In the normal language of quantum gravity, the spin connection is an insanely complicated bit of mathematics that is used to connect the spin (of electrons and suchlike) to gravity (described by curvature of spacetime). In the normal run of things, if you can’t talk about the spin connection, then nobody will take you seriously in the quantum gravity world. Just to give you a bit of context, the spin connection is part of the subject of differential geometry. When I was a final-year student in Cambridge, I started going to a course of lectures on differential geometry, but gave up because I considered it to be too hard. And when I was a professor in QMUL, and I tried to talk to another professor in QMUL about quantum gravity (about which they knew a great deal) the conversation ended rather quickly when I couldn’t talk the talk about spin connections.
But now I find myself in an Aladdin’s Cave of treasures, and I swept with the magic Broom and found the spin connection staring me in the face. To be fair, I did already know more or less what the spin connection is, and what it does and how it works, but now I have a complete description, that unifies all the forces, and quantises them all, so I know exactly what the spin connection is, exactly what it does and exactly how it works. So now I can explain it to an 8-year-old. Are you ready for this?
Forget any idea you may have that mathematics is hard. It isn’t. You just have to look at it in the right way. The right way to think about the spin connection is to take a trip to the Lake District (any lake will do, as long as it’s nice and smooth and has lots of flat stones near it). Take a flat stone, spin it, and watch it skip over the surface of the lake. Now explain how this works, to your 8-year-old. That is how the spin connection works.
Did you see the spin flip as the stone bounced? To explain this, I first need to know whether you are right-handed or left-handed – because left-handed stones (or electrons) spin the opposite way to right-handed stones (or electrons). Anyway, let’s suppose that as you follow the path of the stone, from the perspective of the stone itself, it hits the water spinning clockwise. When it bounces, then from the perspective of the stone, it is sent travelling backwards, which means it is spinning anti-clockwise. That is a spin-flip, OK? Now look at the next bounce. Again, it hits the water spinning clockwise. WTF? How the hell did it do that? How did that spin “spontaneously” change from anti-clockwise to clockwise? What the hell is going on?
Those are the questions that physicists have been asking themselves for 100 years, and they still haven’t got any answers. But you know the answers, don’t you? I know the answer, and any other reasonably intelligent 12-year-old can explain it. It is because gravity affects the spin – when it is going up, it is spinning anti-clockwise, and when it is coming down it is spinning clockwise. So if you want to know anything at all about how electron spins work, you have to consider it in the context of gravity. If you don’t you won’t understand how the spins flip, and you certainly won’t understand why they don’t flip between a pair of entangled particles.
OK, so to explain entanglement, I need you to take a pair of 10-year-old twins to the lake, and make sure one of them is left-handed and the other right-handed. Now get them to skip stones together, so that their spins are opposite. Then every time you measure the spin (that is, when the stone interacts with the water), you will always measure the two to be opposite. But if you measure the spin vertically instead of horizontally, for example by putting a sticky tar-covered wall in the path of the stone, there’s a 50/50 chance of it coming up heads or tails. Of course, in this experiment, you can’t get everything exactly opposite, so the two 50/50 probabilities are independent. That’s what is called decoherence in quantum mechanics (I prefer to call it incoherence, but they consider that to be rude). But if you imagine that you can take away all the differences between the twins, all the air resistance, and everything else except gravity, you will find that the tides will determine whether they come out heads or tails, and because the tides don’t vary much on this scale, the two measurements will still be opposite to each other, almost all the time.
That is how entangled electrons work. It is also how entangled photons work. And it completely explains all of the experimental properties of measurements of entangled particles. If you take away all other interactions, so that you maintain coherence between the two particles, and you measure spins in the same direction, they will always be opposite. That is, if you measure both horizontally, or both vertically, they will always be opposite. For the horizontal measurement, you use up-down axis of gravity to determine the difference between clockwise and anti-clockwise spins. For the vertical measurements, you use the left-right axis instead, and you have to use the tides to tell you which way the electrons are falling (sideways). But it’s still gravity, so it’s still in the spin connection.
So, anyway, I still can’t talk the talk about spin connections. But those people who can talk the talk, can’t walk the walk. If they could, they’d have a theory of quantum gravity that works. What you have to judge is, can I walk the walk? Can I explain how gravity works at a quantum level?
I have shown you how an electron looks like a coin (via Lorentz contraction), spins like a coin, and flips like a coin. It is a well known principle that something that looks like a duck, swims like a duck and quacks like a duck, is a duck. This principle is a form of Occam’s Razor, which used to be widely used in physics. If an electron is a spinner, then there is no need to invent spinors to explain how the electron behaves. The spinor is dead, long live the spinner!
Hidden assumptions 
March 29, 2024 at 9:10 am |
The trouble with physicists, I tend to find, is that they can’t spell. They spell spinner, spinor, and they invent Dirac spinors because they don’t properly understand how Hamilton spinners actually work. They spell spatial, special, and because they don’t understand how Hamiltonian spatial relativity works, they invent Einsteinian special relativity.
They don’t understand that the mathematics of Dirac spinors is exactly the same as the mathematics of Hamilton spinners, so if you understand Hamilton, you don’t need Dirac. They don’t understand that the mathematics of special relativity is exactly the same as the mathematics of spatial relativity, so if you understand Hamilton, you don’t need Einstein.
So the best thing to do with theoretical physics (not experimental physics, obviously) is to throw away everything that has been done since 1973, translate all the previous 100 years of “development” back into Hamilton’s original language, and restart from about 1850.
But, please, please, please, do not turn the clock back to Newton. Do not make the mistake of defining Newtonian “mass” as an abstraction of the concept of “weight”. Hamiltonian mechanics does not have a concept of mass at all. It works directly with the concept of weight, and the fact that the weight of something varies as the gravitational field varies is not a bug, it is a feature.
You see, when physicists write “mass”, it is just a mis-spelling of “mess”. And if theoretical physicists want to get out of the mess they are in, they just have to get out of the mass they are in.
March 29, 2024 at 9:11 am |
Newtonian mass, you see, is just a mess.
March 30, 2024 at 12:53 am |
“… the two measurements will still be opposite to each other, almost all the time. That is how entangled electrons work. It is also how entangled photons work. And it completely explains all of the experimental properties of measurements of entangled particles.”
Two particles are supposedly emitted in opposite directions by the same decay, with correlated spins. I’m sorry but we have to be clear this is a fundamental error. You cannot assume such an emission takes place, because of 2nd quantization. Everytime you think you are emitting a “single” particle or a “pair of them with correlated spins”, you’re actually emitting a vast number along a huge number of paths (the path integral), most of which interfere and thus apparently “cancel out”. This is totally ignored by Einstein, Polansky, Rosen, Bohm, Bell and Aspect.
So until the measurements are made at the detectors, there are never two particles with wavefunction “entanglement” (false “1st quantization”, i.e. QM model used by Aspect’s analysis of experimental data). There are loads of particle emitted and Aspect’s detectors pick up two apparent particles that are actually resultants of a path integral. I urge you to look at the pictures of this path integral effect for reflection of light by mirrors and refraction in prisms in Feynman’s 1985 book QED. Feynman developed the path integral, then had to fight with a bit of help from Dyson and Bethe against Oppenheimer, Einstein, Pauli and Bohr to get it accepted, yet Feynman’s wonderful application to light in his 1985 book QED is censored out by the mainstream of QFT. It is really, really fundamental, it has hard evidence behind it, and it’s being ignored! A photon is not emitted by a light bulb, travelling to your eye. Instead, every single photon that arrives on your retina is a superposition of numerous virtual photons, most of which are out of phase and cancel out. You have to have this model to explain principle of least action, e.g. light takes route of least time if having to go through different media at different velocities (air, glass, water etc). It’s a scandal Aspect uses 1st quantization!
March 30, 2024 at 6:51 am |
I’m simplifying a bit for my 8-year-old audience. I’ll come to the path integral in a week or two, when I think they’re ready for it. Or, more to the point, when I think I’m ready for it.
March 30, 2024 at 7:47 am
Thanks, it’s up to you, but if you want to get the physical handle on the mathematics of of the “path integral” (better a discrete summation of geometric paths), you really need to start with the pictures (suitable for an 8-year-old) in Feyman’s 1985 book QED: the strange theory of light and matter. There’s no equation in that book and most of the text is drivel (except the fun of him kicking the “uncertainty principle” into oblivion in a footnote!), as usual for his books, so don’t read the text, just look at pics.
Just look at the disgrams and convert them into simple equations of geometric paths and allow it to sink in. Feynman was finally getting into applying the path integral to basic everyday physics, and the results are phenomenal. (I’m convinced that this is the way to go. I won’t link to my papers on this at vixra, giving quantitative evidence emission of radiation from electrically charged fundamental particles is at Hawking’s black hole radiation formula rate – pages 32 and 35-6 of my Nov. 2011 paper which needs updating urgently – but Feynman’s new approach enables you to understand all radiation emission and reception correctly, and this explains the zero point field vacuum (dark) energy. You get “ridiculous” numbers from Hawking’s radiation power from a an electron, ~10^53 K temperature and ~10^205 watts/m^2 Hawking radiating power from the black hole electron or 10^92 watts for the entire radiating surface area. When you calculate the exchange forces resulting from such charged massless radiation (most of it can only be exchanged because – being charged and massless – it has infinite magnetic self-inductance so can’t simply propagate unless the B fields are cancelled out by a two-way exchange equilibrium betweek charges, thereby explaining the physics of the Z.P. field), the huge radiating power is needed to offset the very tiny cross-sections and produce observed force couplings. The application of this to “real” photons is that acceleration of charge upsets the symmetry of excharge, resulting in it!
March 30, 2024 at 9:48 am |
I’ll come back to this in a week or two. Right now I’m too busy.
March 30, 2024 at 8:04 am |
I’ve copied this on my blog, with the note: I’m not hoping Wilson will come in to the Feynman view of the world and mathematicize it properly – that would be hoping for too much – but I’m just trying to stop him disappearing down the usual loony route where everyone gets brainwashed by 1st quantization, finds out it fails to work properly to give a mechanical explanation of stuff like “entanglement” (used mostly as an excuse by journal editors to reject any paper/idea that could lead anywhere beyond existing paradigms), then concludes – wrongly – that “nobody understands quantum mechanics”, which was Feynman’s own view back in the 1960s before he made progress in applying simplified path integral – 2nd quantization – to simple atomic and light phenomena!
(Being competent at mathematics and making a foray into this kind of physics makes you a target for those outside physicists with decades long grudges against the mainstream, so apologies for the pressure…)
March 30, 2024 at 9:59 am |
I’m not doing quantisation this week, I’m doing continuous models. Canonical quantisation is garbage, and I now know why. It is the same reason why GR is garbage, it is the simple fact that physicists cannot tell the difference between Hermitian and anti-Hermitian matrices. Well, they can, but they get them mixed up.
In GR, there are 15 anti-Hermitian matrices (SL(4,R)) and 21 Hermitian (Riemann Curvature Tensor+ scale), but there should be 15 Hermitian (Jordan algebra = fermions) and 21 anti-Hermitian (Lie algebra = bosons = gauge symmetries Sp(3,R) of phase space).
The same mistake is made in the Dirac algebra, in which the 6-dimensional Jordan algebra is made into a Lie algebra, and the 10-dimensional Lie algebra is made into a Jordan algebra.
March 30, 2024 at 10:17 am
What I mean is, GR works with Spin(3,3)=SL(4,R) instead of Sp(6,R) because somebody couldn’t tell the difference between a diagonal matrix (1,0;0,-1) and an off-diagonal matrix (0,1;-1,0). The off-diagonal matrix is correct, and the diagonal matrix is incorrect.
Exactly the same mistake is in electro-weak theory, in which gamma_5 is made to square to +1 when it should square to -1.
March 30, 2024 at 3:42 pm
I can see why that’s interesting (if correct). For goodness sake, don’t make an error with this and assert it without checking (otherwise if there’s a trivial error, you become that 8-year old boy who cried wolf…). Usually it’s best to publish a preprint of something radical in draft form as a “suggestion” (without hard assertion) first, and become more assertive about it being factual later after looking at it really critically. Istudied general relativity over 30 years ago, and can explain to you that no physicist really bothers about the details (except to get through exam revision). In a lecture by Penrose, he gave Einstein’s GR field equation, but then saying that, thankfully, he didn’t need to explain the matrices because they were in a textbook.
I’m very glad that you’re going into this, because you get a huge amount of repetition (plagarism?) in books about it by different people, all repeating the same mythology, and then some fool says: “Look, all the textbooks agree so that proves it must be right, or somebody in that lot would have spotted an error!” There used to be a warning in some old 40s and 50s uni general atomic physics books (of my dad’s generation) which quoted the example of electron discoverer JJ Thomson, who discovered x-rays (glass tubes glowing far away from a cathode-ray tube) in 1893. He ignored as some kind of an anomaly until Rontgen published it and won prize and fame. I fear this happens all the more in theoretical physics.
March 30, 2024 at 4:02 pm |
You’re right, of course, and if I were sensible I’d follow your advice. But I’ve cried “wolf” so many times another one or two won’t make any difference. Being reasonable and sensible is no longer part of my motivation. Being right is the only criterion.
March 30, 2024 at 7:27 pm |
I suppose there is a danger that I might be following a lemming’s path towards a failure of mechanical explanations of QM, that has been followed by generations of cranks before me. But I am arrogant enough to believe that I already know where the cliffs are, and can avoid them.
I have never been brainwashed by first quantisation, because I know it doesn’t work, at least not with the standard physics names for the mathematical concepts. The mathematics is fundamentally inconsistent, and I am simply unable to follow an inconsistent mathematical argument. This supposedly elitist attitude gets me into a lot of trouble with physicists, but it is not something I am prepared to compromise on.
March 31, 2024 at 11:17 pm
Yes, first quantization is a path into a swamp filled with debris from many failed “interpretations of QM”. Second quantization, where the field is quantized, is the way forward. It has its own swampland of maths probs even outside the path integral (which should be a discrete summation not calculus, for truly quantized fields!), in my view the whole maths of field descriptions is defective: https://vixra.org/pdf/1301.0187v1.pdf Note at bottom p2, dismissal of Simons’ and Yang’s connection of gauge theory to fibre bundles (Yang set the Maxwell field strength tensor equal to the Riemann tensor). This was a sneaky rebuff to Woit’s love of the fiber bundles topology to link gauge theory to relativity! It leads nowhere but into a sea of greater obfuscation. What’s really needed, IMHO is the exact opposite: Monte Carlo simulations of gauge bosons being exchanged, causing pair production where the field is strong enough (which then polarize, thus absorbing energy and partly shielding the field), and comparing (normalizing) this physical simulation to usual calculations. Anyway, that’s my view. Maybe there are other possibilities.
March 31, 2024 at 2:20 pm |
“I don’t need to explain the matrices because they’re in a textbook”.
I’m speechless. My jaw dropped to the floor.
You DO need to explain the matrices, Professor Penrose, BECAUSE THE TEXTBOOK IS WRONG.
Forgive me for shouting, but I can’t take any more of this FUCKING CRAP.
Forgive me for shouting AND SWEARING, but if even Penrose says that, how the fuck does anyone else stand a chance?