Bertlmann’s socks and the nature of reality

Last year I wrote about quantum entanglement, looking at the history and talking about the physics. I went through John Stewart Bell’s famous 1964 paper On the Einstein Podolsky Rosen Paradox, and talked about Bell’s inequality, which is also known as Bell’s theorem. Now I thought I’d take a look at Bell’s 1980 paper on Bertlmann’s socks and the nature of reality. It’s freely available on a variety of websites, including the CERN document server. Bell was of course a CERN employee.

It has one of the best descriptions of Bell’s theory I’ve ever read

There’s an easy-reading article about it called, as you might expect, Bertlmann’s Socks And The Nature Of Reality. It’s by Will Sweatman and it’s on the Hackaday website. Sweatman said “Our guide will be a chapter from Jim Baggot’s The Quantum Story, as it has one of the best descriptions of Bell’s theory I’ve ever read”. See page 306. Sweatman’s article talks about two separated hydrogen atoms with the opposite spin being measured by Stern-Gerlach magnets, and about a combined probability P+-.

Image from Hackaday, refers to Stanford, origin Weinert 1995

It says quantum theory “gives the value of P+- as ½ cos²(a/2) where a = the angle between the magnet axes”. It also gives the image below, wherein the green cosine curve is predicted by quantum theory, and the red straight line is allegedly predicted by a “realist” local hidden variables theory:

Image from Hackaday from The Quantum Story figure 22

Sweatman’s article came in two parts. The second part was called What Do Bertlmann’s Socks Mean To The Nature Of Reality? He talked about pairs of socks and washing machine temperatures standing in for particle pairs and magnet angles. He gave the expression P+-(a,b) + P+-(b,c) ≥ P+-(a,c) saying “This, ladies and gentlemen, is Bell’s Inequality”. Then he gave magnet angles A = 0°, B = 146°, and C = 282°, and said applying these values to the inequality would yield ½ cos²(73°) + ½ cos²(68°) ≥ ½ cos² (141°), which reduces to 11.2% ≥ 30.1%. He concludes that The numbers are obvious. The predictions from quantum theory violate the Bell inequality. There is no getting around it”. There is, if you know that the Bell’s inequality is merely a statement about a straight-line graph, and that it’s wrong to say that’s what a local hidden variables theory must yield. But back to Bertlmann’s socks.

Speakable And Unspeakable In Quantum Mechanics

The CERN document server version of Bell’s 1980 paper is typewritten with hand-written equations. It’s rather scruffy. There’s a better version in Bell’s 1987 book Speakable And Unspeakable In Quantum Mechanics. Page 139 includes the naïve picture of Bertlmann with one pink sock:

Image from Speakable And Unspeakable In Quantum Mechanics by J S Bell

The other sock is hidden. Some versions of the paper include an abstract, where Bell said the founding fathers of quantum mechanics had convinced themselves that it was necessary to abandon the idea of an objective reality at the microphysical level”. He was referring to Niels Bohr and the Copenhagen school. He also said the idea of local causality was a formidable argument for an objective reality. This was an indirect reference to Einstein and other “realists”. Bell went on to say the founding fathers offered counter-arguments which were, in his opinion, neither very clear nor very convincing. He then said “since then it has been possible to push the analysis a little further” whereupon “correlations appear, according to quantum mechanics, which are not at all like those of everyday life”. The abstract finished by claiming that the quantum mechanical predictions are not reconcilable with an objectively real microphysical world. They are, but let’s press on.

David Bohm’s EPRB gedankenexperiment

In the introduction Bell likened Bertlmann’s socks to David Bohm’s EPRB gedankenexperiment featuring two entangled spin ½ particles emitted in opposite directions, each toward a Stern-Gerlach magnet and a screen. Bell said “each time the experiment is performed each of the two particles is deflected either up or down at the corresponding magnet. Whether either particle separately goes up or down on a given occasion is quite unpredictable. But when one particle goes up the other always goes down and vice-versa”. On page 140 he said it was useful to know how physicists think of particles with spin, and that “In a crude classical picture it is envisaged that some internal motion gives the particle an angular momentum about some axis, and at the same time generates a magnetization along that axis. The particle is then like a little spinning magnet with north and south poles lying on the axis of rotation”. He said when a magnetic field is applied to a magnet, the north pole is pulled one way and the south pole is pulled the other way. If the field is uniform the net force on the magnet is zero. But in a non-uniform field one pole is pulled more than the other and the magnet as a whole is pulled in the corresponding direction. This is true for a magnet, but it’s a mistake to claim the same for a spin ½ particle. See Charles Galton Darwin’s 1927 Nature paper on the electron as a vector wave, which talked of a spherical harmonic for the two directions of spin. An electron is not the same as a magnet.

A magnetic field does not point up

On page 141 Bell went on to say “suppose that the magnetic field points up”, which is another mistake. A magnetic field does not point up. It causes Larmor precession which dates back to 1897. This results in a torque and rotational particle motion. It also rotates light, as per the Faraday effect. Anyway, in a uniform magnetic field, a spin ½ particle like an electron goes round in circles. (If you throw it through the uniform field, the motion is of course helical, but nevermind that). In a non-uniform field, the circles are not perfect circles, so there’s a net motion in some direction. However the field does not point in this direction. We know this because electrons and positrons go round in opposite circles. Bell must surely have known this, he must have seen the bubble-chamber pictures. But he said “a particle with south-north axis pointing up would be pulled up”, whilst one with a south-north axis pointing down would be pulled down. He also said a particle where the south-north axis was perpendicular to the field would not be deflected, and “one oriented at an intermediate angle would be deflected to an intermediate degree”. These claims are misleading, and I think they’re based on a wilful misrepresentation of 1980s science. Bell then gave figures 4 and 5 as shown below:

Bell talked about the experimental results, which match figure 5 on the right, saying they’re very hard to understand in naïve classical terms. He said “it might be supposed for example that the magnetic field first pulls the little magnets into alignment with itself, like compass needles. But even if this were dynamically sound it would account for only one group of deflections”. He also said “to account for the second group would require ‘compass-needles’ pointing in the wrong direction”. That’s exactly what we see in nuclear magnetic resonance, which dates from 1938:

CCASA image by Darekk2 , see Wikipedia

Note this: Nuclear magnetic resonance was first described and measured in molecular beams by Isidor Rabi in 1938, by extending the Stern–Gerlach experiment, and in 1944, Rabi was awarded the Nobel Prize in Physics for this work. Rabi extended the Stern-Gerlach experiment. Bell must have known about this, and about electron paramagnetic resonance too: “the basic concepts of EPR are analogous to those of nuclear magnetic resonance (NMR), but it is electron spins that are excited instead of the spins of atomic nuclei”. And yet he didn’t mention it. On page 142 he swept spin up and spin down under the carpet. Then he gave a non-sequitur about blaming the absence of intermediate deflections on the source, “which is easily tested by turning the Stern-Gerlach magnet”. His figure 6 depicted it:

Note that this means the apparatus isn’t just measuring something, it’s rotating something too, just like polarizing filters rotate light. But Bell didn’t talk about that. Instead he launched into quantum mysticism: “Phenomena of this kind made physicists despair of finding any consistent space-time picture of what goes on the atomic and subatomic scale. Making a virtue of necessity, and influenced by positivistic and instrumentalist philosophies, many came to hold not only that it is difficult to find a coherent picture but that it is wrong to look for one – if not actually immoral then certainly unprofessional. Going further still, some asserted that atomic and subatomic particles do not have any definite properties in advance of observation. There is nothing, that is to say, in the particles approaching the magnet, to distinguish those subsequently deflected up from those subsequently deflected down. Indeed even the particles are not really there”. That’s the absolute antithesis of science. It’s where you end up when you ignore the wave nature of matter and the reality of spin.

Bohr: It is wrong to think that the task of physics is to find out what Nature is

Bell quoted Bohr, Werner Heisenberg, and Pascual Jordan talking about quantum mysticism. Bohr: “It is wrong to think that the task of physics is to find out what Nature is”. Heisenberg: “Particles are not as real, they form a world of potentialities or possibilities rather one of things or facts”. Jordan: “The electron is forced to a decision. We compel it to assume a definite position”. I think Bell was appealing to their authority. On page 143 he said “It is as if we had come to deny the reality of Bertlmann’s socks, or at least of their colours, when not looked at”. Then he talked about the EPR debate headed up by Bohr and Einstein, using the phrase “paradox indeed”, referring to “spooky action at a distance”, and saying Einstein’s phrase “God does not play dice” had not helped. On page 144 Bell quoted Wolfgang Pauli and Max Born in the context of determinism, saying the quotes are meant to “illustrate the difficulty of putting aside preconceptions and listening to what is actually being said”. Then he gave a long Einstein quote “about the independent existence of physical reality in different parts of space”. Then he totally ignored it.

Illustration

That’s because in his section 2 on page 145, Bell gave a straw-man argument. He started by saying “previously, we implicitly assumed for the net force in the direction of the field gradient (which we always take to be in the same direction as the field) a form F cos θ”. This is treating a magnetic field, which causes rotational motion of a charged particle, as if it’s an electric field, which causes linear aka translational motion. He then said “we change this to F cos θ / |cos θ|”. He explained by saying this: “Whereas previously the force varied over a continuous range with θ, it takes now just two values, ±F, the sign being determined by whether the magnetic axis of the particle points more nearly in the direction of the field or in the opposite direction”. He also said no attempt is made to explain this change in the force law, it’s just an ad hoc attempt to account for the observations. Then he said it accounts for the appearance of the two groups of particles. However on page 146 he then said this only reproduces quantum mechanical results at certain magnet angles, namely (a – b) = 0, (a – b) = π/2, and (a – b) = π. The π here is 180° of rotation. The graphs all show an intersection at zero degrees, ninety degrees, and a hundred and eighty degrees because that’s where the straight-line straw man  intersects with the experimental cosine curve:

CCASA image by Richard Gill, see the old version of Bell’s theorem – Wikipedia

Then Bell asked “could we not be a little more clever, and devise a model which reproduces the quantum formulae completely?” His immediate answer was “No. It cannot be done, so long as action at a distance is excluded”. Oh yes it can.

Difficulty with locality

On page 147 Bell tried to justify his assertion by saying an adaptation of the Wigner-d’Espagnat inequality applies. He talked about the situation where socks might survive a thousand washing cycles at 45°, 90°, or 0°C. He used the word “pass” instead of survive, and said the number that could pass at 0°C and not at 45°C, plus the number that could pass at 45°C and not at 90°, is not less than the number that could pass at 0°C and not at 90°C. This fine for socks, but it’s absolutely not fine for a Stern-Gerlach apparatus that rotates as well as measures. But Bell glossed over that, and on page 148 he moved on to pairs of socks and probabilities, saying this:

(the probability of one sock passing at 0° and the other not at 45°) plus
(the probability of one sock passing at 45° and the other not at 90°) is not less than
(the probability of one sock passing at 0° and the other not at 90°)

Then he said you could set up a similar scenario for pairs of particles of the EPRB experiment. You do this by blocking off the down channels in the Stern-Gerlach magnets, “allowing only particles deflected ‘up’ to pass”. Then instead of temperatures “we now have angles a and b at which the Stern-Gerlach magnets are set”. He then essentially said the spins are opposite, so we take the converse of the second term in each bracket giving a statement equivalent to this:

(the probability of a particle passing at 0° and not at 45°) plus
(the probability of a particle passing at 45° and not at 90°) is not less than
(the probability of a particle passing at 0° and not at 90°)

On page 149 Bell said this trivial inequality is not respected by the quantum mechanics probabilities, which are given by ½(sin (a – b) / 2)², where a and b are magnet angles. That means:

½ (sin 22.5°)² plus
½ (sin 22.5°)² is greater than
½ (sin 45°)²

Bell correctly said this works out at 0.1464 ≥ 0.2500, and pointed out that this is not true. He then talked about the logic that leads to the impasse, saying if the magnets are parallel “the result of the experiment on one side immediately foretells that on the other”. Then he said “if we do not accept the intervention on one side as a causal influence on the other, we seem obliged to admit that the results on both sides are determined in advance anyway”. No we don’t. Remember figure 6? When you rotate the magnet it rotates something too, just like polarizing filters rotate light. It’s rotating the plane of the particles passing through. You aren’t just measuring the probability of a local particle passing through, you’re altering that local particle, because that’s what Larmor precession does. You aren’t altering the remote particle via some magical mysterious spooky action at a distance.

General argument

On page 150 Bell moved on to a general argument, talking about imperfections and saying “in the more sophisticated argument we will avoid any hypothesis of perfection”. He also said “you might suspect that there is something specially peculiar about spin ½ particles”, but that “there are many other ways of creating the troublesome correlations”. So “the following argument makes no reference to spin ½ particles”. I think he was trying to distract the reader from the realist explanation. I think that’s because he knew more about spin and magnetism than he’s letting on. That’s presumably why on page 151, 152, and 153, he waxes lyrical about a long box of unspecified equipment with three inputs and three outputs. The inputs are a central “go” and an “a” on one side and a “b” on the other. The outputs are three pieces of paper with “yes” or “no” on them, the first of which appears before the other two. He talked at great length about probability. When you know the trick, you know that Bell used his general argument to replace physics with probabilistic smoke and mirrors.

Envoi

In his conclusion Bell said he would comment on “four possible positions that might be taken on this business – without pretending that they are the only possibilities”. He said the first position was that quantum mechanics may be wrong, but that “the experimental situation is not very encouraging from this point of view”. He said the second position “may be that it is not permissible to regard the experimental settings a and b in the analyzers as independent variables”. He was suggesting there was some kind of deterministic spookiness when it came to deciding the magnet angles. He said the third position was that “we have to admit that causal influences do go faster than light”. He said the fourth position was that Bohr’s intuition was right, and that there is no reality below some classical macroscopic level. Unfortunately the fifth position is missing. That’s the position that Bell was a charlatan on the make. A cup-and-ball conman peddling blarney, bollocks, and bullshit. All the while surrounded by physicists at CERN who would have told him about Larmor precession, particle motion in a magnetic field, and of course Malus’s law. Malus’s law dates from 1809. It features on the arXiv in the context of EPR, but not in Bell’s book:

Malus’s law tells us that measuring the polarization of the local photon doesn’t alter the remote photon, it alters the local photon. It rotates it, in line with I = I₀ cos²θ. The same principle applies to the rotation of the particle plane by the Stern-Gerlach magnets. Talking of which, Bell’s book doesn’t even contain the word silver, even though the Stern–Gerlach experiment was first performed with silver atoms. And unlike Wikipedia, Bell didn’t say “the screen revealed discrete points rather than a continuous distribution, owing to their quantized spin”. When you know all this, and that Clauser and Freedman’s photons were emitted 5 nanoseconds apart and so weren’t even entangled, you ought to know that there is no magical mysterious instantaneous spooky action at a distance.

They cling to their belief despite the lack of evidence

Sadly too many people believe in quantum mysticism. They want to believe. They cling to their belief despite the evidence, just like the insane delusional zealots do. Sometimes I feel like I want to grab hold of people by the buttons and knock some sense into them. No, wearing lipstick and a frock won’t make you a woman, SLAP. No, the electron is not a point particle, SLAP. No, blaming the results of overpopulation on climate change won’t save the planet, SLAP. No, the speed of light is not constant, SLAP. No, howling for the extermination of Jews doesn’t make them the Nazis. SLAP. No, there is no time travel, SLAP. No, importing millions of third-world migrants won’t make your country a better place, SLAP. No, there is no quantum entanglement, and that’s why after more than forty years, there’s no quantum computing either, and never will be. SLAP, SLAP, SLAP. I hope this helps with your future career decisions.

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This Post Has 30 Comments

  1. Just plain Greg....

    “HaHaHa ! HeHeHe ! HoHoHo ! ” Thus spoke The Walrus.
    I’m still laughing heartily as I text; I can literally hear the raucous echos created by the vacuous empty craniums you just Bitch Slapped, John ! LOL 😂

    1. The Physics Detective

      My pleasure Greg. There is so much unfounded convictional belief around that I sometimes wonder about human nature. We see it in all spheres of life, including politics, religion, science, you name it. Here we are in these enlightened times with vastly improved communications and information, and yet conviction seems to be getting worse. As for artificial intelligence, I said “Oh FFS” when I read about Google Gemini. That’s not artificial intelligence. That’s artificial stupidity. Only it would seem that the non-artificial version isn’t much better.

      1. Greg R. Leslie

        WARNING : The following video will make you spit out your morning tea/ coffee. I found These Pearls of Wisdoms on The Yodeling Yoda of Germanic Gidgetry’s bogg blogg : start at 1:10mins to 1:40. At least she is still firmly against CERNS’s completely insane new demands………..

  2. Dredd

    “Sadly too many people believe in quantum mysticism. They want to believe. They cling to their belief despite the evidence, just like the insane delusional zealots do. Sometimes I feel like I want to grab hold of people by the buttons and knock some sense into them.” Some of the are prominent physicists (Small Brains Considered – 7).

    1. The Physics Detective

      Dredd, if every comment of yours is a link to your blog rather than feedback on the article here, you and I are going to fall out. Note that in the black hole charlatans I said this about Penrose:
      .
      But Penrose got the lion’s share. The Penrose who had a big hand in screwing up Einstein’s general relativity. The Penrose who came up with The Emperor’s New Mind and quantum consciousness, which apparently is something to do with quantum gravity, don’t you know? The Penrose who came up with the Penrose diagrams that depict travel through a black hole to some parallel fucking antiverse. The Penrose who has a list of honours as long as your arm, ye gods. What a quack. What a charlatan.
      .
      I don’t think the same about Einstein. Instead I think it’s rather sad that he had little success in physics after he became famous.

  3. Sandra

    I’m disappointed you never mentioned Joy Christian in this article. He even wrote an extensive paper with a title quoting bertlman’s socks. Have you had the time to read that last paper I linked to?
    .
    It’s interesting that we call these inequalities Bell’s inequalities, when in reality they are actually Boole’s inequalities (which are more than 100 years old). The only merit of Bell has been giving them a physical interpretation.
    .
    It’s also interesting that so many subscribe to non-realism when Fine clearly showed in the 80s that Boole inequalities are simply a statement about the existence of joint probability distributions. That is, you can add probabilities up (to get the final inequality) of different experimental runs only if the measurements of different runs commute with each other (i.e. you could think that if you measure angles a and b, in principle the value at angle c would be determined uniquely). The thing that aspect’s experiment proved is that quantum mechanical spin does not have such property. That’s it. Fine is very clear on this as well.

    1. The Physics Detective

      I’m sorry to disappoint Sandra. I took a look at Joy Christian’s paper (https://arxiv.org/abs/1911.11578), but I didn’t cover it because I didn’t think it was a good fit. Bell used a straight-line probabilistic argument to make the grand claim there had to be spooky action at a distance, when the cosine-curve experimental results could be explained simply via a Malus-law-like rotation caused by the apparatus. Proposing that we live in a quaternionic 3-sphere is not a simple explanation, and is, in my view, another grand claim.
      .
      Noted re Boole’s inequalities. I learn something new every day. Thanks. Re your last paragraph:
      .
      It’s also interesting that so many subscribe to non-realism when Fine clearly showed in the 80s that Boole inequalities are simply a statement about the existence of joint probability distributions. That is, you can add probabilities up (to get the final inequality) of different experimental runs only if the measurements of different runs commute with each other (i.e. you could think that if you measure angles a and b, in principle the value at angle c would be determined uniquely). The thing that aspect’s experiment proved is that quantum mechanical spin does not have such property. That’s it. Fine is very clear on this as well.
      .
      This looks like something I need to read about. You will be aware that I use a Möbius strip in my article on the electron. See https://physicsdetective.com/the-electron/. I think John Williamson and Martin van der Mark should have been recognised for their electron model. Sadly Martin is no longer with us.

      1. Sandra

        I understand your point about the quaternionic 3-sphere, but it’s not complicated as it sounds. It’s analogous to the ant walking on the surface of a ball: it thinks it lives on a flat surface, while In reality, it’s a surface embedded in 3 dimensions. I’ll have you know that currently we don’t know what the topology of the universe is. For some time astrophysicists assumed we live in a flat, infinite universe, and use the CMB measurements for this conclusion. But if you take a look at the recent measurements by the Plank satellite, they are in clear disagreement with previous measurement and support with an 8 sigma confidence a closed, curved universe (which corresponds mathematically to a surface of a 3-sphere). It is one of the three general solutions to Einstein’s equations, together with flat and hyperbolic spaces. Nothing set in stone, but interesting nonetheless.
        .
        I see I still haven’t convinced you about the issue using Malus’ law in explaining the entanglement experiments. You start with two photons with the same polarization: if you allow each photon to be rotated locally at the polarizers according to malus law, how do you get a final probability that depends on the difference in angle between the polarizers? What happened to the local dependence on the angle?

        1. The Physics Detective

          Interesting stuff, Sandra. You are in italics.
          .
          I understand your point about the quaternionic 3-sphere, but it’s not complicated as it sounds. It’s analogous to the ant walking on the surface of a ball: it thinks it lives on a flat surface, while In reality, it’s a surface embedded in 3 dimensions. I’ll have you know that currently we don’t know what the topology of the universe is. For some time astrophysicists assumed we live in a flat, infinite universe, and use the CMB measurements for this conclusion.
          .
          See https://en.wikipedia.org/wiki/Shape_of_the_universe which says this: “As of 2023 current observational evidence suggests that the observable universe is spatially flat with an unknown global structure”. It also says this: “Spaces that have an edge are difficult to treat, both conceptually and mathematically. Namely, it is very difficult to state what would happen at the edge of such a universe. For this reason, spaces that have an edge are typically excluded from consideration”. I wrote about this in https://physicsdetective.com/the-edge-of-the-universe/. Astrophysicists often say a flat universe must be an infinite universe. I think the expansion of the universe is evidence that it is not infinite.
          .
          But if you take a look at the recent measurements by the Plank satellite, they are in clear disagreement with previous measurement and support with an 8 sigma confidence a closed, curved universe (which corresponds mathematically to a surface of a 3-sphere). It is one of the three general solutions to Einstein’s equations, together with flat and hyperbolic spaces. Nothing set in stone, but interesting nonetheless.
          .
          I was not aware of this. See https://www.space.com/universe-shape-flat-closed-debate.html . It says this: “The Planck Collaboration itself did a lot of analysis and checking, and came to the conclusion that our universe is really flat, but that some other contaminant is nudging the data to make it look curved”. That’s my understanding. The article then says this: “But more recently, a trio of astronomers performed their own analysis and came to the opposite conclusion: Planck is not a liar, and the universe is indeed curved”. I will look into this. I don’t think space is curved on the scale of the universe, because I view the electromagnetic field as curved space.
          .
          I see I still haven’t convinced you about the issue using Malus’ law in explaining the entanglement experiments. You start with two photons with the same polarization: if you allow each photon to be rotated locally at the polarizers according to malus law, how do you get a final probability that depends on the difference in angle between the polarizers? What happened to the local dependence on the angle?
          .
          Take two polarizers, and shine light through them like this → → . Then rotate the second polarizer. The intensity of the light that passes through both polarizers is given by I = I₀ cos²θ. Now repeat your experiment, but instead of shining light through both polarizers, emit light from in between the polarizers, in opposite directions, like this ← →. The intensity of the light that passes through both polarizers is still given by I = I₀ cos²θ. All you’ve done is changed the direction of the light that went through the first polarizer. I imagine you could do something similar with Stern-Gerlach magnets and spin ½ particles.

      1. The Physics Detective

        When you’re looking at that solar eclipse Greg, keep an eye out for “the dancing motherships”. Or should I say points of light above the Eastern horizon moving away from one another and towards one another and around one another.

  4. Greg R. Leslie

    Instead of doing my own research, what are the ” motherships ” and what causes them Boss ? Are they any relation to the Led Zep album ? Simple minds demands even simpler answers. ….. ……

    1. The Physics Detective

      It’s a UFO sighting I heard about. Very distant points of light, moving very fast, away towards and around one another. They’re well above the atmosphere.

  5. Greg R. Leslie

    Ha Ha Ha !, Yea, Boss the UFO and conspiracy crowd are having a major field day. But this too shall pass, like kidney stones, but remember Y-2K ; Mayan Calander; and all the different Rapture(rupture)Days ? It’ll be fun to video tape the upcoming eclipse and then edit it in a goofy, comical way perhaps?

  6. Greg R. Leslie

    In all seriousness John, with your permission of course; I will forward to you all of my personal unaltered, virgin still photos and possible videos of said upcoming solar eclispe to The Physics Detective. Then possibly disseminated at your pleasure for all to interpret and distill ?

  7. Greg R. Leslie

    Talk to all of you then, on April, 8th, @ 3:08 pm E.S.T..

  8. Greg R. Leslie

    Yea John, the whole electrocaloric, magnetocaloric, pyroelectric, piezoelectric and especially magnetic refrigeration are long,deep Wikipedia rabbit holes to fall down into. The 1st. & 2nd. Laws of Thermodynamics are prominently in play; but unfortunately all articles are defined using S.M. tautology bollockß. Are you an authorized Wikipedia contributor/editor John ?
    The magnectic refrigeration article is super neato, much to learn there.
    So I think your idea of an article on heat and thermodynamics would seem to be an amazingly happy, current coincidence !

    1. The Physics Detective

      Greg: no, I’m not an authorized Wikipedia contributor/editor. At least I don’t think I am. I think I said something on a talk page a few years back, but I’ve never got into editing the articles. I don’t have time for one thing.
      .
      My idea of an article on heat and thermodynamics? Huh? Heat is just motion at the atomic or molecular level. A hot gas is one where the atoms or molecules are moving fast. In a solid they have vibrational motion rather than linear / translational motion. A liquid is somewhere between the two. I wasn’t planning on writing about that. I was planning on writing a short newspaper-style article on quantum entanglement. My boss is away, so I’m in charge for 2+ weeks, and work has been tough. So I haven’t started yet.

  9. Steve Powell

    I’m knot surprised!

  10. Steve Powell

    I head something on TV the other night about lord kelvin, vortices and knots. It wasn’t a science show. Maybe
    NOVA.

      1. Greg R. Leslie

        Can’t forget someone else’s genius The Detective first exposed us to : William Kingdon Clifford.( hope my spelling is correct )

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