Joy Christian's Intro Chapter for book "On the Origins of Quantum Correlations" now available online

[FrediFizzx]

If you ever wondered about the origins of quantum correlations here is a
good explanation,

http://arxiv.org/abs/1201.0775

Enjoy! More available at,

http://arxiv.org/find/grp_physics/1/au:+christian_joy/0/1/0/all/0/1

Best,

Fred Diether

[Joy Christian]

Thanks, Fred, for starting this thread.

There is one issue with regard to my local model for
the EPR correlation that, to my great puzzlement,
keeps popping up (both in some threads here as well
as at SPR). So let me try to address the issue here.

The basic bivariate variables of my model are defined as

A(a, mu) = (-I . a) (mu . a)
= +1 if mu = +I and -1 if mu = -I
and

B(b, mu) = (+I . b) (mu . b)
= -1 if mu = +I and +1 if mu = -I

(cf. eqs. (1.11) and (1.12) of the paper linked by Fred).

Several people have interpreted these definitions as
implying AB = -1 for all a and b, or equivalently
implying A = -B for all a and b. I fail to understand
how anyone can infer this, because -- above all -- mu is
a *random variable*. And since A and B are functions
of mu, A and B are also *random variables.* What is
more, it is clear from their definitions that A and B are
two *different* functions of mu (i.e., they have *different*
functional dependence on mu). Thus it is absurd to
identify A with -B for all a and b, not the least because
A and B are statistically independent events occurring
on a highly non-trivially parallelized 3-sphere.

Since this simple message is not getting through, let
me try to explain this another way: As noted, A(a, mu)
is a random variable and B(b, mu) is another, *different*
random variable. Therefore the product AB(a, b, mu) is
inevitably a third and a *different* random variable itself,
taking its values from the set {-1, +1} for a given a, b, and
mu. In other words, the product AB inevitably takes both
values, +1 and -1, randomly, with some non-vanishing
probabilities. On the other hand, for the special case
when b = a, it is clear from the above definitions of A
and B that AB = -1 for either values of mu. That is to
say, for the special case when b = a, and only for
the special case when b = a, the equality A = -B is
guaranteed to hold, not for all cases of a and b.

Joy Christian

[Ken S. Tucker]

Hi Fred & Joy.

Is this the so-called "hidden variable"...?
quote from above text , "above all -- mu is a *random variable*. "

Would that be a postulate?
Regards
Ken S. Tucker

[Joy Christian]

On Feb 9, 2:11 am, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:

>
> Is this the so-called "hidden variable"...?
> quote from above text , "above all -- mu is a *random variable*. "
>
> Would that be a postulate?
> Regards
> Ken S. Tucker

Yes, that is correct. mu is a "hidden variable."
And it is indeed a postulate. "mu" is just a special
case of the variable Bell denotes by "lambda."

Joy Christian

[harald]

"Joy Christian" <hojo...@gmail.com> wrote in message
news:703da322-0c97-4a15...@m2g2000vbc.googlegroups.com...

Thanks for the precision as I was a bit puzzled by the move from "lambda" to
"mu".

[FrediFizzx]

"Joy Christian" <hojo...@gmail.com> wrote in message

news:9d1047e5-60ec-4e06...@o13g2000vbf.googlegroups.com...

> On Feb 7, 12:55 am, "FrediFizzx" <fredifi...@hotmail.com> wrote:
>
>> If you ever wondered about the origins of quantum correlations here is a
>> good explanation,
>>
>> http://arxiv.org/abs/1201.0775
>>
>> Enjoy! More available at,
>>
>> http://arxiv.org/find/grp_physics/1/au:+christian_joy/0/1/0/all/0/1

> Thanks, Fred, for starting this thread.

You're welcome. I hope people will read and try to understand Chapter 1 of
your forthcoming book linked above as you summarize what I think is a much
more profound aspect of your work. That is the revelation that *all*
quantum correlations can possibly be explained by the topology of a
7-sphere.

Best,

Fred Diether

[Joy Christian]

On Feb 10, 7:32 am, "FrediFizzx" <fredifi...@hotmail.com> wrote:

> You're welcome.  I hope people will read and try to understand Chapter 1 of
> your forthcoming book linked above as you summarize what I think is a much
> more profound aspect of your work.  That is the revelation that *all*
> quantum correlations can possibly be explained by the topology of a
> 7-sphere.

Before we get into *all* possible quantum correlations,
there seems to be much confusion (at least among the
non-experts) about what exactly Bell's theorem is all
about. For example, the following question was recently
put to me on SPR, which reflects the prevalent confusion.
Since my repeated attempts to answer it on SPR has
failed for some reason, may I address the question here?

The question put to me was:

> I do not fully understand your argument since, if
> two random variables A and B are functions of one and
> the same single random variable mu, by definition, they
> cannot be fully independent, since if A is determined
> also B is, at least to a certain extent. If the mapping
> mu -> A is bijective, if A is determined (by measurement)
> B must be even completely determined. Then there is a
> conventional 100% correlation between A and B, but that
> has nothing to do with the Bell-inequality violations by
> quantum entanglement since it's simply a deterministic
> correlation, i.e., a "classical" one.

And my answer was:

Indeed!!! Neither Bell's local-realistic framework, nor its use
of it in my model, has anything to do with quantum
entanglement. Bell's theorem is about classical (possibly
deterministic) theories, reproducing quantum mechanical
correlations -- such as the EPR-Bohm correlation.

Statistically, my argument is no different from Bell's.
He starts with two deterministic functions, A(a, L) and
B((b, L), with a and b as experimental parameters, and L as
"one and the same random variable" as a "hidden" variable
(which can be absolutely anything one wants). He then
declares that the functions A(a, L) and B(b, L) are two
statistically independent random variables. That is to
say, he requires that A does not depend either on b or
on B, and B does not depend either on a or on A. This of
course does not preclude deterministically determined
*correlation* between A and B. The statistical independence
of A and B simply asserts that, given a complete initial
state L, the outcome at one station provides no *additional*
information about the outcome at the other station. Thus,
in technical jargon, the conditions of both "remote outcome
independence" and "remote parameter independence" are duly
satisfied. These two conditions are equivalent to the condition
of Einstein locality. Thus Bell's local-realistic framework is a
completely general framework, within which I have simply
chosen L to be equal to a trivector mu. Moreover, the point
of Bell's local-realistic challenge was to claim that no model
of quantum correlations satisfying the above two conditions
can exist. More precisely, he claimed that statistically
independent local functions of the form

A(a, L) = +1 or -1 and B(b, L) = +1 or -1,

with one and the same single random hidden variable L,
cannot reproduce correlation of the form

< AB > = -a.b.

However, in my paper linked above I have constructed
precisely two such functions A and B that reproduce
the correlation < AB > = -a.b. Moreover, I have shown
that, not only this simple EPRB correlation, but ALL
quantum mechanical correlation can be reproduced as
purely local-realistic (i.e., classical) correlation among
the points of a parallelized 7-sphere.

Joy Christian

[Ken S. Tucker]

Let conditions
I) be Conservation of Energy , CoE
II) be Conservation of Angular Momentum, CoAM
be true in any number of events,prevail.(?)

III) Measurement, is limited by Heisenbergs Uncertainty,
whereby determinism or nondeterminism is philosophy.

Given a bounded experiment, (no quanta in or out of
the boundary), and given (I) and (II) hold, then the 'mu'
is a function of (III).
Would it follow the postulate "mu" inherent to (III)?
Regards
Ken S. Tucker

[Joy Christian]

The answer is No.

What you have described has nothing to do
with Bell’s theorem, or EPR argument, or my
local-realistic model for the EPRB experiment.

Joy Christian

[Ken S. Tucker]

Which conditions would you apply, given to an experimental
physicist?

> What you have described has nothing to do
> with Bell’s theorem, or EPR argument, or my
> local-realistic model for the EPRB experiment.

So is it your position that CoE and CoAM and boundary's
do not apply?

> Joy Christian

Joy, I think some of us need conditions.
Regards
Ken S. Tucker

[FrediFizzx]

"Ken S. Tucker" <dyna...@vianet.on.ca> wrote in message
news:ea6a24a2-357d-45b3...@rk3g2000pbb.googlegroups.com...

The conditions are those given by the EPR/Bohm thought experiment and Bell
type experiments. In a way, the conservation of angular momentum does
apply for the spins of the "entangled" quantum objects.

Best,

Fred Diether

[harald]

"Joy Christian" <hojo...@gmail.com> wrote in message

news:48d4e775-85cf-4cd7...@z31g2000vbt.googlegroups.com...

Exactly.

> Statistically, my argument is no different from Bell's.
> He starts with two deterministic functions, A(a, L) and
> B((b, L), with a and b as experimental parameters, and L as
> "one and the same random variable" as a "hidden" variable
> (which can be absolutely anything one wants). He then
> declares that the functions A(a, L) and B(b, L) are two
> statistically independent random variables. That is to
> say, he requires that A does not depend either on b or
> on B, and B does not depend either on a or on A. This of
> course does not preclude deterministically determined
> *correlation* between A and B. The statistical independence
> of A and B simply asserts that, given a complete initial
> state L, the outcome at one station provides no *additional*
> information about the outcome at the other station.

Wait a moment: the outcome at station B gives us with high probability
(presumably in your model, with 100% probability) the outcome at station A
for certain detector settings. Right?

Thanks,
Harald

[Ken S. Tucker]

On Feb 12, 6:15 pm, "FrediFizzx" <fredifi...@hotmail.com> wrote:
> "Ken S. Tucker" <dynam...@vianet.on.ca> wrote in messagenews:ea6a24a2-357d-45b3...@rk3g2000pbb.googlegroups.com...

Well it's seems fairly straightforward, see,

http://mathworld.wolfram.com/PoincareTransformation.html

which I'll write for this simple application as being,

X'_i = X_i + L_i .

We have 3 CS's A, O , B where O is Origin of an occurence,
transmitted in directions A and B equally from O,

[A] <~~[O}~~> [B}

then we utilize the Poincare Transform to find,

A_i = O_i + a_i

B_i = O_i + b_i

where the a_i and b_i are displacements from O.
Next we introduce the "hidden variable" , " μ " as a
postulate-as Joy suggests,
I presume here, (dropping the formal ' i ' ),

A = O + a μ(a)

B = O + b μ(b)

with μ being the hidden unknown function .

I'm trying to see if my research posted in
" Vectors as axes " generalizing the fundamental
tensor to include the Poincore Transformation,

g_uv = x_u;v - [uw,v]x^w Eq.(4) .

is able to support the hidden variable " μ " using
[uw,v].

Regards
Ken S. Tucker

[Joy Christian]

On Feb 13, 1:25 am, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:

> So is it your position that CoE and CoAM and boundary's
> do not apply?

No. What I am saying is that CoE and CoAM are irrelevant
for the issue raised by Bell. Apart from the EPR criteria of
completeness and reality, the only condition Bell demands
is that of locality. If AB(a, b, L) is a coincidence "click" on
the two spacelike separated detectors of Alice and Bob,
then the only condition Bell demands is

AB(a, b, L) = A(a, L) x B(b, L),

where A(a, L) and B(b, L) are two individual measurement
results of Alice and Bob, L is any initial condition you like,
and a and b are two independent experimental parameters,
chosen freely by Alice and Bob. All other physical details
are irrelevant to the concerns of Bell (or mine for that matter).

Joy Christian

[Joy Christian]

On Feb 13, 8:04 am, "harald" <h...@swissonline.ch> wrote:

> Wait a moment: the outcome at station B gives us with high probability
> (presumably in your model, with 100% probability) the outcome at station A
> for certain detector settings. Right?

Yes; for a = b and a = -b

For all other settings the probability is less than 100%.

Joy Christian

[harald]

"Joy Christian" <hojo...@gmail.com> wrote in message

news:b9804fb5-183e-49ec...@i18g2000yqf.googlegroups.com...

Thanks for the confirmation. However, I had the impression that this is
incompatible with:

"The statistical independence
of A and B simply asserts that, given a complete initial
state L, the outcome at one station provides no *additional*
information about the outcome at the other station."

Perhaps you can eleborate, if you still think that it's correctly
formulated?

The information about the outcome at B can give us information about the
outcome at A that we otherwise would not have. That is "additional"
information as the "complete initial state L" isn't known to us.

Here's a suggestion: perhaps you could say: "If it would be possible to know
the complete initial state L, then"
If that works for you, then I understand what you meant there.

Harald

[Joy Christian]

On Feb 13, 5:45 pm, "harald" <h...@swissonline.ch> wrote:

> >> Wait a moment: the outcome at station B gives us with high probability
> >> (presumably in your model, with 100% probability) the outcome at station
> >> A
> >> for certain detector settings. Right?
>
> > Yes; for a = b and a = -b
>
> > For all other settings the probability is less than 100%.
>
> Thanks for the confirmation. However, I had the impression that this is
> incompatible with:
>
> "The statistical independence
> of A and B simply asserts that, given a complete initial
> state L, the outcome at one station provides no *additional*
> information about the outcome at the other station."

I see no incompatibility here. It simply means that A is
independent of both b and B, and B is independent of
both a and A. This of course does not mean that there
are no correlations between A and B, because both
A and B depend on the "common cause" L. Thus, for
a = b the correlation is -1 with certainty, and for a = -b
the correlation is +1 with certainty, dictated by L = mu.

Joy Christian

[harald]

"Joy Christian" <hojo...@gmail.com> wrote in message

news:5e8efbd1-40e6-43b9...@z31g2000vbt.googlegroups.com...

I explained how I apparently misunderstood what you meant, and your reply
seems to (indirectly) confirm my next remark which you also don't cite.
In other (completely different!) words, the same as Jaynes: additional
information that *we* obtain from the outcome at one station and which
definitely does provide *us* with additional information about the other
station, does not at all imply that information should be sent from one
station to the other station.

[Joy Christian]

On Feb 14, 9:48 am, "harald" <h...@swissonline.ch> wrote:

> I explained how I apparently misunderstood what you meant, and your reply
> seems to (indirectly) confirm my next remark which you also don't cite.
> In other (completely different!) words, the same as Jaynes: additional
> information that *we* obtain from the outcome at one station and which
> definitely does provide *us* with additional information about the other
> station, does not at all imply that information should be sent from one
> station to the other station.

Yes, I recall our discussion, and I think we are now on the same
page. I also see the similarity between your Jayne-like words and
what I had in mind. But I think anthropocentric words like "we" and
"us" should be avoided if possible. They are helpful and descriptive
to understand the distinction between "statistical independence" and
"correlation", but they do not add to the actual contents of physics.
"Measurements" could have been made by automata, or Nature
herself -- no human intervention is necessary.

Just to bring the main idea home, let me describe the essential
point in another way. The instantaneity exhibited by quantum
correlations has been demystified by my classical derivations.
The mystery of instantaneity has been reduced to the mystery
of Dr. Bertlmann's socks discussed by Bell in one of his papers.
Suppose on a cold winter night in the middle of nowhere I reach
out into my pockets to find my winter gloves but find only one of
them, and that one happens to be for the left hand, then instantly,
without lapse of any time, I know with absolute certainty that the
other glove I accidentally left at home is for the right hand. The
speed of information in this case is infinite, but we are not at all
mystified by this speed. Similarly, what I have demonstrated with
my classical derivations of quantum correlations is that apparently
instantaneous changes in correlations marvelled by people like Bell,
Shimony, and Aspect are no more mysterious than the non-locality
exhibited by my hand-gloves, or that exhibited by Dr. Bertlmann's
socks.

Joy Christian

[andyeverett]

Does a three-sphere have three "special" vector fields such that they
don't go to zero at any point and at each point the triple scalar
vector product of the three fields is some constant?

One way to picture a three-sphere is by identifying two three-balls at
their surfaces? Using such a space should I be able to graph the three
different vector fields above? Does this have anything to do with a
three sphere being parallelizable?

Thanks for any help!

[Daryl McCullough]

On Wednesday, February 15, 2012 1:16:24 PM UTC-5, andyeverett wrote:

> Does a three-sphere have three "special" vector fields such that they
> don't go to zero at any point and at each point the triple scalar
> vector product of the three fields is some constant?

This was discussed in sci.math recently.

A point on a unit 3-sphere can be characterized by a unit
4-vector: 4 numbers (x,y,z,w) such that
x^2 + y^2 + z^2 + w^2 = 1. We can represent
such a 4-vector as the Clifford number (w+IR) where I is the
unit tri-vector e_x ^ e_y ^ e_z, and R is the 3-vector
x e_x + y e_y + z e_z. So points in 4-D space can be mapped to
Clifford numbers of the from (w+IR).

If you have two such Clifford numbers representing two different
unit 4-vectors, (w+IR) and (w' + I R'), then the scalar product
of the two 4-vectors is w w' + R.R', where . is the regular
3-vector scalar product. So if (w+IR) is a Clifford number
representing a unit 4-vector, and V is a unit 3-vector, then
let (w' + I R') be defined by:

w' = -(R . V)
R' = w V - (R x V)

where x means the 3-vector cross product. Then the scalar product
of the 4-vectors represented by (w+IR) and (w'+IR') is
w w' + R . R'
= w (- R . V) + R . (w V - R x V)
= -w (R.V) + w R.V - R.(RxV)
= 0
(where I used the fact that R is perpendicular to RxV)

So (w' + I R') represents a 4-vector orthogonal to (w+IR).
It's also a unit 4-vector, if (w+IR) is.

So I've described a function F(X,V) which takes a
unit 4-vector X = (w+IR) and a unit 3-vector V and returns a
unit 4-vector X' = (w' + IR') which is orthogonal to X.
To get three independent vector fields F1(X), F2(X) and
F3(X), let F1(X) = F(X, e_x),
F2(X) = F(X,e_y)
F3(X) = F(X,e_z)

> One way to picture a three-sphere is by identifying two three-balls at
> their surfaces? Using such a space should I be able to graph the three
> different vector fields above? Does this have anything to do with a
> three sphere being parallelizable?

I don't know how the construction I gave works in terms of that
way of constructing a 3-sphere.

[Joy Christian]

On Feb 7, 12:55�am, "FrediFizzx" <fredifi...@hotmail.com> wrote:

Hi Fred,

I would like to address certain misconceptions about the
experimental observations of the EPR correlation. For example,
following issues were raised in a recent discussion of my model
on SPR:

> Experiments output real numbers and their statistics are
> computed using real number arithmetic.

This is a myth that many would like to sustain for some reason.
Experiments *do not* output real numbers. They output "clicks"
on two remotely located detectors, which are thus *events* in
spacetime. These events are recorded as *coincidence counts*
in the actual experimental practice. Thus individual experimental
outputs are most certainly *not* computed using real number
arithmetic. What is summed up at the end of all experimental
runs are these *coincidence counts.* Thus what is summed up,
in truth, are the *simultaneous events* in spacetime. In other
words, correlations between simultaneously observed �clicks�
are nothing but correlations between simultaneous events in
spacetime.

> Whether geometric algebra is used in theoretical modelling
> is irrelevant

I disagree with this view. In my opinion geometric algebra
provides more faithful representation of what is actually
happening in EPR-type experiments than quantum mechanics.
What is more, it provides an explicit local-realistic basis
for the EPR correlation that Bell claimed to be impossible.

> The outcome proposed must be justified from standard real
> number arithmetic.

This is quite misleading. All that is required by experiments,
as well as by quantum mechanics, EPR, and Bell, is that,
IF the outcomes are represented by real numbers such as
A = +1 or -1 and B = +1 and -1, then the correlation between
these outcomes must satisfy

< A > = < B > = 0

and

< AB > = -a.b.

The *extraneous* demand of "standard real number arithmetic" is
thus completely unjustified. What is more, my theoretical model
exactly satisfies the above two equations, with A = +1 or -1 and
B = +1 or -1, as well as what is actually demanded by experiments,
and does so in a completely local and realistic manner.

Joy Christian

[Cl.Massé]

On 18 fév, 20:04, Joy Christian <hojoin...@gmail.com> wrote:

> Hi Fred,
>
> I would like to address certain misconceptions about the
> experimental observations of the EPR correlation. For example,
> following issues were raised in a recent discussion of my model
> on SPR:
>
> > Experiments output real numbers and their statistics are
> > computed using real number arithmetic.
>
> This is a myth that many would like to sustain for some reason.
> Experiments *do not* output real numbers. They output "clicks"
> on two remotely located detectors, which are thus *events* in
> spacetime. These events are recorded as *coincidence counts*
> in the actual experimental practice. Thus individual experimental
> outputs are most certainly *not* computed using real number
> arithmetic.

You are right, they are computed with rational numbers encoded in
binary, because the precision is necessarily finite. And ... we don't
technically know how to do differently. Any data that can be dealt
with is represented by some sort of components or coordinates in the
set of rational numbers. The clicks are represented by 0, no click, or
1, a click, together with indices labelling the context in which they
occur.

Now, I really wonder what all that has to do with quantum non
locality.

OK, I know, I've not read your paper, I don't know that the 3-sphere
is parallelizable etc.

--
X-Phy