://webpages.charter.net/majik1/QMlogic.htm
a delta is equated to an infinite number of integrals of an infinite
product of deltas. But any one of the deltas could be expressed in
terms of the rest of them. So any equation that represents a delta
would have to have the same form for any delta.
Also, each delta in the infinite product is a function of two
variables D(x1-x2). And each of the variables x1 and x2 varies
independently within the range of R in the integration process. This
means for each argument where x1-x2 is positive, there will also be an
argument where x1-x2 is negative as each of x1 and x2 independently
take on all values in the integration range of R.
So the two paragraphs above require that D(x1-x2) must have the same
form as D(x2-x1). Therefore, the exponent of equation [24] with the
requirement that del^2=t_n-t_n-1 cannot be negative for x1-x2 and
positive for x2-x1. That would make the two cases of a different form
and too much of a discontinuity between the two cases.
But we also need D(x1-x2) to be not equal to D(x2-x2) since they
mathematically represent the logic of q1=>q2 which is not equal to
q2=>q1. So my contention is that the only way to get the delta of one
argument to be not equal to the delta of the negative argument and yet
be of the same form is to have the exponent to be complex. Then the
only difference is a phase angle to an absolute magnitude of 1 for
every delta. The real part of the complex exponential is a cos(x)
which is the same for a negative argument. But the complex part is
sin(x) which changes sign for a negative argument.
Having a complex exponential with an absolute value of 1 also seems to
be consistent with a value of 1 or 0 for the discrete version of the
Kronecker delta for every implication. But I'm not sure this is a
necessary or sufficient argument for a complex exponential for the
deltas in the continuous case. Any thoughts would be welcomed.
Mike
May 31, 2012, 7:53:49 PM5/31/12
to
On May 30, 9:06 pm, Mike <maj...@charter.net> wrote:
> OK, let's try this...
>
> Looking at equation [23] at:http://webpages.charter.net/majik1/QMlogic.htm
>
> OK, let's try this...
>
> Looking at equation [23] at:http://webpages.charter.net/majik1/QMlogic.htm
>
> Also, each delta in the infinite product is a function of two
> variables D(x1-x2). And each of the variables x1 and x2 varies
> independently within the range of R in the integration process. This
> means for each argument where x1-x2 is positive, there will also be an
> argument where x1-x2 is negative as each of x1 and x2 independently
> take on all values in the integration range of R.
Yes, Mike, but there is still a 90 degree phase jump as (t1-t2)
> variables D(x1-x2). And each of the variables x1 and x2 varies
> independently within the range of R in the integration process. This
> means for each argument where x1-x2 is positive, there will also be an
> argument where x1-x2 is negative as each of x1 and x2 independently
> take on all values in the integration range of R.
crosses zero because there is still a square-root of (t1-t2) in the
denominator. And yes, there are contributions from both (x1-x2) and
(x2-x1) in the integral, but I'm not sure that there is a
corresponding (t2-t1) for every (t1-t2). Now I'm thing that "t" will
always increase along any path. For the Action integral in the
exponent of the path integral always goes from 0 to some t, and not
from t to 0 as I recall. Is this right?
ben6993
Jun 1, 2012, 11:08:36 AM6/1/12
to
On Jun 1, 12:53 am, Mike <maj...@charter.net> wrote:
(snip)
> Yes, Mike, but there is still a 90 degree phase jump as (t1-t2)
> crosses zero because there is still a square-root of (t1-t2) in the
> denominator. And yes, there are contributions from both (x1-x2) and
> (x2-x1) in the integral, but I'm not sure that there is a
> corresponding (t2-t1) for every (t1-t2). Now I'm thing that "t" will
> always increase along any path. For the Action integral in the
> exponent of the path integral always goes from 0 to some t, and not
> from t to 0 as I recall. Is this right?
Hi Mike
Taking two steps: (q1->q2)(q2->q3) from a general path.
(I won't point to a particular place in your many formulae as my
comment is very general, and you know I am not a physicist nor a
logician.)
You are trying to justify using complex numbers in your work. In my
non-mathematical model, an electron consists of two preons in two
different 4D spaces. At a measurement or singularity the contents of
one preon are tranferred to the other preon.
As I understand it, (q1->q2) means that the set q1 is compressed to a
representative point or singularity at q2. That is equivalent to the
collapse of wavefunction, of set q1, to the point q2.
What is next occurring is the recreation of the next wavefunction,
that of set q2. At the singularity at q2, the contents of the first
preon enter the second preon and fill the second preon creating the
new wave function. That new wave function q2 is later collapsed to a
point q3 as shown by (q2->q3).
In my model, you would need the complex numbers to distinguish between
the compressing of one preon to a singularity in one 4D and the
recreation of the wavefunction for that preon in the second 4D.
In Christian's model, in a nearby thread, an electron can be created
with a random choice of +1 and -1 orientation in a trivector (ie an
oriented unit volume) in Clifford Algebra. So I suppose it may be
that after the singularity the electron swaps its trivector
orientation sign, rather than changes its entire 4D as in my version.
(Clifford algebra is not using 8D, apparently.) This is also
describable by the Moibus strip analogy.
You ask if t always increases along a path. In my model, t can
reverse direction after a singularity That is because a preon has its
own t dimension which may not be pointing in the same direction as the
universe's t direction. Transferring contents into a preon with a
reverse t direction would be equivalent to transferring to an
antimatter preon, eg a component of a positron. The universe is not
here changing its t direction, of course, but the positron's preon is
travelling in the reverse time direction to the t of the universe.
All the best in your work.
Ben
Not a physicist
(snip)
> Yes, Mike, but there is still a 90 degree phase jump as (t1-t2)
> crosses zero because there is still a square-root of (t1-t2) in the
> denominator. And yes, there are contributions from both (x1-x2) and
> (x2-x1) in the integral, but I'm not sure that there is a
> corresponding (t2-t1) for every (t1-t2). Now I'm thing that "t" will
> always increase along any path. For the Action integral in the
> exponent of the path integral always goes from 0 to some t, and not
> from t to 0 as I recall. Is this right?
Taking two steps: (q1->q2)(q2->q3) from a general path.
(I won't point to a particular place in your many formulae as my
comment is very general, and you know I am not a physicist nor a
logician.)
You are trying to justify using complex numbers in your work. In my
non-mathematical model, an electron consists of two preons in two
different 4D spaces. At a measurement or singularity the contents of
one preon are tranferred to the other preon.
As I understand it, (q1->q2) means that the set q1 is compressed to a
representative point or singularity at q2. That is equivalent to the
collapse of wavefunction, of set q1, to the point q2.
What is next occurring is the recreation of the next wavefunction,
that of set q2. At the singularity at q2, the contents of the first
preon enter the second preon and fill the second preon creating the
new wave function. That new wave function q2 is later collapsed to a
point q3 as shown by (q2->q3).
In my model, you would need the complex numbers to distinguish between
the compressing of one preon to a singularity in one 4D and the
recreation of the wavefunction for that preon in the second 4D.
In Christian's model, in a nearby thread, an electron can be created
with a random choice of +1 and -1 orientation in a trivector (ie an
oriented unit volume) in Clifford Algebra. So I suppose it may be
that after the singularity the electron swaps its trivector
orientation sign, rather than changes its entire 4D as in my version.
(Clifford algebra is not using 8D, apparently.) This is also
describable by the Moibus strip analogy.
You ask if t always increases along a path. In my model, t can
reverse direction after a singularity That is because a preon has its
own t dimension which may not be pointing in the same direction as the
universe's t direction. Transferring contents into a preon with a
reverse t direction would be equivalent to transferring to an
antimatter preon, eg a component of a positron. The universe is not
here changing its t direction, of course, but the positron's preon is
travelling in the reverse time direction to the t of the universe.
All the best in your work.
Ben
Not a physicist
Mike
Jun 3, 2012, 12:09:13 PM6/3/12
to
OK, maybe I need to revert to more traditional efforts concerning
complex numbers.
As I understand it, complex numbers in quantum mechanics traditionally
comes from unitary operators which are determined by a conservation of
information requirement.
So maybe all I have to do is to set up the integral for the
information content of my wave-function/path-integral and set the
variation of that to zero. I think that means that the variation
commutes with integration and ends up becoming the variation of the
integrand inside the integral for the information.
But I'd like some help with these assumptions. Maybe someone more
experienced with QM can tell me how connected are the ideas of
information content of a wave-function with unitary operators and
complex numbers. Any help is appreciated.
complex numbers.
As I understand it, complex numbers in quantum mechanics traditionally
comes from unitary operators which are determined by a conservation of
information requirement.
So maybe all I have to do is to set up the integral for the
information content of my wave-function/path-integral and set the
variation of that to zero. I think that means that the variation
commutes with integration and ends up becoming the variation of the
integrand inside the integral for the information.
But I'd like some help with these assumptions. Maybe someone more
experienced with QM can tell me how connected are the ideas of
information content of a wave-function with unitary operators and
complex numbers. Any help is appreciated.
Mike
Jun 9, 2012, 8:31:08 PM6/9/12
to
On Jun 3, 12:09 pm, Mike <maj...@charter.net> wrote:
> OK, maybe I need to revert to more traditional efforts concerning
> complex numbers.
Yep, still grasping at straws. But this may prove useful.
> OK, maybe I need to revert to more traditional efforts concerning
> complex numbers.
Lubos Molt wrote:
"The uncertainty principle forces the complex numbers upon us."
http://motls.blogspot.com/2010/08/why-complex-numbers-are-fundamental-in.html
But the uncertainty principle relies on Fourier transforms since one
needs to find the frequency response in order to calculate the
standard deviation of frequency as part of the uncertainty principle.
That would certainly introduce complex numbers into the calculation.
But Fourier transforms only apply to linear, time invariant systems.
So I need to find out whether equation [23] on my website at:
http://webpages.charter.net/majik1/QMlogic.htm
is a linear, time invariant system or not. If equation [23] represents
a wave-function as I suspect, then it obeys the rules of
superposition, which is another way of saying that it is a linear,
time invariant system. But I'd like to see that more explicitly in my
formulism.
If I am dealing with a linear, time invariant system, then the Fourier
transform can be applied to it, and complex numbers would
automatically enter the picture. But I don't know if a Fourier
transform is necessarily implied by a linear, time-invariant system.
Is finding an uncertainty principle the only reason to use a Fourier
transform? Or is there some use of it more generally on distributions,
for example?
I think I'm on to something with using the Fourier transform. For it
seems to introduce Hilberts spaces, dual spaces and their inner
products, and eigenvectors and eigenvalues besides just introducing
complex numbers. I'm looking into all this, but I have limited
experience. Any insight into all this would be appreciated. Thanks.
Mike
Jun 13, 2012, 1:39:03 AM6/13/12
to
http://www.physicsforums.com/showpost.php?p=3953737&postcount=4
Any help is appreciated.
Mike
Jan 29, 2013, 8:02:07 PM1/29/13
to
I'm still trying to justify complex numbers in the gaussian form of the dirac delta function. And I think I found it. I think all that's necessary to justify the complex nature of the dirac delta is to show that the dirac delta function in this formalism has the same algebraic properties of complex numbers.
So there seems to be a progression of hypercomplex numbers in my formalism from real to complex to quaternions to octonions. And the algebraic property lost with each iteration is that complex numbers lose the property of magnitude, quaternions lose commutativity, and octonions lose associativity. So how does the dirac delta lose the property of magnitude so that complex number are a fair representation? Well, obviously, you can't say which dirac delta is greater or less than another dirac delta function. But the dirac delta is still associative and commutative. Therefore, one can represent the dirac delta with complex numbers at least in my formalism where many are used side by side, right?
So there seems to be a progression of hypercomplex numbers in my formalism from real to complex to quaternions to octonions. And the algebraic property lost with each iteration is that complex numbers lose the property of magnitude, quaternions lose commutativity, and octonions lose associativity. So how does the dirac delta lose the property of magnitude so that complex number are a fair representation? Well, obviously, you can't say which dirac delta is greater or less than another dirac delta function. But the dirac delta is still associative and commutative. Therefore, one can represent the dirac delta with complex numbers at least in my formalism where many are used side by side, right?
Mike
Mar 9, 2013, 2:36:59 PM3/9/13
to
It seems to me it might be easy to hook kids interest
in physics and quantum mechanics, at least at the high
school level.
Every high school student should go through the
exercise of developing a probability distribution by
measuring parts with calipers or meters and puting
them in adjacent bens according to their value to see
how the values are distributed. Probabilites could be
taught by asking how many would have been in that ben
had they tested more. The calculus of integration
could be introduced by showing that the total number
is achieved by adding up each ben using smaller and
smaller bins.
They could then see how nothing is perfect and there
is always noise or errors that enter the production
process. They could measure the width of the variation
of the distribution and discuss what means are available
to reduce the variance.
And here's the hook. Ask them, "Is there any process in
the universe that's perfect - that produces identical
things every time?" The answer, of course, is protons,
neutrons, and electrons, which are identical to each
other within the accuracy of our meters. Show how a
perfect process is represented by the Dirac delta
function. Then state that the properties of these
subatomic particles can actually be derived with the math
of the Dirac delta function. If they know anything about
adding exponents and integration, they can be shown the
path integral of quantum mechanic and the what part is
the lagrangian, etc.
Is this something that seniors in high school could
learn?
in physics and quantum mechanics, at least at the high
school level.
Every high school student should go through the
exercise of developing a probability distribution by
measuring parts with calipers or meters and puting
them in adjacent bens according to their value to see
how the values are distributed. Probabilites could be
taught by asking how many would have been in that ben
had they tested more. The calculus of integration
could be introduced by showing that the total number
is achieved by adding up each ben using smaller and
smaller bins.
They could then see how nothing is perfect and there
is always noise or errors that enter the production
process. They could measure the width of the variation
of the distribution and discuss what means are available
to reduce the variance.
And here's the hook. Ask them, "Is there any process in
the universe that's perfect - that produces identical
things every time?" The answer, of course, is protons,
neutrons, and electrons, which are identical to each
other within the accuracy of our meters. Show how a
perfect process is represented by the Dirac delta
function. Then state that the properties of these
subatomic particles can actually be derived with the math
of the Dirac delta function. If they know anything about
adding exponents and integration, they can be shown the
path integral of quantum mechanic and the what part is
the lagrangian, etc.
Is this something that seniors in high school could
learn?
Mike
Mar 28, 2013, 10:20:37 AM3/28/13
to
On Wednesday, March 27, 2013 6:50:02 PM UTC-4, ben...@hotmail.com wrote:
> I very much like Mike's use of logic to derive quantum equations,
> including the Born rule, but I am not clear where he is going on
> his (sort of?) Theory of Everything. So I can't yet say I like it,
> but I am not against it either. My problem is the difference
> between the rule of logic itself and the application of that rule.
> Mike seems to be implying that if the rule of logic is followed then
> there is only one outcome for the state of the world. I don't
> understand that.
Thanks, Ben, for your comments. I should never be so complacent as to
refuse to consider how I can make myself more clear.
The logic portion of my effort is pretty straight forward logical
manipulations. I manipulate a conjunction (ANDs) of many (infinite)
statements into a disjunction (ORs) of every possible "path" of
implications. A path is a conjunction of implications where the
consequence of one implication is the premise of the next
implication. Hopefully you've had some logic courses.
What's not so conventional is then representing each implication as
a Dirac delta function. This is not a difficult step, and I can try
to explain that if you wish. But the use of the Dirac delta for
implication does introduce a probabilistic distribution at a very
fundamental level. It seems from this I'm not going to get a
deterministic theory, and some physical entities will be
probabilistic at best.
Your concern about differentiating between "the rules of logic
itself with the application of those rules" I take to mean that you
feel that the rules of logic apply to propositions that are
obtained independent of the rules. And I don't really explain where
I get and what exactly are the propositions I use to start with.
I suppose what I'm doing is similar to what's done in special and
general relativity, where each point in the spacetime manifold is
considered to be an "event". Events in this case are where something
might happen which we could just as well describe with a
proposition. So like in GR, I'm representing propositions with
points in a point-set. Then one can consider whether those points
are an element of a set and use the Dirac measure to represent set
inclusion. You can consider my propositions to be points in a
point-set where something may happen.
> You can't expect to use the rule to determine that all houses must at
> this instant be skyscrapers, or all must be mud huts etc. Can you use
> the rule to say that spontaneous symmetry breaking must have led to
> 1 here and 0 over there? I can't see how. It could lead to identifying
> possible optional outcomes for symmetry breaking? But not identifying,
> from logic alone, which way the symmetry broke in particular places?
>From above, I explain how my theory is inherently probabilistic
because of the introduction of the Dirac delta distribution at a
fundamental level. I don't really know at this point if my theory
explains symmetry breaking. I've got some ideas about that, but
they're not fleshed out. But at least I do seem to be getting which
symmetry groups are involved from principle alone before any kind of
breaking occurs. I get the U(1)SU(2)SU(3) symmetry groups by
iterating my formalism.
For those interested, my theory is described at:
http://webpages.charter.net/majik1/QMlogic.htm
Mike
> I very much like Mike's use of logic to derive quantum equations,
> including the Born rule, but I am not clear where he is going on
> his (sort of?) Theory of Everything. So I can't yet say I like it,
> but I am not against it either. My problem is the difference
> between the rule of logic itself and the application of that rule.
> Mike seems to be implying that if the rule of logic is followed then
> there is only one outcome for the state of the world. I don't
> understand that.
Thanks, Ben, for your comments. I should never be so complacent as to
refuse to consider how I can make myself more clear.
The logic portion of my effort is pretty straight forward logical
manipulations. I manipulate a conjunction (ANDs) of many (infinite)
statements into a disjunction (ORs) of every possible "path" of
implications. A path is a conjunction of implications where the
consequence of one implication is the premise of the next
implication. Hopefully you've had some logic courses.
What's not so conventional is then representing each implication as
a Dirac delta function. This is not a difficult step, and I can try
to explain that if you wish. But the use of the Dirac delta for
implication does introduce a probabilistic distribution at a very
fundamental level. It seems from this I'm not going to get a
deterministic theory, and some physical entities will be
probabilistic at best.
Your concern about differentiating between "the rules of logic
itself with the application of those rules" I take to mean that you
feel that the rules of logic apply to propositions that are
obtained independent of the rules. And I don't really explain where
I get and what exactly are the propositions I use to start with.
I suppose what I'm doing is similar to what's done in special and
general relativity, where each point in the spacetime manifold is
considered to be an "event". Events in this case are where something
might happen which we could just as well describe with a
proposition. So like in GR, I'm representing propositions with
points in a point-set. Then one can consider whether those points
are an element of a set and use the Dirac measure to represent set
inclusion. You can consider my propositions to be points in a
point-set where something may happen.
> You can't expect to use the rule to determine that all houses must at
> this instant be skyscrapers, or all must be mud huts etc. Can you use
> the rule to say that spontaneous symmetry breaking must have led to
> 1 here and 0 over there? I can't see how. It could lead to identifying
> possible optional outcomes for symmetry breaking? But not identifying,
> from logic alone, which way the symmetry broke in particular places?
>From above, I explain how my theory is inherently probabilistic
because of the introduction of the Dirac delta distribution at a
fundamental level. I don't really know at this point if my theory
explains symmetry breaking. I've got some ideas about that, but
they're not fleshed out. But at least I do seem to be getting which
symmetry groups are involved from principle alone before any kind of
breaking occurs. I get the U(1)SU(2)SU(3) symmetry groups by
iterating my formalism.
For those interested, my theory is described at:
http://webpages.charter.net/majik1/QMlogic.htm
Mike
Mike
Apr 11, 2013, 7:46:04 PM4/11/13
to
On Thursday, March 28, 2013 9:30:05 AM UTC-4, Mike wrote:
>
> I suppose what I'm doing is similar to what's done in special and
> general relativity, where each point in the spacetime manifold is
> considered to be an "event". Events in this case are where something
> might happen which we could just as well describe with a
> proposition. So like in GR, I'm representing propositions with
> points in a point-set. Then one can consider whether those points
> are an element of a set and use the Dirac measure to represent set
> inclusion. You can consider my propositions to be points in a
> point-set where something may happen.
>
I wonder what this all says about quantum gravity. I seemed
>
> I suppose what I'm doing is similar to what's done in special and
> general relativity, where each point in the spacetime manifold is
> considered to be an "event". Events in this case are where something
> might happen which we could just as well describe with a
> proposition. So like in GR, I'm representing propositions with
> points in a point-set. Then one can consider whether those points
> are an element of a set and use the Dirac measure to represent set
> inclusion. You can consider my propositions to be points in a
> point-set where something may happen.
>
to have kept the point-set of the underlying space-time
manifold as is done in special and general relativity. All I've
done is to treat each event of the space-time manifold as a
proposition and considered the whole manifold as a coexisting
set of consistent propositions. This allowed me to use the
Dirac delta function to mathematically represent the resulting
material implication between each point/event/proposition.
In effect, all I've done is place a Dirac delta function
between each point in the manifold. And when all the exponents
of the Gaussian Dirac deltas are added up, you create a quantum
field theory on the background space-time. This field theory is
as unavoidable as the space-time manifold itself if you assume
each point stands for a proposition which implies every other.
And it doesn't seem to matter how you label the coordinates;
you'd get the same formalism back again. In other words, this
QFT is invariant with changes in coordinates.
However, I don't see in this the necessity of "quantizing" the
background metric, since the assumption naturally results in a
QFT on a pre-existing non-quantized background manifold. My
efforts don't even address how one comes up with a metric,
much less whether it should be quantized or not.
ben...@hotmail.com
Apr 12, 2013, 10:15:27 AM4/12/13
to
On Thursday, 11 April 2013 23:50:02 UTC+1, Mike wrote:
> I wonder what this all says about quantum gravity. I seemed
> to have kept the point-set of the underlying space-time
> manifold as is done in special and general relativity. All I've
> done is to treat each event of the space-time manifold as a
> proposition and considered the whole manifold as a coexisting
> set of consistent propositions. This allowed me to use the
> Dirac delta function to mathematically represent the resulting
> material implication between each point/event/proposition.
> In effect, all I've done is place a Dirac delta function
> between each point in the manifold. And when all the exponents
> of the Gaussian Dirac deltas are added up, you create a quantum
> field theory on the background space-time. This field theory is
> as unavoidable as the space-time manifold itself if you assume
> each point stands for a proposition which implies every other.
> And it doesn't seem to matter how you label the coordinates;
> you'd get the same formalism back again. In other words, this
> QFT is invariant with changes in coordinates.
>
> However, I don't see in this the necessity of "quantizing" the
> background metric, since the assumption naturally results in a
> QFT on a pre-existing non-quantized background manifold. My
> efforts don't even address how one comes up with a metric,
> much less whether it should be quantized or not.
> mass
> I wonder what this all says about quantum gravity. I seemed
> to have kept the point-set of the underlying space-time
> manifold as is done in special and general relativity. All I've
> done is to treat each event of the space-time manifold as a
> proposition and considered the whole manifold as a coexisting
> set of consistent propositions. This allowed me to use the
> Dirac delta function to mathematically represent the resulting
> material implication between each point/event/proposition.
> In effect, all I've done is place a Dirac delta function
> between each point in the manifold. And when all the exponents
> of the Gaussian Dirac deltas are added up, you create a quantum
> field theory on the background space-time. This field theory is
> as unavoidable as the space-time manifold itself if you assume
> each point stands for a proposition which implies every other.
> And it doesn't seem to matter how you label the coordinates;
> you'd get the same formalism back again. In other words, this
> QFT is invariant with changes in coordinates.
>
> However, I don't see in this the necessity of "quantizing" the
> background metric, since the assumption naturally results in a
> QFT on a pre-existing non-quantized background manifold. My
> efforts don't even address how one comes up with a metric,
> much less whether it should be quantized or not.
In my model, a particle, say an electron, has its own spacetime within
it. That spacetime collapses to a singularity each time it has an
interaction. To model that electron between collapses, you would need to
do everything you have already done to model the spacetime of our
universe and do it again within the electron? If you have put a Dirac
delta function between each point in our manifold, then do you need to
replace one(?) of those delta functions by a whole extra bag of them to
model a single electron? But there is a need to identify the bag as not
part of our own metric.
To obtain a mass, which for me is an emergent property just as is the
spacetime metric, that single electron needs to interact with a higgs-
like static field.
You could model the higgs-like static field by having another bag of
delta functions? But where would you put it. The god-like answer is
'everywhere'. The trouble, as it seems to me, is that an n-higgs is too
massive for it to be brought to a singularity by normal events. And if
it doesn't come to a singularity then it won't contribute to the making
of the metric of our spacetime. So you can't find two points in our
spacetime to place it between.
Mass is an emergent effect of the electron field interacting with
the higgs field. And that depends on the structure of the electron,
where the strings (all are left handed threads) in the electron with make
tight curls because of interaction with the higgs field. That gives
inertia, which gives mass. The photon has a different structure of its
strings (left and right threads) and its strings are arranged so that
they do not move in tight curls, but move linearly.
The mass is caused by interactions which are not part of our spacetime. Mass-
giving interactions of the electron lead to the construction of a spacetime
metric, but not to our spacetime metric. They contribute to the making of the
internal spacetime metric of the electron.
Mike
Apr 12, 2013, 2:21:12 PM4/12/13
to
On Thursday, April 11, 2013 6:50:02 PM UTC-4, Mike wrote:
> However, I don't see in this the necessity of "quantizing" the
> background metric, since the assumption naturally results in a
> QFT on a pre-existing non-quantized background manifold.
Actually, the quantum mechanical formalism seems to assume
> However, I don't see in this the necessity of "quantizing" the
> background metric, since the assumption naturally results in a
> QFT on a pre-existing non-quantized background manifold.
a smooth background metric in the (x-x0)^2 of the Gaussian
Dirac delta functions. And since this gives rise to all the
quantum effects, the quantum measurements seem to have
proved that the smooth nature of the background is a
necessity.
If one were to quantize the metric, then I suppose that
there would be measurable effects in the quantum mechanics
as well.
> My
> efforts don't even address how one comes up with a metric,
> much less whether it should be quantized or not.
of complex number to quaternions which are a representation
of the SU(2) symmetry group. And the SU(2) group will
"double cover" the SO(1,3) symmetry group which is a
representation of the symmetry of Lorentz spacetime
of special relativity.
What I don't understand yet is how this flat Minkowski
background metric can change with gravitation in general
relativity.
Hans van Leunen
Apr 15, 2013, 2:19:28 PM4/15/13
to
Op zondag 20 mei 2012 03:16:41 UTC+2 schreef Mike het volgende:
> I've updated my website where I prove that quantum theory can be
>
> derived from pure logic. I improved the notation a bit to make it
>
> easier to read. And I explain how the map from logic to math is
>
> consistent even in the continuous case. I also try to explain a bit
>
> more why the exponent should be complex in the gaussian form of the
>
> Dirac delta function that is used to represent logical implication.
>
> For your inspection at:
>
>
>
> http://webpages.charter.net/majik1/QMlogic.htm
Mike: investigate http://www.e-physics.eu
Hans
> I've updated my website where I prove that quantum theory can be
>
> derived from pure logic. I improved the notation a bit to make it
>
> easier to read. And I explain how the map from logic to math is
>
> consistent even in the continuous case. I also try to explain a bit
>
> more why the exponent should be complex in the gaussian form of the
>
> Dirac delta function that is used to represent logical implication.
>
> For your inspection at:
>
>
>
> http://webpages.charter.net/majik1/QMlogic.htm
Mike: investigate http://www.e-physics.eu
Hans
Mike
May 5, 2013, 11:14:53 PM5/5/13
to
On Thursday, April 11, 2013 6:50:02 PM UTC-4, Mike wrote:
> I wonder what this all says about quantum gravity. I seemed
> to have kept the point-set of the underlying space-time
> manifold as is done in special and general relativity. All I've
> done is to treat each event of the space-time manifold as a
> proposition and considered the whole manifold as a coexisting
> set of consistent propositions. This allowed me to use the
> Dirac delta function to mathematically represent the resulting
> material implication between each point/event/proposition.
> In effect, all I've done is place a Dirac delta function
> between each point in the manifold. And when all the exponents
> of the Gaussian Dirac deltas are added up, you create a quantum
> field theory on the background space-time. This field theory is
> as unavoidable as the space-time manifold itself if you assume
> each point stands for a proposition which implies every other.
> And it doesn't seem to matter how you label the coordinates;
> you'd get the same formalism back again. In other words, this
> QFT is invariant with changes in coordinates.
>
So now it seems that quantum theory is a part of any manifold.
> I wonder what this all says about quantum gravity. I seemed
> to have kept the point-set of the underlying space-time
> manifold as is done in special and general relativity. All I've
> done is to treat each event of the space-time manifold as a
> proposition and considered the whole manifold as a coexisting
> set of consistent propositions. This allowed me to use the
> Dirac delta function to mathematically represent the resulting
> material implication between each point/event/proposition.
> In effect, all I've done is place a Dirac delta function
> between each point in the manifold. And when all the exponents
> of the Gaussian Dirac deltas are added up, you create a quantum
> field theory on the background space-time. This field theory is
> as unavoidable as the space-time manifold itself if you assume
> each point stands for a proposition which implies every other.
> And it doesn't seem to matter how you label the coordinates;
> you'd get the same formalism back again. In other words, this
> QFT is invariant with changes in coordinates.
>
My reasoning is as follows:
1) "every topological manifold is Tychonoff", as stated at:
http://en.wikipedia.org/wiki/Completely_regular_space
2) "X is a Tychonoff space... if it is both completely regular
and Hausdorff", as stated in the above link.
3) Therefore, every topological manifold is completely regular.
4) A completely regular space is defined by:
"X is a completely regular space if given any closed set F and
any point x that does not belong to F, then there is a
continuous function f from X to the real line R such that f(x)
is 0 and, for every y in F, f(y) is 1. In other terms, this
condition says that x and F can be separated by a continuous
function." This is stated in the above link.
5) Since every point in a manifold is a "closed set", then
F in the definition in 4) can be a single point. So every
topological manifold admits a continuous function, f, from
one point, x, to another point, y, such that
f(x)=0, and f(y)=1.
6) The function described in 5) could be considered to be the
integral of a probability distribution, which is 0 when
integrated from x point to x, but is 1 when
integrated from x to y, if that range encompasses all
possibilities.
7) Since 5) and 6) must be true for all points x for a given y,
even for x arbitrarily close to y, and must also be true for
all points y since each point is a closed set required to be
accommodated in the definition, then there must be a Dirac
delta between any two points in the manifold, or at least a
gaussian distribution between any two points even in the limit
where x approaches y.
8) The Dirac delta, or even just a gaussian, can be manipulated
into the Feynman Path Integral of quantum mechanics as I've
posted many time in PF, for example, see:
http://www.physicsforums.com/showpost.php?p=4304005&postcount=25
These manipulations
work also for any gaussians because of the Chapman-Kolmogorov
equation, which I can show if asked.
9) Therefore, every topological manifold is a completely regular
space which must admit Dirac delta functions between any two
points, which can be manipulated into the Path Integral of
quantum mechanics. So every manifold necessarily includes a
quantum mechanical structure in its definition.
Your comments are appreciated.
Mike
May 17, 2013, 7:50:50 PM5/17/13
to
On Sunday, May 5, 2013 10:20:06 PM UTC-4, Mike wrote:
> 9) Therefore, every topological manifold is a completely regular
>
> space which must admit Dirac delta functions between any two
>
> points, which can be manipulated into the Path Integral of
>
> quantum mechanics. So every manifold necessarily includes a
>
> quantum mechanical structure in its definition.
>
>
The previous post might be worth considering more carefully. For it would be extremely interesting if one aspect of manifolds could be interpreted as a metric and a different aspect could be interpreted as a quantum field theory. If metrics and quantum theory are just different sides of the same coin, I wonder what this says about quantum gravity.
> 9) Therefore, every topological manifold is a completely regular
>
> space which must admit Dirac delta functions between any two
>
> points, which can be manipulated into the Path Integral of
>
> quantum mechanics. So every manifold necessarily includes a
>
> quantum mechanical structure in its definition.
>
>
Mike
Jun 23, 2013, 1:31:00 AM6/23/13
to
Just an update. I moved my site to it's own domain name. I'm now at:
http://logictophysics.com/
There I show where the Standard Model symmetries may come from as interations of the quantizing procedure. I also describe where the potential may come from as a weighting function on each of the dirac deltas.
Now I think I know where the symmetry breaking mechanism comes from (not included on the website yet). The symmetries have expression as commutator relations in the algebra and describe how multiplication acts when operands are reversed. But if the weighting function, p(x), multiplying each dirac delta is not constant, then the multiplication property is no longer gauranteed.
As long as the potential is not changing, the weighting funciton derived from it is not changing and there is no interference with the way things multiply. But that's not the case if the potential is changing. Comments welcome, of course.
http://logictophysics.com/
There I show where the Standard Model symmetries may come from as interations of the quantizing procedure. I also describe where the potential may come from as a weighting function on each of the dirac deltas.
Now I think I know where the symmetry breaking mechanism comes from (not included on the website yet). The symmetries have expression as commutator relations in the algebra and describe how multiplication acts when operands are reversed. But if the weighting function, p(x), multiplying each dirac delta is not constant, then the multiplication property is no longer gauranteed.
As long as the potential is not changing, the weighting funciton derived from it is not changing and there is no interference with the way things multiply. But that's not the case if the potential is changing. Comments welcome, of course.
Mike
Jun 24, 2013, 4:39:41 PM6/24/13
to
On Sunday, June 23, 2013 12:40:02 AM UTC-4, Mike wrote:
> Now I think I know where the symmetry breaking mechanism
> comes from (not included on the website yet). The symmetries
> have expression as commutator relations in the algebra and
> describe how multiplication acts when operands are reversed.
> But if the weighting function, p(x), multiplying each dirac
> delta is not constant, then the multiplication property is
> no longer gauranteed.
>
> As long as the potential is not changing, the weighting
> funciton derived from it is not changing and there is no
> interference with the way things multiply. But that's not
> the case if the potential is changing. Comments welcome,
> of course.
This may provide a means of connecting QM with GR. For a
> Now I think I know where the symmetry breaking mechanism
> comes from (not included on the website yet). The symmetries
> have expression as commutator relations in the algebra and
> describe how multiplication acts when operands are reversed.
> But if the weighting function, p(x), multiplying each dirac
> delta is not constant, then the multiplication property is
> no longer gauranteed.
>
> As long as the potential is not changing, the weighting
> funciton derived from it is not changing and there is no
> interference with the way things multiply. But that's not
> the case if the potential is changing. Comments welcome,
> of course.
change in p(x), giving rise to a change in potential, would
be equivalent to keeping p(x) constant and change the value
of x so that the value of the exponential stays the same.
That would be a length contraction instead of a potential
energy increase. I wonder if changing the length instead of
a potential would cause a curvature in the background
consistend with GR.
Mike
Jul 8, 2014, 2:00:02 PM7/8/14
to
It turns out that the wavefunction is a mathematical representation of the material implication of logic. The premise is the way the samples were prepared; the conclusion is the result of a measurement after the system propagates. But a premise can imply a great number of consequences, and so the wavefunction is distributed and does not give one particular result. It takes two data points to calculate a probability. If you have the starting state and the ending state, you can calculate the probability of that happening. Logically, if the preparation (premise) is consistent with the measurement (consequence), then one will imply the other. The consequence (measurement) implying the premise (preparation) is the inverse wavefunction expressed as the complex conjugate. When they are in conjunction with each other, this results in the wavefunction multiplying the complex conjugate of the wave function to give the probability of a particular measured result. It only requires advanced high-school math to understand all this. See details at:
http://www.logictophysics.com
http://www.logictophysics.com
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