Paul Adrien Maurice Dirac was born in 1902 in Bristol, England. His father, Charles, was a Swiss-French immigrant who made his living as a French teacher at a local school and as a private tutor in French. His mother, Florence (Flo), had given up her job as a librarian upon marrying Charles. The young Paul and his older brother Felix found themselves growing up in a very unusual, verging upon bizarre, home environment. Their father was as strict a disciplinarian at home as in the schoolroom, and spoke only French to his children, requiring them to answer in that language and abruptly correcting them if they committed any *faute de français*. Flo spoke to the children only in English, and since the Diracs rarely received visitors at home, before going to school Paul got the idea that men and women spoke different languages. At dinner time Charles and Paul would eat in the dining room, speaking French exclusively (with any error swiftly chastised) while Flo, Felix, and younger daughter Betty ate in the kitchen, speaking English. Paul quickly learned that the less he said, the fewer opportunities for error and humiliation, and he traced his famous reputation for taciturnity to his childhood experience.

(It should be noted that the only account we have of Dirac’s childhood experience comes from himself, much later in life. He made no attempt to conceal the extent he despised his father [who was respected by his colleagues and acquaintances in Bristol], and there is no way to know whether Paul exaggerated or embroidered upon the circumstances of his childhood.)

After a primary education in which he was regarded as a sound but not exceptional pupil, Paul followed his brother Felix into the Merchant Venturers’ School, a Bristol technical school ranked among the finest in the country. There he quickly distinguished himself, ranking near the top in most subjects. The instruction was intensely practical, eschewing Latin, Greek, and music in favour of mathematics, science, geometric and mechanical drawing, and practical skills such as operating machine tools. Dirac learned physics and mathematics with the engineer’s eye to “getting the answer out” as opposed to finding the most elegant solution to the problem. He then pursued his engineering studies at Bristol University, where he excelled in mathematics but struggled with experiments.

Dirac graduated with a first-class honours degree in engineering, only to find the British economy in a terrible post-war depression, the worst economic downturn since the start of the Industrial Revolution. Unable to find employment as an engineer, he returned to Bristol University to do a second degree in mathematics, where it was arranged he could skip the first year of the curriculum and pay no tuition fees. Dirac quickly established himself as the star of the mathematics programme, and also attended lectures about the enigmatic quantum theory.

His father had been working in the background to secure a position at Cambridge for Paul, and after cobbling together scholarships and a gift from his father, Dirac arrived at the university in October 1923 to pursue a doctorate in theoretical physics. Dirac would already have seemed strange to his fellow students. While most were scions of the upper class, classically trained, with plummy accents, Dirac knew no Latin or Greek, spoke with a Bristol accent, and approached problems as an engineer or mathematician, not a physicist. He had hoped to study Einstein’s general relativity, the discovery of which had first interested him in theoretical physics, but his supervisor was interested in quantum mechanics and directed his work into that field.

It was an auspicious time for a talented researcher to undertake work in quantum theory. The “old quantum theory”, elaborated in the early years of the 20th century, had explained puzzles like the distribution of energy in heat radiation and the photoelectric effect, but by the 1920s it was clear that nature was much more subtle. For example, the original quantum theory failed to explain even the spectral lines of hydrogen, the simplest atom. Dirac began working on modest questions related to quantum theory, but his life was changed when he read Heisenberg’s 1925 paper which is now considered one of the pillars of the new quantum mechanics. After initially dismissing the paper as overly complicated and artificial, he came to believe that it pointed the way forward, dismissing Bohr’s concept of atoms like little solar systems in favour of a probability density function which gives the probability an electron will be observed in a given position. This represented not just a change in the model of the atom but the discarding entirely of models in favour of a mathematical formulation which permitted calculating what could be observed without providing any mechanism whatsoever explaining how it worked.

After reading and fully appreciating the significance of Heisenberg’s work, Dirac embarked on one of the most productive bursts of discovery in the history of modern physics. Between 1925 and 1933 he published one foundational paper after another. His Ph.D. in 1926, the first granted by Cambridge for work in quantum mechanics, linked Heisenberg’s theory to the classical mechanics he had learned as an engineer and provided a framework which made Heisenberg’s work more accessible. Scholarly writing did not come easily to Dirac, but he mastered the art to such an extent that his papers are still read today as examples of pellucid exposition. At a time when many contributions to quantum mechanics were rough-edged and difficult to understand even by specialists, Dirac’s papers were, in the words of Freeman Dyson, “like exquisitely carved marble statues falling out of the sky, one after another.”

In 1928, Dirac took the first step to unify quantum mechanics and special relativity in the Dirac equation. The consequences of this equation led Dirac to predict the existence of a positively-charged electron, which had never been observed. This was the first time a theoretical physicist had predicted the existence of a new particle. This “positron” was observed in debris from cosmic ray collisions in 1932. The Dirac equation also interpreted the spin (angular momentum) of particles as a relativistic phenomenon.

Dirac, along with Enrico Fermi, elaborated the statistics of particles with half-integral spin (now called “fermions”). The behaviour of ensembles of one such particle, the electron, is essential to the devices you use to read this article. He took the first steps toward a relativistic theory of light and matter and coined the name, “quantum electrodynamics”, for the field, but never found a theory sufficiently simple and beautiful to satisfy himself. He published The Principles of Quantum Mechanics in 1930, for many years the standard textbook on the subject and still read today. He worked out the theory of magnetic monopoles (not detected to this date) and speculated on the origin and possible links between large numbers in physics and cosmology.

The significance of Dirac’s work was recognised at the time. He was elected a Fellow of the Royal Society in 1930, became the Lucasian Professor of Mathematics (Newton’s chair) at Cambridge in 1932, and shared the Nobel Prize in Physics for 1933 with Erwin Schrödinger. After declining a knighthood because he disliked being addressed by his first name, he was awarded the Order of Merit in 1973. He is commemorated by a plaque in Westminster Abbey, close to that of Newton; the plaque bears his name and the Dirac equation, the only equation so honoured.

Many physicists consider Dirac the second greatest theoretical physicist of the 20th century, after Einstein. While Einstein produced great leaps of intellectual achievement in fields neglected by others, Dirac, working alone, contributed to the grand edifice of quantum mechanics, which occupied many of the most talented theorists of a generation. You have to dig a bit deeper into the history of quantum mechanics to fully appreciate Dirac’s achievement, which probably accounts for his name not being as well known as it deserves.

There is much more to Dirac, all described in this extensively-documented scientific biography. While declining to join the British atomic weapons project during World War II because he refused to work as part of a collaboration, he spent much of the war doing consulting work for the project on his own, including inventing a new technique for isotope separation. (Dirac’s process proved less efficient that those eventually chosen by the Manhattan project and was not used.) As an extreme introvert, nobody expected him to ever marry, and he astonished even his closest associates when he married the sister of his fellow physicist Eugene Wigner, Manci, a Hungarian divorcée with two children by her first husband. Manci was as extroverted as Dirac was reserved, and their marriage in 1937 lasted until Dirac’s death in 1984. They had two daughters together, and lived a remarkably normal family life. Dirac, who disdained philosophy in his early years, became intensely interested in the philosophy of science later in life, even arguing that mathematical beauty, not experimental results, could best guide theorists to the best expression of the laws of nature.

Paul Dirac was a very complicated man, and this is a complicated and occasionally self-contradictory biography (but the contradiction is in the subject’s life, not the fault of the biographer). This book provides a glimpse of a unique intellect whom even many of his closest associates never really felt they completely knew.

**Farmelo, Graham. The Strangest Man. New York: Basic Books, 2009. ISBN 978-0-465-02210-6.**

Here is a one hour lecture by the author in December 2011 at the Perimeter Institute on the life and science of Paul Dirac.

The following are four lectures Paul Dirac gave in 1975 at the University of New South Wales in Australia on the topics which occupied his scientific life. These lectures were recorded on an analogue reel-to-reel video tape recorder, and the digital transcriptions were made from tapes which had substantially deteriorated over the years. The video and audio quality is poor; it is almost impossible to read what Dirac writes on the blackboard; and the audio is contaminated by a 50 Hz hum. Still, this is the only opportunity of which I’m aware to actually experience a Dirac public lecture, an event which so many who had the opportunity to attend one in person find so memorable. The lectures focus on the following topics:

**Lecture 1: Quantum Mechanics**

**Lecture 2: Quantum Electrodynamics**

**Lecture 3: Magnetic Monopoles**

**Lecture 4: The Large Numbers Hypothesis**

Why Paul Dirac, along with Hermann Weyl, is one of my heroes.

Welcome back, John! Hoping that the Festive Season was, indeed, festive…Looking forward to conversation soon; best to Roxie!

John, I very much enjoy your science posts and the discussions they prompt even when I don’t understand everything!

Ricochet is a conversation—if you don’t understand something, feel free to ask a question!

Quantum mechanics is difficult to write about because unlike other theories (for example Newton’s laws of motion, optics, and gravitation; and Einstein’s special and general relativity) quantum theory was elaborated over decades by many contributors. Planck, Bohr, Heisenberg, Dirac, Schrödinger, Born, Pauli, Fermi, Feynman, Schwinger, Tomonaga, Dyson, and many others contributed to the theory, and their contributions built upon one another in a complicated way that requires historians of science to dig into minute details to discover how ideas flowed from one investigator to another as the theory was developed.

I think of Newton’s and Einstein’s work as similar to the works of Bach or Mozart: the product of genius, building upon earlier work to be sure, but largely done in isolation by a single mind. Quantum mechanics is more like a grand work of improvisational jazz where individuals make innovative riffs upon a theme and then others pursue it to discover that its consequences are far more profound.

I do not mean by this to disparage the founders of quantum mechanics: simply to note that they worked in an environment of intellectual ferment where theorists and experimentalists were reading one another’s papers and contributing to a theory whose technological consequences are central to all of the information technologies of this century and the last.

Toward the end of his life, Dirac sometimes lamented that if he had never lived, others would have made his discoveries not long after he did. This is almost certainly the case, but so it is in any rapidly-developing field of science or technology. But Dirac saw it

first.Beautiful, John…Simply beautiful! (In addition to being wonderfully clarifying.)

Dirac need not have been so depressed: recent work suggests that his formulation of QM comes nearest, mathematically, to accurately describing the geometric structure inherent in QM, up to and including possible impact on the physical interpretation of QM. If true, it would be

quitea significant achievement, albeit largely unrecognized for 70 years and more.Well written and informative as usual. Wish I had something more substantial to contribute:

But you must own your own tools!

Excellent post, John. As always.

He’s right, you know.

I like this post.

and this picture:

As a student of quantum mechanics they make you drudge through a semester or two manipulating derivatives and integrals and the explicit form of wavefunctions. Then they teach you Dirac notation with ‘bras’ and ‘kets’ and the whole ugly world of difficult integrals and funny functions like Hermite-Gaussians gets swept under the rug and quantum mechanics becomes this fun, brisk game with nary a derivative or integral symbol in sight (although they are still there you rarely have to break out your favorite table of integrals, or in this day and age Mathematica).

For his development of notation alone, Dirac gets a great deal of graditude from the quantum mechanics that followed him.

Highly recommended for reading John’s posts: Google Chrome extension “Thesaurus: Synonym 4 Right Click”.

Wonderful stuff and a great longish form break from the mindlessness of Twitter.

I just watched Lecture 1. Dirac’s final remarks are very pertinent to my own approach that retrocausality restores Einstein’s determinism, but at a price that violates normal ideas of cause and effect. In other words, God does not play dice with the universe because there are both past and future influences on actual events in the present. Yakir Aharonov has developed this idea in detail in his two vector weak measurement model.

http://en.wikipedia.org/wiki/Weak_measurement

FWIW, we don’t need backward causality to establish a local, realistic model explaining the behavior of QM. See Disproof of Bell’s Theorem by Clifford Algebra Valued Local Variables for details, and Disproof of Bell’s Theorem: Reply to Critics for responses to several criticisms of the first paper.

A major lesson from QM (that doesn’t seem like it

shouldneed reinforcing, but manifestlydoes) is that getting the mathematical formalism,and its attendant philosophy, right is absolutely vital to making real progress. Christian’s replies to several of his critics are extremely embarrassing—to the critics, who, as far as I can tell, completely fail to understand Christian’s re-framing of Bell’s Theorem in terms of Clifford Algebras, which subsumes and extends the algebra relevant to Bell’s Theorem, integrating the anti-commutativity of multivector multiplication necessary for the algebra to agree with experiment while remaining locally realistic.tl;dr You lose the right to be surprised at the nonsense results you get in physics if you aren’t

extraordinarilycareful in your choice of mathematical formalisms. Using the wrong algebra, and accepting the claim that there is “real randomness” in the physical universe, have halted genuine progress in physics for over 70 years now. It’s well past time to accept the truth of EPR-Bohm and the Everett “interpretation” of QM, and leave the ridiculous-on-its-face Copenhagen interpretation behind us.Then maybe we can consign point-set topology to the scrap heap, but one war at a time.

Sometimes reading Ricochet unexpectedly builds extreme levels of empathy. I now know how children with low reading comprehension feel.

Ah. The Dirac Delta Function.

Perhaps the most intimidating concept I ran into on the way to a BSEE. Senior Year. Information theory. An infinitely small pulse with a unit area of “1”. I was ok with complex variables, fields/waves, and transmission lines. But I had severe doubts about proceeding further.

Dirac is gonnna be worth a second look.

A lot of things that intimidated made sense later on.

Thanks for reminding me of “brick walls past”.

-wbajr tbc

Heirarchy of EEs:

Radar

Radio

Digital [“Bit Slice” state machines]

Batteries not included…. I was some where between Digital & Radio;-)

I must apologize! I’m a computer scientist who started out intending to double-major in computer science and theoretical physics, and dropped the physics to stick to the easy stuff. :-) The state of physics since 1927 makes me stabby, and the more I (re)learn the math involved, the stabbier it makes me—without, unfortunately, making me any more comprehensible.

Thankfully, within my son’s lifetime, I expect two revolutions in mathematics (hence physics) to come to fruition, a situation I view with a kind of longing regret that I won’t be around to see them.

no apology needed.

I enjoyed reading every word, I just didn’t comprehend too much of it. But clearly your words make sense to many people. Ricochet comes with an auto-inflate life preserver for moments like that. :)

I also enjoy reading these posts to remind myself of just how profoundly I misspent my youth; nevertheless the more Saturday Night Science posts that I read, the better I understand the parts that I can’t possibly comprehend.

This is from his Wikipedia entry:

Margit, known as Manci, visited her brother in 1934 in Princeton, New Jersey, from her native Hungary and, while at dinner at the Annex Restaurant met the “lonely-looking man at the next table.” This account from a Korean physicist, Y. S. Kim, who met and was influenced by Dirac, also says: “It is quite fortunate for the physics community that Manci took good care of our respected Paul A. M. Dirac. Dirac published eleven papers during the period 1939–46…. Dirac was able to maintain his normal research productivity only because Manci was in charge of everything else.”[25]It is interesting how Dirac’s views on the existence of God evolved. He does not seem to have got past being Agnostic, but did move from Atheism.

It turns out δ isn’t even due to Dirac after all, and has a perfectly sensible algebraic definition. It’s also easy to express using infinitesimals rather than ε-δ (no relation) limits. Infinitesimals were thought to be on logically shaky ground pre-Weierstraß, but this turns out to be quite questionable, and in any event infinitesimals have been made rigorous, not once, but twice. In the latter context, δ must be reconceived, since all functions are continuous, but this has also been done.

It continues to depressstrike me that we had a lot of working mathematics in the 18th and up to the end of the 19th century that got swept away by the madness of “

Mengenlehre, a disease from which future generations will be said to have recovered.” That recovery is underway, cf. the resurrection of Geometric Algebra and the introduction of Homotopy Type Theory, but people my age will miss it coming to any kind of popular fruition.Those papers are not accepted as correct by the majority of mainstream physicists in the field. More on this another time.

Frankly, I find Joy Christian’s argument completely unintelligible and I am not alone in this. One can always introduce mathematical fudge factors without any clear connection to actual experiments to argue against any well-established result. Joy’s introduction of Clifford algebras in the particular way he does it, is not a legitimate move in the quantum game in my opinion. It is basically a bigger more complex alternative theory with a steep learning curve and without any intuitive basis to my mind at least. Bell’s inequality concerns orthodox quantum theory with wave functions that are complex functions of real numbers. There are now many clever experiments in weak measurements using interferometers by Yakir Aharonov’s group whose simplest understanding is in terms of retrocausality. I will provide references another time. In the meantime you may find these of interest:

## Back From the Future

## A series of quantum experiments shows that measurements performed in the future can influence the present. Does that mean the universe has a destiny—and the laws of physics pull us inexorably toward our prewritten fate?

http://newagendasstudyoftime.wordpress.com/events/retrocausality-conference/

Of particular interest is:

10:30–11:30. Lev Vaidman (Tel Aviv). “Can future measurements affect the present?” [Videos: talk; discussion.]You may also be amused by:

“Any intelligent fool can make things bigger and more complex… It takes a touch of genius — and a lot of courage to move in the opposite direction.” – Albert Einstein

I know. So what?

So, I don’t believe Joy’s argument is correct. That is also the consensus in the mainstream of the field. Joy would have to show how his new alternative theory explains for example the Vaidman experiment in the link I gave. Good theoretical physics is more than posing a mathematical model. One must show how key mathematical symbols in the model relate to observations – at least in principle. Furthermore, there is evidence from “brain presponse” experiments of real retro-causal influence that goes beyond even orthodox quantum theory, but that is a long story. In addition, there is way of understanding the cosmological dark energy accelerating our universe’s expansion rate as advanced back-from-the-future Hawking horizon black body radiation. In other words, the retrocausal view is very useful indeed in terms of actual observations.

Arguing from an “intuitive basis” in QM is what got us into the mess we’re in now. Specifically Bohr’s intuition, which was prejudiced in favor of his vacuous “complementarity principle,” as documented in The Infamous Boundary: Seven Decades of Controversy in Quantum Physics. Far from being a “mathematical fudge factor without any clear connection to actual experiments,” Christian’s locally realistic model completely agrees with experiment and is on firmer foundations than Bell’s traditional (scalar) algebra. I refer you to Response #4 of Disproof of Bell’s Theorem: Reply to Critics for details, including a list of the relevant algebraic identities used in Bell’s Theorem, and a detailed explanation as to why replacing a single identity with one from the Clifford Algebra

Cl_{3,0}is necessary in order to avoid singularities—literallygimbal lock—in the scalar algebra. So, far from being an unintuitive fudge, the use of (one identity from) a Clifford Algebra results in an algebra which remains an associative division algebra over the reals, and in fact is relatively commonly known as thequaternionic algebra, an algebra well known to aerospace engineers, roboticists, and computer-game developers, all of whom work in contexts in which gimbal lock is a well-known—and rightly unacceptable—problem.I don’t have a problem with retrocausality, since no physical theory since Newton’s has posited time moving in only one direction, and in particular since Gödel proved that any universe satisfying Einstein’s field equations must include closed time-like curves (the so-called Gödel universes). My appeal here is merely to Occam’s razor: there’s no need to introduce retrocausality to make sense of Bell’s Theorem, because Bell’s Theorem is false—a byproduct of the bad mathematics that infected physics in the early 20th century, when Gibbs’ vector calculus overtook the earlier, better quaternion and, more generally, geometric-algebra-based approaches.

It’s worth adding that Christian is nevertheless only correcting an error of formalism. We already know why Bell’s Theorem doesn’t show what it purports to show, thanks to Does Quantum Nonlocality Exist? Bell’s Theorem and the Many-Worlds Interpretation. The “nonlocality” only arises if you assume the observer obeys classical mechanics, while the observed system obeys quantum mechanics. Only the kind of confusion that has gripped physics ever since Bohr convinced the physics community to stop doing science can come from this.

“Everything should be as simple as possible, but not simpler.” – Albert Einstein“As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.” – Albert EinsteinDear Ghost: If you think you understand Joy Christian’s theory, please explain it in as simple a way that you can without being simpler than is possible. To my mind, it seems a mathematical snow job. I find it completely unintelligible in terms of orthodox quantum theory of observable operators in Hilbert space. Thanks.

PS: For example, your writing:

“and a detailed explanation as to why replacing a single identity with one from the Clifford Algebra

Cl3,0 is necessary in order to avoid singularities—literallygimbal lock—in the scalar algebra. So, far from being an unintuitive fudge, the use of (one identity from) a Clifford Algebra results in an algebra which remains an associative division algebra over the reals, and in fact is relatively commonly known as thequaternionic algebra, an algebra well known to aerospace engineers, roboticists, and computer-game developers, all of whom work in contexts in which gimbal lock is a well-known—and rightly unacceptable—problem.”I see no connection of the above pure mathematics to quantum theory as normally understood by physicsts working in the field. BTW I prefer Bohm’s pilot wave theory to Bohr’s.

Pauli spin matrices, angular momentum operators, Dirac gamma matrices can, I agree, be understood in terms of Clifford algebras. However, they correspond to Hermitian operators on a Hilbert quantum information space. They also correspond elements of a Lie algebra of the Poincare symmetry group.

Does Quantum Nonlocality Exist? Bell’s Theorem and the Many-Worlds Interpretation

Frank J. Tipler

(Submitted on 30 Mar 2000)

“Quantum nonlocality may be an artifact of the assumption that observers obey the laws of classical mechanics, while observed systems obey quantum mechanics. I show that, at least in the case of Bell’s Theorem, locality is restored if observed and observer are both assumed to obey quantum mechanics, as in the Many-Worlds Interpretation. Using the MWI, I shall show that the apparently “non-local” expectation value for the product of the spins of two widely separated particles — the “quantum” part of Bell’s Theorem — is really due to a series of three purely local measurements. Thus, experiments confirming “nonlocality” are actually confirming the MWI.”

This is also essentially Murray Gell-Mann’s position in Ch 11 of “The Quark and The Jaguar.” There are several recent papers showing why this position also has serious problems of interpretation. I will try to find them and post them in the not too distant future. Henry Stapp’s phrasing of the implication of Bell’s theorem includes this option in terms of counter-factual definiteness (CFD).

http://www.stillnessspeaks.com/ssblog/henry_stapp/

http://www-physics.lbl.gov/~stapp/stappfiles.html

e.g. http://www-physics.lbl.gov/~stapp/purported.pdf Here Stapp has a post-quantum theory of retro-causation.

As I said, I favor Bohm’s pilot wave theory with a purely quantum-informational quantum potential Q acting on actual particles and classical boson fields in spacetime. Here everything is quantum mechanical and Q acts nonlocally when entanglement is present. Tipler’s argument does not apply in the Bohm interpretation.

If we restrict the discussion to orthodox quantum theory what you choose to believe is subjective – a matter of taste. There are several paradigms that can equally explain the results of scattering experiments – a space of degenerate equivalent interpretations of a limited set of experiments. However, there is controversial evidence of real retrocausation in our minds, which is a new regime of phenomena. This involves what Antony Valentini calls “signal nonlocality” beyond the orthodox quantum theory.

“It is argued that immense physical resources – for nonlocal communication, espionage, and exponentially-fast computation – are hidden from us by quantum noise, and that this noise is not fundamental but merely a property of an equilibrium state in which the universe happens to be at the present time. It is suggested that ‘non-quantum’ or nonequilibrium matter might exist today in the form of relic particles from the early universe. We describe how such matter could be detected and put to practical use. Nonequilibrium matter could be used to send instantaneous signals, to violate the uncertainty principle, to distinguish non-orthogonal quantum states without disturbing them, to eavesdrop on quantum key distribution, and to outpace quantum computation (solving NP-complete problems in polynomial time).” http://arxiv.org/abs/quant-ph/0203049

I referred to Christian’s Response #4 precisely

becauseit’s as simple as possible, consisting of replacing a single identity in scalar algebra to get quaternionic algebra, probably the simplest, best-understood of the Clifford algebras. This might seem like a “mathematical snow job” if not for the explicit treatment of the fact that the scalar algebra—and remember, Bell’s Theorem rests on this—doesn’t even support 3D rotation correctly—again, as understood perfectly well by aerospace engineers, roboticists, computer game developers, and anyone else concerned with rotation in 3D (or more). In other words, Bell’s Theorem—because of scalar algebra—explicitly (identity 19, in Christian’s Response #4) assumes that multiplication is commutative—as it is for scalars. But this is not the appropriate model to apply to rotations in 3D, because there are values for which the calculation is undefined (that’s what “singularity” means; in a good math/logic/physics/computer-science thesaurus we’d also find “divergence” and/or “crash,” literally as in “the software crashes when it tries to do the computation”—think division by zero) and because rotation is manifestly not commutative, as Christian reminds us with his “rotate a book” example. So Christian correctly changes that identity, andonlythat identity, to correctly account for multiplication in the algebra to be non-commutative—as you obviously know it also is in matrix algebra. More, he ensures that the resulting algebra is one of the only two remaining associative division algebras over the reals—in other words, he takes a “first, do no harm” stance.So the result is physically realistic—not “pure math” at all—precisely because it

doescorrectly model rotation in 3D. It then serves as a locally realistic model for the calculations that Bell’s Theorem, in a stunning piece of ontological overreach, claim area prioriuniversally impossible.So what?

I’m not saying that to be cheeky. I’m observing that you’re making a naked appeal to authority in what is supposed to be a scientific discussion. It carries literally no weight. Christian has the advantage of making explicit the algebraic identities Bell’s Theorem uses; his

extremelyconservative replacement of one of those identities on clear, obvious grounds of physical reality (does the algebra accurately model 3D rotation or not?) while maintaining the algebra’s properties as an associative division algebra; the result is a model that is successfully locally realistic, in contradiction to Bell’s Theorem. Rejecting this is rather obviously philosophy rather than science.I think you might be surprised.

I look forward to further material on problems with Dr. Gell-Mann’s understanding of the Everett “interpretation,” which he does indeed share with Dr. Tipler. Regarding that, let me highly recommend David Wallace’s recent The Emergent Multiverse: Quantum Theory According to the Everett Interpretation. As you may surmise, I accept the Everett “interpretation” (like Dr. Tipler, I put “interpretation” in quotes because it’s

not“an interpretation,” in a sense Wallace makes precise in his book). I particularly think you’ll appreciate the “surprised” link above, given your interest in the relationship between information theory (which I would reframe, in this context especially, as algorithmic information theory) and the quantum mechanics.In the end, I accept the naked results of experiment, minus philosophers attempting to impose their philosophies upon them. This means I accept the conclusion that observers, too, are quantum-mechanical systems, as there is no experiment suggesting otherwise—on the contrary, the meaning of many experiments becomes clear upon accepting this. This means that the Everett “interpretation” is correct. That has interesting

philosophical implications, to be sure—but those implications are strictly subsequent, rather than antecedent, to Everett, and philosophical conclusions that contradict them, including various “paradoxes” arising from otheractualinterpretations, are to be jettisoned wholesale.Ghost wrote:

“My appeal here is merely to Occam’s razor: there’s no need to introduce retrocausality to make sense of Bell’s Theorem, because Bell’s Theorem is false—a byproduct of the bad mathematics that infected physics in the early 20th century, when Gibbs’ vector calculus overtook the earlier, better quaternion and, more generally, geometric-algebra-based approaches. It’s worth adding that Christian is nevertheless only correcting an error of formalism.”

The great majority of physicists active in quantum theory foundations will say that your above position is false. They do not accept Joy Christian’s argument.

Occam’s razor is also vague. When I look at the experiments the simplest explanation to my mind is retro-causality in the sense of John Cramer’s “transactional interpretation” and Yakir Aharonov’s two state vector interpretation in the new regime of weak measurements. BTW, Bell’s argument is only for Von Neumann strong measurements. You might also take a look at the GHZ paper.

“GHZ experiments are a class of physics experiments that may be used to generate starkly contrasting predictions from local hidden variable theory and quantum mechanical theory, and permit immediate comparison with actual experimental results. A GHZ experiment is similar to a test of Bell’s inequality, except using three or more entangled particles, rather than two. With specific settings of GHZ experiments, it is possible to demonstrate absolute contradictions between the predictions of local hidden variable theory and those of quantum mechanics, whereas tests of Bell’s inequality only demonstrate contradictions of a statistical nature. The results of actual GHZ experiments agree with the predictions of quantum mechanics.” http://en.wikipedia.org/wiki/GHZ_experiment