The quantum entanglement story began in 1935 with the EPR paper. That’s where Einstein, Podolsky, and Rosen said quantum mechanics must be incomplete, because it predicts a system in two different states at the same time. Later that year Bohr replied saying spooky action at a distance could occur. Then Schrödinger came up with a paper where he talked of entanglement, a paper where he used his cat to show how ridiculous the two-state situation was, and a paper saying he found spooky action at a distance to be repugnant. He also compared it to Voodoo magic, where a savage “believes that he can harm his enemy by piercing the enemy’s image with a needle”.
Credits: NASA/JPL-Caltech, see Particles in Love: Quantum Mechanics Explored in New Study | NASA
Then in 1952 Bohm came up with two hidden variables papers which retained the spooky action at a distance. He also came up with the EPRB experiment, which was the subject of a paper in 1957. Then in 1964 Bell came up with papers On the Problem of Hidden Variables in Quantum Mechanics and On the Einstein Podolsky Rosen Paradox. Bell said the issue was resolved in the way Einstein would have liked least, and gave a mathematical “proof” which is usually called Bell’s theorem. Then in 1969 we had the CHSH paper on a Proposed Experiment to Test Local Hidden-Variable Theories by Clauser et al. Then in 1972 we had Clauser and Freedman’s Experimental Test of Local Hidden-Variable Theories. Then in 1981 we had Experimental Tests of Realistic Local Theories via Bell’s Theorem by Aspect et al, followed by two further papers in 1982. Then in 1998 we had Violation of Bell’s inequality under strict Einstein locality conditions by Zeilinger et al.
Convinced the physics community in general that local realism is untenable
All these so-called Bell test experiments used photons and polarizing filters. They featured ever-increasing complexity to cater for so-called loopholes, and are said to have “convinced the physics community in general that local realism is untenable”. So much so, that the 2022 physics Nobel Prize was awarded to Clauser, Aspect, and Zeilinger “for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science”. This Nobel prize was awarded exactly a hundred years after Bohr was awarded a Nobel prize in 1922. There’s just one problem. It’s all bullshit.
Quantum bullshit from the man who said reality does not exist until you measure it
The bullshit started in 1935 with Bohr’s reply to the EPR paper. Bohr’s paper was rambling, off-topic, and pretentious. He didn’t address the issue at all. Instead he gave a lofty lecture on complementarity and the double slit experiment, then energy and time, and space and time. In the middle of all the condescending bluster he slipped in this: “an influence on the very conditions which define the possible types of predictions regarding the future behavior of the system”. That’s spooky action at a distance. He also slipped in this: “we see that the argumentation of the mentioned authors does not justify their conclusion”. No, we don’t. We see Bohr ducking the issue. We see quantum bullshit from the man who said reality does not exist until you measure it. From the man who said the Moon isn’t there if nobody looks. From the man who said quantum mechanics surpasseth all human understanding, and you can never hope to understand it, so don’t even try. Bohr even had the gall to say the “quantum-mechanical description of physical phenomena would seem to fulfill, within its scope, all rational demands of completeness”. Even though quantum mechanics doesn’t tell us what a photon is, how pair production works, or what the electron is. Even though it dismisses electron spin as an abstract notion via a spinning faster than light non-sequitur. Despite the hard scientific evidence of the Einstein-de Haas effect, Larmor precession, and the wave nature of matter. And do note the use of the word rational. Bohr was just so patronising. You will not find one person who has a good word to say about his paper. Even Clauser said he found Bohr’s ideas “muddy and difficult to understand”.
A whole layer cake of bullshit
The next load of bullshit came from Bohm with his 1952 papers. I say that because people talk about de Broglie-Bohm theory, and de Broglie won his 1929 Nobel Prize for the discovery of the wave nature of electrons. Did Bohm somehow miss the bit that said matter is, by its nature, a wave motion? He couldn’t have. Which means he was going off on one when he said wavefunction was a mathematical representation of a real field which exerts a force on a particle akin to an electromagnetic field. Especially when he then said it can “transmit uncontrollable disturbances instantaneously from one particle to another”. In one fell swoop Bohm had contradicted the wave nature of matter, dug up spooky action at a distance, and then pulled the stake from its heart. He had resurrected a myth and set it free to stalk the land. Not only that, but in 1957 he ignored the original EPR position v momentum debate, and said spooky action at a distance applied to the Stern-Gerlach measurements of spin ½ particles.
Spindle torus animation by Adrian Rossiter, see antiprism.com, resized and reversed by me via EZgif
He said “if the x component is definite, then the y and z components are indeterminate”. That makes as much sense as saying the South side of a whirlpool is definitely spinning from West to East, but the spin on the East side is indeterminate. Conservation of angular momentum says it isn’t. But Bohm was so full of bullshit he even said “in any single case, the total angular momentum will not be conserved”. On top of that, he said it was only practicable to test the EPR paradox via “the polarization properties of correlated photons”. Photon polarization is nothing like spin ½. This is just a whole layer cake of bullshit from a wannabee mystic who didn’t understand the photon, pair production and annihilation, the electron the positron, or anything else.
A barrelful of blarney
The next shedload of bullshit came in Bell’s 1964 paper. It was a career-promoting Einstein-was-wrong hit piece. A hit piece that peddled Copenhagen mysticism and was as clear as mud. Bell didn’t address the physics of spin ½. Instead he gave a rambling smoke-and-mirrors mathematical “proof” which culminated in him pulling a rabbit out of a hat and making the grandiose claim that “the signal involved must propagate instantaneously”. How on Earth can anybody pretend to prove that via mere mathematics? With no experimental evidence at all? Bell’s whole paper was a barrelful of blarney from a 1960s particle physicist who hadn’t read any of the realist papers from the 1920s and 1930s. In the introduction, he gave some history and referred to Bohm and others. Then he made the claim that non-locality is characteristic of any theory which “reproduces exactly the quantum mechanical predictions”. In section II he talked about an entangled pair of spin ½ particles. He defined terms and to describe a ±1 Stern-Gerlach measurement on particle 1 at magnet angle a, and a similar measurement on particle 2 at magnet angle b. His equation 2 said the expectation value for such measurements was , where λ denoted a set, A being a result of measuring particle 1 and B being a result of measuring particle 2. That’s A for Alice and B for Bob.
Introducing an unwarranted linear relationship
Bell also said a hidden-variable expectation value should equal the quantum-mechanical singlet state expectation value , but that “it will be shown that this is not possible”. Then in section III he said = cos θ. There’s nothing wrong with that. But there’s plenty wrong with his hidden variable in the form of “a unit vector λ, with a uniform probability distribution”. That’s a straw man hidden variable. It’s nothing like the real hidden variable. The real hidden variable is that spin ½ is a real rotation in two orthogonal directions, just like Darwin said in 1928:
Sinusoidal strip by me, GNUFDL spinor image by Slawkb, Torii by Adrian Rossiter, S-orbital from Encyclopaedia Britannica
Stern-Gerlach measurements yielding +1 and -1 just don’t do it justice, especially since a magnetic field causes Larmor precession. Those Stern-Gerlach magnets don’t “measure” spin, they just give you a pointer to it, and whilst doing so, they alter it. So that’s another hidden variable. So Bell’s section III is useless. However section IV is worse than useless, because that’s where the sleight-of-hand lies. In equation 13 Bell said , which means your A and B sets of measurements will be opposite if your magnet angles are the same. Then in his equation 14, he treated a set of measurements as a simple number, and said the expectation value . That’s saying you can get the same results using only your Alice measurements, because they’re the opposite of your Bob measurements. That means you’re introducing an unwarranted linear relationship.
When Bell snuck in that linear relationship, he kicked a cosine under the rug
Then Bell threw in another measurement at angle c, and after a bit of jiggery-pokery came up with expression 15, which is . That’s Bell’s inequality. As to what it means, let me draw you a picture:
One plus your bc term is greater than or equal to your ab term plus your minus ac term, which isn’t really negative. Your expectations add up in a sensible fashion, because there is no magic. You can ignore the rest of Bell’s maths because of this statement: “Nor can the quantum mechanical correlation (3) be arbitrarily closely approximated by the form (2). The formal proof of this may be set out as follows”. It’s not important. What’s important is that when Bell snuck in that linear relationship, he kicked a cosine under the rug. That resulted in a straw man “classical prediction” that takes a linear form. Hence Bell’s inequality is usually illustrated with a picture like the one below, with a red straight-line classical prediction, and a blue curved-line quantum mechanical prediction:
CCASA image by Richard Gill, see Bell’s theorem – Wikipedia. Caption: The best possible local realist imitation (red) for the quantum correlation of two spins in the singlet state (blue), insisting on perfect anti-correlation at zero degrees, perfect correlation at 180 degrees. Many other possibilities exist for the classical correlation subject to these side conditions, but all are characterized by sharp peaks (and valleys) at 0, 180, 360 degrees, and none has more extreme values (±0.5) at 45, 135, 225, 315 degrees. These values are marked by stars in the graph, and are the values measured in a standard Bell-CHSH type experiment: QM allows ±1/√2 = 0.707, local realism predicts ±0.5 or less.
This concerns two spin ½ particles with opposite spins. It’s saying the classical prediction for the correlation at 45° is -0.5, whilst the quantum mechanical prediction is -0.707. Special thanks to Physics Forums and Richard Gill for this picture. It’s from an old version of the Wikipedia Bell’s Theorem article. Gill has written a number of papers on the subject of Bell’s theorem.
In Bell’s toy model, correlations fall off linearly
Don’t think Gill made a mistake with this. That heavyweight Stanford article I mentioned includes Abner Shimony amongst the authors, and says this: “In Bell’s toy model, correlations fall off linearly with the angle between the device axes”. In addition, you can see much the same picture in Alain Aspect’s paper Bell’s Theorem: The Naive View of an Experimentalist:
Image by Alain Aspect
This concerns two photons with the same polarization, so we don’t have the exact same curve, but it’s still cosinusoidal, and the meaning is the same. Again there’s a straight-line classical prediction, and a curved-line quantum mechanical prediction. Aspect mentioned Malus’s Law, which I’ve mentioned previously. It’s to do with optics, and it’s of crucial interest. So much so that I want to show you something from the Wikipedia Bell’s theorem article:
What it’s saying is vectors a and b are orthogonal, whilst vector c is at a 45° angle to both of them. P is a correlation. When you combine a and b, you get a result that’s zero. That’s cos 90°. Combine a and c, or b and c, and you get a result that’s –√2/2, which is –0.707. Note that 0.707 is cos 45°. The claim is that 0.707 is not less than 1 – 0.707 = 0.293, therefore “there is no local hidden variable model that can reproduce the predictions of quantum mechanics”. But there is something that can. Polarizing filters.
Take two polarizing filters and place them in a light beam, one orthogonal to the other. No light gets through. Then take a third filter and put it between the first two at a 45° angle. Now some of the light does get through:
Crossed polarizer images from Rod Nave’s hyperphysics
The third polarizing filter is sometimes presented as something mysterious, but that mystery is based upon a lack of understanding. Darel Rex Finley explained it well in his 2004 article Third-Polarizing-Filter Experiment Demystified – How It Works. He described how a horizontal polarizing filter doesn’t just let through a horizontally polarized light wave. It lets through the horizontal component of a light wave polarized at some angle, also rotating it so that it ends up horizontal. If the light wave is horizontally polarized, it lets it all through. If the light wave is polarized at 22.5° it lets almost all of it through whilst rotating it by 22.5°. If the light wave is polarized at 45° it lets some of it through whilst rotating it by 45°. If the light wave is polarized at 67.5° it lets less of it through whilst rotating it by 67.5°. If the light wave is polarized at 90°, it lets none of it though. Here’s Finley’s depictions:
Polarization images by Darel Rex Finley, see Third-Polarizing-Filter Experiment Demystified – How It Works
There’s an adjacent-over-hypotenuse cosine function at work here. Cos 0° = 1, cos 22.5°= 0.923, cos 45° = 0.707, cos 67.5° = 0.382, cos 90° = 0. As Finley said, there are no spooky quantum properties, and there’s nothing mysterious about it. Instead it’s a straightforward chain of cause and effect yielding rational, comprehensible results. It’s closely related to Malus’s law, which gives the intensity of the transmitted light as I = I₀ cos²θ. There’s a square in there because “the transmitted intensity is proportional to the amplitude squared”. When θ is 0°, all the light gets through, when θ is 90°, none of the light gets through, when θ is 45°, half the light gets through because cos²θ is 0.707 x 0.707 = 0.5. Note that the same is true for a beam of unpolarized light going through a polarizing filter. It’s a mixture of polarizations, and half the light gets through.
It describes a cosine-like curve because that’s how polarizing filters work
It’s similar when your polarizing filters are at opposite ends of an entanglement experiment. You emit a random assortment of photon pairs towards your polarizing filters at A and B, and on average half of them get through A. If your photon pair have the same polarization and your polarizing filters have the same alignment, then if you detect a photon at A you will detect a photon at B. If you rotate filter B round by 90° and repeat, then if you detect a photon at A you will not detect a photon at B. There’s a sliding scale between the two extremes, only it isn’t linear. It describes a cosine-like curve because that’s how polarizing filters work. When you know this, articles like Bell’s Theorem explained, Bell’s theorem and Bell’s Theorem with Easy Math seem totally lame. So does Clauser and Freedman’s experiment. Take another look at their results. Freedman’s inequality is δ = | R(22½°) / R₀ – R(67½°) / R₀ | – ¼ ≤ 0. That’s where R is the coincidence rate for two-photon detection with both polarizing filters in place, and R₀ is the coincidence rate for two-photon detection with no polarizing filters in place. The former divided by the latter is about 0.5 when the two polarizers have the same orientation and so angle ϕ is zero. This is what you’d expect, because on average half the light gets through polarizer A. It isn’t quite 0.5 because polarizers aren’t perfect:
Image from Experimental Test of Local Hidden-Variable Theories by Clauser and Freedman
Then as you rotate polarizer B, the coincidence rate drops off, following a cosine-like curve. Looking at the plot above, at 22½° it’s about 0.4, at 67½° it’s about 0.1, so δ = 0.4 – 0.1 – 0.25 = 0.05. Turning to Malus’s law, the 0.5 relates to a cos² 0° = 1. So for cos² 22.5° we have 0.923 x 0.923 = 0.852 which we divide by 2 to give 0.426. Then for cos² 67.5° we have 0.382 x 0.382 = 0.146 which we divide by 2 to give 0.073. So δ = 0.426 – 0.073 – 0.25 = 0.103. That isn’t less than or equal to zero, so Freedman’s inequality is broken. But not because of some magical mysterious spooky action at a distance. Because of the way polarizers work.
Those photons weren’t entangled at all
Not only that, but Clauser and Freedman’s photons weren’t even entangled. The wavelengths were 581 nanometres and 406 nanometres. They weren’t the same wavelength because the photons were not produced at the same time. Clauser and Freedman referred to an intermediate state lifetime of 5 nanoseconds. Those photons were produced 5 nanoseconds apart. A photon travels 1.5 metres in 5 nanoseconds. By the time the second photon was emitted, the first photon was through the polarizer. Those photons weren’t entangled at all. Aspect used the same calcium cascade. So his photons weren’t entangled either. That’s why you can do a Bell-type Polarization Experiment With Pairs Of Uncorrelated Optical Photons, and get the same result. This is why Al Kracklauer was talking about Malus’s law twenty years ago. And why Dean L Mamas wrote a no-nonsense “realist” paper called Bell tests explained by classical optics without quantum entanglement. It’s brief and to the point, saying this: “The observed cosine dependence in the data is commonly attributed to quantum mechanics; however, the cosine behavior can be attributed simply to the geometry of classical optics with no need for quantum mechanics”. Quite. I found out about this because Gill wrote a paper in 2022 dissing Mamas by moving the goalposts and saying the quantum mechanical cosine is twice the classical cosine. Gill used the trick of changing both polarizer angles. We are dealing with correlations here, so it’s the difference between the polarizer angles that matters, not the difference of each from some reference angle. Cos 2 θ is not equal to 2 cos θ. It’s like what Joy Christian said, the terms do not commute.
Is Spookiness Under Threat?
Note that Gill also wrote a paper dissing Joy Christian, who had the temerity to challenge spooky at a distance in 2007. See Mark Buchanan’s New Scientist article Quantum Entanglement: Is Spookiness Under Threat? It referred to Christian’s paper Disproof of Bell’s Theorem by Clifford Algebra Valued Local Variables. After that, Christian got cancelled for challenging quantum entanglement. He was dropped by the Perimeter Institute and Oxford University, because of people like Gill, who talks about Bell denialists. Scott Aaronson used the same word when he was dissing Christian. He also said he’d “decided to impose a moratorium, on this blog, on all discussions about the validity of quantum mechanics in the microscopic realm, the reality of quantum entanglement, or the correctness of theorems such as Bell’s Theorem”. That’s what you call safe-space censorship. He also said this: “Imagine, for example, that there existed a devoted band of crackpots who believed, for complicated, impossible-to-pin-down reasons of topology and geometric algebra, that triangles actually have five corners. These crackpots couldn’t be persuaded by rational argument”. And so on. Scott Aaronson is a cheerleader for quantum computing.
Physicists Create a Wormhole Using a Quantum Computer
There’s a lot of that sort of stuff in physics. Propaganda and censorship has been par for the course for decades, along with ad-hominem abuse and de-platforming. The tofu-eating wokerati learned it from the tenured academics living a life of ease on the public purse. That’s why you can’t read about people* like Krackleur, Mamas, and Christian in Nature, or in Quanta magazine. Instead you can read how Physicists Create a Wormhole Using a Quantum Computer. Wooo! You can also read how “the power of a quantum computer grows exponentially with each additional entangled qubit”. The problem is that quantum entanglement is bullshit, so entangled qubits are bullshit, so quantum computing is bullshit too. That’s why it still hasn’t delivered anything, and never ever will. What else would you expect when the quantum entanglement story is a fairy tale? It’s a castle in the air, built of bullshit, blarney, and bollocks, all mixed in with straw men and non-sequiturs, all held aloft by hype, hokum and hogwash. It is sophistry peddled by shysters and charlatans. It is cargo-cult pseudoscience promoted by quantum quacks who are spinning you a yarn and playing you for a sucker. The emperor has no clothes, and scientific fraud leaves a nasty taste in the mouth. Remember that the next time you read some jam-tomorrow puff-piece about quantum information science.
* It’s like finding a whole cave wall full of messages from a whole host of different Arne Saknussemms. So many people have been here before. But you only find them once you know you have to search on Entanglement and Malus’s law. Here’s a few:
Disproof of Bell’s Theorem: Further Consolidations by Joy Christian, who refers to Bell’s own derivation of Malus’s law.
A Comparison of Bell’s Theorem and Malus’s Law: Action-at-a-Distance is not Required in Order to Explain Results of Bell’s Theorem Experiments by Austin J Fearnley who said “there is an enforceable duality between results of Malus’ Law experiments and the results from Bell experiments”.
Disentangling entanglement by Antony R Crofts, who said “Violation of the expectation values of Bell’s theorem have been taken to exclude all ‘local realistic’ explanations of quantum entanglement. A simple computer simulation demonstrates that Bell’s inequalities are violated by a local realistic model that depends only on a statistical implementation of the law of Malus in the measurement context”.
Entanglement: A Contrarian View by A F Kracklauer, who said “This comparison is made on the basis of Malus’ Law”.
Polarization Correlation of Entangled Photons Derived Without Using Non-local Interactions by Kurt Jung, who said “In consequence Bell’s inequalities are irrelevant”.
Analyzer Output Correlations Compared for Entangled or Non-entangled Photons by Gary Gordon, who said “Our predicted results for this non-entangled photon case are an exact match to those reported in the literature for the analysis and experimental outcomes for the entangled photon case”.
A New Model for Linear Polarizing Filter by Herb Savage, who said “This new single-photon model for a linear polarizing filter shows the same apparent violation of Bell’s theorem as current loophole-free experiments”.
Fatal_Flaws_in_Bell’s_Inequality_Analyses_Omitting_Malus_Law_and_Wave_Physics_Born_Rule by Arthur S Dixon. who talked about the conscious or negligent omission of Malus’ law in the furtherance of scientific fame and fortune. His reference 43 refers to a paper called Bell’s Theorem and Einstein’s ‘Spooky Actions’ from a Simple Thought Experiment: The Physics Teacher by Fred Kuttner and Bruce Rosenblum who give a reference 11 to Malus’s law on page 128.
Rotational Invariance, Phase Relationships and the Quantum Entanglement Illusion by Caroline H Thompson, along with The tangled methods of quantum entanglement experiments. She said “They appear to be rejecting papers that endanger the accepted dogma”.
Classical Interpretation of EPR- Bell Test Photon Correlation Experiments by Thomas Smid, who said “All experiments are claimed to rule out the existence of Hidden Variables as Bell’s Inequality is violated and the coincidence rate (for initially unpolarized radiation) is observed to follow the well known Malus law”.
Experimental Counterexample to Bell’s Locality Criterion by Ghenadie N. Mardari who said “If polarization measurements are interpreted as transformations, then there is no mystery to explain”.
Visualization of quantum entanglement by Stefan Heusler, who said “Visualization of the angular dependency of the transmission probability pĤ(θ) = |⟨Ĥ|ΩPolarisation⟩|² of vertical polarized light. After many measurements, Malus law is recovered, indicated as red line”.