Joy Christian's Work on Bell's Inequality

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Daryl McCullough

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Dec 22, 2011, 8:32:00 PM12/22/11
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Is there some kind of consensus about the correctness of
Joy Christian's work disproving Bell's Theorem?
(The most succinct paper by Christian on the topic
is here: http://arxiv.org/abs/1103.1879)

Christian's argument does not make a lot of sense to me.
It would be nice to have someone either explain what I'm
missing, or confirm my skepticism of his argument.

--
Daryl McCullough
Ithaca, NY

a student

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Dec 24, 2011, 12:11:53 PM12/24/11
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On Dec 23, 12:32 pm, Daryl McCullough <stevendaryl3...@yahoo.com>
wrote:
> Is there some kind of consensus about the correctness of
> Joy Christian's work disproving Bell's Theorem?
> (The most succinct paper by Christian on the topic
> is here:http://arxiv.org/abs/1103.1879)

There is certainly a consensus of some sort, in the fact that
while Christian has put a number of papers on the arXiv
regarding his "disproof", he has only been able to publish
this work in "a forthcoming book sponsored by fqxi". No
peer reviewed journal has accepted it, AFAIK.

> Christian's argument does not make a lot of sense to me.
> It would be nice to have someone either explain what I'm
> missing, or confirm my skepticism of his argument.

Bell's theorem is about necessary conditions for the
measured outcomes, in a set of joint experiments, to have
predetermined values - under the assumption that the
outcome for one part of the joint experiment cannot affect
the outcome for another part (eg, because they are
carried out in spacelike separated regions).

Christian's model of the singlet state does not assign
predetermined values to the measured outcomes for
spin in various directions (i.e, values of +1 or -1 for each
direction of interest). Hence his model is simply
not relevant to Bell's theorem. Is his model of interest?
No refereed journal seems to think so. In fact, his
model is, algebraically, very similar to the standard
quantum model.

For an excellent and amusing discussion, containing
correspondence with Joy Christian himself, see
http://www.science20.com/alpha_meme/quantum_crackpot_randi_challenge_help_perimeter_physicist_joy_christian_collect_nobel_prize-79614
You can also search this newsgroup for earlier
discussions.

Paul Colby

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Dec 24, 2011, 12:12:52 PM12/24/11
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One of the things I've noticed in reading famous seminal papers
is a remarkable clarity, simplicity and precision in which new ideas
were put forward. The paper linked above exhibits none of these
qualities.

I probably have just as much trouble interpreting the development
as yourself so I can't be counted as one who follows or understands
the paper. However, Equation 4 introduces an algebra with a stochastic
defining relation. This may not be what Bell had in mind as a realistic
local model.

Regards
Paul C.

ben6993

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Dec 24, 2011, 3:37:23 PM12/24/11
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On Dec 23, 1:32 am, Daryl McCullough <stevendaryl3...@yahoo.com>
wrote:
May I just add a point before I feel I cannot intrude as it has become
too complicated for me as a non-physicist. I understand that the
criteria you will be discussing need to be treated rigorously but I will
soon get lost trying to follow Bell's criteria wrt hidden variables.

Say Edward in a lab prepares an electron in a random direction (he knows
that direction and makes a note of it for his private records) and
passes the electron to Fred, nearby, who does not know the direction of
preparation.

Fred's task is to try to find out if he really believes Edward does know
the direction of the electron or if Edward has been pretending to know
and has just passed Fred any old electron off the bench.

To provide statistical information, Edward passes Fred many such
electrons all in random directions, all directions logged in Edward's
private notes.

When Fred makes tests of direction of spin, I assume he will find that
there is a 50/50 change of spin 1 being found in any direction he
chooses. If Edward had passed Fred any old electrons off the bench,
they may have been near a magnetic field which had caused them all to
line up in the same direction. This would become evident to Fred who
would eventually find a preferred direction in his tests.

Returning to the electrons with random directions, would not Fred be
bemused that he found on aggregate that the electrons had random spin
directions, yet Edward claimed to know those directions? Wouldn't Fred
disbelieve Edward and say that what he was doing is impossible? There
can be no hidden variables indicating the spin directions. His 50/50
results proved that to be the case?

So, to act as a proof, every other test is now performed by Edward who
consults his log book, picks the correct test setting and makes a
measurment which always gets the spin measurement correct.

If this experiment can be conducted, and I don't see why not, doesn't it
prove that Edward can have a log book equivalent to the hidden variable?
The electron itself needs no log book as it knows its own spin.

I haven't mentioned entangled pairs yet as they seem to me to be almost
an irrelevancy to the question of hidden variables. Edward could
prepare alternate electrons with exactly opposite spin directions and
pass one to Fred and one to Geoff. Fred would still find 50/50 and
Goeff would likewise find 50/50. Not only would Edward's private log
book enable him to know the outcome for any particlular electron (as
long as Edward could set up the apparatus himself in the appropriate
direction), Edward would know and could prove, if required, that pairs
were oppositely aligned.

Leonard Susskind in his online entanglement course says that if you
prepare an electron in spin state 1 and then immediately re-test it in
the same alignment then it will still be in spin state 1 with 100%
probability. So I do not see why Edward cannot do the tests above.

Joy Christian

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Dec 25, 2011, 4:18:08 AM12/25/11
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On Dec 24, 5:11=A0pm, a student <of_1001_nig...@hotmail.com> wrote:
>
> There is certainly a consensus of some sort, in the fact that
> while Christian has put a number of papers on the arXiv
> regarding his "disproof", he has only been able to publish
> this work in "a forthcoming book sponsored by fqxi". =A0No
> peer reviewed journal has accepted it, AFAIK.
>

You seem to have inside information about this.
I sure would like to know how you came to know
what I have or have not been able to do. I would
also like to know what the word =93only=94 signifies in
your assertion. I suppose it means that Perelman=92s
proof of Poincare conjecture is no good because it
is not even published in =93a forthcoming book
sponsored by fqxi.=94 It is =93only=94 published on the arXiv.

>
> Christian's model of the singlet state does not assign
> predetermined =A0values to the measured outcomes for
> spin in various directions (i.e, values of +1 or -1 for each
> direction of interest).

False. One only has to glance at equations (1) and (2)
of the paper linked above to see that this is a blatantly
false assertion.

>
> Is his model of interest?
> No refereed journal seems to think so.
>

Again, I would like to know your source of information.
Could it be the scholarly blog you have linked? I, for one, do
not know what the refereed journals think about my model.

>
> For an excellent and amusing discussion, containing
> correspondence with Joy Christian himself, see...
>

And you are of course absolutely certain that what is
reported on that scholarly blog is an accurate and
honest claim =96 that the alleged correspondence did
indeed take place. Again, you seem to have some
inside information about the alleged correspondence.

Joy Christian

a student

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Dec 25, 2011, 11:22:47 AM12/25/11
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On Dec 25, 7:37 am, ben6993 <ben6...@hotmail.com> wrote:

[snip]

> I haven't mentioned entangled pairs yet as they seem to me to be almost
> an irrelevancy to the question of hidden variables. Edward could
> prepare alternate electrons with exactly opposite spin directions and
> pass one to Fred and one to Geoff. Fred would still find 50/50 and
> Goeff would likewise find 50/50. Not only would Edward's private log
> book enable him to know the outcome for any particlular electron (as
> long as Edward could set up the apparatus himself in the appropriate
> direction), Edward would know and could prove, if required, that pairs
> were oppositely aligned.

It is indeed trivial to model anti-aligned statistics. It is also
trivial to
model the spin properties of a single electron. However, there is no
deterministic local model of the singlet state, of the type you
suggest.
This is what is so amazing about Bell's theorem, and it is worth
actually reading a proof so that you can appreciate it - there are
plenty of these on the web, including Wikipedia.

Here's a very simple one, making stronger assumptions than are
necessary, to give you the flavour.. Note that it does not actually
use the anti-alignment property anywhere, and hence the example
you give is not actually relevant.

Suppose that Fred can measure the spin of his electron in
either direction f or f', and Geoff can measure in direction g or
g'. Suppose that the outcomes beforehand can be predicted,
and are denoted by F, F', G, G' respectively, where these
take the value +1 if spin is up in that direction, and -1 if spin
is down in that direction.

For each pair of electrons, consider the quantity formed by
the pre-existing values, defined by
B = FG + FG' + F'G - F'G'.
You can easily check yourself that this quantity is equal
to +2 or -2 for each pair. This checking is the only
"difficult" part of the proof. One way to check is to write
B = F(G+G') + F'(G-G').
Note that one of the expressions in brackets must
vanish, and the other equal +/-2, depending on whether
G=G' or G=-G'. But the nonvanishing expression is
multiplied by either F or F', i.e., by +1 or -1. QED.

So, we know that
-2 <= B <= 2.
Now take the average over many pairs. The average
of something less than 2 cannot be greater than 2.
Therefore
-2 <= <B> <= 2.
But from the definition of B, this is the same as
-2 <= <FG> + <FG'> + <F'G> - <F'G'> <= 2.

This is a "Bell inequality" (known as the Clauser-
Horne-Shimony-Holt Bell inequality, after the guys
who found it). Note that each of the individual
expectation values, <FG> etc, can be measured.

Study the above carefully, as it is not that
difficult to follow the logic.

Now, the trick is not to consider the directions f and
g, and f' and g', to be aligned or anti-aligned, as in
your example. The above inequality won't be violated
if you do.

The trick is instead to consider directions in a plane,
with f, g, f' and g' at angles 0, 22.5, 45, and 67.5
degrees, with respect to some fixed direction in the
plane. If you work out the middle part of the
above inequality, for the singlet state and these
directions, using the formula
<FG> = - f.g,
you will easily find that
<B> = 2 sqrt{2} ~ 2.828.
Note that this is much larger than the right hand
side of the inequality, by a whopping 40% !

a student

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Dec 25, 2011, 12:22:54 PM12/25/11
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On Dec 25, 7:37 am, ben6993 <ben6...@hotmail.com> wrote:

Oops - a correction to my previous response to Ben:

I gave inappropriate angles (relevant to polarisation
rather than spin) in the example of a violation.

Noting <FG> = - f.g for the singlet state, the Bell
quantity is
<B> = -f.g - f.g' - f'.g + f'.g'.
Now choose the directions to lie in a plane with, eg,
f', g, f and g' at angles 0, 45, 90 and 135 degrees
from some fixed direction. Then one obtains
<B> = - 2 sqrt{2} ~ - 2.828,
which is about 40% less than the lower bound
of 2 that any local deterministic model must
satisfy.

FrediFizzx

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Dec 26, 2011, 3:55:06 AM12/26/11
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"Daryl McCullough" <stevend...@yahoo.com> wrote in message
news:20050468.72.1324306789748.JavaMail.geo-discussion-forums@vbbhx10...
> Is there some kind of consensus about the correctness of
> Joy Christian's work disproving Bell's Theorem?
> (The most succinct paper by Christian on the topic
> is here: http://arxiv.org/abs/1103.1879)

A comprehensive explanation of that paper is here,
http://arxiv.org/abs/1106.0748

> Christian's argument does not make a lot of sense to me.
> It would be nice to have someone either explain what I'm
> missing, or confirm my skepticism of his argument.

From our private email discussion, you are missing how the 3-sphere
topology works. For those that are interested in learning more about
Joy Christian's model that produces quantum correlations the same as QM
does from classical spherical topology, there have been very
comprehensive discussions on the FQXi blogs which are open to all that
might want to ask a particular question. Or you can ask it here on SPR
if you wish. But I would recommend reading through some of the blog
discussions first.

http://www.fqxi.org/community/forum/topic/995
"On the Origins of Quantum Correlations"
http://www.fqxi.org/community/forum/topic/975
"Quantum Music from a Classical Sphere"

The last discussion culminated in Joy Christian's latest arXiv paper
clearly refuting the arguments against his model in those discussions.
http://arxiv.org/abs/1110.5876

For those that would like to know more about the 3-sphere topology that
Joy Christian uses in his model please watch this video lecture about
Hopf Fibration by Niles Johnson of the University of Georgia.
http://www.youtube.com/watch?v=QXDQsmL-8Us&feature=player_detailpage

Also highly recommended is Joy Christian's paper,
"What Really Sets the Upper Bound on Quantum Correlations?"
http://arxiv.org/abs/1101.1958

Best,

Fred Diether

ben6993

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Dec 26, 2011, 4:01:31 PM12/26/11
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That seems very clearly explained and I may get further this time
before getting lost. So thank you very much. I will work at it.

First I need to think about the overall framework. I need to concede I
was wrong about the difference between electrons prepared by Edward and
singlet electrons. Edward can only prepare a poor man's electron
direction. Take a match (ie electron) using its head as the pointer.
Let it have a random direction in 3D. Take its projection onto the up/
down direction and that gives the laboratory reading of 'up' or 'down'.
But the match itself is not pointing exactly in that up/down direction.
This means that two electrons prepared by Edward as an up and down pair
will not necessarily always give opposite results. They will only
certainly give opposite results when tested up/down. A singlet pair
will produce opposite results in whatever direction they are tested. Ie
their directions are rich in that they are exactly opposite to one
another in a rich sense not a poor one. As if their rich directions were
not quantised, yet we know the electron direction is quantised.

I think that last sentence lets me accept that a particlar electron's
rich direction cannot be described in the laboratory 3D. The laboratory
3D is the world of real measurement and that only allows poor mens'
direction measurements. There is no single observation possible on a
single electron to determine a rich direction. To determine rich
directions requires many measurements on many electrons. And the outcome
is a correlation showing the exact oppositeness of the singlet
directions over all directions tested.

Next is where it gets confusing for me to follow Bell's criteria. In my
first post I said that Edward kept a secret log of data for
individually-produced electrons. However, noone can make a similar log
of data for electron singlets. I also said that Edward's electron
needed no log as it always knew which way its own direction. I think
that the natural starting point should be an assumption that the singlet
electrons also know their own directions. Is there as assumption being
made that because a log book of data cannot be made, then the electron
itself cannot know its own direction? Hence the use of superpositional
states? I can see that our observer knowledge of the singlet
electrons's states are superposed, but I do not see why the electron's
physical states are required to be superposed. It seems more simple to
assume that they are created with opposite rich directions (that we
cannot measure) and keep those directions until they next experience a
measurement event eg interaction with a photon.

Just mentioning two further points: Joy Christian appears to be saying
that Euclidean space is richer than normally thought. I am not expert
enough to agree or disagree, but I can accept that he may be correct. (A
poor man's non-disagreement rather than a rich man's agreement in the
above terminology.) I note that the definition of space that he uses
requires more than 3D plus time. 7D plus time, I think. As an aside,
my own view is that the electron has 12D (4D in the lab; 4D in spin
space 1; and, 4D in spin space 2) and that it has enough structure for
it to maintain its rich direction that we can test, for correlation
only, in the laboratory. The electron does not need to restrict itself
to a 4D laboratory definition of its direction when it has a 12D
structure.

A further complication is that I should not too easily concede that no
log book is possible for singlet electrons. Dr Raedt et al provided
software online to run simulated Bell's or Aspect's experiments. I did
this and have a file of output data which is of the cosine form for
correlated data rather than the sawtooth form that uncorrelated data. I
have these data in a file and yet somehow still don't believe it was
possible. Or it just hasn't sunk in yet. Or I just don't understand it
enough yet.

Daryl McCullough

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Dec 26, 2011, 4:01:53 PM12/26/11
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On Monday, December 26, 2011 3:55:06 AM UTC-5, FrediFizzx wrote:
> "Daryl McCullough" <stevend...@yahoo.com> wrote

> > Christian's argument does not make a lot of sense to me.
> > It would be nice to have someone either explain what I'm
> > missing, or confirm my skepticism of his argument.
>
> From our private email discussion, you are missing how the 3-sphere
> topology works.

I don't see how it is even relevant to my complaints about Christian's
work. I haven't made any claims one way or the other about the topology
of the 3-sphere.

The scenario that seems to me to contradict Christian's model is the
following: Alice and Bob engage in 4 rounds of an EPR-type experiment
for spin-1/2 particles. They produce 4 twin-pairs, and each measures
the spin of one of the two particles along two fixed axes a for Alice,
and b for Bob. Each records his or her result as +1 if he or she
measured spin-up, and -1 if he or she measured spin-down. In four
rounds, the sequence of pairs (Alice's result, Bob's result)
is the following: (+1,+1), (+1,-1), (-1,+1), (-1,-1).

For the purposes of exploring local hidden variables theories,
we assume that Alice's result in each round is determined by
the value of some hidden variable mu during that round, together with
the choice a of her axis. We assume that Bob's result in each round
is determined by mu and his choice b of axis. Since a and b are
held fixed during all four rounds, then the only relevant thing
that changes from one round to the next is the value of mu.

In Christian's model, mu can take on two different values,
which he calls +I and -I, where I is the unit tri-vector
e_x ^ e_y ^ e_z.

My argument against Christian's model is pretty simple,
and to me seems airtight:

(1) Since a and b are fixed for the four rounds, and mu can only
take on two possible values, then there are only two possible
values for the triple (a,b,mu) during the four rounds.
(2) But the results for the four rounds are all different.
(3) Therefore, the results were not determined by a, b, and mu.

That seems a trivially correct argument. I don't see how the
complexities of the topology of the 3-sphere is at all relevant
to the correctness or incorrectness of my 3-step argument against
Christian's model.

Possibly Christian means something different by the phrase
"Alice's result is determined by a and mu" than what I mean by it.
Or maybe he means something different by the phrase "Alice's
result" than what I mean by it. But with the ordinary meanings
of those phrases, Christian's model seems to be falsified by
the hypothetical 4-rounds of EPR experiments.

Joy Christian

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Dec 28, 2011, 2:55:33 PM12/28/11
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On Dec 26, 9:01 pm, Daryl McCullough <stevendaryl3...@yahoo.com>
wrote:
>
> I don't see how it is even relevant to my complaints about Christian's
> work. I haven't made any claims one way or the other about the topology
> of the 3-sphere.
>

Oh, but you most certain have made claims about topology!

As I have tried to explain to you over and over and over and over
again, my model is NOT a contextual hidden variable model. It is a
non-contextual model in which correlations result entirely because
of the non-trivial topology of the physical space. The physical
space in my model is taken to be a parallelized 3-sphere, S^3, not
a non-compact space R^3. You, on the other hand, have implicitly
assumed the physical space to be R^3 without even realizing it.
Therefore your argument has nothing whatsoever to do with my
model. Your implicit assumption of R^3 is betrayed in you casual
reference to my hidden variable mu as "some hidden variable mu."
mu is not some garden variety hidden variable of a contextual kind.
It specifies the orientation of the physical space S^3 within which
the measurement events are taking place. As such these events are
subject to the non-trivial twist in the Hopf fibration of the 3-
sphere.
Consequently, as I have explained in great detail in this paper:
http://arxiv.org/abs/1106.0748 , the four different outcomes, (+1,+1),
(+1,-1), (-1,+1), and (-1,-1), necessarily and deterministically occur
within my model even for the fixed detector directions a and b (but of
course with different probabilites depending on the angle between
a and b). The role played by the topology of the 3-sphere in this
process is further elucidated in detail in Section III of this paper:
http://arxiv.org/abs/1101.1958 .

If, however, one chooses to ignore the premises of my model (as you
have been doing) by replacing it with an old fashioned contextual
hidden variable model set up within a non-compact flat space with a
trivial topology (and that is indeed what you are doing whether you
realize it or not), then there is no topological reason to expect all
four
variations in the measurement outcomes to deterministically come
about for fixed detector directions and a garden variety mu.

Joy Christian

ben6993

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Dec 30, 2011, 3:57:00 AM12/30/11
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On Dec 26, 9:01 pm, Daryl McCullough <stevendaryl3...@yahoo.com>
wrote:
That seems so easy an example that it is almost within grasp. Almost,
but not quite as the trivector is related to tensors and that will
slow down my understanding.

I watched the lecture last night on Hopf Fibration by Niles Johnson:
http://www.youtube.com/watch?v=QXDQsmL-8Us&feature=player_detailpage
and note that the sort of effect in Euclidean space that is being
referred to by the mu variable is, by analogy with reduced dimensions,
like turning a thick elastic band inside out. You can hold the band
with one face in or that face out. Unlike a Moibus strip, which only
has one orientation. This also may explain why this algebra requires
more than 3D to to describe Euclidean space.

The +I value must inhabit spin 1 and the -I value inhabit spin 0, cf
opposite sides of the elastic band. Presumably, this is a suficient
specification always to ensure that opposites spins arise from any
measurement of a +I and -I pairing.

But this means that the +I value is not a pointer in one direction in
space. Not even in a 'rich' direction using my previous terminology
of a non-quantum exact direction. It seems to be somewhat of a fiddle
in the sense that it is a 'pointer indicating spin 1'. So between
then +I and -I quarantee that the two particles have opposite spins.

I am lost wrt tensors but do they (and the trivector) not contain an
element of curl or twist? ie is not the +I and -I indicative of two
opposite twists? Does that not give the required element of
permanently opposite spin no matter what the laboratory test
direction?

If the mu had been a rich or exact non-quantum direction then one
would need to use a different rich direction for mu in every round of
testing by Alice and Bob, as each new particle pairing will be
opposite partners in a random direction. But mu does not seem to be a
pointer in a particlular direction, but a pointer direct to a spin
state. As I said, that seems somewhat of a fiddle by pointing
straight to the answer. But it is not a fiddle if it is supported by
the maths and I cannot comment on that except that I do not disbelieve
it, an will work at improving my geometric algebra.

Anon E. Mouse

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Dec 30, 2011, 3:57:02 AM12/30/11
to

> My argument against Christian's model is pretty simple,
> and to me seems airtight:
>

Your model is very simple. Impossibly so, real spin measures are
fractions of all possible data captures, or a filtered subset thereof,
not 100% captures of integer spins.

Similarly you limit the value of mu, a hypothetical measure of
entanglement, being a unit tri-vector which could take on any complex
value between 1 and -1, in a restricted 2d representation of the
actual 3 space to just two values, represented by the extreme limits.

The data scenario you project is indeed impossible, as far as I can
tell. However, I don't see this as valid criticism of Christian or
Bell.

I am struggling with understanding Christian's work however, would it
be fair, correct to say that the unit tri-vector mu being a 3d
spherical representation of a hypothetical entanglement, when
projected onto a 2d space can yield either form of Bells inequality
due to the insufficiency of 2d projection of 3d forms? If so, I've got
it. If not, I fail.

Best wishes to all this season,

AAG

Daryl McCullough

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Dec 30, 2011, 3:57:03 AM12/30/11
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On Wednesday, December 28, 2011 2:55:33 PM UTC-5, Joy Christian wrote:

> Oh, but you most certain have made claims about topology!

No, what I've said has nothing to do with topology.

Locally, all 3D manifolds look like neighborhoods of R^3; the
distinction between R^3 and S^3 has to do with the connectivity
of neighborhoods. In the particular case of S^3, it is the topology
that results from taking two 3D balls and identifying the two
boundaries (which are 2-spheres). Having the topology of S^3
changes *global* properties of space--for example, it is compact,
whereas R^3 is not--but in a small enough region, it doesn't
change any properties that are locally measurable.

Assuming that an EPR type experiment takes place in a region
that is small compared with the size of the universe, the topology
would not make a difference to results.

> The physical space in my model is taken to be a parallelized 3-sphere,
> S^3, not a non-compact space R^3. You, on the other hand, have
> implicitly assumed the physical space to be R^3 without even realizing
> it.

No, I haven't said anything about topology, and I don't think it
is relevant.

In Bell's derivation of his inequality, the assumptions are
made that there is a pair of detectors a certain distance apart,
that each detector has a setting--an orientation that can be
described by a direction in 3-space--and that the results of a
detection event can have two possible values: spin-up or spin-down
(in the case of spin-1/2 twin-pair EPR experiments). The topology
of space is not relevant, except for the assumption that the two
detection events have a spacelike separation.

> Therefore your argument has nothing whatsoever to do with my
> model. Your implicit assumption of R^3 is betrayed in you casual
> reference to my hidden variable mu as "some hidden variable mu."
> mu is not some garden variety hidden variable of a contextual kind.
> It specifies the orientation of the physical space S^3 within which
> the measurement events are taking place. As such these events are
> subject to the non-trivial twist in the Hopf fibration of the 3-
> sphere.

The first part of that is false--I did not assume anything about
topology. The second part seems irrelevant. As I said, in a small
enough region, topology by itself would not play a role in an
EPR-type experiment. What would play a role is curvature, or
more generally, non-trivial parallel transport. Spin-up in the
+z direction can be changed to spin-up in some other direction
by parallel transport over a significant distance. But neither
topological nor curvature effects would be a source of variability
in an EPR-type experiment; they would effect every round of
the experiment in the same way. Such an effect could not
produce probabilistic behavior.

> Consequently, as I have explained in great detail in this paper:
> http://arxiv.org/abs/1106.0748 , the four different outcomes, (+1,+1),
> (+1,-1), (-1,+1), and (-1,-1), necessarily and deterministically occur
> within my model even for the fixed detector directions a and b (but of
> course with different probabilites depending on the angle between
> a and b).

That paper leaves the most important questions about your model
unanswered. In particular, the interpretation of equation (46) as
a *probabilistic* prediction is not supported by anything leading
up to it.

> If, however, one chooses to ignore the premises of my model (as you
> have been doing) by replacing it with an old fashioned contextual
> hidden variable model set up within a non-compact flat space with a
> trivial topology (and that is indeed what you are doing whether you
> realize it or not),

You haven't shown how topology is even relevant to Bell's theorem.
As I said, topology comes into play when the scale of the experiment
becomes significant, compared to the size of the universe. But that's
not the case in EPR experiments on Earth.

Joy Christian

unread,
Dec 30, 2011, 7:59:20 AM12/30/11
to
On Dec 30, 8:57=A0am, Daryl McCullough <stevendaryl3...@yahoo.com>
wrote:

>
> No, what I've said has nothing to do with topology.
>

But it most certainly does, whether you realize it or
not. You are implicitly assuming a wrong topology of
the physical space in your argument. Worse still, you
are confusing the topology of the space S^3 with the
global topology of the universe. Let me try to explain
this to you one more time. You wrote:

>
> Having the topology of S^3
> changes *global* properties of space--for example, it is compact,
> whereas R^3 is not--but in a small enough region, it doesn't
> change any properties that are locally measurable.
>

This is correct, but this is simply reiterating what
I have explained in my papers. Your argument
relies on comparing two measurement events, one
observed by Alice and the other observed by Bob,
in two remote, space-like separated regions. You,
or Bell, are therefore not justified in ignoring the
global properties of the physical space. It is evident
from my variables A(a, mu) and B(b, mu), which
are defined in small enough local regions, that they
are not affected by the global topology of S^3. Both
of them produce completely random binary numbers,
+1 or -1. But when these numbers are compared at
the end of a large number of runs, one finds that
they are strongly correlated. These correlations are
the result of the global properties of S^3, which
have nothing to do with the global topology of the
universe as a whole. And Just as Dr. Bertlmann's
socks have nothing to do with non-locality, they
have nothing to do with non-locality either.

> Assuming that an EPR type experiment takes place in a region
> that is small compared with the size of the universe, the topology
> would not make a difference to results.
>

Wrong. As I just explained, my argument has nothing
to do with the topology of the universe as a whole.

Have you ever tried to do the Dirac's belt trick? That
is a topological effect, exhibited in a small region of
space. Does that involve the size of the Universe?

Your assertions here are another indication that
you have not understood my argument at all.
My argument has nothing to do with the global
topology of the universe. It has to do with the
topology of S^3, for joint measurement events.

>
> No, I haven't said anything about topology, and
> I don't think it is relevant.
>

But you indeed have, and it is absolutely relevant.

You are assuming wrong topology of space -- R^3
instead of S^3. For example, in your argument you
are assuming two vectors, a and b. How are these
vectors defined? In my model all vectors are defined
as Clifford-algebraic elements. They are defined by
the trivector mu itself, since that is how vectors are
defined in Clifford algebra -- by equations mu /\ a =3D 0
and mu /\ b =3D 0. There is no analogue of these
equations in vector algebra (which is not even an
algebra). This is very important in my model, because
it is based on the even sub-algebra of Cl(3, 0), which
represents the 3-sphere. This is just one example of
how you are making implicit assumptions without
even realizing. You are assuming vectors a and b
which have nothing to do with the vectors of my
model. As a result, your argument has nothing to do
with my model, let alone the actual EPR statistics.

> I did not assume anything about topology.

You most certainly did, but without realizing it.

> ... in a small enough region, topology by itself would
> not play a role in an EPR-type experiment.

You are confusing the topology of space with the
topology of the universe. I am not concerned about
the topology of the universe. I am concerned about
the topology of S^3, as exhibited in Dirac=92s belt trick.

>
> What would play a role is curvature, or more generally,
> non-trivial parallel transport.
>

Curvature is completely irrelevant. It is zero. S^3 is as
flat as a sheet of paper. What is relevant is the torsion
within S^3. Once again, you have not understood my
argument at all, or even the basic physics of the EPR
correlations. And you have not read my papers. As I
have urged you many times before, read my papers
first and try to understand my argument. Read this paper,
for example, to understand how torsion is relevant, but
not curvature: http://arxiv.org/abs/1101.1958

>
> > Consequently, as I have explained in great detail in this paper:
> >http://arxiv.org/abs/1106.0748, the four different outcomes, (+1,+1),
> > (+1,-1), (-1,+1), and (-1,-1), necessarily and deterministically occur
> > within my model even for the fixed detector directions a and b (but of
> > course with different probabilites depending on the angle between
> > a and b).
>
> That paper leaves the most important questions about your model
> unanswered. In particular, the interpretation of equation (46) as a
> *probabilistic* prediction is not supported by anything leading up to it.
>

No it does not. As I have explained to you many times before,
you must read the *whole* paper before making such false
claims. The argument leading up to equation (46) is developed
in equations (1) to (45) that come before equation (46). But you
have not paid any attention to these earlier equations.

> > If, however, one chooses to ignore the premises of my model (as you
> > have been doing) by replacing it with an old fashioned contextual
> > hidden variable model set up within a non-compact flat space with a
> > trivial topology (and that is indeed what you are doing whether you
> > realize it or not),
>
> You haven't shown how topology is even relevant to Bell's theorem.
> As I said, topology comes into play when the scale of the experiment
> becomes significant, compared to the size of the universe. But that's
> not the case in EPR experiments on Earth.
>

Yes I have. As I have explained to you before, the topology
of S^3, and more generally that of S^7, are crucially important
for the existence and strength of quantum correlations. The
global topology of the universe has nothing to do with this.
This is explained in great detail in my papers, which can be
found here:
http://arxiv.org/find/all/1/au:+Christian_Joy/0/1/0/all/0/1

Joy Christian

Robert L. Oldershaw

unread,
Dec 30, 2011, 5:29:11 PM12/30/11
to
On Dec 28, 2:55 pm, Joy Christian <hojoin...@gmail.com> wrote:

> of the non-trivial topology of the physical space. The physical
> space in my model is taken to be a parallelized 3-sphere, S^3, not
> a non-compact space R^3.
------------------------------------------------------------

Could you provide some physical/conceptual description of what
properties an S^3 space would have?

Why "parallelized"?

Thanks,
RLO

Cl.Massé

unread,
Dec 30, 2011, 5:29:32 PM12/30/11
to
"Joy Christian" wrote:

> On Dec 26, 9:01 pm, Daryl McCullough <stevendaryl3...@yahoo.com>
> wrote:
>>
>> I don't see how it is even relevant to my complaints about Christian's
>> work. I haven't made any claims one way or the other about the topology
>> of the 3-sphere.
>
> Oh, but you most certain have made claims about topology!
>
> As I have tried to explain to you over and over and over and over
> again, my model is NOT a contextual hidden variable model. It is a
> non-contextual model in which correlations result entirely because
> of the non-trivial topology of the physical space. The physical
> space in my model is taken to be a parallelized 3-sphere, S^3, not
> a non-compact space R^3. You, on the other hand, have implicitly
> assumed the physical space to be R^3 without even realizing it.
> Therefore your argument has nothing whatsoever to do with my
> model. Your implicit assumption of R^3 is betrayed in you casual
> reference to my hidden variable mu as "some hidden variable mu."
> mu is not some garden variety hidden variable of a contextual kind.
> It specifies the orientation of the physical space S^3 within which
> the measurement events are taking place. As such these events are
> subject to the non-trivial twist in the Hopf fibration of the 3-
> sphere.

You seem yourself not to have understood what is a topological sphere.
Every experiment being local, the global topology of space doesn't even
enter the formula. Similarly, every experiment being made of a
countable number of events (even if infinite,) it is impossible for
those to form a continuous space, however they may be parameterized.
Topology is a well developed mathematical area that doesn't allow
improvisation. In contrast to geometry, it deals with objects as a
whole. They can't be broken down in pieces while keeping working.
Pictorially for the Hopf fibration, you can't link two loops if at least
one of them isn't closed. No link, no (topological) twist.

Daryl McCullough

unread,
Dec 30, 2011, 5:29:53 PM12/30/11
to
On Friday, December 30, 2011 7:59:20 AM UTC-5, Joy Christian wrote:

> Your assertions here are another indication that
> you have not understood my argument at all.

I agree. I don't understand your argument at all.
I'm trying to get to the bottom of what your
argument is about.

> My argument has nothing to do with the global
> topology of the universe. It has to do with the
> topology of S^3, for joint measurement events.

...

> You are assuming wrong topology of space -- R^3
> instead of S^3.

Are you distinguishing between the topology of "space"
and the topology of the "universe"? What do you mean
by that distinction?

> For example, in your argument you
> are assuming two vectors, a and b.
> How are these vectors defined?

You have to use parallel transport in order to relate
two distant direction vectors. But it's ultimately
an operational definition, not a mathematical
definition. For example, take two identical
circular panels. On each, draw three radii at angles
of 0 degrees, 120 degrees and 240 degrees. Line up
the 0 degrees on the two panels. Then move on of
the panels a distance away from the first, along
the direction perpendicular to their surfaces, being
careful not to rotate it as you move.

Then you can perform an EPR-type experiment, in which
one experimenter lines up his Stern-Gerlach experiment
with one of the three radii on on panel, and the other
experimenter lines up his stern-Gerlach experiment with
one of the radii on the other panel. Then you have a
source of twin pairs somewhere between the two.
Empirically, each detection event results either in
deflecting a particle one way in the Stern-Gerlach
device, or the opposite way. The experimenter records
the pair (theta, spin), where theta is one of the three
possibilities: 0, 120 or 240, and where spin is either
+1 for deflection in one direction, or -1 for deflection
in the other direction.

Certainly in this setup, parallel transport is involved,
because in order to get perfect correlation, one must
make sure that the panels are not rotated as they are
moved from one spot to another. But that actually is
not a problem; one can fine-tune the orientations after
the fact by rotating the panels to maximize joint detections
of spin-up when both detectors are oriented at 0 degrees.

I don't see how topology has any relevance to this
setup.

> In my model all vectors are defined
> as Clifford-algebraic elements.
> They are defined by
> the trivector mu itself, since that is how vectors are
> defined in Clifford algebra -- by equations mu /\ a = 0
> and mu /\ b = 0. There is no analogue of these
> equations in vector algebra (which is not even an
> algebra). This is very important in my model, because
> it is based on the even sub-algebra of Cl(3, 0), which
> represents the 3-sphere. This is just one example of
> how you are making implicit assumptions without
> even realizing. You are assuming vectors a and b
> which have nothing to do with the vectors of my
> model. As a result, your argument has nothing to do
> with my model, let alone the actual EPR statistics.

I would say, rather that, it's not clear what your
model has to do with EPR or Bell's argument.

The way I described things above, there is no assumption
being made about the true nature of vectors. We have three
lines drawn on circular panels.

> You are confusing the topology of space with the
> topology of the universe. I am not concerned about
> the topology of the universe. I am concerned about
> the topology of S^3, as exhibited in Dirac's belt trick.

Please, in terms of my description of an EPR-type experiment
above, where does the topology of S^3 come into play?

Joy Christian

unread,
Dec 31, 2011, 12:06:22 PM12/31/11
to
On Dec 30, 10:29 pm, "Robert L. Oldershaw" <rlolders...@amherst.edu>
wrote:
>
> > of the non-trivial topology of the physical space. The physical
> > space in my model is taken to be a parallelized 3-sphere, S^3, not
> > a non-compact space R^3.
>
> ------------------------------------------------------------
>
> Could you provide some physical/conceptual description of what
> properties an S^3 space would have?
>
> Why "parallelized"?
>
> Thanks,
> RLO

S^3 is a one-point compactification of R^3. As
such, S^3 is a compact space, but R^3 is not.

The reason for parallelization has to do with
the original EPR argument. In that argument
there is a criterion of completeness. Unless
this criterion is satisfied, Bell’s argument does
not get off the ground. But as I have argued in
several of my papers, completeness criterion
can only be satisfied if the co-domain of the
functions A(a, L) assumed by Bell is a parallelized
3-sphere. The argument is rather subtle and it is not
possible to reproduce here. Now parallelization
renders the 3-sphere flat, in the sense that its
Riemann curvature vanishes. But the torsion
in a parallelized 3-sphere is not zero, and it is
this non-zero torsion that is responsible for
producing the EPR correlation. In other words,
it is the *discipline of parallelization* within the
manifold of all possible measurement results,
*both actual as well as counterfactual*, that is
responsible for producing the EPR correlation.

Now a parallelized 3-sphere is homeomorphic
to a set of unit quaternions, and hence to the
covering group SU(2) of the rotation group SO(3).
So it is not really surprising why my model works.
I am just doing what Hamilton and Clifford would
have done in 1870 to explain the EPR correlation.
We, on the other hand, have the disadvantage of
knowing quantum mechanics.

Joy Christian

Joy Christian

unread,
Dec 31, 2011, 4:34:21 PM12/31/11
to
On Dec 30, 10:29 pm, "Cl.Mass�" <akia...@fastwebnet.it> wrote:
>
> You seem yourself not to have understood what is a topological sphere.
> Every experiment being local, the global topology of space doesn't even
> enter the formula.
>

What formula? Whose formula? I don't care about Bell's formula,
if that is what you have in mind. Topology enters my formula (i.e.,
my model) and that is all that matters. All one has to do to refute
Bell is to construct a model that reproduces the EPR correlation,
and that is what I have done: http://arxiv.org/abs/1103.1879

>
> Similarly, every experiment being made of a
> countable number of events (even if infinite,) it is impossible for
> those to form a continuous space, however they may be parameterized.
> Topology is a well developed mathematical area that doesn't allow
> improvisation. In contrast to geometry, it deals with objects as a
> whole. They can't be broken down in pieces while keeping working.
> Pictorially for the Hopf fibration, you can't link two loops if at least
> one of them isn't closed. No link, no (topological) twist.

All of this is quite elementary. Your comments simply show that
you haven't actually read my papers. If you do, and if you know
some geometric algebra, then you will see how topological
considerations enter my model.

Joy Christian

Joy Christian

unread,
Dec 31, 2011, 4:34:42 PM12/31/11
to
On Dec 30, 10:29 pm, Daryl McCullough <stevendaryl3...@yahoo.com>
wrote:

>
> I agree. I don't understand your argument at all.
> I'm trying to get to the bottom of what your
> argument is about.
>

I appreciate that. But you will not be able to
understand my arguement until you try to
understand at least the introductory parts of
this paper: http://arxiv.org/abs/1106.0748

>
> Are you distinguishing between the topology of "space"
> and the topology of the "universe"? What do you mean
> by that distinction?
>

There is no need to postulate anything about
the whole universe when analyzing the EPR
experiment. We have a closed system, which
starts out in some initial state and ends up in
two clicks of two detectors in two remote regions
of space, which could be only a meter apart.
There is no need to know anything about the
global or local topology of the universe. What
is important is how one models this local region
of the universe. Usually one models it as R^3.
That is simply wrong, as explained in the intro
of this paper: http://arxiv.org/abs/1106.0748

>
> I would say, rather that, it's not clear what your
> model has to do with EPR or Bell's argument.
>

It is more than evident that my model has
everything to do with the EPR-Bell argument.

>
> The way I described things above, there is no assumption
> being made about the true nature of vectors. We have three
> lines drawn on circular panels.
>

This is your mistake. You are not recognizing
the fact that your innocent looking description is not
so innocent. Without realizing you are modelling
the physical space (incorrectly) as R^3. Our physical
space respects the symmetries of S^3, not R^3, as
can be easily demonstrated by the Dirac belt trick.

>
> Please, in terms of my description of an EPR-type experiment
> above, where does the topology of S^3 come into play?
>

The topology of S^3 comes into play as the correct
model of the physical space. This is what you have
not understood.

Joy Christian

Hendrik van Hees

unread,
Jan 2, 2012, 7:13:25 AM1/2/12
to
As someone who uses relativistic quantum field theory (not only the
vacuum theory of high-energy particle physics but also the many-body
theory in and out of thermal equilibrium to describe relativistic
heavy-ion collisions and the quark-gluon plasma) as a basis for my
everyday work, I already stumble over the first sentence in the abstract
of your paper since locality and (micro-)causality is at the very
foundation of relativistic quantum field theory.

From these features follows also macroscopic causality. The most simple
example is linear-response theory, where in a view lines you get the
retarded, i.e. causal, propagator as the response of the medium to a
(local) perturbation, and from this in going from the microscopic
description to a macroscopic one to classical causality. Of course, in
general you have memory and non-local effects, but this is no
contradiction to locality and micro-causality of quantum field theory.
To the contrary it follows from these features.

Of course, quantum theory is fundamentally different from classical
deterministic theories with respect to non-local correlations, described
by what we usually call "entangled states". The existence of such
non-classical correlations, however, does not contradict locality and/or
causality either. Such correlations exist because of the preparation of
the system in its initial state and their persistence in the quantum
theoretical time evolution of this system for a (sufficiently well)
isolated (i.e., closed) system. Such correlations are exactly described
by the non-Markovian and non-local master equations of non-equilibrium
theory, which is based on locality and micro-causality.

That there cannot be any contradiction between locality and
micro-causality on the one hand and long-ranged correlations described
by entangled states in EPR-like situations is clear from the fact that a
local micro-causal QFT fulfills the linked-cluster theorem, which
ensures that local measurements on a single subsystem cannot reveal its
"entanglement" with another far-away subsystem with which it is
"entangled". You always need to also make well-constructed and thus
correlated measurements on both subsystems to reveal their
"entanglement". E.g., in Aspect/Zeilinger like experiments with
entangled photon pairs ("teleportation experiment"), you have to measure
the polarization state of both photons using a polarizer in the same (or
perpendicular) direction at both places (with observers Alice and Bob,
respectively) to find the 100% EPR-correlation of the polarization
state. Also you have to make sure that you always measure the
correlations of each pair by using a precise enough coincidence
measurement (i.e., precise timing of the registration of the photons at
A's and B's detector). While A's and B's measurements taken for
themselves only reveals totally unpolarized photons, only the analysis
of the coincidence measurement by putting both data sets (including the
precise timing to ensure that only the two measurements on the same
entangled photon pair are considered and taken into account in the
statistical analysis of the correlations) together. There's no
contradiction whatsoever with Einstein causality and locality of quantum
field theory.

In my opinion the whole apparant EPR paradox is not inherent of
relativistic quantum field theory but only in the Copenhagen
interpretation (and all their relatives, assuming some "collapse of the
quantum state" to be a "real physical process") of the foundations of
quantum theory. This is simply cured by taking the Born probablility
interpretation of quantum states really seriously and thus using a
"Minimal Statistical Interpretation". For me that's the only convincing
conclusion from the empirical "proof" of the validity of Bell's
inequality. At the same time it's important to keep in mind what's meant
by "locality", which simple means that local observables (i.e.,
observable quantum-field operators like the energy-momentum tensor,
charge densities, etc.) commute when their arguments denote space-like
separated events and the still possible long-range correlations of
entangled subsystems of (sufficiently isolated and thus closed) larger
systems.

Particularly, I don't see any need to modify the mathematical space-time
structure, at least not in the realm of special relativity; it's of
course still an open question, in how far one has to find a modification
of the space-time model in the connection with a fully consistent
quantum theory of gravity.

On 31/12/11 22:34, Joy Christian wrote:

> I appreciate that. But you will not be able to
> understand my arguement until you try to
> understand at least the introductory parts of
> this paper: http://arxiv.org/abs/1106.0748

--
Hendrik van Hees
Frankfurt Institute of Advanced Studies
D-60438 Frankfurt am Main
http://fias.uni-frankfurt.de/~hees/

a student

unread,
Jan 2, 2012, 1:05:51 PM1/2/12
to
On Jan 1, 7:34 am, Joy Christian <hojoin...@gmail.com> wrote:
> On Dec 30, 10:29 pm, "Cl.Mass " <akia...@fastwebnet.it> wrote:
>
>
>
> > You seem yourself not to have understood what is a topological sphere.
> > Every experiment being local, the global topology of space doesn't even
> > enter the formula.
>
> What formula? Whose formula? I don't care about Bell's formula,
> if that is what you have in mind. Topology enters my formula (i.e.,
> my model) and that is all that matters. All one has to do to refute
> Bell is to construct a model that reproduces the EPR correlation,
> and that is what I have done:http://arxiv.org/abs/1103.1879
>

Polite cough. The Hilbert space model of standard quantum
mechanics reproduces the singlet state correlations, yet does
not refute Bell's theorem. Bell inequalities show that there is
no model of these correlations which is local and deterministic
(some derivations weaken determinism, but not Bell's original
derivation). They are mathematically rigorous. Hence no
model of the correlations, including yours, refutes them.

Second polite cough. You refer to EPR correlations. These
are for the position and momentum coprrelations of two
particles. The EPR state (and Gaussian approximations
thereto) has a positive Wigner function, and hence there is a
classical model for these correlations. This is why the
Bell inequalities are such an important advance over mere
"EPR" correlations.

I've made my opinion of your model(s) clear earlier, in this
thread and others. In short, your papers have no relevance
to the Bell inequalties and their import.

Here, by the way, is an amusing model of the singlet
state which is even simpler than yours, although it uses
a similar algebraic trick.

Alice receives a random unit
vector, V, and Bob receives the vector -V. If Alice
measures in direction A, she writes down the result
+sqrt{3} if A.V is positive, and -sqrt{3} otherwise. Bob
does the same (but relative to -V). What is the
correlation between their measurement results? It is
easily calculated as
E(A,B) = -A.B,
i.e, the same as the singlet state prediction. And
look how local and realistic the model is! (and
no topology required - clever me!).

But I'm not waiting for my Nobel prize Joy, and
neither should you. Did you spot the flaw? - Bell
inequalities are about products of outcomes
labelled as +/-1, not about products of outcomes
labelled as +/-sqrt{3}. Similarly, they are not
about products of outcomes labelled as bivectors
etc as per your models, nor even about products
of outcomes labelled as spin operators as in the
standard QM model.

Daryl McCullough

unread,
Jan 2, 2012, 1:04:51 PM1/2/12
to
On Friday, December 30, 2011 3:57:02 AM UTC-5, Anon E. Mouse wrote:
> > My argument against Christian's model is pretty simple,
> > and to me seems airtight:
> >
>
> Your model is very simple. Impossibly so, real spin measures are
> fractions of all possible data captures, or a filtered subset thereof,
> not 100% captures of integer spins.

I certainly understand the difficulties of experimental analysis
in determining which events are part of a twin pair, and which
events are noise. But those complexities don't seem relevant to
Christian's arguments about Bell's theorem.

> Similarly you limit the value of mu, a hypothetical measure of
> entanglement, being a unit tri-vector which could take on any complex
> value between 1 and -1, in a restricted 2d representation of the
> actual 3 space to just two values, represented by the extreme limits.

Christian specifically limited the possible values of mu to real
tri-vectors. Yes, if it were allowed to be complex, that would
allow more possibilities, but his model does not involve complex
tri-vectors.

> The data scenario you project is indeed impossible, as far as I can
> tell. However, I don't see this as valid criticism of Christian or
> Bell.

I didn't mean it as a criticism of Christian, I meant it as
a way of asking a question about it. I don't understand how,
if the hidden variable mu can only take on two values (which
he assumes it does), how one can get 4 different outcomes,
if everything is deterministic (which I thought he was claiming).
If things are not deterministic, then I don't understand where
the additional nondeterminism is coming from in his model.

Daryl McCullough

unread,
Jan 2, 2012, 1:06:09 PM1/2/12
to
On Saturday, December 31, 2011 4:34:42 PM UTC-5, Joy Christian wrote:

> > The way I described things above, there is no assumption
> > being made about the true nature of vectors. We have three
> > lines drawn on circular panels.

> This is your mistake. You are not recognizing
> the fact that your innocent looking description is not
> so innocent. Without realizing you are modelling
> the physical space (incorrectly) as R^3.

Nothing I've said makes any such assumption. All I described
was an operational procedure for relating detector orientations
at distant locations. As I said, there is an assumption that
it is possible to do parallel transport, to move an object
along a path without rotating it, but that is not a matter
of topology.

> Our physical space respects the symmetries of S^3, not R^3, as
> can be easily demonstrated by the Dirac belt trick.

I'm *NOT* disputing your claims about the topology of space.
I'm asking the following question:

> > Please, in terms of my description of an EPR-type experiment
> > above, where does the topology of S^3 come into play?
>
> The topology of S^3 comes into play as the correct
> model of the physical space. This is what you have
> not understood.

That's why I asked the question: *how* does S^3 versus R^3
come into play? It's not that helpful to just repeat the
claim that it does.

Joy Christian

unread,
Jan 2, 2012, 5:41:57 PM1/2/12
to
On Jan 2, 12:13 pm, Hendrik van Hees <h...@fias.uni-frankfurt.de>
wrote:
>
> As someone who uses relativistic quantum field theory (not only the
> vacuum theory of high-energy particle physics but also the many-body
> theory in and out of thermal equilibrium to describe relativistic
> heavy-ion collisions and the quark-gluon plasma) as a basis for my
> everyday work, I already stumble over the first sentence in the abstract
> of your paper since locality and (micro-)causality is at the very
> foundation of relativistic quantum field theory.
>

I presume you mean this sentence of mine:
"Unlike our basic theories of space and time,
quantum mechanics is not a locally causal theory."

If you are disputing this sentence then your disagreement
is not with me but with EPR, Bell, and the majority of the
physics community. I agree with the conclusion of EPR,
Bell, and the majority of the physics community that quantum
mechanics is not a locally causal theory.

What you are implicitly assuming in your discussion is the
signalling locality of the relativistic theories. It is well known
that quantum mechanics is perfectly compatible with the
signalling locality of relativistic theories. Quantum mechanics,
however, harbors a peculiar form of *no-signalling non-locality*,
as discovered by EPR and clarified by Bell. It is in the latter
sense of no-signalling non-locality that quantum mechanics
is not a locally causal theory. This conclusion is not in dispute.
Evidently you are unaware of these subtle nuances in local
causality brought out by the EPR-Bell debate. What you
have discussed is entirely irrelevant to that debate.

Joy Christian

Joy Christian

unread,
Jan 2, 2012, 5:52:14 PM1/2/12
to
On Jan 2, 12:13 pm, Hendrik van Hees <h...@fias.uni-frankfurt.de>
wrote:
>
> As someone who uses relativistic quantum field theory (not only the
> vacuum theory of high-energy particle physics but also the many-body
> theory in and out of thermal equilibrium to describe relativistic
> heavy-ion collisions and the quark-gluon plasma) as a basis for my
> everyday work, I already stumble over the first sentence in the abstract
> of your paper since locality and (micro-)causality is at the very
> foundation of relativistic quantum field theory.
>

Hendrik van Hees

unread,
Jan 3, 2012, 10:15:52 AM1/3/12
to
On 02/01/12 23:52, Joy Christian wrote:

> I presume you mean this sentence of mine:
> "Unlike our basic theories of space and time,
> quantum mechanics is not a locally causal theory."

Yes, I do not understand this claim, but obviously we have a different
understanding of what we call "local" and "causal".
>
> If you are disputing this sentence then your disagreement
> is not with me but with EPR, Bell, and the majority of the
> physics community. I agree with the conclusion of EPR,
> Bell, and the majority of the physics community that quantum
> mechanics is not a locally causal theory.

I know the original EPR paper and some of the tests of the violation of
Bell's inequality, but I'm not an expert in this field.
>
> What you are implicitly assuming in your discussion is the
> signalling locality of the relativistic theories.

Of course, and that's the only "locality" and "causality" that's
relevant for consistency of QT with the relativistic space-time
structure. As soon as you give up Copenhagen-like collapse assumptions,
which are not necessary to successfully apply quantum theory to the
description of nature, there is no contradiction between (atl least
special) relativistic space-time structure and quantum theory. For me,
the criticism of EPR agains QT is in fact a criticism against its
Copenhagen interpretation.

Of course, whether you consider a probabilistic description, as implied
by Born's Rule and the Minimal Statistical Interpretation as "complete"
is another question. As long as there is no better non-probabilistic
theory, I think, we have no choice to accept quantum theory as it is.

> It is well known
> that quantum mechanics is perfectly compatible with the
> signalling locality of relativistic theories. Quantum mechanics,
> however, harbors a peculiar form of *no-signalling non-locality*,
> as discovered by EPR and clarified by Bell.

I guess, what you mean here is entanglement as described in my posting,
but that's indeed not related with signal propagation. These are
long-ranged correlations, but the experimentally well-established
conclusions from these non-classical correlations do not contradict
Einstein causality and locality of interactions in relativistic local QFTs.

> It is in the latter
> sense of no-signalling non-locality that quantum mechanics
> is not a locally causal theory. This conclusion is not in dispute.

Of course not, but I think the wording is very misleading, and one
should clearly distinguish causality and locality in the sense of
relativistic local QFTs (what you call "signalling causality and
locality") from the possibility to prepare states where distant
subsystems are entangled. These I would call "long-range quantum
correlations", and their existence does not contradict the causal
structure of special relativistic space-time.

> Evidently you are unaware of these subtle nuances in local
> causality brought out by the EPR-Bell debate. What you
> have discussed is entirely irrelevant to that debate.

Yes, that's what I never understood, and I hope to learn it from this
discussion: What is still under debate concerning the EPR paper?
Relativistic quantum field theory is of course not a closed subject in
the sense that there are many open mathematical questions, but as far as
I can see these have nothing to do with the EPR debate. The prediction
of entanglement, i.e., of "long-ranged quantum correlations" has been
experimentally verified with high statistical significance and the
predictions of (minimally interpreted) quantum theory have been
quantitatively verified too. So what's still an open question concerning
the EPR (or more generally the old Einstein-Bohr debate)? In my opinion,
there's no necessity for a new theory beyond quantum theory if there are
no experimental facts disproving quantum theory.

Joy Christian

unread,
Jan 3, 2012, 1:20:19 PM1/3/12
to
On Jan 2, 6:05�pm, a student <of_1001_nig...@hotmail.com> wrote:

>
> Polite cough ....... Bell inequalities show that there is
> no model of these correlations which is local and deterministic
> (some derivations weaken determinism, but not Bell's original
> derivation). �They are mathematically rigorous. �Hence no
> model of the correlations, including yours, refutes them.
>

I beg to differ.

Bell's theorem, as any other no-go theorem in physics, is based
on many hidden assumptions. For example, it can be of relevance
to physics at all if and only if the measurement functions presupposed
by Bell, namely A(a, L) and B(b, L), satisfy the completeness
criterion
of EPR. If they do not satisfy the completeness criterion, then Bell's
theorem is not worth a penny. In Bell's own words: "Let this more
complete specification be affected by means of parameters L."

The first thing I have shown in my work is that the functions of L
presupposed by Bell cannot possibly satisfy the completeness
criterion of EPR. Thus Bell's theorem does not even get off the
ground. IT IS A NON-STARTER: http://arxiv.org/abs/0904.4259.

Next, I have produced an explicit local and deterministic model
that exactly reproduces the EPR-Bohm correlation. This model,
which can be found in this paper: http://arxiv.org/abs/1103.1879,
clearly shows that, given A(a, L) = +1 or -1 and B(b, L) = +1 or -1
as defined by equations (1) and (2) of the paper, the correlation
between the numbers +1 and -1, as understood by Galton and
Pearson over a century ago, is exactly equal to -a.b.
So much for Bell's imposibility theorem and your cough.

Next, I go on to show that, not only the EPR-Bohm correlation,
but ALL quantum mechanical correlations can be reproduced
in a purely local, deterministic, non-contextual, and realistic
manner. I demonstrate this fact by first explicitly reproducing the
correlations predicted by Bell, GHZ, and Hardy states, and then
by providing a clear-cut framework to reproduce correlaions
predicted by any conceivable arbitrary quantum mechanical
state. These results can be found in these two papers:
http://arxiv.org/abs/0904.4259 and
http://arxiv.org/abs/1101.1958.

I the last paper I also bring out the true topological reasons for
the existence and strength of all quantum correlations, and the
existence of the upper bound on all quantum correlations. Note
that, contrary to your misleading toy example, by correlation
I mean exactly what Bell, GHZ, Hardy, Galton, and Pearson
meant by correlaion. Namely, expectaion value between the
numbers +1 and -1. The evidence is all there in my work if you
are willing to see it. You are of course under no obligation to
see the evidence. You are completely free to remain in denial.
I am in no position to stop you from misrepresenting my work.

Joy Christian

Joy Christian

unread,
Jan 3, 2012, 1:20:21 PM1/3/12
to
You can do whatever you like operationally.
That is not the question one has to answer
to rebut Bell�s claim. His claim was that no
THEORETICAL model can be constructed to
reproduce the EPR correlation. I construct
such a model (an explicit and clear cut one)
by recognizing two related facts about our
physical space. The first is the fact that the
algebra of the orthogonal directions in the
physical space is the Clifford algebra Cl(3, 0).
Second, that the bivector (or even) subalgebra
of the algebra Cl(3, 0) represents a 3-sphere,
albeit a parallelized one. It is a well recognized
fact, since Hamilton and Clifford, that vector
algebra, which you are implicitly assuming in
all of your considerations, is not capable of
representing the physical space correctly. It
is good enough for most applications in physics
but not all. Based on these considerations, as
explained in several of my papers, it is clear, at
least to me, that the correct model of the EPR
correlation must be based on the parallelized
3-sphere and its algebraic representation, the
even sub-algebra of Cl(3, 0). What you have
described, however, is a naive operational
procedure that does not respect the true
symmetries of our physical space. It is then not
surprising that any model of the EPR experiment
you construct based on your procedure would not
be able to reproduce the EPR correlation. We
already know that much from Bell.The idea is to
go beyond Bell, and that is what I have done.

Joy Christian

Tom

unread,
Jan 3, 2012, 1:20:22 PM1/3/12
to
Deterministic means non-probabilistic, it doesn't imply non-
statistical.
In fact, any real measurement in a bounded length of time begs
statistical inference. An example I posted on FQXi explicitly
shows that Bell-Aspect results are subsumed by Joy Christian's
framework. http://fqxi.org/data/forum-attachments/2_Ferryman_Puzzle_rev.pdf

Tom

Cl.Mass??

unread,
Jan 3, 2012, 10:45:04 PM1/3/12
to
"Joy Christian" <hojo...@gmail.com> a ?crit dans le message de
news:458a9f6f-1324-4bc2...@z12g2000yqm.googlegroups.com...

> You can do whatever you like operationally.
> That is not the question one has to answer
> to rebut Bell?s claim. His claim was that no
You not yet have explained how local algebraic considerations turn into global
topological ones. However you parameterize space, it remains topologically
equivalent to R^3, whatever basic, metric, connection, parallelization you
choose. To prove the contrary, you have to exhibit a homeomorphism between R^3
and S^3. That's the paper you still have to write and which, I concede it to
you, we haven't read.

Daryl McCullough

unread,
Jan 3, 2012, 10:44:31 PM1/3/12
to
On Tuesday, January 3, 2012 1:20:19 PM UTC-5, Joy Christian wrote:

> Bell's theorem, as any other no-go theorem in physics, is based
> on many hidden assumptions. For example, it can be of relevance
> to physics at all if and only if the measurement functions presupposed
> by Bell, namely A(a, L) and B(b, L), satisfy the completeness
> criterion of EPR. If they do not satisfy the completeness criterion,
> then Bell's theorem is not worth a penny. In Bell's own words:
> "Let this more complete specification be affected by means of
> parameters L."

I think that's a misunderstanding of Bell's argument. He wasn't in
any way claiming that the functions A(a,L) and B(b,L) are in any
sense "complete" descriptions of physical reality. He was assuming
that they are "more complete" (that is, they contain more information)
than the pure probabilistic predictions of quantum mechanics.

Cl.Mass??

unread,
Jan 3, 2012, 10:46:20 PM1/3/12
to
"Joy Christian" <hojo...@gmail.com> a ?crit dans le message de
news:59b6e7a2-b7b4-4f4d...@q8g2000yqa.googlegroups.com...

> This is your mistake. You are not recognizing
> the fact that your innocent looking description is not
> so innocent. Without realizing you are modelling
> the physical space (incorrectly) as R^3. Our physical
> space respects the symmetries of S^3, not R^3, as
> can be easily demonstrated by the Dirac belt trick.

In the belt trick, there are two fixed points that are topologically identified.
Actually, all the points of a 2-sphere surrounding the belt are identified,
which is equivalent to a point at infinity. But that is possible only because
there is a rigid material frame around it. There is not such thing in a
Bell-type experiment, at least in your model. In that instance, the Dirac belt
trick demonstrates nothing.

Joy Christian

unread,
Jan 4, 2012, 3:00:16 AM1/4/12
to
On Jan 4, 3:46=A0am, "Cl.Mass??" <akia...@fastwebnet.it> wrote:
> "Joy Christian" <hojoin...@gmail.com> a ?crit dans le message denews:59b6=
e7a2-b7b4-4f4d-8...@q8g2000yqa.googlegroups.com...
>
> > This is your mistake. You are not recognizing
> > the fact that your innocent looking description is not
> > so innocent. Without realizing you are modelling
> > the physical space (incorrectly) as R^3. Our physical
> > space respects the symmetries of S^3, not R^3, as
> > can be easily demonstrated by the Dirac belt trick.
>
> In the belt trick, there are two fixed points that are topologically iden=
tified.
> Actually, all the points of a 2-sphere surrounding the belt are identifie=
d,
> which is equivalent to a point at infinity. =A0But that is possible only =
because
> there is a rigid material frame around it. =A0There is not such thing in =
a
> Bell-type experiment, at least in your model. =A0In that instance, the Di=
rac belt
> trick demonstrates nothing.

Incorrect.

In any EPR experiment there are two particles rotating
with respect to each other. They are rotating (or spinning)
in tandem, with each particle providing a material frame for
the other. This is explained in greater detail in this paper:
http://arxiv.org/abs/0806.3078 .

Joy Christian

Joy Christian

unread,
Jan 4, 2012, 3:00:18 AM1/4/12
to
On Jan 4, 3:45=A0am, "Cl.Mass??" <akia...@fastwebnet.it> wrote:
> "Joy Christian" <hojoin...@gmail.com> a ?crit dans le message denews:458a=
9f6f-1324-4bc2-8...@z12g2000yqm.googlegroups.com...
> You not yet have explained how local algebraic considerations turn into g=
lobal
> topological ones. =A0However you parameterize space, it remains topologic=
ally
> equivalent to R^3, whatever basic, metric, connection, parallelization yo=
u
> choose. =A0To prove the contrary, you have to exhibit a homeomorphism bet=
ween R^3
> and S^3. =A0That's the paper you still have to write and which, I concede=
it to
> you, we haven't read.

S^3 is *not* homeomorphic to R^3. They differ by one
point at infinity.

The explanation of how local algebraic considerations
turn into global topological ones is already built into the
framework of geometric algebra I have been using.

Joy Christian

Joy Christian

unread,
Jan 4, 2012, 3:00:19 AM1/4/12
to
On Jan 3, 3:15=A0pm, Hendrik van Hees <h...@fias.uni-frankfurt.de>
wrote:
> Einstein causality and locality of interactions in relativistic local QFT=
I highly recommend Bell's last paper: La nouvelle cuisine (1991) (it
is in Einglish),
http://ebooks.cambridge.org/chapter.jsf?bid=3DCBO9780511815676&cid=3DCBO978=
0511815676A033

His last paper will explain the problem I have solved in my papers.

Joy Christian



,
http://books.google.co.uk/books?id=3DFGnnHxh2YtQC&pg=3DPA232&dq=3Dbell++la+=
nouvelle+cuisine&hl=3Den&ei=3DmhSwTpLfIMiW8gOeuc3IAQ&sa=3DX&oi=3Dbook_resul=
t&ct=3Dresult&resnum=3D1&ved=3D0CC8Q6AEwAA#v=3Donepage&q=3Dbell%20%20la%20n=
ouvelle%20cuisine&f=3Dfalse

Daryl McCullough

unread,
Jan 4, 2012, 10:17:07 AM1/4/12
to
On Tuesday, January 3, 2012 1:20:22 PM UTC-5, Tom wrote:

> Deterministic means non-probabilistic, it doesn't imply non-
> statistical.
> In fact, any real measurement in a bounded length of time begs
> statistical inference. An example I posted on FQXi explicitly
> shows that Bell-Aspect results are subsumed by Joy Christian's
> framework. http://fqxi.org/data/forum-attachments/2_Ferryman_Puzzle_rev.pdf

Thanks for that reference, although I don't understand the
discussion at all. I do understand Lamport's point about
Buridan's Ass. It's discussed very clearly in the paper:
http://research.microsoft.com/en-us/um/people/lamport/pubs/buridan.pdf
I'm looking for level of clarity in a discussion about Christian's
model, and I haven't found it yet.

I can see the relevance of Lamport's Buridan's principle to EPR type
experiments: When trying to decide whether an electron is spin-up or
spin-down, there will be (if Lamport is correct) a number of cases
for which it cannot be decided in a bounded amount of time. Roughly
speaking, the spin direction is determined by the deflection of
the electron in a magnetic field, but for sufficiently high-velocity
electrons, the deflection will be negligible. To me, this seems to
mean that the theoretical correlations predicted by quantum mechanics
will not be precisely mirrored by any actual experiment. I don't see
why that observation is relevant to Christian's model, however.

In the paper you cite, it is said that "Joy Christian's time-dependent
model is deterministic with definite probabilities on the interval
[0,1]." First of all, I didn't see time-dependence
in Christian's model. Second, I don't understand how the statistical
prediction comes out of Christian's model:

Probability that Bob's detector measures spin-up
given that Alice's detector measures spin-up
= sin^2(theta/2), where theta is the angle between
the two detector orientations.

You make the distinction between a model that is probabilistic
and a model that is statistical. I'm not sure that I understand
the distinction between the two, unless by statistical you mean
the apparent nondeterminism that results from ignoring fine-grained
details.

Joy Christian

unread,
Jan 4, 2012, 12:40:35 PM1/4/12
to
This is misleading. Please read the first paragraph
of Bell's famous paper. He starts by summarizing the
EPR argument and builds on it to develop his own
argument. EPR's is a logically impeccable argument
which shows, once and for all, that the description
of physical reality provided by quantum mechanics
is necessarily incomplete. The EPR argument itself is
of course based on four premises, one of them being
the completeness criterion. Bell's goal was to show
that these premises are inconsistent. In particular,
the reality and completeness criteria of EPR are
incompatible with their locality criterion. Bell thought
he had succeeded in showing this in his theorem. He
was wrong, as at least I have shown in my papers.

I do not like to flaunt my credentials in this matter.
But since there are people out there who seem to
think that I am just some fruitcake who has not really
understood Bell's argument, let me point out that
I have been in this business since 1983 and have
learned about the EPR-Bell debate at the feet of
the greatest authority on the subject, namely Abner
Shimony, and have been privileged enough to have
had discussions with Bell himself on the matter on
several occasions. So I think I know a thing or two
about Bell's motivation and his theorem.

Joy Christian

FrediFizzx

unread,
Jan 5, 2012, 2:57:01 AM1/5/12
to
"Daryl McCullough" <stevend...@yahoo.com> wrote in message
news:23014116.2246.1325257872446.JavaMail.geo-discussion-forums@vbak19...
> On Friday, December 30, 2011 3:57:02 AM UTC-5, Anon E. Mouse wrote:
>> > My argument against Christian's model is pretty simple,
>> > and to me seems airtight:
>> >
>>
>> Your model is very simple. Impossibly so, real spin measures are
>> fractions of all possible data captures, or a filtered subset thereof,
>> not 100% captures of integer spins.
>
> I certainly understand the difficulties of experimental analysis
> in determining which events are part of a twin pair, and which
> events are noise. But those complexities don't seem relevant to
> Christian's arguments about Bell's theorem.

Well, the statistics involved sure is a part of his argument. Which is
something else that you are missing in your own argument.

>> Similarly you limit the value of mu, a hypothetical measure of
>> entanglement, being a unit tri-vector which could take on any complex
>> value between 1 and -1, in a restricted 2d representation of the
>> actual 3 space to just two values, represented by the extreme limits.
>
> Christian specifically limited the possible values of mu to real
> tri-vectors. Yes, if it were allowed to be complex, that would
> allow more possibilities, but his model does not involve complex
> tri-vectors.

I suspect you don't understand what the tri-vectors are structure-wise in
the model.

>> The data scenario you project is indeed impossible, as far as I can
>> tell. However, I don't see this as valid criticism of Christian or
>> Bell.
>
> I didn't mean it as a criticism of Christian, I meant it as
> a way of asking a question about it. I don't understand how,
> if the hidden variable mu can only take on two values (which
> he assumes it does), how one can get 4 different outcomes,
> if everything is deterministic (which I thought he was claiming).
> If things are not deterministic, then I don't understand where
> the additional nondeterminism is coming from in his model.

Joy has responded to the above several times now. I wish you would answer
my question that I have asked you several times in the private email
discussion. In the "Restoring..." paper, do you understand everything up to
the top of page 4? If not, what don't you understand? We were willing to
go thru all the math with you so that you might obtain an understanding of
the question you are asking but it is impossible to proceed unless we know
what you understand and what you don't understand. Also.... did you watch
the Niles Johnson video about Hopf Fibration? It seems that since you have
not answered these questions asked of you several times now, that you really
don't have an interest in gaining a better understanding of what Joy has
done. You are horribly stuck in R^3 "flatland".

You might ask yourself, How does a singlet state pair of quantum objects
produce 4 outcomes with no hidden variables? The answer is easy if you
bother to actually try to understand that Joy has shown how via 3-sphere
topology. In fact, Joy has shown in the following linked paper how *all*
quantum correlations might be produced via 7-sphere topology. Which is
actually much more profound than any "disproof" of Bell. Space may have
properties that control or "guide" the behavior of quantum objects and those
properties are probably not revealed on a macroscopic level.

http://arxiv.org/abs/1101.1958

Best,

Fred Diether



Tom

unread,
Jan 5, 2012, 2:57:02 AM1/5/12
to
On Jan 4, 10:17=A0am, Daryl McCullough <stevendaryl3...@yahoo.com>
wrote:
> On Tuesday, January 3, 2012 1:20:22 PM UTC-5, Tom wrote:
> > Deterministic means non-probabilistic, it doesn't imply non-
> > statistical.
> > In fact, any real measurement in a bounded length of time begs
> > statistical inference. An example I posted on FQXi explicitly
> > shows that Bell-Aspect results are subsumed by Joy Christian's
> > framework. =A0http://fqxi.org/data/forum-attachments/2_Ferryman_Puzzle_=
rev.pdf
>
> Thanks for that reference, although I don't understand the
> discussion at all. I do understand Lamport's point about
> Buridan's Ass. It's discussed very clearly in the paper:
>http://research.microsoft.com/en-us/um/people/lamport/pubs/buridan.pdf
> I'm looking for level of clarity in a discussion about Christian's
> model, and I haven't found it yet.
>
> I can see the relevance of Lamport's Buridan's principle to EPR type
> experiments: When trying to decide whether an electron is spin-up or
> spin-down, there will be (if Lamport is correct) a number of cases
> for which it cannot be decided in a bounded amount of time.

Not a number of cases. 100% of the cases. As Lamport writes,

"A real Stern-Gerlach apparatus does not produce the discrete
statistical distribution of electron trajectories usually ascribed to it
in simplified descriptions. Instead, it produces a continuous
distribution having two maxima, but with a nonzero probability of
finding an electron in any finite region between them. Trying to decide
if the electron is deflected up or down then becomes just another
instance of the problem of making a discrete decision based upon a
continuous input value, so nothing has been gained by measuring the
discrete spin value."

It is critical to understand that when we are dealing with a continuous
function framework, as Lamport cites and which Joy treats, there is no
counterpart quantum mechanical measurement theory to: "Buridan=92s Law
of Measurement. If x < y < z, then any measurement performed in a
bounded length of time that has a nonzero probability of yielding a
value in a neighborhood of x and a nonzero probability of yielding a
value in a neighborhood of z must also have a nonzero probability of
yielding a value in a neighborhood of y."

The discrete decision ("Is the value greater or less than y"?) produces
a set of yes-no answers -- what Joy identifies as a fair coin in his
explanations -- that correlate 100% of each classical position of the
detector settings to at least one quantum state. That's all that is
required for mathematical completeness -- EPR and Bell's theorem are
based on classical assumptions, not quantum. As Lamport points out:

"Buridan=92s Principle rests upon mathematical concepts of continuity
and boundedness that are not physically observable. No real experiment,
having finite precision, can demonstrate the presence or absence of
continuity, which is defined in terms of limits. No experiment can
demonstrate that an arbiter requires an unbounded length of time to
reach a decision. An experiment in which the arbiter failed to decide
within a week does not prove that it would not always decide within a
year."

>Roughly
> speaking, the spin direction is determined by the deflection of
> the electron in a magnetic field, but for sufficiently high-velocity
> electrons, the deflection will be negligible. To me, this seems to
> mean that the theoretical correlations predicted by quantum mechanics
> will not be precisely mirrored by any actual experiment. I don't see
> why that observation is relevant to Christian's model, however.

My example shows that unitarity of Bell-Aspect results (0.5 + 0.5)
is subsumed in a full cycle of 4 pi rotations of fixed and oscillating
variables, consistent with Joy's framework..

>
> In the paper you cite, it is said that "Joy Christian's time-dependent
> model is deterministic with definite probabilities on the interval
> [0,1]." First of all, I didn't see time-dependence
> in Christian's model.

A continuous function has time-reverse symmetry. When that symmetry is
broken by the initial condition, the topology is orientable and the
system is time dependent.

> Second, I don't understand how the statistical
> prediction comes out of Christian's model:
>
> Probability that Bob's detector measures spin-up
> given that Alice's detector measures spin-up
> =3D sin^2(theta/2), where theta is the angle between
> the two detector orientations.

Remember -- the framework is not probabilistic, and thus obviates
assumptions that support probability theory. You are only assuming what
is to be proved, on the principle of equally likely outcomes. That
principle does not apply here.

> You make the distinction between a model that is probabilistic
> and a model that is statistical. I'm not sure that I understand
> the distinction between the two, unless by statistical you mean
> the apparent nondeterminism that results from ignoring fine-grained
> details.

I only make a distinction between statistical analysis and probabilistic
measure. The measure is classical and therefore non-probabilistic, but
the set of results that I think should be clear in what Lamport said,
will give us continuous correlation between every possible detector
setting and at least one quantum state. We're dealing with a continuous
range of values, not discrete and equally likely probabilities.

I think Lamport's example using Kepler's orbits is excellent:

"Kepler's first law states that the orbit of a planet is an ellipse.
This is not experimentally verifiable because any finite-precision
measurement of the orbit is consistent with an infinite number of
mathematical curves. In practice, what we can deduce from Kepler's law
is that measurement of the orbit will, to a good approximation, be
consistent with the predicted ellipse."

Joy's mathematical framework -- like Kepler's law -- makes the right
prediction. But only real measurement can show that it is physically
true. Which in fact, is the case in all mathematically complete
physical theories -- because otherwise we cannot in principle avoid
either singularities or the assumption of nonlocality.

Tom

FrediFizzx

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Jan 5, 2012, 8:27:22 AM1/5/12
to

Jos Bergervoet

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Jan 5, 2012, 11:02:18 AM1/5/12
to
On Jan 5, 8:57=A0am, Tom <thray...@aol.com> wrote:
...
> Joy's mathematical framework -- like Kepler's law -- makes the right
> prediction. =A0But only real measurement can show that it is physically
> true.

Has it been coded in a computer program already? Since it
is a local and realistic model then this is by definition possible.
Just some operations on a few bi-vectors or quaternions would
suffice! And then "simulated measurements" will either show
you correlations with the quantum-mechanics value (if Christian
is right) or just the classical value (if Bell is right).

Simply converting the equations to Matlab or Fortran gives you
the answer! I'm convinced Christian would agree with this.

--
Jos

Daryl McCullough

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Jan 5, 2012, 1:50:53 PM1/5/12
to
On Thursday, January 5, 2012 2:57:01 AM UTC-5, FrediFizzx wrote:
> "Daryl McCullough" <stevend...@yahoo.com> wrote

> > I certainly understand the difficulties of experimental analysis
> > in determining which events are part of a twin pair, and which
> > events are noise. But those complexities don't seem relevant to
> > Christian's arguments about Bell's theorem.
>
> Well, the statistics involved sure is a part of his argument.

So you are saying that the statistics of errors (missed detections
and false detections) are analyzed in his model? Where?

> > Christian specifically limited the possible values of mu to real
> > tri-vectors. Yes, if it were allowed to be complex, that would
> > allow more possibilities, but his model does not involve complex
> > tri-vectors.
>
> I suspect you don't understand what the tri-vectors are structure-wise in
> the model.

I understand Clifford algebras. But you're certainly
right, I don't understand how tri-vectors are used in predicting
the probability that Alice will measure spin-up given that Bob
measured spin-up. That's why I started this thread, to see if
anyone can explain how these probabilities are derived in
Christian's model. To respond that I don't understand is just
to repeat the premise of this thread.

> > I didn't mean it as a criticism of Christian, I meant it as
> > a way of asking a question about it. I don't understand how,
> > if the hidden variable mu can only take on two values (which
> > he assumes it does), how one can get 4 different outcomes,
> > if everything is deterministic (which I thought he was claiming).
> > If things are not deterministic, then I don't understand where
> > the additional nondeterminism is coming from in his model.
>
> Joy has responded to the above several times now.

Not in any clear way. Empirically, we find that if
Bob measures spin up along his choice of axis b,
then Alice will measure spin-up along her axis a
a fraction of the time

sin^2(theta/2)

where theta is the angle between the two axes. I've
asked repeatedly how that probabilistic result is
derived within Christian's model. I don't care so
much about the details of computing with Clifford
algebras--what's missing is a clear statement of
what it is that Christian is claiming:

Is he claiming that Alice's result is a deterministic
function of mu and her axis choice a, or not? If
he is, then where is the probabilistic aspect
coming from? What does the sin^2(theta/2) represent?

> I wish you would answer my question that I have asked
> you several times in the private email discussion.

Asking which line I had trouble with is completely
pointless. The problems I have with Christian's model are much
more basic than not understanding a specific mathematical
derivation. I don't understand what he is even claiming.

Is he claiming, in the spin-1/2 EPR experiment, that
Alice's result is a deterministic function of her
axis choice a and the value of the "hidden variable"
mu? That is, is he claiming (in the case where Alice's
axis a is held fixed) that in two different rounds of
an EPR experiment in which Alice recorded "spin-up"
during one round and "spin-down" during a second round,
that that means that mu took on different values for
those two rounds?

That's a very basic question, and I can't seem
to get an answer from anyone who claims to understand
Christian's model.

FrediFizzx

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Jan 6, 2012, 1:34:21 AM1/6/12
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"Daryl McCullough" <stevend...@yahoo.com> wrote in message
news:15720230.219.1325768845268.JavaMail.geo-discussion-forums@vbbeg7...
> On Thursday, January 5, 2012 2:57:01 AM UTC-5, FrediFizzx wrote:

>> I wish you would answer my question that I have asked
>> you several times in the private email discussion.
>
> Asking which line I had trouble with is completely
> pointless. The problems I have with Christian's model are much
> more basic than not understanding a specific mathematical
> derivation.

I didn't ask which line you had trouble with. I asked if you understood
everything up to the top of page 4. And if you don't, what specifically
don't you understand? We can't answer your question(s) unless you are
willing to get thru all the math with an understanding that is necessary to
properly explain it.

> I don't understand what he is even claiming.

Not sure how that could be when he has explained it to you several times
now. What does "On the Origins of Quantum Correlations" tell you?

http://arxiv.org/abs/1201.0775
New paper

Best,

Fred Diether


Tom

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Jan 6, 2012, 3:14:34 AM1/6/12
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On Jan 5, 11:02=A0am, Jos Bergervoet <jos.r.bergerv...@gmail.com> wrote:
> On Jan 5, 8:57=3DA0am, Tom <thray...@aol.com> wrote:
> ...
>
> > Joy's mathematical framework -- like Kepler's law -- makes the right
> > prediction. =3DA0But only real measurement can show that it is physically
> > true.
>
> Has it been coded in a computer program already? Since it
> is a local and realistic model then this is by definition possible.
> Just some operations on a few bi-vectors or quaternions would
> suffice! And then "simulated measurements" will either show
> you correlations with the quantum-mechanics value (if Christian
> is right) or just the classical value (if Bell is right).
>
> Simply converting the equations to Matlab or Fortran gives you
> the answer! I'm convinced Christian would agree with this.
>
> --
> Jos

Hi Jos,

No, I don't think so, though Joy can speak for himself. The problem is
that infinities will show up in this calculation, just as with the
infinite set of curves in the Kepler example, because the motion is
infinitely orientable. Yes, we can make assumptions of boundary
conditions based on topology and initial condition, to get a reasonable
simulation. However, also referring back to Lamport's example, how
convincing could that be to a Bell loyalist assuming nonlocality? Not
at all, I would think -- infinite parameters simply implies GIGO.

Physically, the measurements have to be empirical to get a physical
result (which is how we know of Kepler's elliptical orbits, and not by
assuming an ellipsis).

Tom

harald

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Jan 6, 2012, 3:34:43 AM1/6/12
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"FrediFizzx" <fredi...@hotmail.com> wrote in message
news:9mmci8...@mid.individual.net...
> "Daryl McCullough" <stevend...@yahoo.com> wrote in message
> news:15720230.219.1325768845268.JavaMail.geo-discussion-forums@vbbeg7...
>> On Thursday, January 5, 2012 2:57:01 AM UTC-5, FrediFizzx wrote:

[..]
>> I don't understand what he is even claiming.
>
> Not sure how that could be when he has explained it to you several times
> now. What does "On the Origins of Quantum Correlations" tell you?
>
> http://arxiv.org/abs/1201.0775
> New paper

Thanks, at least the introduction of that paper ("book"?) looks clearer than
the earlier ones - he first explains what Bell claimed* (indeed, already
that is often misunderstood!) and next he replaces Bell's first equation
(1.1) which he deems to be wrong, by his equation (1.3).

Harald

* I spotted a little omission in one sentence: "Bell attempted to prove that
no theory satisfying this criterion" should be "Bell attempted to prove that
no theory satisfying this criterion and perfectly reproducing quantum
mechanics"



Daryl McCullough

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Jan 6, 2012, 4:42:45 AM1/6/12
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On Thursday, January 5, 2012 2:57:01 AM UTC-5, FrediFizzx wrote:

> Joy has responded to the above several times now. I wish you would answer
> my question that I have asked you several times in the private email
> discussion. In the "Restoring..." paper, do you understand everything up to
> the top of page 4? If not, what don't you understand?

Let's start way back, on page 4, equations (16) and (17) of the paper
http://arxiv.org/abs/1106.0748

Those two equations say: (the A and B below are
script-A and script-B in Christian's paper)

A(alpha,mu) = {-I . a-tilda}{ +mu . a-tilda }
= +1 if mu = +I
= -1 if mu = -I

B(beta,mu) = {+I . b-tilda}{ +mu . b-tilda }
= -1 if mu = +I
= +1 if mu = -I

Now, ordinary mathematics would say that these two equations
imply that, for all alpha, beta and mu,

A(alpha,mu) = - B(beta,mu)

In other words, this model seems to predict perfect
anti-correlation between Alice's result and Bob's
result. That is, assuming that A(alpha,mu) = +1
means that Alice will measure spin-up, and
B(beta,mu) = +1 means that Bob will measure spin-up.
That would seem to mean that if Alice measures
spin-up, then Bob will measure spin-down with
100% probability. In contrast, the quantum
prediction is that if Alice measures spin-up,
then Bob will measure spin-up with probability
sin^2(theta/2), where theta is the angle
between Alice's detector orientation and
Bob's detector orientation.

So, either (1) A and B do not represent predictions
about what Alice and Bob will measure, or (2) Christian's
model does not agree with the predictions of quantum
mechanics, or (3) Alice and Bob share different values
of mu, or ...

Cl.Mass�

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Jan 6, 2012, 4:43:07 AM1/6/12
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>> In the belt trick, there are two fixed points that are topologically
>> identified. Actually, all the points of a 2-sphere surrounding the belt are
>> identified, which is equivalent to a point at infinity. But that is possible
>> only because there is a rigid material frame around it. There is not such
>> thing in a Bell-type experiment, at least in your model. In that instance,
>> the Dirac belt trick demonstrates nothing.

"Joy Christian" <hojo...@gmail.com> a �crit dans le message de
news:d1503675-1f55-4f82...@p42g2000vbt.googlegroups.com...
>
> Incorrect.
>
> In any EPR experiment there are two particles rotating
> with respect to each other. They are rotating (or spinning)
> in tandem, with each particle providing a material frame for
> the other. This is explained in greater detail in this paper:
> http://arxiv.org/abs/0806.3078 .

To be so, there must be a constraint such that the wave function has the
same value everywhere on a 2-sphere surrounding the whole setup. That
is not the case. Note that it is a strongly non-local constraint.

A similar idea is already used in a speculative (but consistent that
time) theory, the strand model: http://motionmountain.net/research.html
But that is possible because it isn't in the framework of quantum
theory.

Joy Christian

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Jan 6, 2012, 5:27:40 AM1/6/12
to
On Jan 6, 9:43am, "Cl.Mass " <akia...@fastwebnet.it> wrote:
> >> In the belt trick, there are two fixed points that are topologically
> >> identified. Actually, all the points of a 2-sphere surrounding the bel=
t are
> >> identified, which is equivalent to a point at infinity. But that is=
possible
> >> only because there is a rigid material frame around it. There is no=
t such
> >> thing in a Bell-type experiment, at least in your model. In that in=
stance,
> >> the Dirac belt trick demonstrates nothing.
>
> "Joy Christian" <hojoin...@gmail.com> a crit dans le message denews:d1503=
675-1f55-4f82-8...@p42g2000vbt.googlegroups.com...
>
>
>
> > Incorrect.
>
> > In any EPR experiment there are two particles rotating
> > with respect to each other. They are rotating (or spinning)
> > in tandem, with each particle providing a material frame for
> > the other. This is explained in greater detail in this paper:
> >http://arxiv.org/abs/0806.3078.
>
> To be so, there must be a constraint such that the wave function has the
> same value everywhere on a 2-sphere surrounding the whole setup. That
> is not the case. Note that it is a strongly non-local constraint.
>

What wave function? There are no wave functions
in my model. It is a classical, local-realistic model.

>
> A similar idea is already used in a speculative (but consistent that
> time) theory, the strand model:http://motionmountain.net/research.html
> But that is possible because it isn't in the framework of quantum
> theory.
>

Neither is my model.

Bell's theorem is not about wave functions or quantum
mechanics; it is about classical, local-realistic theories.

Joy Christian

Daryl McCullough

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Jan 6, 2012, 11:10:25 AM1/6/12
to
On Wednesday, January 4, 2012 12:40:35 PM UTC-5, Joy Christian wrote:
> On Jan 4, 3:44 am, Daryl McCullough <stevend...@yahoo.com> wrote:

> > I think that's a misunderstanding of Bell's argument. He wasn't in
> > any way claiming that the functions A(a,L) and B(b,L) are in any
> > sense "complete" descriptions of physical reality. He was assuming
> > that they are "more complete" (that is, they contain more information)
> > than the pure probabilistic predictions of quantum mechanics.
>
> This is misleading. Please read the first paragraph
> of Bell's famous paper. He starts by summarizing the
> EPR argument and builds on it to develop his own
> argument.

The paper is available here: http://philoscience.unibe.ch/documents/TexteHS10/bell1964epr.pdf

I don't think it supports your claim. You said, specifically:

"For example, it can be of relevance
to physics at all if and only if the
measurement functions presupposed
by Bell, namely A(a, L) and B(b, L),
satisfy the completeness criterion of EPR."

Bell does not say anything about the functions A(a,L) and
B(b,L) satisfying any completeness criterion. He is talking
about completeness in terms of the parameter L. L is supposed
to be a parameter (or set of parameters) specifying the state
of the spin-1/2 particle prior to the measurement of its spin.
Bell says:

"...Since we can predict in advance the result of measuring
any chosen component of sigma-2...it follows that the result
of any such measurement must actually be predetermined...this
predetermination implies the possibility of a more complete
specification of the state.

"Let this more complete specification be effected by means
of parameters lambda."

It seems clear to me that he's talking about the completeness
of the parameters lambda, not the functions A(a,lambda) and
B(b,lambda). The point of the latter two functions is that
*if* the outcome of an experiment is predetermined by some
hidden variable lambda, (as well as the settings a and b)
then there exists functions A and B that specify the outcomes
as a function of a,b and lambda. There is no claim being
made that A and B in any sense are complete characterizations
of the state of the particle.

> EPR's is a logically impeccable argument
> which shows, once and for all, that the description
> of physical reality provided by quantum mechanics
> is necessarily incomplete.

I don't agree that it is logically impeccable, but
that's another topic.

> The EPR argument itself is
> of course based on four premises, one of them being
> the completeness criterion. Bell's goal was to show
> that these premises are inconsistent. In particular,
> the reality and completeness criteria of EPR are
> incompatible with their locality criterion. Bell thought
> he had succeeded in showing this in his theorem. He
> was wrong, as at least I have shown in my papers.

Well, the whole point of this thread is that I
don't see how your model shows what Bell was wrong.
Bell was arguing about the nonexistence of deterministic
functions A(a,lambda) and B(b,lambda) such that
A and B always return either +1 or -1 and such that
A(a,lambda) = +1 iff Alice measuring the spin of
a particle with parameter lambda along direction a
will measure spin-up, and -1 iff she will measure
spin-down, and B(b,lambda) similarly predicts the
outcomes of Bob's measurement of spin along an axis
b. I don't see that you have shown the existence of
such functions A and B.

> I do not like to flaunt my credentials in this matter.
> But since there are people out there who seem to
> think that I am just some fruitcake who has not really
> understood Bell's argument, let me point out that
> I have been in this business since 1983 and have
> learned about the EPR-Bell debate at the feet of
> the greatest authority on the subject, namely Abner
> Shimony, and have been privileged enough to have
> had discussions with Bell himself on the matter on
> several occasions. So I think I know a thing or two
> about Bell's motivation and his theorem.

But your claims seem to contradict claims made by
both Bell and Shimony (Shimony summarizes the various
arguments here: http://plato.stanford.edu/entries/bell-theorem/

FrediFizzx

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Jan 6, 2012, 11:11:05 AM1/6/12
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"Joy Christian" <hojo...@gmail.com> wrote in message
news:a414ec28-d874-4c5c...@m20g2000vbf.googlegroups.com...
I reiterate; you have successfully shown that Bell's theorem does not make
proper contact with physical reality as concerns EPRB type scenarios. Easy
to see if one actually studies what you have done.

> I do not like to flaunt my credentials in this matter.
> But since there are people out there who seem to
> think that I am just some fruitcake who has not really
> understood Bell's argument, let me point out that
> I have been in this business since 1983 and have
> learned about the EPR-Bell debate at the feet of
> the greatest authority on the subject, namely Abner
> Shimony, and have been privileged enough to have
> had discussions with Bell himself on the matter on
> several occasions. So I think I know a thing or two
> about Bell's motivation and his theorem.

Hear! Hear! It might actually be helpful if you did flaunt your
credentials more. I think this is the second time in hundreds of
discussions that I have read or been involved in that you mention the above.

But one only has to read / study your papers with *serious intent* to
realize that you are in fact an expert in this field. I am a bit
disappointed that many of the criticisms here in this current discussion are
"generic" and not based on more specific details of your work. People...
please study the content in the papers and if you don't understand parts of
them, I am sure Joy would be happy to try to explain those parts to you.
You might be surprised if you can get past your prejudices. See my post at
the beginning of this thread for important links. Or for all,

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

Best,

Fred Diether

Jos Bergervoet

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Jan 6, 2012, 11:11:58 AM1/6/12
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On Jan 2, 7:05 pm, a student <of_1001_nig...@hotmail.com> wrote:
...
> ... she writes down the result
> +sqrt{3} if A.V is positive, and -sqrt{3} otherwise. Bob
> does the same (but relative to -V). What is the
> correlation between their measurement results? It is
> easily calculated as
> E(A,B) = -A.B,
> i.e, the same as the singlet state prediction. And
> look how local and realistic the model is! (and
> no topology required - clever me!).

Do you mean that Christian did not normalize the
correlation properly: E(A,B) / sqrt(E(A,A) E(B,B)) ?
Is there an equation in his paper where you could
simply insert the correct normalization and settle
this whole dispute?

And do you think that using S^3 instead of R^3 is
therefore not the essential distinction at all?

--
Jos

Daryl McCullough

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Jan 6, 2012, 11:12:32 AM1/6/12
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On Thursday, January 5, 2012 2:57:02 AM UTC-5, Tom wrote:
>Daryl McCullough wrote:

> > I can see the relevance of Lamport's Buridan's principle to EPR type
> > experiments: When trying to decide whether an electron is spin-up or
> > spin-down, there will be (if Lamport is correct) a number of cases
> > for which it cannot be decided in a bounded amount of time.
>
> Not a number of cases. 100% of the cases.

I read through Lamport's paper again, and it seems to me that
he is ambiguous about whether he is saying it applies in *every*
case, or in certain cases. He states (Section 2, page 4):

"A survey article on reaction times mentions two models that
describe the time needed to make a binary decision. Both models
predict that the decision time increases to infinity as the
stimulus approaches the point at which the correct decision
changes from zero to one."

That would seem to say that only ambiguous cases would
require infinite time. The claim that *every* binary
decision requires infinite time is completely contra