Bell Theorem Simulation

[John Reed]

After I wrote Joy's simulation from the Java code, I decided to work up my
own simulation. This simulation also is written in Mathematica and tries to
follow
Aspect's experiments as closely as possible. I tried to keep it simple
without
adjustable parameters. I used Pauli matrices to generate a complete set
of bivectors. Alice and Bob's detectors are represented by bivectors in the
y-z
plane, and Bob's detector is incremented in 10 degree angles from 0 to 180
degrees
from Alice's detector which is fixed. At each angle, 5000 random 3D
bivectors are
generated, and the inner products of each with Alice's and Bob's detectors
are found.
If both of these are above a threshold and are positive, a coincidence is
recorded.

I am not able to come up with the Bell Sine curve with this simulation. I
only get a
straight line from {0, 0.5} to {180, 0}. This program includes a coin flip
in each
calculation of the coincidences to randomly select a right or left hand
bivector basis.
Leaving the coin flip out does not make any difference in the final counts
of coincidences.

Can anyone offer suggestions on how I can come up with the Sine curve in my
results?
I'll be happy to try any suggestions. Also, if there is any interest in
this simulation, I
can send the code to be posted as was done with my other program.

John Reed

[Joy Christian]

Hi John,

I do not wish to discourage you, but this will be a rather negative
comment. Regardless of the details of your simulation, I can guarantee
you that you will not be able to get either the sin^2 curve for the probabilities or the cosine curve for the correlations in your simulation.
The reason is pure and simple: Bell's theorem. It is a mathematical
theorem that proves, ones and for all, that no procedure like what you
are considering will ever produce the cosine correlation. There are also
some corollaries of Bell's theorem, specifically aimed at simulation
attempts of the kind you are considering, which prove that you will not
be able to generate correlations or probabilities stronger than the
straight line you are getting. Of course, if you somehow let some
information pass on from one side to the other non-locally, or exploit
some kind of a loophole like the detector loophole, then you will be
able to get stronger correlations. One such example which exploits the
time-window loophole can be found here: http://rugth30.phys.rug.nl/eprbdemo/simulation.php

Best,

Joy

[ben...@hotmail.com]

John:

About three years ago, I tried to make Bell's curves for myself with data in a
spreadsheet. And of course that failed. Similarly, the Randi challenge is
impossible to meet, where the inputted data are on a 2D spreadsheet.

Joy's time-window loophole example is based on a model by Dr Raedt et al. Dr
Raedt published his Fortran source code a few years ago and I transcribed his
fortran code into excel VB and confirmed for myself that the software produced
the Bell's curves.

Dr Raedt introduced a random variable associated with each particle which he
used as a time of flight measure for the particle. The Aspect experiment also
presumably needed to take some steps to ensure that the correct pairs of
particles were being correlated.

Joy:

Entanglement plays no role in your model. But can I ask whether 'chance' plays
a role in the outcomes?

I distinguish between chance as observed by laboratory staff, and chance as in
whether or not a particle must follow exactly the course that it did. At theta
= 0 and theta = 180 deg, the outcomes are perfectly correlated (-1 and +1
respectively). That implies for me that the particles have no choice where to
fall as the relationship is exact. Your simulation does not distinguish
between ++ and -- nor between +- and -+ so there is potential for a 50/50
chance to occur there as in QM. But I see that as a chance only in the eyes of
the observer who does not see the dimensions of the particles. I imagine a
particle, with its access to more dimensions, as having no chance in its
outcome?

[Joy Christian]

Ben,

Good question. My local model is a classical, deterministic model.
It obeys the laws of mechanics specified by Newton. Thus chance
plays the same role in my model as it does in the classical world
of Newton. Given the initial state lambda, a particle in my model
has no choice but to follow exactly the course it did. But even in
the classical world we have irreducible randomness. In practice it
is impossible to predict whether a coin I toss will land heads or
tails, or whether it will rain a few days from now or not. This is
due to the so-called "random errors" in the classical world. In the
language of philosophy we can say that chance in my model is purely
epistemic, not ontological. It arises due to random errors in how
the vector e gets aligned with the vectors a and b. Mathematically
this is specified by the so-called "probability density function",
or PDF, as discussed in the footnote 1 on pages 18 and 19 of my
paper. In other words, I agree with the following remarks of yours:

"I distinguish between chance as observed by laboratory staff, and
chance as in whether or not a particle must follow exactly the course

that it did. At theta=0 and theta=180 deg, the outcomes are perfectly

correlated (-1 and +1 respectively). That implies for me that the
particles have no choice where to fall as the relationship is exact."

But I am not sure about the last couple of sentences you wrote. In
particular, the lack of distinction in my model between ++ and --
outcomes and +- and -+ outcomes for AB is purely accidental. The
50/50 chance for the product AB = +1 or -1 is due to the 50/50
chance in the initial state lambda. This chance, as you say, is a
chance only in the eyes of the observer, not in the particle itself.

Best,

Joy

[John Reed]

Thanks for your reply. I'm very confused about all this. First you
write many papers disproving Bell's theorem, which I thought
I understood. It seemed to be a matter of using Clifford
algebra to express the physical components of the
experiment, and not getting locked into one particular
set of bivectors, right or left hand. The trick seemed to be in
choosing the bivector coordinate system randomly for each
experiment, then repeating the experiment over and over.
Averaging these together would give the correct Bell violating
proof. I wrote up this simulation to reflect that hypothesis.
Now you say Bell's theorem won't allow this to work. You seem
to be using Bell's theorem to disprove an argument to disprove
Bell's theorem. I can only think that Bell's theorem may be
correct after all.

John

"Joy Christian" wrote in message
news:45b8da3f-8ff3-4850...@googlegroups.com...

[Joy Christian]

John,

Sorry about the confusion. There is nothing wrong with Bell's
theorem as a mathematical theorem. One cannot disprove a proven
mathematical theorem. The difficulty for Bell arises in how he
applies his mathematical theorem to physics. Let me quote Abner
Shimony to state what is meant by Bell's theorem as it is applied
to physics: "...no physical theory which is local and realistic in
a specified sense can reproduce all of the statistical predictions
of quantum mechanics." When I say I have disproved Bell's theorem
I mean I have disproved the quoted statement. Contrary to the claim
made in the statement, I have constructed precisely a local and
realistic framework for physics that Bell and CHSH thought was
impossible to construct. You have understood this framework almost
correctly. But there is a subtlety in it that you are missing. In
your simulation above what you are doing wrong is reducing the
Clifford-algebraic structure to ordinary numbers in a manner that
is subject to Bell's mathematical theorem. The trick is to get
around Bell's theorem, not confront it. To do that one must first
understand the error Bell made in how he applied his theorem to
physics. I have explained his error in some detail on my blog: http://libertesphilosophica.info/blog/. I hope the argument I
spell out there is clear enough for you to follow. The bottom
line is that one must correlate points of a parallelized 3-sphere
to recover the strong correlation. In your simulation you are
correlating points of a real line, just like Bell, and hence your
simulation is subject to his theorem. My model, on the other hand,
gets around Bell's theorem by correlating points of a 3-sphere.

Best,

Joy

[FrediFizzx]

"John Reed" <88ka5...@sbcglobal.net> wrote in message
news:l4ccq6$snl$1...@dont-email.me...

> Can anyone offer suggestions on how I can come up with the Sine curve in
> my results?

It is impossible the way you are doing it. Same reason why the "challenge"
will never work to violate Bell.

Email me the Mathematica notebook and I will post it.

Best,

Fred Diether

[ben...@hotmail.com]

Thank you for confirming the lack of chance in the evolution of a particle.
Can I also say/ask a few more things about the way to interpret the nature of
particles. Spacetime, as in (x,y,z,t), is not enough information to show the
lack of chance in a particle's evolution. It needs a more detailed algebra eg
Clifford Algebra which I could represent as say (w,x,y,z,t) where w could
(maybe?) be as minimal as a dichotomous 0 or 1. But if one conflates or
compactifies or removes the w dimension of CA to leave just spacetime, then
chance will appear because for w=0 the particle could be in state spin + while
for w=1 the particle could be in state spin -.

In other words, spacetime includes a double cover with both w=0 and w=1 values
simultaneously. This is like the moibus strip with the ice skater spinning
+wise on one side of the strip and spinning -wise on the other side. CA lets
you work with the full details of the strip whereas spacetime does not.

However, even if one has been using CA in calculations, as soon as those
calculations are turned into individual observations in spacetime, ie
laboratory outcomes of the kind reported at the detectors, say A = + and B = -,
then the correlation is lost as spacetime observations do not contain enough
details.

To sum up: working in CA allows one to calculate the details required to give
the Bell's corelations but, as soon as the individual outcomes at the detector
are recorded, those observations are recorded as spacetime events and the
correlation is lost.

So how did the simulation work? I apologise if I am misunderstanding the java
software, but here is my interpretation which is subject to my not
understanding it properly. As long as the 'double cover' events are not
separately recorded then one can keep the Bell correlation. The software
increments PlusResult, separately for each theta, when the results at A&B are
either +&+ or -&-. The software increments MinusResults when the results at
A&B are either +&- or -&+. Presumably, this use of paired results aggregates
the double cover results in a way that does not destroy the correlation because
the individual results are not treated separately.

PlusResults should give P = sin^2(eta/2) and MinusResults should give
P = cos^2(eta/2). However, since the model gives P(+&+) = P(-&-) and
P(+&-) = P(-&+) then the graph plotted can be either of P(+&+) or P(-&-) for
one curve and either of P(+&-) or P(-&+) as the other curve. The
probablitities being halved to P = 0.5*sin^2(eta/2) and P = 0.5*sin^2(eta/2),
and it is these two probabilites that are plotted in the simulation. (Well, at
least it seems to be that way in the part of the simulation that I have
[approxinately] replicated.)

The Randi challenge appears to be odd in the light of the geometry of
CA. (x,y,z,t) does not hold enough details to obtain the Bell curves. Particle
behaviour seems to break Bell's Inequality, hence to model particle behaviour
one needs to put (x,y,z,t) and the Randi challenge to one side and look at QM
or Joy's model or other such models. If you use QM you get entanglement and
possibly FTL action at a distance. If you take a CA space, and combine that
with Joy's opinion that within CA the particles have no 'chance' or choice in
their evolutions, then all depends on the particles' interactions with the local geometry of CA.

[John Reed]

"Joy Christian" wrote in message

news:d6d39fa3-7898-4eaf...@googlegroups.com...

Thanks for the references. I need to read more on this to become
more familiar with your theory. I don't think I'm seeing this the same
way you are. I have a Ph.D in physics so I understand the experiments
but I can't fit them into this new framework very well yet. If the ideas
you have are correct it would answer a lot of questions.

John

[Joy Christian]

Ben,

Although you have used non-technical language, you have summarized
the central ideas behind my model almost correctly. Let me therefore
jump straight to your main question: How did the simulation work?

To understand this, we must first ask: How can we make sure that a
result A observed by Alice occurred at the same time as the result
B observed by Bob? The usual functions A(a, e) and B(b, e) clearly
do not contain this information explicitly. In the usual picture
there is no way of knowing---theoretically---that the results A and
B occurred simultaneously. Within the 3-sphere, on the other hand,
we have one of its natural properties to help us in this regard.
Because a 3-sphere remains closed under multiplication, we can
proceed to deduce the simultaneity information as follows:

Let (v, i, j, k) and (w, x, y, z) represent two distinct points of
a unit 3-sphere, with v = +/-1 and w = +/-1 corresponding to the
results A and B, respectively. Then, a third point (u, f, g, h) of
the 3-sphere given by the product

(u, f, g, h) = (v, i, j, k) (w, x, y, z),

and corresponding to the product AB, provides us the missing
simultaneity information. We can also make this more explicit by
introducing a time parameter, t, and writing

(u, f, g, h; t) = (v, i, j, k; t) (w, x, y, z; t).

Now in the measurement limit we have v = +/-1 and w = +/-1, and
therefore we necessarily have u = +/-1. What is more, we now know
when, say, v = +1 occurred simultaneously with w = +1. Clearly, the
results v = +1 and w = +1 can occur simultaneously only when we have
u = +1. So all we need to do is calculate the probability for u to
have the value +1. This is what is described in equations (A33) and
(A34) of my paper. So, to answer your question, the simulation works
by adding the missing simultaneity information into the results A and
B as above, but without compromising their locality.

Does this answer your question?

Best,

Joy

[FrediFizzx]

"John Reed" <88ka5...@sbcglobal.net> wrote in message

news:l4heql$vdg$1...@dont-email.me...

> Thanks for the references. I need to read more on this to become
> more familiar with your theory. I don't think I'm seeing this the same
> way you are. I have a Ph.D in physics so I understand the experiments
> but I can't fit them into this new framework very well yet. If the ideas
> you have are correct it would answer a lot of questions.

Hi John,

Here is a verbal description of Joy's model that I posted on the FQXi blogs
awhile ago. Perhaps it will help.

"Einstein thought (via EPR) that quantum mechanics was not complete. Not
that it was wrong but that it was missing something. Of course everyone
thinks that in 1964, Bell put an end to that proposition. Fast forward to
2007 and Joy Christian discovered what was missing! And that is the topology
of a parallelized 3-sphere applied to the EPR-Bohm scenario. The 3-sphere
topology is really not anything that is all that radical or new. It
basically involves spinors that we already knew about from quantum theory
and math. But no one ever applied it to the problem before like Dr.
Christian did. When you come right down to thinking about it, it really is a
natural choice to try. Lo and behold, it actually works to solve Einstein's
problem with QM! Basically said, space has similar properties to say...
fermions.

Now, since the 3-sphere topology is parallelized, it has zero curvature
(flat) but non-zero torsion (twist). Dr. Christian, in his model, has
normalized the topology to a unit 3-sphere so that points on the 3-sphere
can be +1 or -1. However, an interesting thing is that the topology also has
a left or right handed orientation. Basically opposite. So the signs of the
1's become flipped in the two different orientations. When the particle pair
is created in the EPR-Bohm scenario, there is a 50-50 chance in Nature that
the orientation of that particular pair's topology will be left or right
handed. That is Dr. Christian's hidden variable. And this is all involving
physical postulates here. That hidden variable coupled with the torsion of
the topology (space) is what gives us quantum correlations in the EPR-Bohm
scenario."

If you have any questions at all while you are studying the model, you can
ask here or on Joy's blog or feel free to send me an email if you would
rather not ask publicly.

Best,

Fred Diether

[mich...@gmail.com]

I have posted an event-by-event simulation of EPR which reproduces the QM results at https://github.com/minkwe/epr-simple/ (comments welcome)

It appears it should be possible to do the same for Joy's model. As a first step, I have ported the code written by Chantal Roth to python https://github.com/minkwe/jcspython/ but I need to understand a little what is going on:

Specifically, can I use the Ca1,Ca2,Cb1,Cb2 functions to generate the +1/-1 results at each station? If so, how?

[Joy Christian]

On Tuesday, October 29, 2013 4:10:02 AM UTC, mich...@gmail.com wrote:
> I have posted an event-by-event simulation of EPR which reproduces the QM results at https://github.com/minkwe/epr-simple/ (comments welcome)
>
>
>
> It appears it should be possible to do the same for Joy's model. As a first step, I have ported the code written by Chantal Roth to python https://github.com/minkwe/jcspython/ but I need to understand a little what is going on:
>
>
>

Hi Michel,

> Specifically, can I use the Ca1,Ca2,Cb1,Cb2 functions to
> generate the +1/-1 results at each station? If so, how?

No, that won't work. Ca1, Ca2, Cb1, and Cb2 do not have enough
information within them to generate the strong correlation.

I looked at your program, but I do not yet understand how you
are able to produce the strong correlation. My hunch is that
your program involves either exploiting some sort of detector
loophole or non-locality. I will ask Chantal to have a look.

Best,

Joy

[ben...@hotmail.com]

On Sunday, 27 October 2013 16:40:02 UTC, Joy Christian wrote:
...

>
> Does this answer your question?
> Best,
> Joy

Hi Joy,

Your reply was very useful, thank you. I have seen your S3 diagram with the
three points A, B and AB on it before, but now you have added more about its
relevance here, I can now see it is being used in the simulation software. I can
understand what you mean about AB being used to show simultaneity of A and B and
I suppose that is a neat avoidance of needing to use the variable t to show
simultaneity which would be more difficult.

I hope you will comment on chirality of particles and world fields. Say a pair
of particles in the simulation was a LH electron (say spin +) and a RH positron
(spin -). When I first saw your model three years ago, I don't think I had even
heard of the Higgs field and I had great difficulty understanding what world
your CA was trying to represent. I was thinking in terms of (x,y,z,t) with some
kind of large-scale twist and wondering how the twist in the universe could get
something back to its starting point so quickly! But I see the double cover
version now. Anyway, I see the Higgs field as being static wrt spin only
because of a tension between its own simultaneous + and - counterbalancing
spins. I picture your model as a + and - particle pair being produced somehow
within one of the + spin fields of the Higgs. I don't really see why the pair
should evolve restricted within the + field alone, but that may be due to
something akin to not having access to places outside their starting horizons.
Alternatively, the pair could evolve, by [an acceptable kind of] chance, within
a - spin of the Higgs field. I wondered if you had considered other options and
why you ruled them out? For example the electron could evolve within the +
field of the Higgs and the positron could evolve within the - field of the
Higgs, or of some Higgs-like vacuum field? This is related to one of the
criticisms that CA maths does not allow the use of opposite curvature tensor
bases in the same equation.

To extend that idea to locomotion of particles, again I see the higgs field as
static with respect to electric charge because of a tension between simultaneous
+ and - charges within the higgs field. I also see the photon as having a
similar counterbalancing of + and - charges in its field. To get speed c, a
photon would have its + charge field interacting with the higg's - field and at
the same time the photon's - field interacting with the higg's + field. Though
again I cannot see why the motion should be restricted to such interactions.

Best wishes

Ben

[Joy Christian]

Hi Ben,

I see the chirality of the 3-sphere within my model somewhat differently.
I see it more geometrically then how you have described it. Perhaps Fred
can comment more from the particle physics perspective, but in my view
the chirality (within my model) has to do with the initial orientation of
the 3-sphere. To understand this, recall that in the EPR-Bohm experiment
each run of the experiment is a distinct physical process. Suppose at the
start of a run a neutral pion decays into an electron and a positron (and
of course a photon). Then, at the start of this process Nature must make
a choice between the two possible orientations of the 3-sphere (which is
taken as a physical space in my model). Now what do I mean by an
orientation of the 3-sphere? Well, imagine a tiny little 3-dimensional
tangent space (a flat 3D space) attached to every single point of the
3-sphere. Then, by orientation I mean a choice of a basis (or a frame)
for each of these tangent spaces. But there are two possible sets of
such bases. We can have either right-handed frames or left-handed frames
defining the tangent spaces of the 3-sphere. A choice between these two
possible sets must be made to be able to describe the physics of each
run consistently. My hypothesis then is that Nature must make a choice,
with 50/50 chance for each orientation, to carry out physics consistently.
In Bell's language, this choice of an orientation is taken as an initial
state, or a hidden variable in my model. You already know all this, but
I am repeating it to stress how geometrical the picture I have in mind is.
It is also important to realize that an orientation of a manifold (like
that of a 3-sphere) is both a local and a global property at the same time.
It is local in the sense that a basis is chosen at each point of the
3-sphere. But since this choice must be made consistently throughout the
3-sphere, its orientation is also a global (or a topological) property.
Now the question is: How would an electron, which appears to have spin up
in the right-oriented 3-sphere, look like from the perspective of a
left-oriented 3-sphere? Well, you already know the answer to this question:
It would look like an electron with spin down, in analogy with the Mobius
strip example. Note that, contrary to some fallacious claims, no two
orientations (or the corresponding algebras) ever get mixed in this picture,
because, as I already mentioned, each run of the experiment is a separate
physical process. So, to sum up, unlike you, I have used as little particle
physics as possible in my description, following Newton’s maxim of
"Hypotheses non fingo."

Best,

Joy

[FrediFizzx]

<ben...@hotmail.com> wrote in message
news:67703110-b790-4723...@googlegroups.com...

> I hope you will comment on chirality of particles and world fields. Say a
> pair
> of particles in the simulation was a LH electron (say spin +) and a RH
> positron
> (spin -).

A left handed electron can be either spin up or down. Same with a RH
positron.

> When I first saw your model three years ago, I don't think I had even
> heard of the Higgs field and I had great difficulty understanding what
> world
> your CA was trying to represent. I was thinking in terms of (x,y,z,t)
> with some
> kind of large-scale twist and wondering how the twist in the universe
> could get
> something back to its starting point so quickly! But I see the double
> cover
> version now.

I am not sure what you mean by "something back to its starting point so
quickly".

> Anyway, I see the Higgs field as being static wrt spin only
> because of a tension between its own simultaneous + and - counterbalancing
> spins. I picture your model as a + and - particle pair being produced
> somehow
> within one of the + spin fields of the Higgs. I don't really see why the
> pair
> should evolve restricted within the + field alone, but that may be due to
> something akin to not having access to places outside their starting
> horizons.
> Alternatively, the pair could evolve, by [an acceptable kind of] chance,
> within
> a - spin of the Higgs field. I wondered if you had considered other
> options and
> why you ruled them out? For example the electron could evolve within the
> +
> field of the Higgs and the positron could evolve within the - field of the
> Higgs, or of some Higgs-like vacuum field? This is related to one of the
> criticisms that CA maths does not allow the use of opposite curvature
> tensor
> bases in the same equation.

What you wrote above seems to be speculation. I believe that Joy's model
works best with considering the void to be permeated with a Dirac field in
addition to a Higgs field. Remember, since the Higgs boson is massive, it
has to be very short ranged. And believed to be zero spin and no charge.
However, the difference between the parallelized 3-sphere topology and
charged fermions is that in the topology, you will have a sign flip after
180 degrees and with the fermion you get a sign flip in 360 degrees. I
haven't quite reconciled that yet.

Best,

Fred

[Joy Christian]

This is easy to understand. The angle of rotation and the angle between
the directions of spins are related by a factor of 2: eta_ab = psi/2. So
180 degrees change in eta_ab is 360 degrees change in the rotation angle.

Best,

Joy

[ben...@hotmail.com]

Hi Joy:

Your reply was very helpful, thank you. Do you have anything at all to help
visualize the 7-sphere? Your 7-sphere paper is one which I have not even tried
to read as the geometry seems so daunting.


Hi Fred:

On Thursday, 31 October 2013 06:00:03 UTC, FrediFizzx wrote:
> A left handed electron can be either spin up or down. Same with a RH
> positron.

Oops. Yes, agreed. I should not have written "spin +". I was thinking of
"chirality" but wrote "spin". Either chiral structure can have either spin at a
detector. The chirality is a hidden variable. Joy writes about helicity very
clearly in his reply. Sorry.

Ben wrote:
> > kind of large-scale twist and wondering how the twist in the universe
> > could get
> > something back to its starting point so quickly! But I see the double
> > cover version now.

Fred wrote:
> I am not sure what you mean by "something back to its starting point so
> quickly".

Three years ago, I was wrongly thinking of a large scale twist in a 3D
universe. A universe-sized radius of curvature gets you back (maybe!) to a
starting point after an aeon. That was obviously no use. Travelling around a
very small radius of curvature, however, gets something back to its starting
point quickly enough but that is the territory of strings or maybe microscopic
BHs and that did not seem to be the correct territory for CA either.

I think that I follow the Dirac belt analogy. It involved a 3D body rotating
around a 3D body and getting back to its starting point after a 720 degree
rotation. It does not involve using extra dimensions beyond 3D, but if there
were a small compactified extra dimension, with a very small radius of
curvature, then a rotation of a body around that curvature would need 720
degrees for a full rotation. And as in Joy's similar point, in his reply, this
would be a global effect as the curled up extra dimension would be accessible
everywhere in our 3D.


<snip my earlier writing>
Fred replied:

> What you wrote above seems to be speculation. I believe that Joy's model
> works best with considering the void to be permeated with a Dirac field in
> addition to a Higgs field. Remember, since the Higgs boson is massive, it
> has to be very short ranged. And believed to be zero spin and no charge.
> However, the difference between the parallelized 3-sphere topology and
> charged fermions is that in the topology, you will have a sign flip after
> 180 degrees and with the fermion you get a sign flip in 360 degrees. I
> haven't quite reconciled that yet.

Yes, I admit to using speculation. Sorry for not being clearer. I often do
write that I am not a physicist, but forgot here. The trouble is that I can
visualize (maybe speculatively and wrongly) multiple dimensions using
particle/fields easier than I can using geometry. In my model, the electron
has colour charges but they are neutral overall. But just because the mean
colour charge is zero does not mean that colour is irrelevant to the electron.

In some ways I think Joy is fortunate that the 7-sphere is not needed to cater
for the electron behaviour. Well, Joy would be OK because he could re-write a
model using the 7-spere. But I would not be able to follow it yet.

In my speculation, the full dimensions of space would need to cater for four
short range particle properties (red colour charge, green colour charge, blue
colour charge, weak isospin) and two long range ones (electric charge, spin). I
see all those as containing opposing chiral properties eg red is chirally
opposite to antired. The world could subdivide into different chiral parts for
any of those six variables. AFAIK that is all there is. I do not know how
many dimensions that makes in total. A world or vacuum field could subdivide so
long as it has both chiralities within it. IMO the Higgs could do this. If the
Dirac field provides for the creation of e-/e+ pairs then the Dirac field can do
this too.

What is a 3-sphere? Joy notes that at each point on a 3-sphere one can have
two chirally opposite small 3D tangential spaces. So that is in total a 3-
sphere plus 6D? Yet the whole space is supposed to be 5D? Presumably the two
3D spaces can be thought of as one 3D space because each 3D space is somehow
exclusive of the other space, and that must be why a particle stays within its
starting chiral space. [And that is why the maths for one curvature should not
be mixed with the maths for the other curvature at the same time.] So we have
the 3-sphere plus 3D. And the 3-sphere is just the surface of a sphere and so
is just 2D. Hence 2D+3D=5D is the total dimensions?

I suppose that the radius of curvature of the 3-sphere is indeterminate? But
could it be a compactified string dimension?

Best wishes to you both.

Ben

[ben...@hotmail.com]

Fred: a postscript

I probably am speculating too much about charge being a chiral property. That
is because, in my own non-mathematical model, a charge and a preon are
confounded together. A LH preon and a RH antipreon both always have an anti-
colour property. Maybe the colour charge is not chiral, but in my model I
cannot see a colour charge being made in a space without it being carried by a
preon, and the preon is chiral and may(?) need a chiral vacuum field to be
created in.

If none of the charges were chiral, then you could construct a total space from
two 3-spheres. One for spin (rather, chirality) and is 2D and one for weak
isospin (chirality really) and is also 2D. That gives total dimensions of
either 2D+2D + the tangential 3D = 7D in total. Or 2D * 2 +3D = 7D again.

If spheres were nested one could add their dimensions, if they were crossed one
could multiply their dimensions.

If the charges are also included, nested, that would give a total of 2D * 6 +3D
=15D. If they are included, crossed, then the total dimensions are 2D^6 + 3D =
67 dimensions. (I know one should not really cross spin with weak isospin as
you do not get the latter with all chiral structures.)

Best wishes

Ben

[Joy Christian]

Hi Ben,

7-sphere is much more difficult to visualize than a 3-sphere. One way to
visualize it is as a 4-sphere worth of 3-spheres. You can imagine it as a
3-sphere attached to every point of a 4-sphere. Just as a 3-sphere can be
imagined as a 1-sphere (i.e., a circle) attached to every point of a
2-sphere (i.e., the surface of a tennis ball), you can imagine a 7-sphere
as a 3-sphere attached to every point of a 4-sphere. If you are more
ambitious than this, then you can try to follow this video by Niles Johnson:
http://www.youtube.com/watch?v=II-maE5HEj0.

As for your question about the 3-sphere, it is simply a three-dimensional
space, like the ordinary space, but with a spherical geometry. You have got
its dimensionality all wrong. A 3D tangent space at each of its points is
just a mathematical device to understand its manifold structure (or its Riemannian geometry). Let us start with the surface of the globe. Locally
it looks flat, doesn't it? But we know that earth is not flat. However, we
can think of a flat local segment of the surface of the earth at one location
as its tangent space at that location. The tangent space is therefore 2D. Then
we can think of the round surface of the earth as a collection of all such 2D
tangent spaces at all of its locations. As you can see, it is just a
mathematical way of thinking about it. This way of thinking of the surface of
the earth does not change its dimensionality---it is still 2D. Now you can
imagine the same for the 3-sphere, with a collection of 3D tangent spaces.
This does not change the dimensionality of the 3-sphere, which, as I mentioned,
is just a three-dimensional surface. You can visualize it as an ordinary 3D
space, but with an intrinsic (or Riemannian) curvature characterizing its
points. This is much easier to understand in the language of Riemannian
geometry. Similarly, although it is much harder to visualize a 7-sphere, in
the language of Riemannian geometry it is not too difficult to understand.
Also, one does not have to be a physicist to understand any of these things.
We certainly do not need to know anything about the string theory, for example.
But knowing a bit of Riemannian geometry helps.

Best,

Joy

[ben...@hotmail.com]

On Friday, 1 November 2013 16:40:11 UTC, Joy Christian wrote:

> .....

> as a 3-sphere attached to every point of a 4-sphere. If you are more
> ambitious than this, then you can try to follow this video by Niles Johnson:
> http://www.youtube.com/watch?v=II-maE5HEj0.

> .....

> As for your question about the 3-sphere, it is simply a three-dimensional
> space, like the ordinary space, but with a spherical geometry. You have got
> its dimensionality all wrong. A 3D tangent space at each of its points is

> ....

Hi Joy,

Thank you once again for your advice, the link, and your patience. I can't
expect more help as this must be quite trivial and frustrating for you as I am
not seeing the geometry correctly yet, so I really have appreciated your help.

I did say at the beginning that I found it difficult to visualise the 3-sphere.
I have watched the Niles Johnson video on the 7-sphere and it is very
interesting. I need to go away and start again on working out how to visualise
the 3-sphere geometry from scratch. Well, not quite from scratch as I see the
dynamic equilibrium tension within scalar vacuum fields as causing the CA
version of the geometry of space, and the video only reinforced my view.

I used CA to follow your papers. But that used a shut-up-and-calculate
method based on partitions of the whole space into geometric objects: 1, a, b,
c, ab, ac, bc, abc, without, as I said, being able to visualise it properly,
especially the torsion in the abc part and why the total space is 5D. But I
will work on it. I have books on metrics and topological spaces and there may
be online courses so I could start there. It is all a matter of what is at the
top of my TODO list, and I suppose the geometry of space ought to be at the
very top.

I notice that elsewhere you speak of the next 50 years. Do you envisage the
mathematics of QM being recast using CA over this period or will the two
approaches be complementary? When I first noticed this spf website over three
years ago, it had discussions contrasting QM and CA and one view was that CA
was just an alternative approach so "why bother" to use CA when one had QM. At
the time I thought that the CA approach must prevail as a geometrical approach
must be the more easy to visualise. I still think that despite not finding the
CA so easy to visualise myself yet!

Thanks again.

Ben

[Joy Christian]

Hi Ben,

Although just a 3D space, the 3-sphere is indeed difficult to visualize.
This is one of the reasons why my ideas are not well understood by
professional physicists. Perhaps this paper might help you to visualize
the 3-sphere better: M. A. Peterson, Am. J. Phys. 47, 1031 (1980).

I think the mathematics of orthodox quantum mechanics is likely to be
favoured by physicists in practice, partly because of their intellectual
inertia and partly because operationally it is a very efficient and
successful tool for calculating and predicting new physical phenomena
(at least at the microscopic scale). However, the usual interpretation
of this operational tool in terms of concepts like superposition,
entanglement, and non-locality are unlikely to survive. Eventually
physicists will recognize that these concepts are not fundamental to
nature. They are just artefacts of a particular interpretation of the
orthodox formalism. From my work and from some other works it is becoming
clear that Clifford-algebraic approach provides conceptually much cleaner
understanding of the physical phenomena. It is also not impossible that
Clifford-algebraic underpinning of quantum mechanics may lead to
predictions of new physical phenomena that are not predicted by orthodox
quantum mechanics. My ultimate ambition is of course to be able to
contribute to the understanding of the theory of quantum gravity, where
orthodox quantum formalism has led to insurmountable difficulties. So,
to answer your question, the next 50 years in physics are likely to
benefit enormously from the Clifford-algebraic approaches I and others
are exploring. In particular, the combination of Clifford algebra and
division algebras seen in my work is likely to provide advantages going
far beyond the simple ease to visualize things better.

Best,

Joy

[Joy Christian]

On Tuesday, October 29, 2013 4:10:02 AM UTC, mich...@gmail.com wrote:

Hi Everyone,

Michel Fodje has written a code for the EPR-Bohm correlation based
on Chantal's simulation of my model. It can be downloaded from here:
https://github.com/minkwe/epr-simple/. Michel and I have been
communicating about his code and that has led to some remarkable
improvements. I think it would be instructive if someone else can
try to translate Michel's code (which is written in Python) into
some other programming language (such as Java or Mathematica).

Best,

Joy

[John Reed]

"FrediFizzx" wrote in message news:bd54ko...@mid.individual.net...

Hi Fred,

I've read through some of the papers dealing with simulations. Joy's math
looks correct. The papers by Gill and Moldoveanu are not in my opinion.
I have some questions about the equations in the 4 Sept. paper by Joy. In
equation A27 of that paper two normalization constants appear, Na and Nb.
Where do they come from and what do they represent?

A more general question deals with the claim of locality. The bivectors
representing Script A and Script B are certainly local. However when the
bivector product of these two is taken, that represents a third bivector
which is then analyzed. That bivector is no longer local since it includes
contributions from the A and B bivectors. This reminds me of what Bohr
said about quantum mechanics experiments. He said it is all one reality
and you can't break it up into pieces as EPR wanted to do. I think what
you have here is another way of looking at quantum mechanics.

Something else comes to mind about macroscopic domain experiments
to verify this theory. In computers, quantum chips are now being
developed. They use qubits which represent quantum bits. These
have the ability to be in a superposition of states allowing them to do
calculations it would take a classical computer much longer to do. The
researchers developing these have found they need to be super cooled.
The superposed states are very sensitive. I think it will be found that
macroscopic experiments using exploding balls will not work. It will be
impossible to maintain quantum superposed states for these large objects.

Best regards,
John

[Joy Christian]

Hi John,

Let me answer your questions to Fred.

> I've read through some of the papers dealing with simulations. Joy's math
>
> looks correct. The papers by Gill and Moldoveanu are not in my opinion.

You can say that again!

> I have some questions about the equations in the 4 Sept. paper by Joy. In
>
> equation A27 of that paper two normalization constants appear, Na and Nb.
>
> Where do they come from and what do they represent?

Na and Nb are normalization factors. Recall that 3-sphere is defined by
a set of *unit* quaternions. Therefore all quaternions appearing in my
papers are normalized to unity. Equation A27 is a scalar part of the
*product* of two such unit quaternions. Thus it is automatically a unit
quanternion (because 3-sphere remains closed under multiplication). This
is why both Na and Nb appears in A27. If you carry out geometric product
of the quaternions defined in A28 and A29, then you will see where Na and
Nb are coming from.

> A more general question deals with the claim of locality. The bivectors
>
> representing Script A and Script B are certainly local. However when the
>
> bivector product of these two is taken, that represents a third bivector
>
> which is then analyzed. That bivector is no longer local since it includes
>
> contributions from the A and B bivectors. This reminds me of what Bohr
>
> said about quantum mechanics experiments. He said it is all one reality
>
> and you can't break it up into pieces as EPR wanted to do. I think what
>
> you have here is another way of looking at quantum mechanics.

I disagree. What I am doing is purely local, classical physics. Bohr
was wrong. Einstein was right. The variable A and B strictly satisfy
the locality condition specified by Einstein and spelt out by Bell.
This condition is best understood as a factorizability condition.
Consider a joint system, which includes contributions from both A
and B bivectors. Let us write this joint system as J(A, B). In my
framework this system can be represented by a unit quaternion, which
in turn represents a point of a unit, parallelized, 3-sphere. Now the
question is: Can this system satisfy the factorizability (or locality)
criterion of Einstein and Bell, or will it be non-factorizable as
claimed by Bohr? Well, any quaternion can be written as a product of
two or more quaternions, and bivectors are just special cases of
quaternions. Thus we can write

J(A, B) = A * B,

where * represents a geometric product. So, contrary to Bohr's opinion,
all systems are factorizable. What is more, 3-sphere is a classical space.
There is no superposition, entanglement, or non-locality in this space.

> Something else comes to mind about macroscopic domain experiments
>
> to verify this theory. In computers, quantum chips are now being
>
> developed. They use qubits which represent quantum bits. These
>
> have the ability to be in a superposition of states allowing them to do
>
> calculations it would take a classical computer much longer to do. The
>
> researchers developing these have found they need to be super cooled.
>
> The superposed states are very sensitive. I think it will be found that
>
> macroscopic experiments using exploding balls will not work. It will be
>
> impossible to maintain quantum superposed states for these large objects.


I think it will be found that macroscopic experiments using exploding

balls exhibit "quantum" correlations, just as I have predicted in my
paper: http://arxiv.org/abs/1211.0784. In the experiment proposed in
this paper there is no superposition of states. It is a purely classical
experiment. When the experiment is finally done, the world will be
"astounded", to used the word of one of my colleagues and friend. People
will then begin to understand what I have been talking about. There is no
boundary between "the classical" and "the quantum." The boundary is only
in our minds.

Best regards,

Joy

[John Reed]

"Joy Christian" wrote in message

news:7dca8576-f9da-4c34...@googlegroups.com...

>
>


Hi John,

Let me answer your questions to Fred.

I think factoring is beside the point. Here's a posting that appeared
in sci.physics.research a month or so ago:

"A crucial step in generating the outcomes that is the basis of the
cosine curves in Christian's paper is the following line of code
(in module JoyChristianSimulation.java):

double C_ab = (-Math.cos(eta_ae + phi_op) * Math.cos(eta_be + phi_or) +
Math.cos(eta_cross) *
Math.sin(eta_ae + phi_oq) * Math.sin(eta_be + phi_os))/((N_a)*(N_b));

where anything with an a in the subscript depends on Alice's detector
angle setting a, and anything with a b in the subscript depends on
Bobs's detector angle setting b, and eta_cross depends on both.

But this of course is manifestly non-local, since in this code
computed outcomes depends on *both* detector settings simultaneously."

At the time I wasn't familiar enough with the theory to understand the
importance of this posting, but it states my thoughts on this very well.
You
can't make the claim that this program is "manifestly local" with the
calculations being done with this algorithm.

> Something else comes to mind about macroscopic domain experiments
>
> to verify this theory. In computers, quantum chips are now being
>
> developed. They use qubits which represent quantum bits. These
>
> have the ability to be in a superposition of states allowing them to do
>
> calculations it would take a classical computer much longer to do. The
>
> researchers developing these have found they need to be super cooled.
>
> The superposed states are very sensitive. I think it will be found that
>
> macroscopic experiments using exploding balls will not work. It will be
>
> impossible to maintain quantum superposed states for these large objects.


I think it will be found that macroscopic experiments using exploding
balls exhibit "quantum" correlations, just as I have predicted in my
paper: http://arxiv.org/abs/1211.0784. In the experiment proposed in
this paper there is no superposition of states. It is a purely classical
experiment. When the experiment is finally done, the world will be
"astounded", to used the word of one of my colleagues and friend. People
will then begin to understand what I have been talking about. There is no
boundary between "the classical" and "the quantum." The boundary is only
in our minds.

That still doesn't explain why the researchers weren't able to do the Bell
violating qubit calculations without super cooling. There is a boundary
between classical and quantum and it's temperature.

Best regards,

Joy

[Joy Christian]

Hi John,

Elsewhere I have answered the issues you have raised. Any simulation
code by itself has no meaning without knowing what it is that is being
simulated, or demonstrated. In the case of my manifestly local model,
what is being simulated is the correlation between the points of a
parallelized 3-sphere. C_ab is just a statistical tool---a probability
density function---for calculating *joint* probabilities of simultaneous
detections of what is remotely observed by Alice and Bob, independently
of each other. The key to understand this are the pair of equations
(A33) and (A34) on the page 21 of http://arxiv.org/abs/1301.1653.

Equation (A34) is a special or limiting case of equation (A33),
when C_a, C_b, and C_ab all happen to be equal to +1 or -1.

Now, we can see from the right-hand-side of (A34) that when,
for example, Alice observes +1 result and Bob also observes +1
result, the product AB of their simultaneously observed results
is necessarily equal to +1. But from the left-hand-sides of (A33)
and (A34) we see that AB = +1 is equivalent to the condition
C_ab = +1. By similar reasoning applied to all four cases of
simultaneous observations made by Alice and Bob, we can see that
it is necessary and sufficient to just calculate the different
values of C_ab to determine what results Alice and Bob will be
observing, independently of each other. Thus, although the tool
C_ab involves both a and b as you note, it does not provide any
non-local exchange of information between Alice and Bob. In
other words, since C_ab is simply a tool representing the
geometrical constraints of the 3-sphere, we can use it to our
advantage without fear of any conceptual muddle. What saves
locality is the factorization of the observed results A and B,
as shown in the equation (A34) of the paper. This equation is
simply the famous locality condition of Bell, for deterministic
local models such as mine: http://arxiv.org/abs/1301.1653.

The above comments are essentially a repeat of what I explained
elsewhere. But since then Michel Fodje has written a program to
verify my model which does not use C_ab for the calculation of
either the probabilities or the correlation. He uses only C_a
and C_b to do the job. Here is the website from where you can
download his program: https://github.com/minkwe/epr-simple/

As for qubits or any other system requiring super-cooling to
violate Bell inequality, all that indicates is that the system
under consideration was not appropriate for exhibiting strong
correlations. You can crudely say temperature is the boundary,
but that is hardly the boundary that concerned either Einstein
or Bell. (see, for example, the quote from John Bell on my
blog: http://libertesphilosophica.info/blog/).

Best regards,

Joy

[ben...@hotmail.com]

On Monday, 4 November 2013 00:02:11 UTC, Joy Christian wrote:
> ...

> Michel Fodje has written a code for the EPR-Bohm correlation based
> on Chantal's simulation of my model. It can be downloaded from here:
> https://github.com/minkwe/epr-simple/.

> ...

Here is an extract from the readme file found on the above linked site:
λ = {e, p, s}, e ∈ [0..2π), p ∈ [0..π/4), s = {1/2, 1}
e' = e + 2πs
A(a,λ) = sign(-1ⁿ cos n(a − e)) if ½|cos n(a − e)|² > pᵏ, 0 otherwise
B(b,λ) = sign(-1ⁿ cos n(a − e')) if ½|cos n(a − e)|² > pᵏ, 0 otherwise
where n = 2s, k=π

The formula for B(b,λ) has the variable 'a' rather than 'b' on the r.h.s. Is
that simply a typo error?

[Joy Christian]

Hi Ben,

I hope it is just a typo.

Also, I prefer to write his threshold condition as

|cos n(a - e)| > \/2 p^(π/2).

This way of writing makes it clear that this is a condition
on the probability density function I discuss in footnote 1
on page 18 of my paper.

Best,

Joy

[mich...@gmail.com]

Hi Ben,
It is a typo in the description which has now been fixed. I've also changed the functional form to that suggested by Joy. If you want to inspect the source code, you can take a look at the epr.py file which is very readable. I can answer any questions you or anyone may have about what the code is doing. But anyone can also code up the equations in the description and verify that it works.

[FrediFizzx]

[A note for those that might be on a newsreader where the equations below
don't render correctly: try changing your encoding to Unicode UTF-8. Yeah,
its supposed to be ASCII plain text only for UseNet but what the heck it
seems to work.]

<mich...@gmail.com> wrote in message
news:cc7c6dbf-7a2f-42fd...@googlegroups.com...

Thanks Michel,

I was looking at the source code for epr.py and I am wondering how and where
does the 3-sphere geometry enter? I am not a programmer but I suspect numpy
has something to do with it.

Best,

Fred Diether

[mich...@gmail.com]

>
> Thanks Michel,
>
>
>
> I was looking at the source code for epr.py and I am wondering how and where
>
> does the 3-sphere geometry enter? I am not a programmer but I suspect numpy
>
> has something to do with it.
>
>
>
> Best,
>
>
>
> Fred Diether

Hi Fred,
The 3-sphere is not explicit in the program, although Joy can probably answer better how you can interpret it in terms of the 3-sphere. Originally, it wasn't explicitly written according to the 3-sphere geometry but after some discussion with Joy, and changing some of the equations we got it to the current form.

Numpy is just a math library for python. I may add a code walk-through document for those who are not programmers.

/Michel

[John Reed]

"Joy Christian" wrote in message

news:292211a7-b05b-48b1...@googlegroups.com...


Hi John,

The above comments are essentially a repeat of what I explained
elsewhere. But since then Michel Fodje has written a program to
verify my model which does not use C_ab for the calculation of
either the probabilities or the correlation. He uses only C_a
and C_b to do the job. Here is the website from where you can
download his program: https://github.com/minkwe/epr-simple/

Hi Joy,

I have looked at the code for this new simulation. If we lived in a
two dimensional world, it would mean something, but I don't see any
connection to the previous simulations or the experiments dealing
with Bell's theorem. There is no reference to Clifford algebra,
bivectors or a parallelized three sphere. It's all now just picking
random numbers and taking the cosine of their difference. What
is the meaning of that? The experiments are done in three dimensions.

Best regards,
John

[Joy Christian]

Hi John,

Michel has streamlined the notation in my paper to make his simulation
more comprehensible to someone who does not know, or wish to know, the
details of my physical model. It is simply a different implementation of
the original simulation of my model by Chantal. What Michel has done is
to take the C_a and C_b functions from my paper, streamline the notation,
and use the sin^2(p) function appearing in the integration discussed in
the footnote 1 of my paper to generate the correct statistics for the
correlation, without using the C_ab part of Chantal's simulation (which,
as you know, has been misinterpreted by various people). I suppose it all
boils down to what appeals to you. Many people in the computer science
community will appreciate Michel's simulation more than Chantal’s. I myself
see them as two complementing simulations of one and the same physics.

Best regards,

Joy

[mich...@gmail.com]

> Hi Joy,
>
>
>
> I have looked at the code for this new simulation. If we lived in a
>
> two dimensional world, it would mean something, but I don't see any
>
> connection to the previous simulations or the experiments dealing
>
> with Bell's theorem. There is no reference to Clifford algebra,
>
> bivectors or a parallelized three sphere. It's all now just picking
>
> random numbers and taking the cosine of their difference. What
>
> is the meaning of that? The experiments are done in three dimensions.
>
>
>
> Best regards,
>
> John

Hi John,
Thanks for looking at the code. The important thing to note is that every component of the real experiments is represented in the simulation. There is a source, there are particles, and there are detectors. The simulation lays out the behavior of each component and combines them in exactly the same way as in real experiments. But it is only still just a simulation, a model. The model can be interpreted geometrically but the important point is that it irrefutably violates the CHSH, reproduces the QM expectations and does it in completely local and realistic manner which was claimed to be impossible for any model to do, 1D, 2D or 3D.

Regards,
Michel.

[heine.r...@gmail.com]

On Thursday, November 7, 2013 11:00:51 PM UTC+1, mich...@gmail.com wrote:
[...]

> Hi John,
>
> Thanks for looking at the code. The important thing to note is that every component of the real experiments is represented in the simulation. There is a source, there are particles, and there are detectors. The simulation lays out the behavior of each component and combines them in exactly the same way as in real experiments. But it is only still just a simulation, a model. The model can be interpreted geometrically but the important point is that it irrefutably violates the CHSH, reproduces the QM expectations and does it in completely local and realistic manner which was claimed to be impossible for any model to do, 1D, 2D or 3D.
>
>
>
> Regards,
>
> Michel.

Yes, but your code achieves this by exploiting the detection loophole. It has been known at least since 1970 that Bell's theorem can be circumvented this way (*). However, the dectection loophole was decisively closed by a recent experiment by Christensen et al.

(*) Pearle, P. (1970) "Hidden-Variable Example Based upon Data Rejection,"

[Joy Christian]

In my view your objection to Michel's simulation is not justified,
and neither is your objection to Chantal's simulation of my model.

What you are missing is a very basic point about my model.
Unfortunately many people have been missing this point about my
model for many years. The point is this: EPR-Bohm correlations are
correlations among the points of a unit parallelized 3-sphere [or
the group SU(2)]. They are NOT correlations among the points of a
real line, as Bell and his followers have been assuming. I mention
this, because you will not understand my comments below without
understanding this basic point. You can find further discussion
about it on my blog: http://libertesphilosophica.info/blog/.

Now to the objections you have raised to Chantal's and Michel's
simulations of my local model: I have already addressed above your
misunderstanding of what C_ab stands for in Chantal's simulation.
Michel's simulation does not use the probability density function
C_ab used in Chantal's simulation, but instead uses the probability
density functions C_a and C_b directly, together with the constraint

|cos (x - e)| > 1/2 sin^2(t).

This constraint has nothing to do with the detection loophole as far
as my 3-sphere model is concerned. In the measurement results defined
by Michel, the initial or complete state lambda is a set {e, t}, where
e from [0.. 2pi) and t from [0 .. pi/2) are two random hidden variables
shared by both Alice and Bob, such that the above constraint holds for
all feely chosen detector angles x. In my model this constraint arises
from the geometry and topology of the 3-sphere. One can see this from
footnote 1 on pages 18 to 19 of my paper. The crucial point here is
that the initial state of the particle is defined by both e and t, not
just by e. More precisely, it is defined by the set {e, t}, *together*
with the above constraint. In other words, the distribution of the
particles is defined by the set {e, t}, *together* with the above
constraint. Therefore it has nothing to do with any loopholes, or the
efficiencies of the detectors. Every particle that emerges in the initial
state {e, t} ends up being detected by the detector setup at angle x,
with 100% efficiency, just like in Chantal's simulation, or in my
theoretical model.

In my 3-spherical view, Chantal's and Michel's simulations nicely
complement each other. Both of them reproduce the quantum mechanical
predictions exactly, but using very different strategies. Of course,
my analytical model stands on its own, without needing a simulation
for its validity.

Best regards,

Joy

[mich...@gmail.com]

> Yes, but your code achieves this by exploiting the detection loophole. It has been known at least since 1970 that Bell's theorem can be circumvented this way (*). However, the dectection loophole was decisively closed by a recent experiment by Christensen et al.

Thanks for mentioning the Christensen paper. To add to what Joy has already explained, I generated a table from my simulation, similar to their table 1. As you can see, my code achieves higher efficiency than they achieve.

Settings Sing.(A) Coinc. Sing.(B) Trials <AB>_sim <AB>_qm
a ,b 3595 3194 3585 4342 -0.910 -0.924
a ,b' 3689 2946 3649 4392 -0.388 -0.383
a',b 3525 3124 3531 4237 -0.924 -0.924
a',b' 3562 3162 3546 4266 -0.923 -0.924

If that paper has *decidedly* closed the loophole, then obviously my simulation cannot be said to "exploit" it.

[John Reed]

"Joy Christian" wrote in message

news:a619e913-b01f-4821...@googlegroups.com...

I don't understand how Michael can claim his simulation represents
real experiments. I wrote up Chantal's simulation in Mathematica
and it agrees with the output from her program. I have looked at the
Python code of Michael, and I understand what he's done, but it does
not represent the experiments and it is not the same as Chantal's
by any stretch of the imagination. Chantal's code represents the
detectors and particles in three dimensions. Michael's does everything
in two dimensions. That's more than just streamlining the code or
removing the nonlocal term. It's an entirely different geometric
setting and there's no comparison between the two. There's no
way you can compare Michael's simulation to the real experiments.

Best regards,
John

[heine.r...@gmail.com]

In the code, the particle is discarded/not detected based on this constraint, i.e., conditioned upon the detector setting. This is the very definition of the detection loophole.

> In the measurement results defined
>
> by Michel, the initial or complete state lambda is a set {e, t}, where
>
> e from [0.. 2pi) and t from [0 .. pi/2) are two random hidden variables
>
> shared by both Alice and Bob, such that the above constraint holds for
>
> all feely chosen detector angles x. In my model this constraint arises
>
> from the geometry and topology of the 3-sphere. One can see this from
>
> footnote 1 on pages 18 to 19 of my paper. The crucial point here is
>
> that the initial state of the particle is defined by both e and t, not
>
> just by e. More precisely, it is defined by the set {e, t}, *together*
>
> with the above constraint.

Well, if the initial state depends on the constraint, it depends on the detector settings, and then the whole thing is most certainly nonlocal.

>In other words, the distribution of the
>
> particles is defined by the set {e, t}, *together* with the above
>
> constraint. Therefore it has nothing to do with any loopholes, or the
>
> efficiencies of the detectors. Every particle that emerges in the initial
>
> state {e, t} ends up being detected by the detector setup at angle x,
>
> with 100% efficiency, just like in Chantal's simulation, or in my
>
> theoretical model.

This is certainly not true in Michel's code, where he gets a lot of single detections. Since all particles in the code are generated in pairs, that means that some particles go undetected.

[mich...@gmail.com]

If I write a simulation of malus law which simply takes two angles a and b and calculates Icos^2(a-b), I doubt you will criticize it as only 2D. So why a different standard here? Of course I could make it more complicated and generate vectors in 3D and then calculate angles between vectors, and in the end still use exactly the same equations. Is this really the only "criticism" you have of the simulation? Did you program the equations in Mathematica? Did you verify that the equations work as claimed?

[Joy Christian]

I disagree, John. Bell's argument has nothing to do with dimensionality,
and nor does Michel's simulation. Bell's claim is very simple. He said:
Given two measurement functions A(a, L) = +1 or -1 and B(b, L) = +1 or
-1, where a and b are any freely chosen experimental parameters (such as
the angles a and b in Michel's simulation) and L is any kind of functions
called "hidden variables", then the correlation between such numbers
A(a, L) and B(b, L) cannot exceed the strength of the linear correlation.
In particular, they cannot possibly produce cosine correlation (see, for
example, Bell's original paper, or any of his papers from his book). But
Michel's simulation (not to mention my analytical model and Chantal's
simulation) produces precisely the cosine correlation between such numbers
A(a, L) and B(b, L). Bell's is a pure and simple mathematical claim.
This claim is proven wrong by Michel's simulation by itself, let alone my
analytical model, or Chantal's simulation of it. Now I fully appreciate
your desire to see physics, dimensionality, Clifford algebra, etc. But
they have nothing whatsoever to do with Bell's mathematical argument.

Best,

Joy

[hei...@gmail.com]

Plug the data from your table into the CH-inequality (2) in their paper. You will find that the inequality is not violated, while it is violated with Christensen's data.

[Joy Christian]

On Saturday, November 9, 2013 3:09:41 PM UTC, heine.r...@gmail.com wrote:


> In the code, the particle is discarded/not detected based on this constraint, > i.e., conditioned upon the detector setting. This is the very definition of > the detection loophole.

This is true in the "flatland" of Bell and his followers, but not
true in my 3-sphere model of the physical reality. Let me repeat what
I wrote above: What you are missing is a very basic point about my model.

Unfortunately many people have been missing this point about my model
for many years. The point is this: EPR-Bohm correlations are correlations
among the points of a unit parallelized 3-sphere [or the group SU(2)].
They are NOT correlations among the points of a real line, as Bell and
his followers have been assuming. I mention this, because you will not
understand my comments below without understanding this basic point.

> Well, if the initial state depends on the constraint, it depends on the
> detector settings, and then the whole thing is most certainly nonlocal.

No, the initial state does not *depend* on the constraint. The initial
sate {e, t} is what it is. The constraint arises as a consequence of
the geometry and topology of the 3-sphere. We cannot arbitrarily
declare something "non-local" simply because it does not fit into our
preconceptions. This is why Bell formulated the notion of non-locality
in a mathematically very precise terms. I will not repeat his formulation
here, because it can be found in most of his as well as my papers on the
subject. The important thing is that not only my analytical model, but
also Michel's and Chantal's simulations are manifestly local in precisely
the sense defined by both Einstein and Bell.

> This is certainly not true in Michel's code, where he gets a lot of single
> detections. Since all particles in the code are generated in pairs, that
> means that some particles go undetected.

It depends on what you mean by detection. From the perspective of my
model the detection is predetermined by the state {e, t}, not just by e.
The entire perspective thus changes, as I noted in my previous post.

[Joy Christian]

On Saturday, November 9, 2013 6:19:29 PM UTC, hei...@gmail.com wrote:

>
> Plug the data from your table into the CH-inequality (2) in their paper. You will find that the inequality is not violated, while it is violated with Christensen's data.

The CH-inequality is violated by my analytical model and in Chantal's
simulation---see eqs. A43 and A44 of http://arxiv.org/abs/1301.1653.

The CH-inequality is violated in Michel's simulation as well, provided
the hidden variable (or the initial state) is taken as the set {e, t}
as I explained above, and not simply as e. If you take only e as the
initial state neglecting the 3-sphere topology, then CH-inequality may
or may not be violated in Michel's simulation (I hope he checks this).

[mich...@gmail.com]

> Plug the data from your table into the CH-inequality (2) in their paper. You will find that the inequality is not violated, while it is violated with Christensen's data.

You can't compare them like that.
1) The particles in the simulation for the data presented are electrons, not photons. You will have to change the spin parameter from 1/2 to 1 to simulate photons (and the results will match QM without any other change).
2) The simulation is of "maximally entangled" particles. To simulate non-maximally entangled particles, you will have to modify the code for the source.
3) The a,a',b,b' angles in my table correspond to the usual Bell-test angles 0, 22.5, 45 and 67.5 while they use the angles (-3.8, 25.2, -25.2 and -3.8).

Will you be convinced if I do all of the above and violate the CH inequality??

Let me ask you another question which concerns the CH inequality (and all other Bell inequalities):

Do you think the expression f(x,y) + f(x,z) - f(y,z) <= S is valid, if the domain of all three functions is different.

[John Reed]

wrote in message
news:c28c4e7c-3fd5-44fd...@googlegroups.com...

Sorry for the confusion. I thought you were trying to simulate an actual
experiment, for
example the Aspect experiment. The first line of your explanation says:
"A Simple event-by-event simulation of the EPR experiment". Those
experiments
were all 3D.

I programmed Chantal's program up in Mathematica and I'm able to
get identical results to hers. I have not programmed your version up
yet, but it wouldn't be difficult to do. I haven't done that yet since I
wasn't sure of its relation to the previous discussion which seemed
to center around the 3 sphere, quaternions and bivectors. I do have a
Mathematica program that uses bivectors to do all the calculations but
so far that has not matched Chantel's results.

Best regards,
John

[Michel Fodje]

> Sorry for the confusion. I thought you were trying to simulate an actual
>
> experiment, for
>
> example the Aspect experiment. The first line of your explanation says:
>
> "A Simple event-by-event simulation of the EPR experiment". Those
>
> experiments
>
> were all 3D.

As has been explained to you already, it *is* a simulation of the EPR experiment, just as Malus law is not a 2D law. Just because you did not see bivectors and 3-spheres does not change that.

I thought you had a legitimate criticism that the simulation does not reproduce the strong QM correlation. But you are not even saying that. This 2D vs 3D stuff is just a red-herring in my opinion.

Regards,
Michel.

[heine.r...@gmail.com]

On Saturday, November 9, 2013 11:23:36 PM UTC+1, Michel Fodje wrote:
> > Plug the data from your table into the CH-inequality (2) in their paper. You will find that the inequality is not violated, while it is violated with Christensen's data.
>
>
>
> You can't compare them like that.
>
> 1) The particles in the simulation for the data presented are electrons, not photons. You will have to change the spin parameter from 1/2 to 1 to simulate photons (and the results will match QM without any other change).
>
> 2) The simulation is of "maximally entangled" particles. To simulate non-maximally entangled particles, you will have to modify the code for the source.
>
> 3) The a,a',b,b' angles in my table correspond to the usual Bell-test angles 0, 22.5, 45 and 67.5 while they use the angles (-3.8, 25.2, -25.2 and -3.8).
>
>
>
> Will you be convinced if I do all of the above and violate the CH inequality??

By all means, make an attempt. But you will find that none of the three changes you suggest will enable you to beat the CH-inequality.

[Michel Fodje]

Here is what I asked you:
* Will you be convinced if I do all of the above and violate the CH inequality??

* Let me ask you another question which concerns the CH inequality (and all other Bell inequalities): Do you think the expression f(x,y) + f(x,z) - f(y,z) <= S is valid, if the domain of all three functions is different.

It didn't escape my attention that you answered none of those questions? Why should I bother to do all those things if you'll just turn around and nitpick on some else.

[Joy Christian]

This exercise would be largely academic. For the measurement functions
A(a; e, t) and B(b; e, t) defined by Michel, the probabilities of observing
the outcomes +1 and -1 are exactly 1/2, with 100% detector efficiency. This
is because the state of the particle is defined by the set {e, t}, not just
by e. And every particle that emerges in a state {e, t } necessarily gets
detected by the detector. Moreover, the probabilities of joint observation
of the results A (a; e, t) and B(b; e, t) is exactly those predicted by
quantum mechanics. Therefore the CH-inequality is necessarily violated in
Michel's simulation. Any analysis based on just e is simply inconsistent
with how the functions A(a; e, t) and B(b; e, t) are defined by Michel.

[ben...@hotmail.com]

On Sunday, 10 November 2013 00:05:54 UTC, John Reed wrote:
> ...

> I programmed Chantal's program up in Mathematica and I'm able to
> get identical results to hers. I have not programmed your version up
> yet, but it wouldn't be difficult to do. I haven't done that yet since I
> wasn't sure of its relation to the previous discussion which seemed
> to center around the 3 sphere, quaternions and bivectors. I do have a
> Mathematica program that uses bivectors to do all the calculations but
> so far that has not matched Chantel's results.
> Best regards,
> John

Hi John

Will you clarify, please...
In the first sentence of your paragraph you say you have obtained identical
results to Chantal. I think that you made public your Mathematica code
obtaining Chantal's results so that sentence should be accurate. So what does
your final sentence mean? I.e what results of Chantal have you not been able to
replicate yet?

Best wishes

Ben

[heine.r...@gmail.com]

See this paper for a model similar to yours:

http://arxiv.org/pdf/quant-ph/9905018

It should answer all your questions.

[Michel Fodje]

It doesn't. And neither have you, despite the questions being very straight forward. Why the resistance?

[Joy Christian]

Similar is not the same. See my post above. In Michel's model the initial
state of the emitted particles is defined by the pair (e, t), not just by
e, where e and t are related by the geometrical constraint

|cos (x - e)| > 1/2 sin^2(t) for all x.

Therefore the probabilities of observation are exactly 1/2, with 100%
detector efficiency at both stations. The issues of efficiency, sampling
bias, or detection loophole does not even arise, let alone exploited as
in the paper you link. The CH-inequality is thus necessarily violated in

[John Reed]

wrote in message
news:f8596fce-9087-4f45...@googlegroups.com...

Hi Ben,

I'm trying to simulate the Aspect experiments using bivectors, and until
yesterday
I wasn't able to get anything but the usual straight line plots. However,
yesterday I tried combining both Alice and Bob's observations with a
bivector
product. The product bivector is very interesting, no longer a straight
line,
but looks like the curve that comes out of the Aspect experiments. I
need to do more work with this before I can say it means something.

Best regards,
John

[heine.r...@gmail.com]

On Monday, November 11, 2013 5:58:11 PM UTC+1, Michel Fodje wrote:
> It doesn't. And neither have you, despite the questions being very straight forward. Why the resistance?

That paper I linked to, by Gisin and Gisin, was originally published in 1999 in Physics Letters A. It should at least make you realize that you are not the first person to have written a local hidden variable model that reproduces the quantum correlations. Of course they never intended their model to be taken seriously as a real model of reality, but rather to give an example of how simple such a model can be if we introduce some detection inefficiency.

Now to your questions: I thought I answerd the first one, but anyway. Yes, I would be convinced. Alternatively, I would also be convinced if you rewrote the code so that detector efficiency was 100%, as that was achieved in an experiment by Rowe et al. [1] using ions instead of photons.

Your second question went unanswered because without further qualifications, it makes no sense to me. But I can add that as a general principle, at the end of the day the domain of any physical theory must be the space of observable experimental outcomes, for example binary clicks in a detector.

[1] http://deepblue.lib.umich.edu/bitstream/handle/2027.42/62731/409791a0.pdf?sequence=1

[Michel Fodje]

The paper says 88% you say 100%. My simulation has 96%. Go figure.

[Michel Fodje]

> That paper I linked to, by Gisin and Gisin, was originally published in 1999 in Physics Letters A. It should at least make you realize that you are not the first person ...

I don't recall that I claimed my simulation was the first to reproduce the correlations. Maybe that's what you assumed.

> Your second question went unanswered because without further qualifications, it makes no sense to me. But I can add that as a general principle, at the end of the day the domain of any physical theory must be the space of observable experimental outcomes, for example binary clicks in a detector.

If the domain of a physical theory *must be* observable outcomes, as you say, why then are you so hung up with non-detections? If the model reproduces observable results, why do you care about unobserved particles? QM says nothing about unobserved particles, experimenters know nothing about particles they did not observe yet you expect my simulation to account for both observed and unobserved. Isn't that a double standard?

However, I wasn't talking about the domain of a physical theory but rather the domain of a function -- the set of values over which the function applies. Let me answer the question and tell you why it is important.

The expression:

f(x,y) + f(y,z) - f(x,z) < S

Is ONLY valid if the domain of f(x,y), f(y,z), f(x,z) are exactly the same. For this reason, ALL Bell inequalities are invalid *when* applied to the EPR experiment and QM in which each term is obtained from a different set of particles.