Bell's Theorem and the New Statistics.
Jay Sulzberger
On Thu, 4 Jul 1996, Jack Sarfatti wrote:
> From: sarf...@ix.netcom.com (Jack Sarfatti )
> Newsgroups: sci.physics
> Subject: Re: Bell's theorem and the New Statistics.
> Date: 4 Jul 1996 23:31:39 GMT
>
> In <4rgm87$a...@news1.t1.usa.pipeline.com>
> egr...@nyc.pipeline.com(Edward Green) writes:
> >
> >'ja...@panix.com (Jay Sulzberger)' wrote:
> >
> >[Careful and explicit development]
> >
> >>Bell's Theorem. No Einstein-Podolsky-Rosen-Bohm circuit has as its
> >>input
> >>output behavior the Two Electron Singlet Thirds function.
> >
> >Thank you very much for a careful statement of (a) Bell's Theorem.
> >
>
> What is the "Two Electron Singlet Thirds function" ? Sounds goofy. But
> maybe I'm wrong. Please define it mathematically.
>
>
We do not here attempt the Army manual level of clarity. But the Two
Electron Singlet Complete function, write it as pc, is the probabilistic
function pc:S^1xS^1 --> { u, d }x{ u, d }, where S^1 is the circle,
given, for any phi in S^1 and theta in S^1, by:
pc( O1 = u and O2 = u | PHI = phi and THETA = theta ) =
1/2*sin^2( (phi-theta)/2) )
pc( O1 = u and O2 = d | PHI = phi and THETA = theta ) =
1/2*cos^2( (phi-theta)/2) )
pc( O1 = d and O2 = u | PHI = phi and THETA = theta ) =
1/2*cos^2( (phi-theta)/2) )
pc( O1 = d and O2 = d | PHI = phi and THETA = theta ) =
1/2*sin^2( (phi-theta)/2) )
Notation: PHI refers to the first S^1, THETA to the second, O1 to the
first { u, d }, and O2 to the second. Again pc is not a deterministic
function of S^1xS^1 but only a probabilistic one, also called a
probabilistic gate. Given phi and theta pc(phi,theta) is a probability
distribution on { u, d}x{ u, d }, here certainly not some Dirac delta.
In case the value of pc(phi,theta) were always a delta function we would
call pc an ordinary, or deterministic, function.
Please excuse abuse of notation in above.
According to the standard texts, say Dirac's, or David Bohm's, if we have
two electrons which are in the singlet state, and we set a Stern-Gerlach
device to angle phi to look at the first electron, and we set another
Stern-Gerlach device to look at the second electron, then pc gives the
probabilities of getting the various results (O1 = u and O2 = u),
(O1 = u and O2 = d), (O1 = d and O2 = u), (O1 = d and O2 = d).
In the Einstein-Podolsky-Rosen-Bohm set-up we explode the two electrons
away from each other, one going to the left, one going to the right, and
in the left experimental chamber we have a Stern-Gerlach device, and also
in the right, we have another Stern-Gerlach device. pc gives us the
results, again, only probabilistically, that quantum mechanics predicts.
Shortly pc is the prediction of quantum mechanics. Note that, of course,
we must arrange things so that the electrons' polarizations remain
undisturbed, otherwise we have to put another gate (or perhaps several
gates) in the arm with the disturbance, or two gates, one in each arm, if
both electrons are disturbed in their polarizations, ah, their 'spins'.
If instead of allowing all possible values for PHI we only allow the
values 0 and 2*pi/3, and for THETA the values 0 and -2*pi/3, we obtain
from pc, by the operation of restriction, the function I have called
p, the Two Electron Singlet Thirds function. Why 'Thirds'? Well look down
the axis of our experimental set-up. The possible settings of I1 and I2
divide the circle of angles into thirds. Note that both Stern-Gerlach
devices can be set to 0, but the other two angles only one device now
gets to be set at.
If no Einstein-Podolsky-Rosen-Bohm circuit can compute Two Electron
Singlet Thirds function p, then, a fortiori, no Einstein-Podolsky-Rosen-Bohm
circuit can compute the Two Electron Singlet Complete function pc.
Again, the quantum version of our (classical) circuit does indeed, we
believe, compute pc. That is, if our source is an exploding singlet pair
of electrons, and our other gates are Stern-Gerlach devices.
Please forgive obscurity of above.
I remain, as ever, your fellow reader of usenet, Jay Sulzberger.
PS. I shall be grateful for the correction of any numerical slips in the
definitions of pc and p.
Jay Sulzberger
On Thu, 3 Jul 1996, Edward Green wrote:
> From: egr...@nyc.pipeline.com(Edward Green)
> Newsgroups: sci.physics
> Subject: Re: Bell's Theorem
>
> 'Rams...@hermes.bc.edu (Keith Ramsay)' wrote:
>
> >Now for an inequality: p1q1+p2q1+p1q2-p2q2<=2.
> >This is not so hard. The LHS is linear in each variable
> >separately, so if it is ever >2, it is >2 for some values
> >of p1,p2,q1,q2 which are 0 or 1. The only way to get more
> >than two of the + terms, p1q1, p2q1, and p1q2, to be 1 is
> >by making p1=p2=q1=q2=1, but this makes p2q2 also 1, leaving
> >us with a LHS of just 2. I am not sure that this is the very
> >original inequality of Bell, but it is closely related.
>
> And this inequality is violated by experiment? Most odd.
>
> For the probabilities are all well defined in the absence of quantum
> mechanics, so this seems more in the nature of a tautology than an
> optional prediction. Perhaps we in effect redefine them in the course of
> doing the experiment.
I wish I had my work and Bell's before me. Bell published his theorem
while I was in high school, or just out of it. Within a year I read it. I
did not get it. What on earth are these probabilities? The only thing I
could see was the Einstein-Podolsky-Rosen-Bohm circuit. No probabilities
of events such as:
'the outcome on the right would be u if we had done the measurement with
the device set at -2*pi/3, instead of at 0, as we did'
Hunh? Why should there be any such event? There generally is not, for more
complicated circuits. Indeed for simple variants of the hoary old Markov
chain, which succeed in giving a completely classical completely local
explanation for the behavior of a single electron, subjected to a series of
'spin measurements' (What nonsense!, rather interactions with a
Stern-Gerlach device.).
The above comment is just what any student of probability circa 1960
would have said. I am sure many did, and like me, were not able to get
the paper.
So about every two years for the next 16 or so years, I tried again. each
time the same failure. What on earth is he doing? What is the point?
Then I read one line from an uncollected work of Mermin, and I got it.
There is a non-trivial theorem, which I call Bell's First Theorem,
which shows that the following two spaces are isomorphic as convex sets:
1. IOEPRB = { p:LIxRI --> LOxRO | p is computed by some EPRB circuit }
2. BKP = { (Mab,Mbc,Mcd,Mda) | there exists a joint distribution
call it prob, on the four variables a,b,c,d, such that
Mab = the marginal down to the variables a, and b
Mbc = the marginal down to the variables b, and c
Mcd = the marginal down to the variables c, and d
Mda = the marginal down to the variables d, and a }
'marginal' is to be read as 'the marginal of prob'.
Now once we have this first theorem, we can work entirely with the convex
set BKP, the Boole-Kolmogorov polyhedron.
The incorrect, but nearly universally accepted, theorem you implicitly
appealed to, is that BKP simply consists of all quadruples of
distributions that satisfy:
M(ab->b)(Mab) = M(bc->b)(Mbc)
M(bc->c)(Mbc) = M(cd->c)(Mcd)
M(cd->d)(Mcd) = M(da->d)(Mda)
M(da->a)(Mda) = M(ab->a)(Mab)
where M(xy->x)(Mxy) = the distribution on x derived by starting
with the distribution Mxy on x and y,
and marginalizing out y, to get down to just x.
(The above conditions are called the Kolmogorov consistency conditions.
They are not, in this case, sufficient for something to lie in KBP.)
Call this polyhedron the NSP, for no signalling polyhedron.
Well, BKP is not equal to NSP. The Two Electron Singlet Thirds function,
once we have passed over to the space containing the KSB, lies in NSP, but
not in BKP. BKP is strictly contained in NSP.
I think your earlier claim, staked in the mud, is equivalent, once one
has Bell's First Theorem, to:
NSP = BKP .
By the way, note that if the associated (hyper)graph, every BKP has one,
were acyclic in the sense of databases, then indeed, NSP = BKP .
The hypergraph here, which is just an ordinary graph, is the cycle
{ ab, bc, cd, da } . In the cyclic case you always need further conditions.
Now in all cases, acyclic or not, the smallest affine space in which NSP
lies, is the same as the smallest affine space in which BKP lies. This
was noted by Feynman in a talk he gave at MIT which I did not go to. This
shows that the only way to distinguish points lying in BKP from points
lying in NSP, is by some extra inequalities, which they must satisfy.
Such extra inequalities are called Bell's Inequalities.
>
> and 'aeph...@helios.physics (Aephraim M. Steinberg)' wrote:
>
> >However, probabilities are not
> >experimentally observable quantities; only detection events are.
> >Extending the inequality to apply to measurable entities
> >generally entails introducing certain supplementary assumptions
> >or "loopholes" before tests are possible in the lab.
>
> Well, probabilities are not "observable" in the sense of a direct meter
> reading on a single trial ("Probability shows point eight, sir!"), but
> they are certainly "observable" in the ordinary sense of relative
> frequencies; i.e., if we carry out a large number of trials of an
> apparently stable apparatus we expect with certainty that the relative
> frequencies will converge to the probabilities.
>
> Lurking here may be some confusion over total and marginal probabilities,
> or (equivalently) over the sample space. We can indeed estimate
> probabilities and correlations in the lab, and by repeating a stable
> experiment indefinitely we can achieve a precision that silences any
> reasonable objection. These estimates must with *certainty* eventually
> satisfy any tautologous inequalities we have derived by assuming that the
> estimated quantities are indeed probabilities! If they do not, I contend
> we are not discovering some strange new "quantum probabilities", but
> simply not estimating what we claimed we were going to estimate.
>
> 'aeph...@helios.physics (Aephraim M. Steinberg)' also wrote:
>
> >Testing any version of this involves having the ability to vary
> >certain parameters at positions A and B, and assume that the
> >parameters are being varied independently. Thus _any_ test
> >will rely on the unprovable assumption that one's decision to turn
> >a knob a certain way at A is independent of someone else's decision
> >to turn another knob a certain way at B. This seems a reasonable
> >assumption, although one can always postulate a completely deterministic
> >world which happens to mimic quantum mechanics, and thus appears
> >to violate the inequality although it is in fact local.
>
> Indeed, even a posited practical superluminal signalling device could be
> "explained" by considering that our seemingly independent choice of what to
> send was somehow conditioned by a *prior* signal arriving from an
> intermediate point, which also controlled the reception. But I see no
> need to drag such ideas in here, and I certainly *don't* base any
> skepticism on such an idea. It is the *absence* of dependence, of the
> possibility of driving the output of one detector by altering the other,
> that makes me skeptical of the idea of non-locality..
>
> If nature conspires to make pratical communication based on some "Aspect
> effect" impossible then I do not believe it is possible to even seriously
> discommode the hypothesis of "Physically Independent though Statistically
> Dependent Results" at the separated detectors. (I know this is just what
> Bell claims to do). Whatever we choose as the orientation (in a
> generalized sense) what we will observe is an increasingly accurate
> estimate of a stable underlying distribution of time coupled detections
> given these orientations, and we can always infer that this distribution
> was read into the photon pairs at birth.
Tremendous psychic speed at the bend. g-forces large.
Again, the Kolmogorov Consistency Conditions are not sufficient for the
consistency of collections of putative joint marginals. (Consistency here
just means they all come from some big joint distribution on all the
variables at once.) In spite of the famous theorem of Probability 101
called the Kolmogorov Consistency Theorem, which seems to many to say that
they are. Generally you need, in addition, the Bell's Inequalities.
>
> The statisical mud is deep here. I don't pretend to see entirely clearly,
> but I think it is deep enough that even experts are liable to fall into
> hidden traps.
I believe most professors of probability if asked what are the conditions
that (Mab,Mbc,Ncd,Mda) lie in BKP would confidently state that the
Kolmogorov Conditions are necessary and sufficient. However, I have had
one get it right. Also a very good carpenter once got all of the Bell's
Inequalities for the 4 cycle, a,b,c,d taking values in { u, d }, while
having a coffee on the dias at harvard Square, about ten years ago. He
gazed off into space for about ten minutes then got it. I did warn him
that it was a question with an obvious, but wrong, answer.
>
> --
>
> Ed Green / egr...@nyc.pipeline.com
>
> "Every one being allowed to learn to read, ruineth in the long run not
> only writing but also thinking." -- Nietzsche
>
I see I am now writing stuff too compressed to be useful. So I stop.
Jay Sulzberger.
PS. Sorry for inconsistent notation. We should really write A,B,C,D
instead of a,b,c,d, but then what do you do about M, which is of a
different logical level.
Jay Sulzberger
On Thu, 4 Jul 1996, Edward Green wrote:
> Newsgroups: sci.physics
> Subject: Re: Bell's Theorem and the New Statistics
>
> 'rto...@kcbbs.gen.nz (Ray Tomes)' wrote:
>
> >...Several people in this group
> >have claimed that the existing experiments are inconclusive
> >because they do not measure the time of the events to
> >sufficient accuracy to prove that slower than light
> >signalling was not the cause of correlations. I want to
> >demonstrate that efforts in this direction are pointless.
>
> Thanks Ray. That is pretty much my thinking. Supposing that the two
> measurement events may talk to each other via v <= c signals is looking
> for a "loophole". But as you know my hunch is that it is not a loophole we
> should be looking for, but a faulty premise. For the measurements to
> talk to each other this way via "ordinary" signals is no less perverse than
> for them to talk to each other via superluminal signals! It's the idea
> that these distant events somehow "follow each other's careers from afar
> with considerable interest" that excites my skepticism. Superluminal
> signalling is small change compared to that.
>
> >The lines show the direction of causal effects.
> >
> >[1] What is assumed to happen [2] What the experiments don't eliminate
>
> [see original for graphics]
>
> >Suppose that a clock was set up to send signals to A and B
> >so that the events there could be timed to adequate
> >accuracy to ensure that [2] above is not what is happening.
> >Would this prove anything?
> >
> >I believe not. If nature is so perverse (or whatever you
> >want to call it) that EPR effects follow a diagram like [2]
> >above then nature can equally well do the SAME THING with
> >the TIME signals. In other words the clock signals could
> >also follow the same path. Please don't tell me that this
> >is stupid, because I know. But it is no more stupid than
> >believing that diagram [2] is right in the first place. If
> >nature were this perverse then there would be no way to
> >eliminate this possibility.
>
> Right. The key here seems to be that nature is supposedly shown to be
> perverse. The "need better time measurement" response seems to consider
> that we have not yet proven that nature must be perverse in *that* way, we
> must also still consider the possibility that she is perverse *this* way.
> I believe she actually leads a normal lifestyle. :-)
>
> Proponents of each side impute the other with taking nature to be *more*
> perverse. Each accuses the other of worrying about frippery like "can the
> creation event "control" our choice of detector angles?", or "if we had
> chosen a different detector angle, would we have gotten some other
> definite result", and so forth. (Well, in fairness, not everyone
> belongs to a side. But these things are voiced).
>
> Following Jay Sulzberger's excellent post, I find myself even more
> convinced for now that no extrodinarity causality is needed (which may
> disappoint him, since I think he had the opposite end in mind :-).
I shall do something which is a bit unfair. I shall tell you what is
around the bend, but, of course, you have to get around the bend yourself.
No extraordinary causality is needed. All you need is the ordinary rules
of ordinary quantum causality. Indeed quantum mechanics agrees that the
left hand electron sends no signal to the right hand chamber, nothing to
the right hand electron, nothing to the right hand device, nothing to
their combination. And nothing goes the other way either. And they do not
conspire and secretly meet in the middle. No, they are just quantum
objects, and their version of no collusion is quite different from that of
classical objects. The underlying topology of influence given for the
Einstein-Podolsky-Rosen-Bohm set-up given by the directed graph of my
earlier post is the same. Just as relativity left Maxwell's equations
unchanged and instead changed the concepts of here/now vs. there/then, so
quantum mechanics leaves intact every diagram of influence known to
physics. It just changes the meaning of the word 'is'.
> I'm
> not sure yet why I think the probabilistic gate model may not be an
> adequate representation (and as always, I may simply be wrong), but I
> want to borrow his nice causation diagram:
>
> 'ja...@panix.com (Jay Sulzberger)' wrote:
>
> >Let C be circuit built of probabilistic gates having the following graph:
>
> _____
> | |
> | |
> |_____|
> / \
> / \
> \ / \ /
> \ / \ /
> \_____ / \_____/
> | | | |
> | | | |
> |_____| |_____|
> | |
> | |
> | |
>
> The top box represents the photon source, whence information flows to the
> two detector boxes. The extra wires on top of the detector boxes represent
> choice of some detector parameter ("orientation"), and the bottom lines
> are the output, the actual measurements. I just want to use this diagram
> to describe information flow; I'm not keeping to detailed model Sulzberger
> gives.
>
> A lot seems to be made out of changing the detector orientation, and
> whether we do it while the photons are in flight, and so forth. These
> concerns reflect both of the "No, *you* are the one who thinks nature is
> more perverse" arguments above; viz: the possibility that a homonucleus
> sitting on the source is monitoring the detector positions with radar and
> adjusting his nefarious output accordingly, and the worry that, somehow,
> we can't seem to perform the experiment with the detectors set to both
> values simultaneously!
>
> This is a characteristic feature of laboratory measurement, that we can
> only set an input to a single value at a time and must depend on the
> continuity of nature and the stability of the experiment to allow us to
> repeat it with another value later. (If the output is random then of
> course we must repeat both setting enough times to sketch out the
> distribution.) This is normal everyday stuff, but somehow in the
> presence of quantum mechanics, we go all queer inside, and start wondering
> about the mystical meaning of it all, because everything involved with
> quantum mechanics is weird. ;-)
>
> Now, just bear with me a moment longer while I sketch out a crude
> informational picture using this diagram.
>
> "A pair of photons is created", and two information packets propagate
> outward along the wires from the source. Never mind *what* this
> information is, or whether it fully determines the measurements. Think of
> it as some parameters to plug into probability distributions if you like.
> Correlated at birth, thereafter divorced.
Yes. Yes, and yes. This is exactly what our circuit diagram formalizes.
The rules of classical locality are just the rules by which one goes from
the behavior of all the gates to the total bahavior of the whole circuit,
and then, by just 'marginalizing out' the internal wires, gets the input
output behavior of the gate.
We could have quantum gates in our circuit. They are different things from
classical gates. But they too have their own proper rules of (quantum)
locality. Again one goes from the behavior of all the gates to the total
behavior of the whole circuit, then to the input output behavior.
Again, if we used the proper quantum gates we can get a quantum circuit,
whose underlying graph, that is, whose diagram of influence, is as we
have drawn, and whose input output behavior is the Two Electron Singlet
Thirds function. Aspect tried to do so, and yes, his set-up is not quite
clean, but you have discussed the unlikelihood that Nature is as dull in
her plots as the repulsively boring theories of conspiracy of the poor
paranoid. As we know the real conspiracy is always deeper, funnier, and
much more frightening. Not so cozy, let us say.
>
> Now, imagine this information reaching the detectors. At some time, maybe
> last Tuesday, maybe while the photon is already on its way, with a wicked
> gleam in our eye, we have set both detectors to definite angles. By
> assumption, for each choice of angles there is some definite expected
> correlation between measurements on the two legs, but no possibility of
> signalling. Therefore, *for each orientation*...
>
> [Long pause for thought...]
You are coming into the bend. You are going faster than you think, and in
a direction not easy to feel, yet.
>
> Well Ray, it looks like I may have to eat crow (eat byte?) I begin to
> see, just vaguely, how some data structure might conceivably exist that
> cannot be reproduced by such models, yet do not allow for signalling. At
> least I no longer think it can be dismissed out of hand. And that lets the
> cat in the door.
Confucius says in the Analects "First comes the rectification of names."
Nobody on earth who deals with 'local realistic theories' calls them
anything other than:
1. circuits of probabilistic gates, or
2. influence, or path, or Bayesian, diagrams, or
3. hyperbolic partial differential equations,
except for physicists and professors of philosophy studying 'quantum
weirdness'. If you are such, then you call these things 'local realistic
theories', and now you are stuck. Because if you look up 'local realistic
theories' in the card catalogue, you do not get the references to the work
of the computational complexity people, who call them 1, the work of the
statisticians, who call them 2, or the work of the differential equations
folk, who call them 3.
>
> Can nature really be doing this to us? Is she not the nice girl we thought
> she was? I still cannot believe this of her, but Othello is whispering
> the damning evidence in my ear. I begin to doubt.
>
> Well, I had such a pleasant scoff above that I can't bear to erase it, so
> I will just post the whole thing anyway. If this nonsense really is true,
> and for every reference frame, then I fear we will have to call Louis
> Savain back in and have him help us demolish the illusion of space. Let us
> pray it does not come to that.
Jay Sulzberger
On Fri, 5 Jul 1996, Edward Green wrote:
Newsgroups: sci.physics
Subject: Re: Bell's theorem and the New Statistics.
> 'sarf...@ix.netcom.com (Jack Sarfatti )' wrote:
>
> >What is the "Two Electron Singlet Thirds function" ? Sounds
> >goofy. But maybe I'm wrong. Please define it mathematically.
>
> See Sulzberger's original post. He did so very carefully. I just quoted
> it without the development.
May I also apologize here for writing in one of my posts recently I1 and
I2, and O1 and O2, which would have better been written as LI, RI, LO,
and RO, as I had them in my first post.
It turns out that the usual textbooks of probability do not get enough
pedantic formal definitions through to the student right at the beginning,
and some of the obscurity of Bell's Theorem is due just to lack of proper
elementary definitions. The texts would indeed have to be somewhat
longer to do it right.
Jay Sulzberger.
Jay Sulzberger
On Fri, 5 Jul 1996, Jay Sulzberger wrote:
> Newsgroups: sci.physics
> Subject: Re: Bell's Theorem and the New Statistics.
<stuff deleted>
The material is hard enough without slips of the fingers.
I wrote:
>
> (The above conditions are called the Kolmogorov consistency conditions.
> They are not, in this case, sufficient for something to lie in KBP.)
>
> Call this polyhedron the NSP, for no signalling polyhedron.
> Well, BKP is not equal to NSP. The Two Electron Singlet Thirds function,
> once we have passed over to the space containing the KSB, lies in NSP, but
> not in BKP. BKP is strictly contained in NSP.
What I should have written is:
(The above conditions are called the Kolmogorov Consistency Conditions.
They are not, in this case, sufficient for something to lie in BKP.)
Call this polyhedron the NSP, for no signaling polyhedron.
Well, BKP is not equal to NSP. The Two Electron Singlet Thirds function,
once we have passed over to the space containing both BKP and NSP, lies in
NSP, but not in BKP. BKP is strictly contained in NSP.
OK. End of correction of slips.
We should mention at this point that there is a third set of points.
We have IOEPRB (isomorphic to BKP), and the NSP, the polyhedron
of probabilistic functions p:LIxRI --> LOxRO which do not allow signaling.
(In the last we have silently applied the isomorphism.)
Of course, we also have IOQEPRB defined by:
3. IOQEPRB = { p:LIxRI --> LOxRO | p is computed by some quantum EPRB
circuit }
We should really now call IOEPRB IOCEPRB.
IOQEPRB is not a polyhedron. Rather it has curved faces.
So here is the diagram of strict inclusions:
IOCEPRB < IOQEPRB < NSP .
I have not given the isomorphism guaranteed by Bell's First Theorem, so
this may all be somewhat unclear.
Recently the comparative study of the classical computer and the quantum
computer has become popular. Bell's Theorem is part of this study.
Jay Sulzberger.
Jack Sarfatti
In <4ri83j$k...@panix3.panix.com> ja...@panix.com (Jay Sulzberger)
writes:
>
>We do not here attempt the Army manual level of clarity. But the Two
>Electron Singlet Complete function, write it as pc, is the
probabilistic
>function pc:S^1xS^1 --> { u, d }x{ u, d }, where S^1 is the circle,
>given, for any phi in S^1 and theta in S^1, by:
>
> pc( O1 = u and O2 = u | PHI = phi and THETA = theta ) =
> 1/2*sin^2( (phi-theta)/2) )
>
> pc( O1 = u and O2 = d | PHI = phi and THETA = theta ) =
> 1/2*cos^2( (phi-theta)/2) )
>
> pc( O1 = d and O2 = u | PHI = phi and THETA = theta ) =
> 1/2*cos^2( (phi-theta)/2) )
>
> pc( O1 = d and O2 = d | PHI = phi and THETA = theta ) =
> 1/2*sin^2( (phi-theta)/2) )
>
>
>Notation: PHI refers to the first S^1, THETA to the second, O1 to the
>first { u, d }, and O2 to the second. Again pc is not a deterministic
>function of S^1xS^1 but only a probabilistic one, also called a
>probabilistic gate. Given phi and theta pc(phi,theta) is a probability
>distribution on { u, d}x{ u, d }, here certainly not some Dirac delta.
>In case the value of pc(phi,theta) were always a delta function we
>would call pc an ordinary, or deterministic, function.
>
>Please excuse abuse of notation in above.
OK, I recognize the above joint probabilities as the standard
predictions of ordinary quantum mechanics confirmed by all the
experiments that are accepted as correct. But why use all that
fancy math which only clouds the physics? What new info do you get
from using the fancy math?
>Shortly pc is the prediction of quantum mechanics.
Yes, that's fine.
>Note that, of course,
>we must arrange things so that the electrons' polarizations remain
>undisturbed, otherwise we have to put another gate (or perhaps several
>gates) in the arm with the disturbance, or two gates, one in each arm,
>if
>both electrons are disturbed in their polarizations, ah, their
>'spins'.
You mean like a quantum eraser experiment?
>
>
>If instead of allowing all possible values for PHI we only allow the
>values 0 and 2*pi/3, and for THETA the values 0 and -2*pi/3, we obtain
>from pc, by the operation of restriction, the function I have called
>p, the Two Electron Singlet Thirds function.
You mean you are looking for a special case where the difference
between Bell's locality inequality and the QM prediction is maximal?
>
>
>If no Einstein-Podolsky-Rosen-Bohm circuit can compute Two Electron
>Singlet Thirds function p, then, a fortiori, no
>Einstein-Podolsky-Rosen-Bohm
>circuit can compute the Two Electron Singlet Complete function pc.
You just lost me. QM can certainly predict the joint probability
when PHI and THETA have those special values. But don't you mean
that Bell's locality inequality gives a significantly different
prediction for those cases? What is a "Einstein-Podolsky-Rosen-Bohm
circuit"? This appears to be less with more. It is not a standard
term so why do you use it?
>
>Again, the quantum version of our (classical) circuit does indeed, we
>believe, compute pc. That is, if our source is an exploding singlet
>pair of electrons, and our other gates are Stern-Gerlach devices.
OK, I think you are saying what I am saying but you certainly have
beat around the bush. :-)
>
>
>Please forgive obscurity of above.
You are forgiven - but what's your point in doing all this? :-)
Jack Sarfatti
In <4rihii$n...@panix3.panix.com> ja...@panix.com (Jay Sulzberger)
writes:
>> Superluminal signalling is small change compared to that.
If your criterion for a "signal" is a shift in the local probability
caused by a spacelike-separated change in a knob setting, then
Eberhard's theorem forbids it. However, in the new theory with
"back-action" which is beyond ordinary quantum theory because of the
nonunitary "friction" term in the GRW density matrix evolution
equation, such signalling is possible as shown in
http://www.hia.com/hia/pcr/valentin.html
My theory saus that superluminal signalling of thsi kind can only
happen in sentient quantum systems in which thermal decoherence is
screened out so that the back-action becomes the dominant mechanism.
This is in agreement with Brian Josephson's paper on "Biological
Utilization of Nonlocality" published in Foundations of Physics and
with Stapp's paper in Phys Rev. A July 15, 1994 p.18.
Brian J Flanagan
iOn 5 Jul 1996, Jack Sarfatti wrote:
> In <4ri83j$k...@panix3.panix.com> ja...@panix.com (Jay Sulzberger)
> writes:
>
> >Please excuse abuse of notation in above.
BJ: I only find myself wishing (once again) that we could use standard
mathematical notation in this forum.
>
> fancy math which only clouds the physics? What new info do you get
> from using the fancy math?
BJ: Quantifiable predictions?
>
> >both electrons are disturbed in their polarizations, ah, their
> >'spins'.
>
> You mean like a quantum eraser experiment?
>
BJ: This *is* a bit jumbled.
> >
> >Please forgive obscurity of above.
>
> You are forgiven - but what's your point in doing all this? :-)
>
BJ: I'd also like to know what an EPR-B circuit is, please.
Jack Sarfatti
In
<Pine.A32.3.91.960705210608....@black.weeg.uiow
edu> Brian J Flanagan <bfla...@blue.weeg.uiowa.edu> writes:
>
>BJ: I only find myself wishing (once again) that we could use standard
>mathematical notation in this forum.
This is coming soon. Adobe and Microsoft are coming out with a new web
program that will allow all fonts including symbol on the internet.
Edward Green
'ja...@panix.com (Jay Sulzberger)' wrote:
>I shall do something which is a bit unfair. I shall tell you what is
>around the bend, but, of course, you have to get around the bend yourself.
>No extraordinary causality is needed. All you need is the ordinary rules
>of ordinary quantum causality. Indeed quantum mechanics agrees that the
>left hand electron sends no signal to the right hand chamber, nothing to
>the right hand electron, nothing to the right hand device, nothing to
>their combination. And nothing goes the other way either. And they do
not
>conspire and secretly meet in the middle. No, they are just quantum
>objects, and their version of no collusion is quite different from that of
>classical objects. The underlying topology of influence given for the
>Einstein-Podolsky-Rosen-Bohm set-up given by the directed graph of my
>earlier post is the same. Just as relativity left Maxwell's equations
>unchanged and instead changed the concepts of here/now vs. there/then, so
>quantum mechanics leaves intact every diagram of influence known to
>physics. It just changes the meaning of the word 'is'.
Then I am indeed only half way there, as you said. Now you are opening a
higher vista, when I am still panting from the first climb, and in danger
of falling off the ledge.
The underlying topology of influence is the same as classically? They
don't talk to each other? There is no collusion?
I have a lot of homework to do. I guess I'll just have to buy the book.
Edward Green
>with a new web program that will allow all fonts including
>symbol on the internet.
what you mean is that all fonts would be available on usenet, the basis of
"this forum".
That would be helpful, but I fear it would lessen the equal democratic
access. Part of the charm of usenet is that anybody with a plain text
terminal can communicate as well as anybody else. Completely equalitarian.
Nonetheless, technology must advance eventually, and rather than allow
new fonts and pretty graphics, what I think would really be useful is the
addition of a scratchpad -- i.e., the ability to easily embed sketchs and
hand written equations. People have objected to this on the basis of
bandwidth, but, heck, we already have binary newsgroups, and bandwidth
becomes cheaper all the time.
I think this would be the most transparent, user-friendly and informal way
of extending the abilities of the net.
Matthew J. McIrvin
In article <4rr0hk$n...@news1.t1.usa.pipeline.com>,
> new fonts and pretty graphics, what I think would really be useful is the
> addition of a scratchpad -- i.e., the ability to easily embed sketchs and
> hand written equations. People have objected to this on the basis of
> bandwidth, but, heck, we already have binary newsgroups, and bandwidth
> becomes cheaper all the time.
>
> I think this would be the most transparent, user-friendly and informal way
> of extending the abilities of the net.
This scratchpad already exists in a clumsy way, and making it elegant would
probably not be very hard in principle.
The clumsy way is to scribble out, say, a GIF file with whatever painting
program you have, and then attach the resulting file using MIME and Base64
or uuencoding. Many modern newsreading programs can be set to automatically
decode the attachment and display the result using the viewer of your
choice as a helper application. If somebody did this now, I'd be able to
see it by clicking a big button on my screen. (My newsreader also makes
the attachment process fairly easy.)
Making it elegant would just involve incorporating a very simple paint
program into the newsreader.
The bandwidth involved might be large compared to text, but nowhere near
as large as in most binaries groups, because the pictures could just be
black and white line drawings-- the compression algorithms built into the
popular image formats work wonders on those.
Even greater savings might be achieved by representing the drawings in
vector form, unless they are very complicated.
The drawback is, again, the problem of Net democracy. Not everybody has
software that handles attachments nicely; I see them only as the ability
to get a binary by clicking on a button, but to some they just show up as
pages of ASCII gobbledygook. (I was going to attach a 500-byte scrawl
of the Dirac equation to this post, but I suspect that even that would
make people angry.) Presumably the passage of time will fix this
to some extent.
--
Matt McIrvin <http://world.std.com/~mmcirvin/>
Edward Green
'mmci...@world.std.com (Matthew J. McIrvin)' wrote:
>The drawback is, again, the problem of Net democracy. Not everybody has
>software that handles attachments nicely; I see them only as the ability
>to get a binary by clicking on a button, but to some they just show up as
>pages of ASCII gobbledygook. (I was going to attach a 500-byte scrawl
>of the Dirac equation to this post, but I suspect that even that would
>make people angry.) Presumably the passage of time will fix this
>to some extent.
someway of decoding attached files using my software.
But, based on no evidence whatsoever, it seems to me that sometime next
decade the installed hardware base would have progressed so that an
industry wide standard to do this transparently would be possible. A
stylus pad would seem desirable.
Matt McIrvin
In article <4s0j3t$5...@news1.t1.usa.pipeline.com>,
egr...@nyc.pipeline.com(Edward Green) wrote:
> But, based on no evidence whatsoever, it seems to me that sometime next
> decade the installed hardware base would have progressed so that an
> industry wide standard to do this transparently would be possible. A
> stylus pad would seem desirable.
I just played with a recent incarnation of the Apple Newton MessagePad
that was running the Newton 2.0 OS. It was a demo model in a store,
completely untrained to recognize my handwriting. To my utter
astonishment, the thing worked perfectly! It read my handwriting
and didn't miss a letter. They seem to have finally gotten it right,
albeit a few years too late.
Now what I want is for someone to build handwriting recognition that can
understand equations. This seems to me to be the ideal application for
handwriting recognition. I find typing easier than handwriting, *except*
when I am typing equations, in which case I would love to be able to just
write them on a pad and instantly code them in. A stylus pad of this sort
with some major computing horsepower, and Mathematica or the equivalent
built in, would be heavenly.
Of course, for transmitting them over the net, you don't need this sort of
capability, just a simple graphics tablet of the type you can buy today,
and an elegant means of attaching, say, black-and-white GIFs built into
the news posting software, which *almost* already exists.
Ken Muldrew
mmci...@world.std.com (Matt McIrvin) wrote:
>I just played with a recent incarnation of the Apple Newton MessagePad
>that was running the Newton 2.0 OS. It was a demo model in a store,
>completely untrained to recognize my handwriting. To my utter
>astonishment, the thing worked perfectly! It read my handwriting
>and didn't miss a letter. They seem to have finally gotten it right,
>albeit a few years too late.
>Now what I want is for someone to build handwriting recognition that can
>understand equations. This seems to me to be the ideal application for
>handwriting recognition. I find typing easier than handwriting, *except*
>when I am typing equations, in which case I would love to be able to just
>write them on a pad and instantly code them in. A stylus pad of this sort
>with some major computing horsepower, and Mathematica or the equivalent
>built in, would be heavenly.
About 4 years ago there was a lot of noise from one of the original
people behind Lotus about a handheld calculator with handwriting
recognition. This was supposed to be easier than the Newton project
because people were more uniform in writing numbers and there are
fewer of them to recognize. I can't remember what level of sw was
planned, but I doubt that symbolic math was to be included. Sadly,
I've not heard anything about it since. Perhaps someone will write the
necessary code for the Newton; I think I'd hawk my guitar if it had
Mathematica built in.
Ken Muldrew
kmul...@acs.ucalgary.ca
Matt McIrvin
In article <4s64vk$17...@ds2.acs.ucalgary.ca>, kmul...@acs.ucalgary.ca
(Ken Muldrew) wrote:
> Sadly,
> I've not heard anything about it since. Perhaps someone will write the
> necessary code for the Newton; I think I'd hawk my guitar if it had
> Mathematica built in.
I suspect you'd need better hardware and OS than what's in a Newton to
make Mathematica work well, handwriting recognition considerations aside.
However, I'm sure someone could at least give it the equivalent of the
HP48 operating system-- an equation-recognizing gizmo could then replace
the 48's slow and awkward equation-entry mode. Beef up the integration
routines a little and it would be pretty nice to carry around.