Great story, John. I think it's kind of ironic that W. Edwards Deming -- the father of statistical process control -- found his first customers among the Japanese. After all, a statistical method that puts power in the hands of the individual production worker seems to go against the grain of Japanese business culture, of which one Japanese manager I knew said, "the nail that sticks up gets hammered down."
And then they proceeded to kick our butts, by exporting American ingenuity. :-)
Hi Tom,
Actually it is more simple that what you describe. It is just due to the non-communitivity in the algebra. Which is familiar by just rotating a book two different ways. Anyways, the classical local realistic model does in fact produce the prediction of QM, -a.b.
I just respond to the remark "GAViewer sounds like 'graphic arts drawing' tool to me, and would not be built to select between a right or left mathematical handedness".
GAViewer is a research tool built by the authors of Geometric Algebra for Computer Science: Leo Dorst, Daniel Fontijne, Stephen Mann; see http://www.geometricalgebra.net/
I wouldn't call it a "graphic arts drawing tool".
It is built to select between right or left handedness: if "a b" is a right-handed geometric product then "b a" is left-handed.
The challenge to program Joy Christian's model in GAViewer is still open. Going back to Christian's 2007 paper there would not appear to be much work to do: the model is contained in formulas (16) to (19). Albert Jan Wonnink has therefore got about half way - he has done the second half. Only the first half still to do.
This essay appears indeed highly erudite but I wonder how much the author has understood of the authors he is citing. Let me illustrate this with the citations he gives to papers in an area I know well: Bell inequalities.
Instead of plugging the Joy Christian model, Thomas Ray is now plugging Hess and Philipp, who more than ten years ago published a bunch of papers with the main theme that Bell had forgotten about time. Actually, if you take the care the read Bell's famous Bertlmann's socks paper, you will see that Bell was very aware of the role of time, and gave specific experimental instructions so that one would *not* be able to blame a violation of his inequality on time.
Apart from an erudite verbal discussion of the issue of time in these experiments, Hess and Philipp also professed to have constructed a local hidden variables model which reproduced the singlet correlations but unfortunately -- inevitably, of course, by Bell's theorem -- their elaborate construction concealed a little math error. They forgot one of three subscripts somewhere deep in the computations and failed to normalise a measure to be a probability measure. This was pointed out by myself and others, and the model died a natural death. The time issues they raised *are* interesting. The possibility of a memory loophole was already being studied by several researchers including myself. All this activity led to Jan-Ake Larsson and myself discovering a "new" loophole in Aspect type experiments due to the fact that experimenters do not use a framework of predetermined time intervals for measurements. Instead, the detection times of two photons being close to one another is used to post-select the pair i.e. to discard all detection events which seem not to be paired. Disaster! A very non-local selection of which outcomes to keep, which to throw away. Biased sampling ... It turns out to be a far *worse* loophole than the famous detection loophole.
Later Hess used the Larsson-Gill approach to build simulation models for past experiments with these defect, together with Hans de Raedt. In his recent book, Hess claims that Larsson and I had *stolen* the idea from him. Well we were certainly inspired by his work, and as he pointed out, other people had noticed that there was an issue, before him.
The hidden title of Hess' book (published as "Einstein was Right!") is "Karl Hess was always right, at least, in retrospect".
Then a second authority whom Ray quotes is my friend Han Geurdes from the Netherlands who recently got a paper published in the journal RIP (results in physics) which is Elseviers' answer to predatory journals where, I am sorry to say, the author gets to pay an exhorbitant fee to have just about anything published. Geurdes' amazing insight is that an experimentally observed correlation might differ by some amount, in either direction, from the "true" theoretical correlation, hence that a local realist simulation model of a loophole free Bell-CHSH type experiment can easily produce a result larger than 2. The paper is discussed on PubPeer: https://pubpeer.com/publications/DBFF182E87F04FB92102CAC7E33046
Yes! The measured value of some physical quantity might be larger than the true value! Disaster? The end of experimental physics?
Smart people have already known that about half the time, the "observed" value of CHSH would be bigger than 2, half the time it would be smaller. That's why physicists who actually do experiments make sure that the sample size is rather larger and they compute a standard error and do a statistical significance test in order to show that the deviation they have observed above 2 could not be ascribed to merely chance variation around a "true" value equal to 2.
Regarding Bell, EPR and all that I note that Ray does *not* refer to Christian's work so I wonder if this means that he has now abandoned support of that direction?
Before spending just a few words on that, it should be mentioned that Doran and Lasenby's book on geometric algebra contains two whole chapters "doing" spin half, the singlet state, and all that, with geometric algebra. It is very elegant, and very interesting, and just the tip of the iceberg in this area. The only thing they don't do is provide a local realist model for the singlet correlations. (For obvious reasons ... Bell's theorem).
However it seems that geometric algebra is not so popular in this area any more. I suppose it did a good job at describing all the facts - all the facts which are also described in the conventional Hilbert space approach. It links them nicely to geometry. But it didn't take us any further. And just like the conventional Hilbert space approach, it does not tell us what is going on "under the hood" event by event. It is "just" another (mathematically isomorphic) way to derive the probabilities of what happens.
My recent analysis of Christian's early works including a tutorial on geometric algebra is on viXra: http://vixra.org/abs/1504.0102 "Does Geometric Algebra Provide a Loophole to Bell's Theorem?"
and Ray has given a link to a pdf discussing my paper here: http://fqxi.org/data/forum-attachments/Continuing_misguided_attacks_by.pdf
The point I want to make is that time and time again in this essay, I am sorry to say, the essayist does show that he does not know what he is talking about. IMHO. Sorry.
Gill's wordy reply support's Karl Hess's claim that Gill "makes himself a pretzel" to defend his views while disparaging constructive alternatives with irrelevant misdirection.
" ... Bell was very aware of the role of time, and gave specific experimental instructions so that one would *not* be able to blame a violation of his inequality on time".
Uh ... yeah. That's the core of what Hess-Philipp (and I) have been saying. The Bell-Aspect program does no more than prove its own assumptions.
Gill's "friend" Han Geurdes is cited (not quoted) as an example of a trivial proof that "The free will to choose both a proposition and the negation of that proposition is contradictory of free will in any physical sense." And I have discussed this with Han -- it is in fact, Gill himself who characterized the proof as 'trivial,' in the PubPeer discussion to which he refers, and I happen to agree with the characterization. The fact that it is trivial only underscores its importance to measure theory.
I have never "plugged" Joy Christian or anyone else. It is Gill who is so enamored of personality cults that he confuses science with scientist. At any rate, Joy Christian's program does not contradict the contents of the essay -- I just didn't need it to make my point.
Time and events to follow will reveal whether "the essayist knows what he is talking about." And whether the voice of authority is stronger than rational science.
Tom
Hi Fred,
Yes. Except that one cannot realize the full rotation in less than 4 dimensions. Early on, what made Joy's framework attractive to me is that it is compatible with Minkowski space. I tried every way I knew to create discontinuity in the result and thus falsify it. This is the same approach Gill uses in "finding" a nonexistent algebraic error.
And even though David Hestenes has been silent on the issue -- I cannot justify an alleged error based on quaternion algebra, when Christian clearly extends the measure space to octonions. "Spacetime algebra," therefore, fulfills time evolution without having to refer to time, given the extended measure space.
Best,
Tom
I have never doubted Richard Gill's sincerity and expertise in defending Bell's theorem orthodoxy. He is certainly misguided, though, in his assumption that Bell's Bertlmann's Socks analogy eliminates the issue of a missing time parameter.
Consider Bell's illustrations 4 & 5. Bell (and Gill) would have us believe that the Stern-Gerlach magnet rotation produces separated groups (quantum mechanical pattern) of particle detections as a result of fundamental quantum non-locality.
Einstein, however -- using the mathematical convention of Minkowski space -- never considered this spatial parameter independent of the time parameter. The problem arises in the microscopic scale. Every point of spacetime in relativity carries its own clock independent of scale, a point that Karl Hess and Walter Philipp made quite elegantly to apply on the quantum microscopic scale, and which Gill's (with Weihs, Zeilinger and Zukowski) criticism -- despite his claim -- fails to refute.
A modified version of the 2-slit experiment (Young), where particles are sent one at a time through the slits -- and nevertheless arrange themselves in the classical wave interference pattern as if each particle "knows" where the other went -- is local and time dependent. It is unmotivated, other than by mere assumptions of quantum entanglement and non-locality, that measurement scale affects hidden-variable continuity in the spacetime subspace of local measure. (I have an existence proof of this claim that I am not yet ready to discuss publicly.)
In the words of Hess-Philipp " ... a properly chosen sum of what we call setting dependent subspace product measures (SDSPM) does not violate Einstein-separability and does lead to the quantum result ..."
Tom
Bertlmann's Socks link: https://hal.archives-ouvertes.fr/jpa-00220688/en/
Tom,
I thought your approach to the essay topic via the mathematics of probabilities was rather challenging in the first place, and it is provocative of further questioning of what we *do* with math. On the surface its quite a simple thing to correlate probabilities to a space frame, like throwing darts. But having come to understand some of your theoretical thinking, you are reaching well beyond that concept.
I have known a number of people for years whom, once I dealt with it enough working with them, I came to recognize that they don't see things in a geometric sense though they are quite adept at shooting pool, operating cranes, or racing automobiles. They might rough out a sketch on a scrap of paper of how they want a site laid out for a small footer and spacing pilasters, but there will be no proportion at all in the sketch and it will as likely show the short dimension of a rectangle as the longer length. It is the numerical relationship that they see and the actual spatial relationship only in a moment to moment instinctive reaction. The final result, here to there.
There have been recent advances in brain mapping and studies of mathematic abilities that make me wonder. Even though algebra comes from geometry, do we as a species have an inherent disjunct between our spatial perception with its temporal dimension, and the perception of mathematical relationships in an abstract dimension? Brain scans of 'math whizzes' at work show areas larger than common, consuming high levels of oxygen. But is that only in the abstract, does it correspond to a sense of spatial environment?
That correspondence at a foundational level is what you seem to be driving at in your essay. And a perceptual lack of such a correspondence almost guarantees a perception of non-locality as the reality. Good luck getting that across, jrc
John, you are leaving your footprints on my mind, and I do appreciate it.
I am at work on a paper -- partial draft attached -- that shows rigorously and conclusively how Gill et al, fail to refute Hess-Philipp. They got it wrong, because their assumptions based on Bell's theorem are wrong.
Gill claims, "They forgot one of three subscripts somewhere deep in the computations and failed to normalise a measure to be a probability measure."
Gill fails to realize that normalization of a complete function in spacetime -- which is deterministic -- is not equivalent to normalization of an algebraic function in probability space. The attachment explains.
All best,
Dear Tom
Thanks for adding the link to Bertlmann's socks! Required reading for anyone interested in Bell and all that.
You mentioned: Hess-Philipp " ... a properly chosen sum of what we call setting dependent subspace product measures (SDSPM) does not violate Einstein-separability and does lead to the quantum result ..."
Unfortunately, their mathematical proof contained a fatal error. As of course it had to: if their model had been correct, it would have contradicted Bell's theorem. Of course, not many people actually worked through the pages and pages of computations using all kinds of advanced math stuff.
Before promoting the Hess-Philipp construction you should take a look at http://arxiv.org/abs/quant-ph/0204169 (Europhys. Lett. (2003) 61, 282-283) and http://arxiv.org/abs/quant-ph/0208187 (PNAS 2002, 99: 14632-14635). Hess and Philipp did acknowledge their mistake in one of their many later publications and came up with an incredible story about some elements of reality not being elements of reality and how hard it was to decide what was real and what was not real! Because they did need a *nonlocal* hidden variable to get their maths to work. Hence it was obviously not an element of reality. (I guess that Walter Philipp, the mathematician, realised that there was a mathematical error; I suspect that Karl Hess, the physicist, left the hard math stuff to his friend and colleague).
Well that sounds to me like BS. But of course, people like those guys must always be right.
Richard, I do not share your disparaging opinion of Hess and Philipp.
Computability is an issue separate from elements of reality. I understand the difference between nonlocal hidden variables (string theory is a theory of nonlocal hidden variables) and local realism. If we take Einstein on his own terms ("all physics is local") then metaphysically real elements are also local.
Our latest posts crossed. My attachment explains why I think you are wrong about the Hess-Philipp program. I don't see that you even addressed separability -- it is not at all a matter of experimenter choice.
Best,
Tom
A good example of how Bell (and Gill et al) confuse local realism with non-local probability is the abuse of terminology, Gill's "non-local distribution."
There is no such thing as a non-local probability distribution in a physical model. In fact, a demonstration of this fact is integral to Hess-Philipp's introduction of the time parameter.
John Cox has an elegant way of bringing the issues in line with everyday experience.
Having devoted part of my misspent youth to the pool table, John's reference to the relation between shooting pool and moment-to-moment instinct got me thinking about Hess-Philipp's timelike correlated parameters (TLCPs) .
Because initial condition changes with time, moment-to-moment action (event by event in QM simulation terms) avoids action at a distance " ... by letting the probability measure be a superposition of setting-dependent subspace product measures with two important properties: (i) the factors of the product measure depend only on parameters of the station that they describe, and (ii) the joint density of the pairs of setting-dependent parameters in the two stations is uniform."
The multiple time scales of a pool game range from the interval of contact of hand with cue, cue with cue ball, cue ball with object ball, ball with rail, etc. These are well understood causal events whose outcomes are all dependent on initial condition and energy content in the specified interval.
Gill, et al, criticism of Hess-Philipp completely avoids the causal framework -- they claim, " ... "(Hess-Philipp) forgot one of three subscripts somewhere deep in the computations and failed to normalise a measure to be a probability measure" -- which is completely irrelevant to the point made by H-P above (and well supported by the mathematics of the paper). Normalization of probability density in a time dependent causal relation is independent of energy density and initial condition. Hess-Philipp show that initial energy condition determines joint probability -- while Gill et al avow that (" ... because of Bell's theorem" as Gill claims) probability is prior to measurement. The measurement protocol of Bell-Aspect merely demonstrates its own prior conclusion.
While Gill et al are completely off the mark in convincing themselves that they have refuted Hess-Philipp -- the science of complex systems, in line with Bar-Yam's theory of multi-scale variety, supports timelike correlated parameters at multiple scales: http://home.comcast.net/~thomasray1209/ICCS2007PP.ppt
Tom
Tom,
I had meant to get back and discuss more about your fine essay. But time is running out, so at least I can give you an appropriate score.
Best,
Edwin Eugene Klingman
More should be said about why the Karl Hess and Walter Philipp PNAS paper of 2001 is a breakthrough in our understanding of time dependent systems, because it accents the physical identities among time, information and energy that characterizes complex systems -- and as the authors make explicit, the problem of decidability between Einstein and Bohr.
Criticisms of Hess-Philipp have failed to even address the key issues of Einstein separability and special relativity that drive the paper's conclusions. The critics know that these issues cannot be confronted head-on, because they are well-understood physical principles that cannot be refuted.
Let's return to a point I made in my essay (p.6), that Einstein's original quest for E = mc^2 substituted the Lagrangian (a system's energy content) for the E term, where E was then generalized to rest energy, so we get that famous equation. The continuous values of the Lagrangian, however -- vary with mass -- local measured. In reply to critics, Philipp-Hess simplified their explanation of the model (attached), such that " ... Imagine the time axis wrapped around a circle of circumference that corresponds to a time interval related to a simple measurement and normalized to 1. We suppose that for a fixed N each interval [(m в€' 1)/N, m/N ], m = 1, 2, . . . , N of arc length 1/N on the circle gets about its proper share of time measurement points over the measurement period." The authors go on to show time correlations that the critics ignore, and reproduce quantum correlations in a complete framework of distributed time-dependent energy/information. These results satisfy Einstein separability and special relativity in a way that the critics do not and cannot:
Because a continuous range of time-dependent energy values attends every classical measure, normalization of the time interval locally does not imply a global normalization (as Gill claims) -- because of the special relativity limit. Each measure carries its own time stamp, and it is always local.
Tom,
I'm glad I managed to get to your essay. Again I found little to disagree with, but then I'm now down to speed-reading so resolution is reduced! There's also now little time for discussion, which I suspect may be a blessing, though our fundamental views may have more in common than is often apparent. Certainly I found the essay beautifully 'bookended' with Bronowki's quote (always a guiding star for my own work) and your concluding paragraph.
"In聽 this聽 game聽 of聽 unlimited 聽possibilities called mathematics, our bet is 聽 on聽human聽imagination."
As you're a mathematician I'm particularly impressed with that. I see you're struggling to make the break point so I hope my score helps.
best wishes.
Peter
Peter,
Thank you, that's very kind. There's no mystery to why my score languishes below the cut -- never in my memory, from the first time I entered these competitions (which dates from the very beginning), has a fully relativistic viewpoint in foundational physics gotten due respect, while some of the fringiest views in quantum theory have won big prizes. So I have long abandoned any illusions I might have had. It is enough that the FQXi forum gives voice to a minority viewpoint that it de facto opposes, and I am grateful to the Institute for that, even when I think it could do more.
There is an even lower score than mine, given for a far better essay by Vesselin Petkov, and -- I expect -- is low for the same reasons. I am going to do a lazy thing, and quote Vesselin's reply to a recent forum participant, because it matches my opinion: " ... if Minkowski had lived to see the advent of general relativity, he would have realized, as a mathematician, that the mathematical formalism of general relativity implies that gravitational phenomena are merely manifestation of the non-Euclidean geometry of spacetime (not an interaction). Einstein made a gigantic step by linking gravity with spacetime geometry, but even he was unable to overcome the seemingly self-evident 'fact' that gravitational phenomena are caused by gravitational interaction (which, unfortunately, is still the accepted view in physics)."
Things are changing. I got an Email from The Minkowski Institute Press just a few days ago that they are publishing Cristi Stoica's PhD thesis (congratulations, Cristi!) , which is relativity-based, with a perturbative path to quantum gravity (my own solution is non-perturbative, but we are pretty close).
In regard to your own defense of conventional quantum theory in the Bertlmann's Socks analogy, I applaud your expansion of the pedagogy, and give high marks for that. It is deservedly among the best of Bell's output.
If you don't mind, I am going to do another lazy thing, and reproduce this reply in your forum.
All best,
Tom
We don't agree most times but we get to exchange ideas. It is good to rate those who are here come rain come shine and who have also contributed a nice essay. We continue our arguments (or 'quarrels') after the contest. You should now be able to make the list.
Akinbo
Dear Tom,
I'm sorry but it's late and I don't have time to comment properly, except to say that I really enjoyed your essay a lot; I hope to be able to comment properly tomorrow if the system still allows. I believe too that Vesselin should have received more attention. For what it's worth, you have my vote.
Alma
