Theory of Everything (TOE)
Mike
I've taken graduate level math-physics, but not any advanced probability
studies per se.
I'm trying to come up with the most general probability formula for a state of
affairs starting with absolutely no information about a system (the universe).
I wish to find out if there are any properties of this formula or set of
formulae that might account for all possibly observable phenomena.
Specifically, I'm wondering if this formula may be used to derive the number of
dimensions and the direction of time, and possibly other derivations that might
be interpreted as physical forces. That seems like quite a task, I'm know. But
you never know how hard or easy it may be until you first see the formulae you
start with.
And what makes me think this is the way to go? Consider the following: From
nothing, the fact that the universe exists is an absolute certainty. There is
no new information contained in this event (information, as defined by
Shannon). And the entropy of the event is zero, which can happen with delta S =
Q/T for any amount of heat, Q, added to the system at temperature, T,
approaching infinity. But where can the universe go from here?
The only alternative to absolute certainty is uncertainty described by
probabilities. And there is no telling what properties emerged, but it is
certain that any distinction of events or attributes would be described by
differing properties. We don't have information as to how and what properties
emerged to describe the various distinctions. But the universe must have broken
down into properties with associated probabilities. And that's where I'm at. I
don't know how many properties is takes to describe the universe (probably
infinite), and I don't know the probability associated with each property. And
I don't know the conditional probabilities or how the properties may overlap.
But I'm thinking that if I can get the most general formula for the probability
of a conjunction of properties and perhaps how to normalize all possibilities
when there may be overlap, this in itself may reveal how properties (physical
states) may differ. And these differences may be interpreted as physically
observable measures.
Formula 13 on page:
http://www.fmi.uni-sofia.bg/vesta/Virtual_Labs/prob/prob3.html
has a term for the conjunction of properties (events) if I read it right. Can
this be isolated? Can we take the log of both sides and possibly convert it to
an integral? Or does it make no sense to have a differential change between
properties?
Any help is appreciated
Thank you.
Mike.
Dale A Trynor
Mike wrote:
> I wonder if you would like to help? I'm not sure exactly how to get started.
> I've taken graduate level math-physics, but not any advanced probability
> studies per se.
>
I have no idea if I have anything to offer, however sense the theory on my site is
dependent on ZPE and because it relates to uncertainty you might get a puny nugget
of some idea from it. If the site is rite it would mean that ZPE puts matter in its
place so that space can exists, as well as determine what the speed of light and or
time is for any universe. Of course such changes in time and light are only
observable relating to something else.
Its a mess and I am presently rewriting and updating it.
www.alternatescience.com
tadchem
"Mike" <no....@please.com> wrote in message
news:DXr_6.3080$zB.47...@e3500-chi1.usenetserver.com...
> I wonder if you would like to help? I'm not sure exactly how to get
started.
> I've taken graduate level math-physics, but not any advanced probability
> studies per se.
>
> I'm trying to come up with the most general probability formula for a
state of
> affairs starting with absolutely no information about a system (the
universe).
Therefore, it is unknown what objects exist within the system or what
processes can occur within the system.
> I wish to find out if there are any properties of this formula or set of
> formulae that might account for all possibly observable phenomena.
To establish a formula, one must have at the barest minimum two nameable
objects or quantities (call them A and B) and an operation that compares
them. Such comparison must default to either = (which asserts the objects
are the same) or <> (which asserts that they are not the same).
Since we don't know whether or not there is more than one nameable quantity,
nor the nature of teh comparisons, there can only be one nameable quantity
which identifies whatever may or may not be contained within the system. I
call this quantity "shit."
A similar analysis applied to the concept of a mathematical operation leads
one to the conclusion that, in the absence of a defineable operation on a
system which may or may not be empty, one can only assert that at least one
undefined operation may exist. Since the word "exist" fails to imply the
dynamic nature inherent in a process as opposed to the simple concept of
"being" which can be applied to an operation-free system, I define this
operation with the word "happen."
By combining the concept of an undefineable quantity that may or may not
exist within the system with the concept of an undefineable operation that
may or may not occur within the system, we arrive quickly at the most
fundamental of all logical statements that can be made about a system, even
when nothing is known about the contents or processes that may be found
therein:
"Shit happens."
In my personal theology, this would be the very first utterance of a
creative deity to bring a universe into existence, triggering such events as
the Big Bang.
> Specifically, I'm wondering if this formula may be used to derive the
number of
> dimensions and the direction of time, and possibly other derivations that
might
> be interpreted as physical forces. That seems like quite a task, I'm know.
But
> you never know how hard or easy it may be until you first see the formulae
you
> start with.
Once you have accepted the Tao of objects vs processes, of nouns vs verbs,
of being vs doing, the justaposition of the most general of all possible
[objects/nouns/beingness] with the most general of all possible
[processes/verbs/doingness] as I hace cited abouve, all else is detail...
:)
Tom Davidson
Brighton, CO
Donald G. Shead
you just happened;-?
--
Donald G. Shead <http://pages.cthome.net/donsr/>
Such a tangled web we weaved when first we practiced to perceive.
"tadchem" <tadche...@earthlink.net> wrote in message
news:Gtv_6.2230$ef.2...@newsread2.prod.itd.earthlink.net...
John Gonsowski
Mike wrote:
> I wonder if you would like to help? I'm not sure exactly how to get started.
> I've taken graduate level math-physics, but not any advanced probability
> studies per se.
>
> I'm trying to come up with the most general probability formula for a state of
> affairs starting with absolutely no information about a system (the universe).
> I wish to find out if there are any properties of this formula or set of
> formulae that might account for all possibly observable phenomena.
> Specifically, I'm wondering if this formula may be used to derive the number of
> dimensions and the direction of time, and possibly other derivations that might
> be interpreted as physical forces. That seems like quite a task, I'm know. But
> you never know how hard or easy it may be until you first see the formulae you
> start with.
Well Tony Smith has kind of been there done that... information-wise the
empty set void is the Cl(-1) Clifford algebra... Since Simplex physics above
the Planck energy and the A-D-E LIE algebra series below the Planck energy
both derive from Clifford algebra, this in a nutshell is your TOE. John
Mike
be used to formulate all of math and physics. But is that the same as proving
the tautology that the laws of physics can be derived from nothing more then
the necessary truths of mathematics? I don't think so.
"John Gonsowski" <gons...@us.ibm.com> wrote in message
news:3B3C877C...@us.ibm.com...
John Gonsowski
Mike wrote:
> I've read that Clifford algebras (GA) is a powerful mathematical tool that can
> be used to formulate all of math and physics. But is that the same as proving
> the tautology that the laws of physics can be derived from nothing more then
> the necessary truths of mathematics? I don't think so.
Well you can prove math, you can't really prove physics except sort of
by experimentation and even that isn't as good as you get with math. The
big problem is you can't check everything by experimentation, for example
you can't check out anything above the Planck energy. But given that
Clifford Algebra and the A-D-E series kind of constructs itself naturally
using set theory beginning with the empty set, it is natural to think that
physics does the same thing - you just have to match up physics
variables with the math ones correctly and I believe Tony Smith has done
that (down at low energy he does have the right number of particles
with correct masses and force strengths). John
Mike
restrictions only as required by logical consistency? I mean, without any
observation or experiments to confirm it, has he been able to deduce the laws
of physics from nothing more then what must have been required by logic? If so,
then it would seem that not everything that is mathematical is physical, though
we believe that everything physical is mathematical. So can you give me an
example of what logical restrictions he places on the math that serves as a
kind of boundary value problem from which correct equations are derived? Or is
it more the case that he's been able to mathematically simplify all the
empirical formulae of physics into one equation (or a few) that degenerates
into the various forces under certain circumstances? Personally, I believe that
the former must be at least theoretically the case. Since we would assume that
we will not find any contradictions in nature, it must be that this restriction
itself must generate the laws by which nature operates.
And for those reading this thread for the first time, I repeat the original
quest.
Alex Hilgendorf
would have on this topic.
Thanks,
Alex Hilgendorf
Madison, WI
Mike <no....@please.com> wrote in message
news:DXr_6.3080$zB.47...@e3500-chi1.usenetserver.com...
John Gonsowski
Mike wrote:
> Is it the case, then, that he's been able to reduce physics to mathematics with
> restrictions only as required by logical consistency? I mean, without any
> observation or experiments to confirm it, has he been able to deduce the laws
> of physics from nothing more then what must have been required by logic? If so,
> then it would seem that not everything that is mathematical is physical, though
> we believe that everything physical is mathematical. So can you give me an
> example of what logical restrictions he places on the math that serves as a
> kind of boundary value problem from which correct equations are derived? Or is
> it more the case that he's been able to mathematically simplify all the
> empirical formulae of physics into one equation (or a few) that degenerates
> into the various forces under certain circumstances? Personally, I believe that
> the former must be at least theoretically the case. Since we would assume that
> we will not find any contradictions in nature, it must be that this restriction
> itself must generate the laws by which nature operates.
>
Well above the Planck energy you basically have all of Clifford Algebra and
the Clifford 8-fold periodicity structure, the only "unknowable" thing is the
(very large) number of finite bits that makes up everything. The finite number
of bits is responsible for the discrete (Planck length) spacetime rather than
continuous spacetime. Below the Planck energy you have the fundamental
A-D-E series of A0-A1-A2-D3-D4-D5-E6-E7-E8. This series supposedly
shows up naturally at the Planck energy phase transition point so this
would represent your naturally arising boundary restriction. There's tons
of other LIE algebras not part of the A-D-E series, it's kind of like all the
math not directly on the path arising from the empty set doesn't get used.
This A-D-E series just describes fundamental dimensions/particles...
everything else is a chaos created composite and it is certainly impossible
to have math to follow everything up to the cosmology level though
actually early cosmology starts to become more of a fundamental particle/
dimension thing but at very high energy (but below the Planck energy).
John
EL
Mathematics is the descriptive language of physics.
Yet we should realise that mathematics include many levels of abstractions to mach the world under consideration. The human being
have discovered that his observation is the mean world of nature as far is he is concerned. That is why the level of abstraction
must increase in both directions, whether for extreme details of emergent orders from chaos or great complexities as observed in the
galactic level and cosmic clusters. The proper criterion when utilising a descriptive tool is to define what is being described and
in terms of what. Now that brings us to the ultimate complexity level and abstraction when we wish to understand the influence of
the extremely elementary particles discovered on the structure of the observable zone of the universe. Therefore, we have a set of
formulas handling the level of emergence from chaos (according to our ability to observe), and that set is at the Planck's length
and other primordial quanta. With such tools we investigate the world of elements. The world of elements is the starting point for
many disciplines including molecular chemistry, crystallography, metallurgy, etc.. On higher levels we begin to see the world of
mixtures and heterogeneous structures, as in biology and geology etc... Once all what on earth was being handled satisfactorily,
astronomy and astrophysics come in with yet a different set of formulas and topologies. Crossing worlds with mathematics is a
nightmare. That is why Gravitation stands unsolved universally because it is the least influencing the most. Gravitation is a
property of particles emerging from chaos with a spin and a magnetic momentum, yet the force is accumulative and not pronounced
until the complexity build up reaches the planetary level as a minimum.
Therefore there is no such thing as a finite set of equations that can quantify everything.
Kind regards.
EL
"John Gonsowski" <gons...@us.ibm.com> wrote in message news:3B3DD04E...@us.ibm.com...
EL
May I have the honour of the inquiry?
What is the title and the publisher's name please?
the ISBN would be appreciated too.
Kind regards.
EL
"Alex Hilgendorf" <ahilg...@Voyager.net> wrote in message news:3b3db100$0$12826$272e...@news.execpc.com...
Mike
Mr. Tony Smith says, "I was led to the math structures by such observations
as the 4-dimensional nature of physical space-time and the gauge
groups of the Standard Model."
But I am more interested in why nature would have 4-dimensions in the first
place.
Mike
"EL" <hem...@lilac.ocn.ne.jp> wrote in message
news:9hklqh$qfe$1...@taliesin.netcom.net.uk...
> [EL]
> Mathematics is the descriptive language of physics.
> Yet we should realise that mathematics include many levels of abstractions to
mach the world under consideration. The human being
> have discovered that his observation is the mean world of nature as far is he
is concerned. That is why the level of abstraction
> must increase in both directions, whether for extreme details of emergent
orders from chaos or great complexities as observed in the
> galactic level and cosmic clusters
To suggest that physics is an emergent order from chaos is the antithesis of my
efforts. It suggests that there is no real order or consistency at the basis of
reality. And I think you will find it impossible to technically or
theoretically proof the existence of chaos since chaos is by definition has no
order or logic to it.
It may, however, be possible to show that no matter the truth-value of the
starting premise that the conclusion would still be true. This is a validly
logical argument.
EL
Mr. Tony Smith says, "I was led to the math structures by such observations
as the 4-dimensional nature of physical space-time and the gauge
groups of the Standard Model."
But I am more interested in why nature would have 4-dimensions in the first
place.
[EL]
The answer to your question is not in the realm of physics, Mike.
When you ask "WHY", the most probable field that can handle the issue is philosophy.
In philosophy, a cause is self redundant and if you capture a cause you shall immediately ask for the cause of the cause. I do have
such an answer, but there is no guarantee that my answer shall heal your soul or quench your thirst.
The reason behind the 4-dimensions is that nature is dynamically chaotic by default.
Such a natural state of the background is practically what we call "nothingness".
A single event by itself is not evident.
The relation between two events is indeterminate.
The relation between three static events is such that any two are related in terms of the third.
Without motion events could have never happened.
Motion demands periodicity of observation to compare moments and discover the evolution of motion.
The four dimensions are founded on that logic.
But then, you can still ask "but why". ;-)
EL
tadchem
> "Mike" <no....@please.com> wrote in message
news:Lgl%6.433$JB.14...@e3500-chi1.usenetserver.com...
>
> Mr. Tony Smith says, "I was led to the math structures by such
observations
> as the 4-dimensional nature of physical space-time and the gauge
> groups of the Standard Model."
The Standard model has been shown to have problems, such as the oscillation
of neutrinos (shown to account for the sonar neutrino "deficit", but not
described by the standard model).
> But I am more interested in why nature would have 4-dimensions in the
first
> place.
The electromagnetic radiation that provides us the majority of the
information we have about the universe only requires four, so that is all we
"see." Superstring theory shows that 10 dimensions are necessary and
sufficient for describing that behaviour of all known particles and waves.
We just don't see the dimensions required to handle the quanta of quarks -
hypercharge, charm, strangeness, etc. - because EM radiation doesn't use
them.
Tom Davidson
Brighton, CO
Alex Hilgendorf
who waste space on serious newsgroups".
;)
EL <hem...@lilac.ocn.ne.jp> wrote in message
news:9hklqi$qfe$2...@taliesin.netcom.net.uk...
EL
I read the red rose for T. S. Eliot.
I read Hamlet for Shakespeare.
Now you are telling me to read your book, such that I could later say:
I read "the toe for "Mr. Dumbasses" who is also known as Alex Hilgendorf who waste space on serious newsgroups"?
May I ask, why did you choose such a "phucked" up name to write by and sign with?
Are you telling me that You ARE a dumb ass who is wasting my time?
Fine, fine.
<sigh>
EL
"Alex Hilgendorf" <ahilg...@Voyager.net> wrote in message news:3b3ff41d$0$14442$272e...@news.execpc.com...
John Gonsowski
> as the 4-dimensional nature of physical space-time and the gauge
> groups of the Standard Model."
>
> But I am more interested in why nature would have 4-dimensions in the first
> place.
In Tony's model, spacetime is actually 16 dimensions, 4-complex outer physical
ones and 4-complex internal "curled up " ones. How one historically gets to
where one ends up and what one ends up with are two different things. The
16 dimensions are the 16 root vectors that get added to D4 to form D5. So
nature has 4 outer real spacetime dimensions because of D5. The real-
imaginary differentiation comes from the ends of the D5 5th axis; the inner-
outer differentiation is more difficult to see... from root vectors only, it
looks to me like the inner-outer distinction is an opposite ends of the
7th axis thing (E7 string theory quantum stuff)... Tony actually makes
reference to more complicated things like meta-Clifford algebras,
light cone structure, time slices, etc. in relationship to the inner-outer
differentiation... the reduction from 8 to 4 (complex) dimensions of
spacetime is also responsible for the three generations of
matter/antimatter (they are actually "composite" particles rather than
fundamental ones in Tony's model). John
John Gonsowski
tadchem wrote:
> "> Mr. Tony Smith says, "I was led to the math structures by such
> observations
> > as the 4-dimensional nature of physical space-time and the gauge
> > groups of the Standard Model."
>
> The Standard model has been shown to have problems, such as the oscillation
> of neutrinos (shown to account for the sonar neutrino "deficit", but not
> described by the standard model).
There are possible extensions to the standard model for including
neutrino oscillations: "Igor Kulikov has shown that the Gravitational
Equivalence Principle can be violated in quantum field theories at
finite temperature. In the D4-D5-E6-E7-E8 VoDou Physics model, all
3 flavors of neutrino are massless at tree level. ( The tree-level
massless character of the neutrino means that its Compton Radius
Vortex is probably effectively as large as our universe. ) Therefore,
at tree level, the D4-D5-E6-E7-E8 VoDou Physics model has no
neutrino mixing due to the Kobayashi-Maskawa mass-related matrix,
and so has no tree-level neutrino mixing by the MSW mechanism.
However, the tree-level massless neutrinos of the D4-D5-E6-E7-E8
VoDou Physics model could be mixed by Violation of the gravitational
Equivalence Principle, in two ways: VEP by direct flavor-dependent
coupling to the background gravitational potential. Quantum qVEP
because the equality of the inertial and gravitational masses loses
operational meaning beyond flavor-dependent quantum uncertainty
As of June 2001, VEP is consistent with Solar Neutrino Experiments
but may not be consistent with high-energy Atmospheric Neutrino
Experiments, while qVEP for massless neutrinos is consistent with
Solar Neutrino Experiments and may be consistent with Atmospheric
Neutrino Experiments." (from Tony's website)
> > But I am more interested in why nature would have 4-dimensions in the
> first
> > place.
>
> The electromagnetic radiation that provides us the majority of the
> information we have about the universe only requires four, so that is all we
> "see." Superstring theory shows that 10 dimensions are necessary and
> sufficient for describing that behaviour of all known particles and waves.
> We just don't see the dimensions required to handle the quanta of quarks -
> hypercharge, charm, strangeness, etc. - because EM radiation doesn't use
> them.
String theory actually curls up the extra dimensions. All dimensions also
have complex rather than real structure which causes them to be modeled
for string theory as circular rather than linear.
tadchem
>
>
> tadchem wrote:
<snip>
> > The Standard model has been shown to have problems, such as the
oscillation
> > of neutrinos (shown to account for the sonar neutrino "deficit", but not
> > described by the standard model).
>
> There are possible extensions to the standard model for including
> neutrino oscillations:
The "standard model" makes no allowance for neutrino oscillations.
You can add "extensions" as you see fit, but then, it's no longer "the
Standard Model," is it?
It's sort of an oxymoron - a contradiction in terms - like a "chopped stock
car," or an "original upgrade," or "compassionate conservatism," or
"military intelligence," or "governmental organization."
Tom Davidson
Brighton, CO
EL
"tadchem" <tadche...@earthlink.net> wrote in message news:Ip807.14011$eL5.1...@newsread1.prod.itd.earthlink.net...
<snip>
> There are possible extensions to the standard model
> for including neutrino oscillations:
The "standard model" makes no allowance for neutrino oscillations.
You can add "extensions" as you see fit,
but then, it's no longer "the Standard Model,"
is it?
It's sort of an oxymoron - a contradiction in terms - like a "chopped stock
car," or an "original upgrade," or "compassionate conservatism," or
"military intelligence," or "governmental organization."
Tom Davidson
Brighton, CO
[EL]
Hahaha! Absolute agreement. :)
But how did you come to memorise such funny oxymoronic contradictory expressions?
Cannot we make an extension to the standard "meter" with a couple of millimetres when they come to measure my land in a survey? That
should be KEWL. :) I can sell it the next day immediately. :)
Take care.
EL
John Gonsowski
tadchem wrote:
> "The "standard model" makes no allowance for neutrino oscillations.
>
> You can add "extensions" as you see fit, but then, it's no longer "the
> Standard Model," is it?
>
> It's sort of an oxymoron - a contradiction in terms - like a "chopped stock
> car," or an "original upgrade," or "compassionate conservatism," or
> "military intelligence," or "governmental organization."
Well the standard model certainly has an incomplete picture of gravity
and people often talk about gravity and the standard model as
seperate models. So I guess you could say technically that the
neutrino oscillation extension is an extension to the gravity theory that
someday has to be unified with the standard model. The standard
model name is already a misnomer of sorts, it's really too messy to
be called standard. SU(5) GUT, A-D-E series, string theory, etc. are
examples of ideas meant to both unify the standard model with
gravity and make order of the standard model mess. I personally
vote for the A-D-E series (which kind of unifies SU(5) GUT and
string theory). John
Paul Colby
> I'm trying to come up with the most general probability
> formula for a state of affairs starting with absolutely no
> information about a system (the universe).
Why would you expect to be able to say
anything if you have *no* information? For
example, if the system is a die with 6 faces
then you know you have a die with 6 faces.
This is a lot of information right there. Since
you concede knowing you have a universe
then what do you know about the states?
Doesn't it take information simply to know
the cardinality of the states of a system? Now,
once one has states, what does that mean?
What is a state of the universe? I would
think an answer to that question contains
a vast amount of what I call information.
Regards
Paul Colby
Mike
"Paul Colby" <paulc...@earthlink.net> wrote in message
news:d1H07.892$G_1....@newsread2.prod.itd.earthlink.net...
>
> "Mike" <no....@please.com> wrote in message
> news:DXr_6.3080$zB.47...@e3500-chi1.usenetserver.com...
>
> > I'm trying to come up with the most general probability
> > formula for a state of affairs starting with absolutely no
> > information about a system (the universe).
>
> Why would you expect to be able to say
> anything if you have *no* information?
I'm hoping that the general equation itself will yield results that can be
interpreted as physical dimensions, forces, and events. But there may also need
to be other restrictions on the formula. One might be that the conditional
probabilities cannot be zero since everything in the universe effects
everything else. I wonder if this is also necessary to prevent a divide by zero
operation in the use of the general formula.
The problem I presently have is one in which to express this general formula
for the probability of a conjunction of as yet unknown properties in terms of a
continuous variable for which analytical techniques can be applied. We can
always then use the Dirac delta function to transform the continuous formula
into a discrete formula if such is the case.
I can transform from each possibility in the sample space to a unique value of
a variable. Then all properties takes on various probabilities as the variable
is incremented through its range. Or I can assign a unique continuous variable
to transform each properties from sample space to that variable space. Then I
would have to integrate with a multiple integral of infinite dimensions. I
don't know at this point which approach will cover all the possible conditional
probabilities. I'll look into it when I get time.
me...@cars3.uchicago.edu
>
>"Paul Colby" <paulc...@earthlink.net> wrote in message
>news:d1H07.892$G_1....@newsread2.prod.itd.earthlink.net...
>>
>> "Mike" <no....@please.com> wrote in message
>> news:DXr_6.3080$zB.47...@e3500-chi1.usenetserver.com...
>>
>> > I'm trying to come up with the most general probability
>> > formula for a state of affairs starting with absolutely no
>> > information about a system (the universe).
>>
>> Why would you expect to be able to say
>> anything if you have *no* information?
>
>I'm hoping that the general equation itself will yield results that can be
>interpreted as physical dimensions, forces, and events.
No equation yields results which are not already present in the
equation and the assumptions behind it.
Mati Meron | "When you argue with a fool,
me...@cars.uchicago.edu | chances are he is doing just the same"
Paul Colby
>
> "Paul Colby" <paulc...@earthlink.net> wrote in message
> news:d1H07.892$G_1....@newsread2.prod.itd.earthlink.net...
> >
> > "Mike" <no....@please.com> wrote in message
> > news:DXr_6.3080$zB.47...@e3500-chi1.usenetserver.com...
> >
> > > I'm trying to come up with the most general probability
> > > formula for a state of affairs starting with absolutely no
> > > information about a system (the universe).
> >
> > Why would you expect to be able to say
> > anything if you have *no* information?
>
> I'm hoping that the general equation itself will yield
> results that can be interpreted as physical dimensions,
> forces, and events.
An equation equates *things*. One must define these
*things* and what it means to equate them. A probability
measure is a mapping of a set onto the reals. What is
this set? The state of a system in QM is a vector direction
in a Hilbert space. What is it in your "general equation"?
I would be willing to bet that advances in physical theory
will have as much to do with what we must use to describe
nature as in how these *things* are manipulated. Needless
to say I think your approach is hopelessly general.
<cut>
> The problem I presently have is one in which to express
> this general formula for the probability of a conjunction
> of as yet unknown properties in terms of a continuous
> variable for which analytical techniques can be applied.
Sound like upper level management approach, generalities
punctuated with absurdities.
> We can always then use the Dirac delta function to transform
> the continuous formula into a discrete formula if such is the
> case.
>
> I can transform from each possibility
Possibility for what?
Have you listed them all?
Can you list them all?
> in the sample space
What is the sample space? All this will need
definition before you go equating things.
> to a unique value of a variable.
Is this a real, complex quaturnion?
>Then all properties takes on various probabilities as the variable
> is incremented through its range.
All properties of what? Maybe one variable won't be enough.
> Or I can assign a unique continuous variable to transform
> each properties from sample space to that variable space. Then I
> would have to integrate with a multiple integral of infinite dimensions. I
> don't know at this point which approach will cover all the possible
conditional
> probabilities. I'll look into it when I get time.
>
The time will never come, trust me.
Regards
Paul Colby
EL
Do you know the difference between a formula and a language?
*************************************************************
"Mike" <no....@please.com> wrote in message news:nD117.1063$eF2.2...@e3500-chi1.usenetserver.com...
Mike
<me...@cars3.uchicago.edu> wrote in message
news:uW117.33$45....@news.uchicago.edu...
> In article <nD117.1063$eF2.2...@e3500-chi1.usenetserver.com>, "Mike"
<no....@please.com> writes:
> >
> >"Paul Colby" <paulc...@earthlink.net> wrote in message
> >news:d1H07.892$G_1....@newsread2.prod.itd.earthlink.net...
> >>
> >> "Mike" <no....@please.com> wrote in message
> >> news:DXr_6.3080$zB.47...@e3500-chi1.usenetserver.com...
> >>
> >> > I'm trying to come up with the most general probability
> >> > formula for a state of affairs starting with absolutely no
> >> > information about a system (the universe).
> >>
> >> Why would you expect to be able to say
> >> anything if you have *no* information?
> >
> >I'm hoping that the general equation itself will yield results that can be
> >interpreted as physical dimensions, forces, and events.
>
> No equation yields results which are not already present in the
> equation and the assumptions behind it.
So what is the equation and the assumptions behind it from which we get the
mathematical expression of the laws of physics?
Mike
"Paul Colby" <paulc...@earthlink.net> wrote
> > > "Mike" <no....@please.com> wrote
> > > > I'm trying to come up with the most general probability
> > > > formula for a state of affairs starting with absolutely no
> > > > information about a system (the universe).
> > >
> > > Why would you expect to be able to say
> > > anything if you have *no* information?
> >
> > I'm hoping that the general equation itself will yield
> > results that can be interpreted as physical dimensions,
> > forces, and events.
>
> An equation equates *things*. One must define these
> *things* and what it means to equate them. A probability
> measure is a mapping of a set onto the reals. What is
> this set? The state of a system in QM is a vector direction
> in a Hilbert space. What is it in your "general equation"?
a vector direction in possibility space
If this searched for equation yields orthogonal functions which can be used to
describe every possible state, then would that give the number of dimension
that exist in the universe?
> I would be willing to bet that advances in physical theory
> will have as much to do with what we must use to describe
> nature as in how these *things* are manipulated. Needless
> to say I think your approach is hopelessly general.
You've got to start somewhere, and you never know until you try.
>
> <cut>
>
> > The problem I presently have is one in which to express
> > this general formula for the probability of a conjunction
> > of as yet unknown properties in terms of a continuous
> > variable for which analytical techniques can be applied.
>
> Sound like upper level management approach, generalities
> punctuated with absurdities.
Do you KNOW of an absurdity in this approach?
>
> > We can always then use the Dirac delta function to transform
> > the continuous formula into a discrete formula if such is the
> > case.
>
> >
> > I can transform from each possibility
>
> Possibility for what?
> Have you listed them all?
> Can you list them all?
All I know at this point is that it does break down to properties with
probabilities. And I'm asking if there are further restrictions and
mathematical tools that can be used on this most general equation that can
eventually lead to physical interpretations.
>
> > in the sample space
>
> What is the sample space? All this will need
> definition before you go equating things.
If there are more than one way to write this equation, then they can be
equated. Also, there might be some normalizing techiques that equate things to
one. Or it may be that if we differentiate the probability of one property with
respect to the probability of another property there may be differential
equations that we can work with that further describes the characteristics of
the physical properties.
me...@cars3.uchicago.edu
What is the equation from which you get the axioms of geometry?
tadchem
<snip repost>
> So what is the equation and the assumptions behind it from which we get
the
> mathematical expression of the laws of physics?
"Shit happens." All else is just detail ;)
Tom Davidson
Brighton, CO
Paul Colby
>
> "Paul Colby" <paulc...@earthlink.net> wrote
>
> > > > "Mike" <no....@please.com> wrote
>
> > > > > I'm trying to come up with the most general probability
> > > > > formula for a state of affairs starting with absolutely no
> > > > > information about a system (the universe).
> > > >
> > > > Why would you expect to be able to say
> > > > anything if you have *no* information?
> > >
> > > I'm hoping that the general equation itself will yield
> > > results that can be interpreted as physical dimensions,
> > > forces, and events.
> >
> > An equation equates *things*. One must define these
> > *things* and what it means to equate them. A probability
> > measure is a mapping of a set onto the reals. What is
> > this set? The state of a system in QM is a vector direction
> > in a Hilbert space. What is it in your "general equation"?
>
> a vector direction in possibility space
>
> If this searched for equation yields orthogonal functions
> which can be used to describe every possible state, then
> would that give the number of dimension that exist in the
> universe?
>
No. How do you know you got them all? I defy you
to explain what one is beyond the "a state of the
universe". Please note that in all physical theories
which are currently accepted the concept of state
is rather well defined in terms of some mathematical
structure.
One can be quite specific if one sticks to current
quantum theory. AFAIK it is generally believed that
the set of states (for a field) is a seperable Hilbert
space (i.e. containing a countable dense set). If there
is a finite number of fields then naive arguments say
that the Hilbert space for everything is also seperable.
Okay, there's a model which is consistent with current
theory. Bang away and let us know what you discover.
I don't hold out much hope unless you first add
vast amounts of other assumptions to the pot. All
seperable Hilbert spaces with countably infinite basis
look exactly the same as far as I can see. The physics
isn't in the states per say its in the operators.
> > I would be willing to bet that advances in physical theory
> > will have as much to do with what we must use to describe
> > nature as in how these *things* are manipulated. Needless
> > to say I think your approach is hopelessly general.
>
> You've got to start somewhere, and you never know until you try.
Wow, that's original. No one's ever thought of that before.
Why not start with what *is* known. Oh right, I forgot
old age thinking will get me no where.
> >
> > <cut>
> >
> > > The problem I presently have is one in which to express
> > > this general formula for the probability of a conjunction
> > > of as yet unknown properties in terms of a continuous
> > > variable for which analytical techniques can be applied.
> >
> > Sound like upper level management approach, generalities
> > punctuated with absurdities.
>
> Do you KNOW of an absurdity in this approach?
Yes, calling "it" an approach.
> >
> > > We can always then use the Dirac delta function to transform
> > > the continuous formula into a discrete formula if such is the
> > > case.
> >
> > >
> > > I can transform from each possibility
> >
> > Possibility for what?
> > Have you listed them all?
> > Can you list them all?
>
> All I know at this point is that it does break down to
> properties with probabilities. And I'm asking if there
> are further restrictions and mathematical tools that can
> be used on this most general equation that can
> eventually lead to physical interpretations.
Sigh, I assume you don't know the
equation or even what it equates.
Kinda hard to give you concrete
suggestions at this juncture, but let's
try. My favorite equation is A = B.
I usually simplify things by noting
that A=B allows me to throw away
B altogether and simply write A.
Now, A can be tossed out because
we don't know what it's for anyway.
> >
> > > in the sample space
> >
> > What is the sample space? All this will need
> > definition before you go equating things.
>
> If there are more than one way to write this
> equation, then they can be equated. Also, there
> might be some normalizing techiques that equate
> things to one. Or it may be that if we differentiate
> the probability of one property with respect to the
> probability of another property there may be
> differential equations that we can work with that
> further describes the characteristics of the physical
> properties.
>
Sounds like trying to nail jelly to a tree.
Regards
Paul Colby
Mike
"Paul Colby" <paulc...@earthlink.net> wrote
> > All I know at this point is that it does break down to
> > properties with probabilities. And I'm asking if there
> > are further restrictions and mathematical tools that can
> > be used on this most general equation that can
> > eventually lead to physical interpretations.
>
> Sigh, I assume you don't know the
> equation or even what it equates.
> Kinda hard to give you concrete
> suggestions at this juncture, but let's
> try. My favorite equation is A = B.
> I usually simplify things by noting
> that A=B allows me to throw away
> B altogether and simply write A.
> Now, A can be tossed out because
> we don't know what it's for anyway.
I did not start this thread in order to brag of my knowledge. I was hoping to
get a little help from those who have the time and are more mathematically
inclind than I am.
It may be that our present form of physical laws is just a perspective of what
we are capable of observing. For instance, since we are stuck in this 4
dimensional perspective, we cannot phathom the events that may be occuring in
other dimensions if they exist. There may be a limit to our knowlege of how the
universe works if we go strictly by observation.
No, I do not know the starting equation at the moment. But I do know how it
might be derived. I do know for an absolute certainty that the universe exists.
From there it can only break down to various properties each with a probability
less than 1 (less than absolute certainty). Any event or particle in the
universe can only be described as the conjunction of various properties.
Equation 13 on page:
http://www.fmi.uni-sofia.bg/vesta/Virtual_Labs/prob/prob3.html
and Equation 10 on page:
http://www.fmi.uni-sofia.bg/vesta/Virtual_Labs/prob/prob5.html
both have a term involving the probability of a conjustion of properties
(a.k.a. events).
The text on page:
http://www.fmi.uni-sofia.bg/vesta/Virtual_Labs/prob/prob4.html
describes how to map events (properties) from the sample space to random
variables.
All that remains is to write equation 10 and/or 13 in terms of a random
variable(s). Then we can start manipulating it to see what characteristics and
restrictions these states (conjunction of properties) can have.
Since this much, in any event, must absolutely be the case, I think it is worth
while to write it down. I will put more effort into it when I get the time,
unless one of you would like to be the first to do so. If you do not reply with
the desired equation, I must assume you do not have the time or mathematical
talent to do so.
Good luck,
Mike.
Paul Colby
Well, I've tried to suggest that your "approach" is a tad too general for
definition and clearly I've failed to convince you of this. That's fine
since it's better to think of wrong ideas than to not think at all. Quantum
phenomena are known not to follow classical probability theory.
One can throw classical probability theory at the problem all day and
not get any closer to nature simply because classical probability theory
doesn't work in this realm. So, if you fail to find a solution I'll assume
not that you lacked talent as a mathematician but rather that you fail to
understand what physics says about the world and how it operates.
Regards
Paul Colby
tadchem
<snip repost>
> It may be that our present form of physical laws is just a perspective of
what
> we are capable of observing.
General Relativity Theory includes the concept of "invariance," the idea
that physical laws can be formulated in such a way that they are independent
of any observer of any particular frame of reference.
>For instance, since we are stuck in this 4
> dimensional perspective, we cannot phathom the events that may be occuring
in
> other dimensions if they exist. There may be a limit to our knowlege of
how the
> universe works if we go strictly by observation.
The "observable" universe is the only universe we have in which we can test
and either verify oir contradict physical theory. Actually the observable
universe includes any arbitrary number of dimensions. I have personally
worked in "phase space" which contains at least 6 times Avogadro's number
(6.02252x10^23) of dimensions. If one can measure the quantity associated
with the dimension (length, time, charge, speed, spin magnetic moment, or
whatever) it is a measurable and therefore physical dimension.
The problems arise when the "quantity" associated with a purported dimension
has not been clearly enough defined that it is amenable to careful
measurement of calculation. This is the problem with many "new age"
theories that claim to overturn conventional physics. There are no means of
independently and repeatibly comparing certain properties with an objective
scale.
There *IS* a limit to the observable universe. The limit is in our ability
to make measurements, which is constantly improving.
> No, I do not know the starting equation at the moment. But I do know how
it
> might be derived. I do know for an absolute certainty that the universe
exists.
> From there it can only break down to various properties each with a
probability
> less than 1 (less than absolute certainty). Any event or particle in the
> universe can only be described as the conjunction of various properties.
>
> Equation 13 on page:
> http://www.fmi.uni-sofia.bg/vesta/Virtual_Labs/prob/prob3.html
>
> and Equation 10 on page:
> http://www.fmi.uni-sofia.bg/vesta/Virtual_Labs/prob/prob5.html
>
> both have a term involving the probability of a conjustion of properties
> (a.k.a. events).
Are you aware that there are certain assumptions behind the mathematics of
probability, and that these assumptions do not always hold when one tries to
manipulate empirical or theoretical probabilities?
Often events are not independent, and the probabilites of certain outcomes
depend on the outcomes of previous events. This is well understood to
anyone who has ever studied the game of craps.
> The text on page:
> http://www.fmi.uni-sofia.bg/vesta/Virtual_Labs/prob/prob4.html
>
> describes how to map events (properties) from the sample space to random
> variables.
One of the corollaries to Murphy's Law is "Random Variables Aren't." While
randomness may be approximately correct enough for "fair" dice and "fair"
coins, it doesn't apply to the structure of the universe. One there are two
or more material objects with mass, physical laws determine that the
evolution of the system is far less than random.
In the statistical mechanics of phase space, the *initial conditions* may be
random or totally arbitrary, but the progress of changes of the system is
deterministic. Physical laws require conservation of eneergy, conservation
of matter, conservation of charge, conservation of angular momentum, and
evolution of a complex system to the most probable (maximum entropy) state,
among other things.
Tom Davidson
Brighton, CO
Mike
Thanks for the warning. Could you give an example of how QM violates classical
probability theory? At this point, however, there may be so much math and
intuition from getting from the equation I seek and the observable phenomena
that I don't think it is appropriate to comment on its ability to succeed.
I wonder, though, have I failed to convince you that it should be developed for
its own sake simply because we know that it must be?
Mike
I appreciate your discourse on the subject. But I am not so interested in how
we mathematically describe the observations that we measure. For this is simply
a curve fitting empirical exercise. It does not tell us that any of it is
necessary on the basis of total consistency. For it does not reduce to logic. I
prefer an approach that starts with inescapable requirements and hopefully
discern the laws of physics from that.
tadchem
> I appreciate your discourse on the subject. But I am not so interested in
how
> we mathematically describe the observations that we measure. For this is
simply
> a curve fitting empirical exercise. It does not tell us that any of it is
> necessary on the basis of total consistency. For it does not reduce to
logic. I
> prefer an approach that starts with inescapable requirements and hopefully
> discern the laws of physics from that.
Aristotle tried that - deducing the nature of the universe from first
principles. His entire philosophy got blown out of the water by empirical
measurements - and not very precise ones at that.
Thank you Tycho and Copernicus.
Tom Davidson
Brighton, CO
Paul Colby
>
> "Paul Colby" <paulc...@earthlink.net> wrote in message
> news:g9027.2273$6O3.1...@newsread1.prod.itd.earthlink.net...
> >
> > "Mike" <no....@please.com> wrote in message
> > news:B5_17.185$k86.2...@e3500-chi1.usenetserver.com...
> > >
> > > "Paul Colby" <paulc...@earthlink.net> wrote
> > >
<cut>
> >
> > Well, I've tried to suggest that your "approach" is a tad too general
for
> > definition and clearly I've failed to convince you of this. That's fine
> > since it's better to think of wrong ideas than to not think at all.
Quantum
> > phenomena are known not to follow classical probability theory.
> > One can throw classical probability theory at the problem all day and
> > not get any closer to nature simply because classical probability theory
> > doesn't work in this realm. So, if you fail to find a solution I'll
assume
> > not that you lacked talent as a mathematician but rather that you fail
to
> > understand what physics says about the world and how it operates.
> >
> > Regards
> > Paul Colby
>
> Thanks for the warning. Could you give an example of how QM violates
> classical probability theory?
Quantum mechanics abound with examples. The two slit experiment for
the particle of your choosing doesn't obey the usual classical probability
rules. The probability of a photon landing on a screen at x is the is *not*
the sum of the probabilities of going through each slit. One must add
complex probability amplitudes and take the absolute square to obtain
the probability.
> At this point, however, there may be so much math and intuition from
> getting from the equation I seek and the observable phenomena that
> I don't think it is appropriate to comment on its ability to succeed.
>
Sure it's appropriate. Your chances are 0 because you don't
know the basic physics. How are you going to divine where
the basic physics comes from?
> I wonder, though, have I failed to convince you that it should be
> developed for its own sake simply because we know that it must be?
>
I think it's great but see no chance of this happening
without one applying one boat load of known physics
to start with. You certainly have to get the basic rules
right and that isn't classical probability theory.
Regards
Paul Colby
Mike
"Paul Colby" <paulc...@earthlink.net>
> >
> > Thanks for the warning. Could you give an example of how QM violates
> > classical probability theory?
>
> Quantum mechanics abound with examples. The two slit experiment for
> the particle of your choosing doesn't obey the usual classical probability
> rules. The probability of a photon landing on a screen at x is the is *not*
> the sum of the probabilities of going through each slit. One must add
> complex probability amplitudes and take the absolute square to obtain
> the probability.
I fail to see how particles acting like waves contradicts the fundamentals of
probability theory. If the total probability of alternatives were not additive,
for example, then that would violate classical probability theory. But we find
in QM that this additive nature of alternatives is exactly what gives us the
interference patterns that seems like the result of wave interference.
>
> > At this point, however, there may be so much math and intuition from
> > getting from the equation I seek and the observable phenomena that
> > I don't think it is appropriate to comment on its ability to succeed.
> >
>
> Sure it's appropriate. Your chances are 0 because you don't
> know the basic physics. How are you going to divine where
> the basic physics comes from?
That would be the quest. Let's not give up at the start.
>
> > I wonder, though, have I failed to convince you that it should be
> > developed for its own sake simply because we know that it must be?
> >
>
> I think it's great but see no chance of this happening
> without one applying one boat load of known physics
> to start with. You certainly have to get the basic rules
> right and that isn't classical probability theory.
If such an effort resulted in predictions that we know for an absolute
certainty would not happen, then we know our intuition has led us down the
wrong path.
Mike
"tadchem" <tadche...@earthlink.net> wrote
> I
> > prefer an approach that starts with inescapable requirements and hopefully
> > discern the laws of physics from that.
>
> Aristotle tried that - deducing the nature of the universe from first
> principles. His entire philosophy got blown out of the water by empirical
> measurements - and not very precise ones at that.
Are you saying that the universe is not logical at its very core?
>
> Thank you Tycho and Copernicus.
If their theories got blown out of the water, it is only because they did not
start with basic enough truths, or if they did, then they applied some wrong
assumptions or restrictions. What did these people know about math or logic.
They did not have calculus, symbolic logic, or advanced probability theory as
we have today.
me...@cars3.uchicago.edu
>
>"tadchem" <tadche...@earthlink.net> wrote
>> I
>> > prefer an approach that starts with inescapable requirements and hopefully
>> > discern the laws of physics from that.
>>
>> Aristotle tried that - deducing the nature of the universe from first
>> principles. His entire philosophy got blown out of the water by empirical
>> measurements - and not very precise ones at that.
>
>>
>
>start with basic enough truths, or if they did, then they applied some wrong
>assumptions or restrictions.
LOL.
Paul Colby
>
> "Paul Colby" <paulc...@earthlink.net>
>
> > >
> > > Thanks for the warning. Could you give an example of how QM violates
> > > classical probability theory?
> >
> > Quantum mechanics abound with examples. The two slit experiment for
> > the particle of your choosing doesn't obey the usual classical
probability
> > rules. The probability of a photon landing on a screen at x is the is
*not*
> > the sum of the probabilities of going through each slit. One must add
> > complex probability amplitudes and take the absolute square to obtain
> > the probability.
>
> I fail to see how particles acting like waves contradicts the fundamentals
of
> probability theory.
Then you fail to see a very fundamental point.
> If the total probability of alternatives were not additive,
> for example, then that would violate classical probability theory.
In all but the most special cases (eigenstates) the probability
is not addative for alternatives. Example, the particle may
pass through slit 1 or slit 2. The probability is not the sum
of these two alternatives.
> But we find in QM that this additive nature of alternatives is
> exactly what gives us the interference patterns that seems like
> the result of wave interference.
Who is this "we" you speak of? Feel free to show this for the
two slit case.
> >
> > > At this point, however, there may be so much math and intuition from
> > > getting from the equation I seek and the observable phenomena that
> > > I don't think it is appropriate to comment on its ability to succeed.
> > >
> >
> > Sure it's appropriate. Your chances are 0 because you don't
> > know the basic physics. How are you going to divine where
> > the basic physics comes from?
>
> That would be the quest. Let's not give up at the start.
> >
> > > I wonder, though, have I failed to convince you that it should be
> > > developed for its own sake simply because we know that it must be?
> > >
> >
> > I think it's great but see no chance of this happening
> > without one applying one boat load of known physics
> > to start with. You certainly have to get the basic rules
> > right and that isn't classical probability theory.
>
> If such an effort resulted in predictions that we know for
> an absolute certainty would not happen, then we know
> our intuition has led us down the wrong path.
>
Good thinking. I'd be willing to bet false or incorrect
approaches far outnumber correct ones. You've said
nothing that would lead one to think a general discussion of
classical probability theory would yield a correct approach
let alone a fruitful one.
Regards
Paul Colby
tadchem
<snip>
> > Aristotle tried that - deducing the nature of the universe from first
> > principles. His entire philosophy got blown out of the water by
empirical
> > measurements - and not very precise ones at that.
>
> Are you saying that the universe is not logical at its very core?
The Universe is flawlessly logical. The logic of the human intellect is
flawed. That is why all physical science *must* be subject to empirical
verification. It show us the flaws in our logic.
> > Thank you Tycho and Copernicus.
>
> If their theories got blown out of the water, it is only because they did
not
> start with basic enough truths, or if they did, then they applied some
wrong
> assumptions or restrictions. What did these people know about math or
logic.
> They did not have calculus, symbolic logic, or advanced probability theory
as
> we have today.
Tycho made the observations that proved the perfect universe deduced by
Aristotle (the "Harmony of the Spheres") was confounded by epicycle upon
epicycle, all without logical basis in Aristotle's model. Copernicus showed
that the data of Tycho was consistent with a *heliocentric* solar system.
Yes, there were flaws in Aristotle's assumptions. Aristotle *assumed" that
the Universe was perfect, that the gods would not make an imperfect
universe. He also assumed that since the planets made loops around the
earth and the gods put the planets there, then the loops would be "perfect"
loops. Geometrically, he "knew" that a perfect loop was a circle.
There will *ALWAYS* be flaws in the assumptions made by the human intellect.
You and I are not Gods, with Perfect Ideas.
It only remained for Kepler to deduce the ellipticity of orbits that
violated Aristotle's "perfect" circles, and for Newton to systematize it all
with a new paradigm: F = G * M1 * M2 / r^2 - the inverse square law of
gravity. This turned out to be much simpler than Aristotle's "perfect"
spheres and circles. It took only about 2000 years to find a better idea
for holding the solar system together than Aristotle's.
"What did these people know about math or logic" you ask? Of Aristotle?
Man, are you IGNORANT!!!
Aristotle (read his "Organon", which he wrote in 350 B.C. where he analyzed
knowledge and classified the typed of reasoning) was the culmination of the
classic tradition of Socrates, Plato, Pythagoras, Archimedes, and many other
people, who would be geniuses even by modern standards. They INVENTED
logic, geometry, philosophy, analytical mathematics, engineering, and so
much more than you can now imagine.
They did not have calculus (co-invented by Newton and Leibnitz in the late
17th century), symbolic logic (also developed by Leibnitz in the 17th
century), or probability theory (which has been developing ever since the
time of Descartes, the early 17th century). They did the best they could
with the tools they had available, and some clever fellows developed better
tools to solve tougher problems, as we do now, and as will continue in the
future.
The ancient Greeks and Romans didn't even have "times tables," but they
could THINK. One or two thousand years in the future, children will be
probably taught mathematics in school that we can't even imagine right now.
By believing we are somehow superior (i.e. less likely to make errors of
logic) because our tools have been more developed than theirs is to indulge
yourself in the same kind of chronological chauvinism that denies that the
ancient Egyptians could have built the pyramids, or the mediaeval Chinese
could have built the Great Wall.
People are people. Some are clever; some are naive; some are stupid; some
can be taught.
Where are you in that list?
Tom Davidson
Brighton, CO
Mike
"tadchem" <tadche...@earthlink.net> wrote
> By believing we are somehow superior (i.e. less likely to make errors of
> logic) because our tools have been more developed than theirs is to indulge
> yourself in the same kind of chronological chauvinism that denies that the
> ancient Egyptians could have built the pyramids, or the mediaeval Chinese
> could have built the Great Wall.
>
What does it matter? We are ALWAYS obligated to do the best we can with the
tools we have whether it turns out that we were right or wrong.
John Gonsowski
Mike wrote:
> I fail to see how particles acting like waves contradicts the fundamentals of
> probability theory. If the total probability of alternatives were not additive,
> for example, then that would violate classical probability theory. But we find
> in QM that this additive nature of alternatives is exactly what gives us the
> interference patterns that seems like the result of wave interference.
Bosonic string theory is certainly related to probability theory, the wierd
part is that negative probabilities show up, which is of course not a
particularly "classical" thing but it works and is also related to the
E7 LIE algebra and its associated Jordan-like algebra. John
Mike
"John Gonsowski" <gons...@us.ibm.com> wrote in message
news:3B49ABA7...@us.ibm.com...
probabilities were positive by definition, so if you come up with negative
values then it cannot be a probability. And aren't probabilities derived as the
square of a function? Then how could it be negative unless you are dealing with
complex numbers? I thought we multiplied complex conjugates to get a real
number for the probability. Are you saying that string theory assigns a complex
number to represent real things? Or are we now lost in notation?
Mike
and just don't know it.
John Gonsowski
Mike wrote:
> perhaps you are now dealing with the relative difference between probabilities
> and just don't know it.
No it's actually real negative probabilities. The negative probabilities
(negative amplitude at this point) is assigned to different paths for
getting from one place to another and at the end things do get
squared so that the total probability (relative to going someplace
else) is positive... but if you look at the contributions of the many
paths between two points, some paths are contributing negative
amplitudes and thus in effect negative probability; this is very
diffferent than anything in "classical" probability theory. The
best quote about this I could find quickly is:
"Cerf and Adami have shown that information theory of quantum
computers can give negative conditional entropies for quantum
entangled systems. Therefore negative virtual information can be
carried by particles, and quantum information processes can be
described by particle-antiparticle diagrams much like particle
physics diagrams."
John
Mike
"John Gonsowski" <gons...@us.ibm.com>
What do you suppose negative information means? Positive information means that
something unusual happened. There is more information contained in the highly
improbable event. There is zero information in the absolute certain event. What
could negative information be other than an event which cancels out unusual
events, a force to impose order and conformity?
Mike
Conditional entropy? Excuse my ignorance. It's been awhile since I studied
these things in detail. Is that the entropy of a conditional probability, for
instance, the probability of observing A once B has occurred,
P(A|B)=P(A^B)/P(B)? If so, then the entropy, S=k*log(P(A|B))=
k*(log(P(A^B))-log(P(B))). Normally we would have that P(A^B) is closer to zero
than P(B). So log(P(A^B)) would be more negative than log(P(B)), and thus a
total negative entropy. So far everything seems consistent. I suppose, however,
that when the change in entropy is compared to some starting state that the net
change in entropy ends up being greater than zero.
Mike
In other words, if the event could have happened, then it would have only lead
to it not happening. A self-negating event, with a self particle and a negating
particle.
tadchem
>
> "John Gonsowski" <gons...@us.ibm.com>
<snip>
> > "Cerf and Adami have shown that information theory of quantum
> > computers can give negative conditional entropies for quantum
> > entangled systems. Therefore negative virtual information can be
> > carried by particles, and quantum information processes can be
> > described by particle-antiparticle diagrams much like particle
> > physics diagrams."
> What do you suppose negative information means?
John is working on an amnesia beam...
Tom Davidson
Brighton, CO
John Gonsowski
Mike wrote:
> In other words, if the event could have happened, then it would have only lead
> to it not happening. A self-negating event, with a self particle and a negating
> particle.
It's a little messier than that since it is kind of arbitrary what you call
negative
information and what you call positive, they each can negate each other. It
doesn't matter whether you end up net positive or net negative at the end
since it gets squared at the end. Nothing really seems like normal information
until you get past the squareing. It's the idea of destructive interference for
waves and the picture doesn't seem any less wierd information-wise.
John Gonsowski
Mike wrote:
> Conditional entropy? Excuse my ignorance. It's been awhile since I studied
> these things in detail. Is that the entropy of a conditional probability, for
> instance, the probability of observing A once B has occurred,
> P(A|B)=P(A^B)/P(B)? If so, then the entropy, S=k*log(P(A|B))=
> k*(log(P(A^B))-log(P(B))). Normally we would have that P(A^B) is closer to zero
> than P(B). So log(P(A^B)) would be more negative than log(P(B)), and thus a
> total negative entropy. So far everything seems consistent. I suppose, however,
> that when the change in entropy is compared to some starting state that the net
> change in entropy ends up being greater than zero.
The only other place I've seen conditional entropy mentioned is in reference
to trying to explain Hawking black hole stuff... it is the idea that perhaps the
Hawking radiation holds negative entropy to keep the total entropy of the
black hole system from getting bigger than allowed. Somehow negative
conditional entropy is allowed to get as negative as its system could have
been positive. I think what is going on in this case is that there is some kind
of borrowing from or rather into the vacuum. For quantum computers, the
vacuum borrowing idea doesn't help alot since all the paths are going to
the same place and since both positive and negative act like the vacuum to
each other. I think for the quantum picture there's some not so easy to
picture physically information game going on using the information
found in the quantum propagator phase degree of freedom. John