Proof Of NO LOCAL Hidden Variables From Magnets

Abstract: Looked at it the right way, the Stern Gerlach experiment with three consecutive magnets oriented various ways, show that there can’t be LOCAL hidden variables. No need, to exhibit nonlocality, for the precise, but obscure logic of the Bell Inequality. The argument here is less mathematically precise, but more intuitive.

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Stern-Gerlach Magnets (SGM) reveal an aspect of the Quantum, namely the quantization of (some sort of) angular momentum. SGM launched in 1922 the saga of Quantum Spin (it turns out to be connected to deep pure geometry which had been developed independently by Élie Cartan, a decade earlier). Drive an electron, or (appropriate) atomic beam through a SGM, and one will get two dots, one up, one down. Whatever the axis of the SGM [1]. (The SGM is just a magnetic field with a specific linear direction.) 

That means, at the emotional level that, at the smallest scale, spin, the electronic (sort of) angular momentum, or the orbital (sort of) angular momentum, reduce to UP and DOWN. First surprise. (This is actually the case of Spin 1/2, the simplest, such as for an electron; we are trying to learn the most from the simplest case.)

Say the first SGM is vertical (magnetic field along “z axis”) and a second SGM is horizontal (mag field along “x axis”). Call them respectively SGMV and SGMH. So SGMH produces LEFT-RIGHT beams. Put SGMH across the UP beam coming out of SGMV. One could call that beam SGMV (UP). Once goes through SGMH, one will get 50-50 LEFT-RIGHT. No surprise there.

Now say one selects the RIGHT beam coming out SGMH. Call that beam SGMH (UP; RIGHT)… because first the beam went up, then the beam went right.  

Naively one would expect, from classical mechanics, that SGMH (UP; RIGHT) to have kept a memory of its initial source as SGMV(UP). 

That would be to assume that beam SGMV (UP) and its descendant SGMH (UP;  RIGHT) to have kept some memory, in other words that some that the beams through the first SGMV and then the second SGM to harbor some LOCAL HIDDEN VARIABLES.

But that’s not the case. 

Indeed, please run SGMH (UP; RIGHT) into a second SGMV (that is a Stern Gerlach Magnet parallel to the first magnet SGMV… Call that second vertical Stern Gerlach Magnet SGMV2 One gets fifty-fifty UP and DOWN coming out of SGMV2. It is as if the initial Stern Gerlach, SGMV, never happened. (This set-up is presented in Feynman Lectures on Physics III, Chapter 6, Spin 1/2)

So if there were local hidden variables carried after SGMV that is in the beam SGMV (UP), they got somehow completely eradicated by getting into the beam SGMH (RIGHT).

So these proposed local hidden variables do not stay hidden inside the “particle”: an outside agent can erase them…. Thus those putative local hidden variables aren’t really “local” anymore: the environment impacts them, outside of the particle, and drastically so, just as the potential impacts the phase of an electron in the Bohm-Aharonov experiment… non locally.

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One can rerun the experiment, by using both beams SGMH (RIGHT) and SGMH (RIGHT), mixing them up. Then it turns out that SGMV2 deflects ONLY UP. So simply going through magnet SGMH, WITHOUT selecting a beam (either SGMH(LEFT) or SMGH (RIGHT)) doesn’t do anything: a collapsing of the Quantum space available to the Quantum wave, selecting either left or right space, is what does something.

Conventional Quantum Physics, newish, path integral version, phrases this by saying one can’t say which path has been followed [2] to keep the information SGV UP or SGV DOWN.  Copenhagen Interpretation of Quantum (CIQ) simply says that selecting beam SGMH (RIGHT) is a measurement thus collapses the wave function… SQPR says roughly the same thing.

In any case, this eradication of the influence of SGMH on the “particle” by just keeping open the OTHER beam, which the putative local hidden variable “particle” is by definition NOT taking, is itself a NONLOCAL effect, thus once again demolishing the “LOCAL Hidden Variable” concept. (One could say that one beam is entangled with the other…)

The advantage of this conceptual approach is that it exhibits directly the nonlocality… without hermetic complications [3]. It also shows the interest of a more philosophical rather than purely formalistic approach to physics.

Patrice Ayme
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[1] Wolfgang Pauli in 1924 was the first to propose a doubling of the number of available electron states due to a two-valued non-classical “hidden rotation“. In 1925, George Uhlenbeck and Samuel Goudsmit suggested the simple physical interpretation for spin of a particle spinning around its own axis… But clearly that doesn’t fit what is observed. Pauli built a mathematical machinery which reflected the observed GSM behavior. It turned out to be a particular case of deep mathematical work from the French mathematician Élie Cartan who was born and initially educated in the small Alpine coal mining village of La Mure, and rose through merit in the republican educational system. It’s a bit like taking the square root of space. I don’t understand it, neither did the extremely famous mathematician Atiyah…

It is easy to be blinded by the math. But actually the math describes an observed physical behavior. Now this behavior may arise from deeper geometrical reason 

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[2] In SQPR, the “particles” are preceded by the linear guiding waves. Blocking some of them triggers “collapse”. By selecting SGMH (RIGHT) one clearly collapses the linear guidance.

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[3] Stern Gerlach Magnets also directly illustrates Spin, as did in the first few lines above (magnetic field —> two dots!) The Pauli machinery is often how Spin is introduced in Quantum Physics courses, but that, philososophically is confusing the formalism derived from what is observed with the observation itself.

Happy In the Sky With New Logics: Einstein’s Error II

Einstein assumed reality was localized and definite in one of his famous 1905 papers, and physics never recovered from that ridiculous, out-of-the-blue, wanton, gratuitous error. (The present essay complements the preceding one found in the link). 

At the origin of Quantum Mechanics is Max Planck’s train of thought. Max demonstrated that supposing that electromagnetic energy was EMITTED as packets of energy hf explained the two obvious problems of physics; h is a constant (since then named after Planck), f is the frequency of the light.

Then came, five years later, Einstein. He explained the photoelectric effect’s mysterious features by reciprocating Planck’s picture: light’s energy was RECEIVED as packets of energy hf. Fine.   

However, so doing Einstein claimed that light, LIGHT IN TRANSIT, was made of “LICHT QUANTEN” (quanta of light), which he described as localized. He had absolutely no proof of that. Centuries of observation stood against it. And the photoelectric effect did not necessitate this grainy feature in flight, so did not justify it.  

Thus Einstein introduced the assumption that the ultimate description of nature was that of grains of mass-energy. That was, in a way, nothing new, but the old hypothesis of the Ancient Greeks, the atomic theory. So one could call this the Greco-Einstein hypothesis. The following experiment, conducted in 1921, demonstrated Einstein was wrong. Thus the perpetrator Walther Gerlach, did not get the Nobel, and the Nobel Committee never mentioned the importance of the experiment. Arguably, Gerlach’s experiment was more important than any work of Einstein, thus deserved punishment The Jewish Stern, an assistant of Einstein, got the Nobel alone in 1944, when Sweden was anxious to make friends with the winning “United Nations”: 

Two Points. The Classical Prediction Is A Vertical Smear. It Is Also Einstein’s Prediction. And That Smear Is Incomprehensible In Einstein’s View Of The World.

Yet, Einstein’s advocacy of nature as made of grains was obviously wrong: since the seventeenth century, it was known that there were wave effects ruling matter (diffraction, refraction, Newton’s rings). That was so true, Huyghens proposed light was made of waves. Around 1800 CE Young and Ampere proposed proofs of wave nature (2 slit experiment and Poisson’s dot). The final proof of the wave theory was Maxwell’s completion and synthesis of electromagnetism which showed light was an electromagnetic wave (travelling at always the same speed, c).

Einstein’s hypothesis of light as made of grain is fundamentally incompatible with the wave theory. The wave theory was invented precisely to explain DELOCALIZATION. A grain’s definition is the exact opposite.

There is worse.

Spin was discovered as an experimental fact in the 1920s. Interestingly it had been discovered mathematically by the French Alpine mathematician Elie Cartan before World War One, and stumbled upon by Dirac’s invention of the eponymous equation.  

The simplest case is the spin of an electron. What is it? When an electron is put in a magnetic field M, it deviates either along the direction of M (call it M!) or the opposite direction (-M). This sounds innocuous enough, until one realizes that it is the OBSERVER who selects the direction “M” of M. Also there are two angles of deviation only. (The Gerlach experiment was realized with silver (Ag) atoms, but the deviation was caused by a single electron therein.)

Einstein would have us believe that the electron is a grain. Call it G. Then G would have itself its own spin. A rotating charged particle G generates a magnetic field. Call it m. If Einstein were correct, as the direction of M varies, its interaction between the grain G magnetic field m will vary. But it’s not the case: it is as if m did not count. At all. Does not count, at all, whatsoever. It’s all about M, the direction of M.

So Einstein was wrong: there is no grain G with an independent existence, an independent magnetic filed m.

Bohr was right: Einstein was, obviously, wrong. That does not mean that Bohr and his followers, who proclaimed the “Copenhagen Interpretation” were right on other issues. Just like Einstein hypothesized something he did not need, so did the Copenhagists.

Backtrack above: M is determined by the observer, I said (so bleated the Copenhagen herd). However, although M can changed by an observer, clearly an observer is NOT necessary to create a magnetic field M and its direction.

Overlooking that blatant fact, that not all magnetic fields are created by observers, is the source of Copenhagen confusion.

We saw above that correct philosophical analysis is crucial to physics. Computations are also crucial, but less so: a correct computation giving correct results can be made from false hypotheses (the paradigm here is epicycle theory: false axiomatics, the Sun did not turn around the Earth, yet, roughly correct computations produced what was observed).

Out of Quantum Theory came Quantum ElectroDynamics (QED), and, from there, Quantum Field Theory (QFT).  

QED is one of the most precise scientific theory ever. However, there is much more precise: the mass of the photon is determined to be no more than 10^(-60) kilogram (by looking at whether the electromagnetic field of Jupiter decreases in 1/d^2…).

Nevertheless, QED is also clearly the most erroneous physical theory ever (by an order of 10^60). Indeed, it predicts, or rather uses, the obviously false hypothesis that there is some finite energy at each point of space. Ironically enough, it is Einstein and Stern (see above) who introduced the notion of “zero point energy” (so, when Einstein later could not understand, or refused to understand, Quantum Electrodynamics, it was not because all the weirdest concepts therein were not of his own making…)

The debate on the Foundations of Quantum Physics is strong among experts, all over the map, and permeated with philosophy. Thus don’t listen to those who scoff about whether philosophy is not the master of science: it always has been, it is frantically so, and always will be. It is a question of method: the philosophical method uses anything to construct a logic. The scientific method can be used only when one knows roughly what one is talking about. Otherwise, as in Zeroth Century, or Twentieth Century physics, one can go on imaginary wild goose chases.

From my point of view, Dark Matter itself is a consequence of the True Quantum Physics. This means that experiments could be devised to test it. The belief that some scientific theory is likely incites beholders to make experiments to test it. Absent the belief, there would be no will, hence no financing. Testing for gravitational waves was long viewed as a wild goose chase. However, the Federal government of the USA invested more than one billion dollars in the experimental field of gravitational wave detection, half a century after an early pioneer (who was made fun of). It worked, in the end, splendidly: several Black Hole (-like) events were detected, and their nature was unexpected, bringing new fundamental questions.

Some will say that all this thinking, at the edges of physics and philosophy is irrelevant to their lives, now. Maybe they cannot understand the following. Society can ether put its resources in making the rich richer, more powerful and domineering. Or society can pursue higher pursuits, such as understanding more complex issues. If nothing else, the higher technology involved will bring new technology which nothing else will bring (the Internet was developed by CERN physicists).

Moreover, such results change the nature not just of what we believe reality to be, but also of the logic we have developed to analyze it. Even if interest in all the rest faded away, the newly found diamonds of more sophisticated, revolutionary logics would not fade away.

Patrice Ayme’