I think when you’ve absorbed a lot of material, especially the old material, you get a handle on the theory of everything. The Einstein digital papers are important for this. That’s where you learn how gravity works. You learn that light curves because the speed of light is spatially variable. Not because it follows the curvature of spacetime. You learn that a gravitational field is a place where a space is neither homogeneous nor isotropic in a non-linear fashion. Hence when you plot your metrical measurements of space and time, your plot is curved:
Gravity probe B image courtesy of NASA, from the Wikipedia Curved Space article
However space is not. A gravitational field is not a place where space is curved. Once you know this, you start wondering about misleading claims like matter tells space how to curve, and why some contemporary authors contradict what Einstein said. It makes you do your own research and think for yourself. Then you ask yourself if there’s a place where space is curved. Then you start reading things like James Clerk Maxwell’s 1861 paper On Physical Lines of Force. He talked about displacement current, and said light consists of “transverse undulations of the same medium which is the cause of electric and magnetic phenomena”. That might sound naïve, but it isn’t. Because when an ocean wave moves through the sea, the sea waves. When a seismic wave moves through the ground, the ground waves. So, what waves when a light wave moves through space? The answer is space. And wherever space is waving, space is curved.
A field is a state of space
I think that’s the start of the theory of everything. It is, in essence, William Kingdon Clifford’s 1870 space theory of matter. It’s also Einstein’s pure geometrical marble. It isn’t Kaluza-Klein theory with some curled-up extra dimension, it’s simpler than that. Maxwell combined the electric field and the magnetic field, saying each is an aspect of the greater whole called the electromagnetic field, then Einstein described a field as a state of space. So, how many states of space can there be at any one place? The answer is one. That makes you think about the last line of Einstein’s E=mc² paper. He said radiation conveys inertia between the emitting and absorbing bodies. That means a photon isn’t just some electromagnetic wave propagating through space at c. There’s a gravitational aspect too, and the electromagnetic aspect and the gravitational aspect can not be separated. As to how it hangs together, it’s easier than you think.
There’s only one wave there, not two
A photon doesn’t consist of an electric wave E and a magnetic wave B orthogonal to one another. The so-called electric wave is merely the spatial derivative of the real wave. The so-called magnetic wave is merely the time derivative. See the Wikipedia electromagnetic radiation article: “the curl operator on one side of these equations results in first-order spatial derivatives of the wave solution, while the time-derivative on the other side of the equations, which gives the other field, is first order in time”. For an analogy, imagine you’re in an orange canoe at sea, riding over a 10m tsunami. As the wave approaches, your canoe tilts upward. The degree of tilt denotes E, whilst the rate of change of tilt denotes B. The degree of tilt increases along with the rate of change of tilt. When you’re halfway up the wave, both are at a maximum. Then the tilt starts to decrease, until you’re momentarily at the top of the wave. At this point your canoe is horizontal and has momentarily stopped tilting. Hence it’s a place where E and B are zero, even though the potential is at a maximum. Then as you go down the other side, the situation is reversed. We can plot it like this:
That’s what a photon is like. There’s only one wave there, not two. As for the cells in the upper portion of the picture, note that most of them are twisted, with a spin-1 characteristic. You have to rotate them by 360° before they look the same again. Now look up the centre, where the cells are rectangular. They have a spin-2 characteristic. You only have to rotate them by 180° before they look the same again. You might associate the former with virtual photons and the latter with virtual gravitons, but that’s missing the trick. You should associate twisted cells with electromagnetism, and flattened cells with gravity. But in doing so, you should note that the twisted cells are also flattened. This is the direction of travel for unification and TOEs. Not some GUT that predicts the existence of magnetic monopoles, and not the 25 “fundamental” fields of the Standard Model.
All photons have a common amplitude
As for what the photon is, there are some outstandings. Does it have an all-round symmetry, like a lemon rather than the upper half of a lemon? Does it have a corkscrew rotation like a lemon with a twist, because circular polarization is more fundamental than linear polarization? I’m not sure. But I am sure that the photon has a quantum nature. All photons have energy E=hf. Planck’s constant of action h is common to all photons, regardless of their frequency f. Action has the dimensionality of momentum × distance, and there’s a distance that’s hiding in plain sight. Look at the pictures of the electromagnetic spectrum. Note how the wave height is always the same regardless of wavelength? As to why, I think of Robert Kemp’s quantization of electromagnetic change, and of light in space moving down a lossless transmission line of its own making. It’s as if space has some kind of elastic limit, so that all photons are like a plucked guitar string. The pluck is always the same, so all photons have a common amplitude regardless of wavelength. I wonder if that was what Hermann Weyl was groping for in his original 1918 gauge invariance paper on Gravitation and Electricity. That’s the paper where he said “in general one cannot separate gravitation and electromagnetism in an arbitrary manner”. And “a geometry will come about that will, surprisingly, explain not only the gravitational phenomena, but also the electromagnetic field”. I’m sure he was right.
Pair production occurs because photons interact with photons, and because this interaction is strong
Something else I’m sure about is that displacement current does what it says on the tin. Because there’s a hole in the heart of quantum electrodynamics, and it’s the size of Texas. See the UCL small tutorial in gamma-gamma physics. It says this: “From Quantum Electro Dynamics (QED) we know that photons cannot couple directly to each other, since they don’t carry charge, but they can interact through higher order processes: a photon can, within the bounds of the uncertainty principle, fluctuate into a charged fermion/anti-fermion pair, to either of which the other photon can couple”. It’s flat out wrong. A 511keV photon does not magically morph into a 511keV electron and a 511keV positron. A 511keV electron and a 511keV positron do not magically morph back into a single 511keV photon. And pair production does not occur because pair production occurs. Pair production occurs because photons interact with photons, and because this interaction is strong.
Each wave ends up displacing its own path into a closed path
When you know about displacement current and the Williamson/van der Mark electron and Hans Ohanian’s paper on spin, and about the wave nature of matter and about spinors, you can envisage what’s going on. Each wave displaces the other wave into itself. Then each wave ends up displacing its own path into a closed path. A spin ½ “spinor” path, where the minimum and maximum field-variation combine to leave you with an all-round phase-invariant standing field:
Sinusoidal strip by me, GNUFDL spinor image by Slawkb, see Wikipedia
Of course, a photon is not some flat sinusoidal strip. It’s a wave in three-dimensional space. Likewise the electron is not some Möbius strip. To depict it we have to inflate the Möbius strip like it’s a flattened inner tube. We inflate it to a torus, then we keep on inflating past the horn-torus stage to the spindle-sphere stage. Only then does it start to resemble an S-orbital electron:
Torus animations by Adrian Rossiter, S-orbital image from the 2010 Encyclopaedia Britannica
However even that isn’t quite the right picture, because the electron is not some purple sphere with a surface. The electron’s field is what it is, and that field doesn’t have an outer edge. So think of the sphere as something like the eye of the storm, a place where the Poynting vector is going round and round at the speed of light in sweet spherical harmony. Then you get a better picture of what the electron is:
Photon depiction by me Electron depiction by me
It’s a 511 keV electromagnetic wave in a double-loop spin ½ chiral closed path, with a toroidal topology and a spherical geometry, and a g-factor of 2.002319. Like I said, the minimum and maximum field-variation combine to form an all-round phase-invariant standing field. Then we call it charge. But we don’t call it a photon any more. We call it an electron. Or a positron, which has the opposite chirality. However it has the same 511 keV mass, because only one wavelength will do to make an electron or a positron. Because only one wavelength is a 2π multiple of the common amplitude that underlies Planck’s constant of action h. That wavelength is 2.42 x 10ˉ¹² m, and the common amplitude is 3.86 x 10ˉ¹³m. There’s two orthogonal components to the spin so it’s a bispinor rotation, where the two elements of wave motion mesh like gears. Interestingly, the Planck length is √(ħG/c³), and when you replace the √(ħG) with a 4π spherical solid angle, you find that 4π/√c³ = 2.42 x 10ˉ¹² m. A medical doctor called Andrew Worsley told me about that. Here he is on researchgate talking to Daniel Baldomir, who co-wrote the Geometry of Electromagnetic Systems with Percy Hammond.
This standing field isn’t really standing of course
That geometry is in essence twisted space. As per the photon, you can associate the twisted cells in the electron depiction with electromagnetism, and the flattened cells with gravity. What flattened cells? The twisted cells. The twisted cells are flattened. Then you can take note of what Frank Wilczek said: “the proper quantum mechanical description of electrons involves wave functions, whose oscillation patterns are standing waves”. But the standing wave isn’t really standing. Standing waves never are. That’s why if you’ve got an optical cavity that consists of a pair of facing mirrors, when you kick away one of the mirrors the light comes out at c. It might look like it accelerated to c in an instant from a standing start, but it didn’t. It was always moving at c. In similar vein electron spin looks static, but it isn’t. It’s dynamical. That’s why the electron goes round in circles in a uniform magnetic field. It’s subject to Larmor precession. It’s rather like the gyroscopic precession of a boomerang. The positron is like a left-handed boomerang that goes round the other way. The electron and the positron go round in circles because they’re “dynamical spinors”. Because spin is real. Not because photons are popping in and out of existence, spontaneously, like worms from mud. And that means the electron’s electromagnetic field isn’t fundamental. So charge isn’t fundamental either. The photon field-variation is more fundamental. The wave is more fundamental than the field.
Space is twisted
It all makes sense once you see it. See page 26 of Schrödinger’s paper quantization as a problem of proper values, part II. He said “let us think of a wave group of the nature described above, which in some way gets into a small closed ‘path’, whose dimensions are of the order of the wave length”. Also see Maxwell’s subtitle in On Physical Lines of Force: the theory of molecular vortices. Maxwell referred to Ampère as the Newton of electromagnetism, and said this: “a motion of translation along an axis cannot produce a rotation about that axis unless it meets with some special mechanism, like that of a screw”. Hermann Minkowski said something similar in Space and Time. Because it’s the screw nature of electromagnetism featuring linear electric force and rotational magnetic force. Not the point-particle nature of electromagnetism featuring magic and mysticism. It’s not unlike gravitomagnetism where there’s a space-time vortex and frame-dragging, and where “space is twisted”:
Gravity-probe B image by James Overduin, Pancho Eekels and Bob Kahn
Don’t forget that gravity probe B precesses. Or that Oliver Heaviside came up with gravitomagnetism via a gravitational and electromagnetic analogy. To depict the electromagnetic field you combine the radial electric field lines with the concentric magnetic field lines, like Maxwell did in his 1871 paper Remarks on the Mathematical Classification of Physical Quantities. He referred to Helmholtz and vortex motion, and to William Thomson aka Lord Kelvin of vortex atom fame. He also referred to Peter Tait, who performed experiments on vortices and came up with the knot zoo. Maxwell had previously written to Tait talking about a worble embracing itself. He said it was the simplest indivisible whorl. In 1913 Gustav Mie talked of knot singularities in the field, nowadays we might call it the trivial knot. That’s what the electron is. It’s also a vortex. An optical vortex. Ditto for the positron. We make electrons and positrons out of light, we can refract them and diffract them, they have a magnetic moment, and when we annihilate them, we get the light back. There are no magical mysterious creation and annihilation operators. Just light changing direction.
The electron and the positron aren’t throwing photons back and forth
When you know all this, you know why matter can never go faster than light: because it’s just light in a closed path, and because light can’t go faster than light. You also know what E=mc² is all about. The photon has momentum because a wave in an open path has a resistance to change-in-motion. The electron has mass because a wave in a closed path has a resistance to change-in-motion. It’s that simple. The inertia of a body depends upon its energy-content not on anything else. Then when you know that counter-rotating vortices attract, you soon work out why the electron and the positron move the way they do. For example, in positronium, the electron and the positron aren’t throwing photons back and forth. They move towards one another and around one another because each is a dynamical spinor in frame-dragged space. There’s a linear electric force and rotational magnetic force because their spin is real, not because unseen “gauge bosons” are popping into existence and nudging them just so:
Leftside CCASA image by Manticorp/Rubber Duck, see Wikipedia, rightside drawing by me
That means there are no messenger particles. Like Cathryn Carson said in the peculiar notion of exchange forces part I and part II, the exchange-particle idea worked its way into QED from the mid-1930s, even though Heisenberg used a neutron model that was later retracted. Now it’s stuck, so the Standard Model can’t tell you how a magnet works. It can’t even tell you why two wires with currents flowing in the opposite direction repel one another. It can’t tell you why when you turn one wire over they now attract. Nor can it tell you that this “trace” force is there because the linear and rotational forces don’t quite balance. Or why when you stop the current, there’s an even weaker trace force there. The force that we call gravity.
The TOE that Maxwell missed
That’s the TOE that Maxwell missed. He used Newton’s equation V = √(m/ρ), which we nowadays write as c = 1/√(ε0μ0). But it looks like he didn’t read Opticks query 20 about the aethereal medium growing denser by degrees. Or query 30 where Newton said “are not gross bodies and light convertible into one another?”. So Maxwell never lined up his transverse undulations like ducks in a row, then pushed them together so that they were all slightly out of phase:
So he never saw that the result was a gravitational field. A place where space is neither homogeneous nor isotropic. Where light beams curve downwards because the speed of light is spatially variable:
Image credit: NASA (I removed the moon and added the lattice lines and the light beam)
A place where electrons fall down because of the wave nature of matter, because the horizontal component curves downwards. A place where energy is conserved, where internal kinetic energy is converted into external kinetic energy, leaving you with a mass deficit. Which makes you realise something.
Much is wrong with the Standard Model
Once you’ve got a handle on electromagnetism and gravity, you realise just how much is wrong with the Standard Model. It doesn’t explain the photon, or how pair production works, or the electron. It offers no concepts of why charged particles move the way that they do, because it has no concept of the screw nature of electromagnetism. Here we are two hundred years after Ampère, and the Standard Model can’t explain how a magnet works. Or why magnetic monopoles do not exist, what charge is, or mass. It can’t even explain the proton. Is it three quarks, or zillions of quarks? Are the gluons virtual, or not? The Standard Model can’t tell you. Then when you ask why you’ve never seen a quark or a gluon, out comes the fairy story about quark confinement. But if you’re sharp you will notice that this confinement doesn’t apply to two-quark pions. You’ll also notice that like the electron and the positron, the proton can be diffracted, and goes round in circles in a uniform magnetic field. Then like the electron and the positron, the proton is subject to a grad-b drift in a non-uniform magnetic field. And like the electron and the positron, you can annihilate it with its antiparticle to yield gamma photons. You don’t have to be Hercule Poirot to spot that the proton g-factor is 5.585. You don’t have to be Miss Marple to notice that it’s nearly three times the electron g-factor. And you don’t have to be Sherlock Holmes to work out that the proton is just the next knot in the knot table:
CCASA image by Arpad Horvath see Wikipedia Public domain image by Jim Belk, see Wikipedia
The next knot in the knot table is the trefoil. A trefoil is tricolourable, as per the picture above. Now trace around that trefoil anticlockwise from the bottom left calling out the crossing-over directions: up down up. Now what are the chances of that? Of course, it helps if you’ve read what Williamson and van der Mark said about space being curved and charge being topological. And about identifying a quark with a confined photon state which is not sufficient in itself to complete a closed loop. It “would then only be possible to build closed three-dimensional loops from these elements with qqq and q̄q combinations”. That means the QCD strong force that keeps a proton together is the same as the strong force that keeps an electron together. It’s the photon-photon interaction that’s missing from QED.
Neutrinos are more like photons than electrons
After that you start to think about other things. For example, if you know that an electron is a photon in a particular configuration, you know that the neutrino Is not very similar to an electron at all. As far as we know neutrinos travel at c. Nobody has ever seen a neutrino travelling at anything other than c. The SN1987A supernova took place circa 168,000 years ago. Some reports say an initial burst of neutrinos arrived 7.7 hours before the light. No reports say the neutrinos arrived after the light because they were moving slower than the light. And if a neutrino travels at c, it has no mass, end of story. It’s a non-sequitur to say neutrino oscillations mean a neutrino has mass. The photon has momentum because a wave in an open path has a resistance to change-in-motion. The electron has mass because a wave in a closed path has a resistance to change-in-motion. And if neutrinos travel at c they’re on an open path. That’s why they have no charge, because charge is what you call it when you wrap and trap a sinusoidal photon field-variation in a spin ½ configuration. So neutrinos are more like photons than electrons. Neutrinos are rotational waves rather than transverse waves.
The nuclear force is electromagnetic
Things go down like dominoes after that. Once you have an appreciation of the electron and the proton and the neutrino, you know what makes up a neutron. Then you pay attention to the way Rutherford thought of the neutron as a close-coupled proton-electron combination. You also pay attention to what his protégé James Chadwick said on page 2 of his 1933 Royal Society Bakerian lecture: “the electric field between a neutron and a nucleus is small except at distances of the order of 10-12 cm”. Then you pay attention to electron capture, and you realise this is something else which does what it says on the tin. The electron is captured. It’s pulled into the proton, like an unfortunate worker in an industrial accident is pulled into a set of rollers. The electron is mangled into the proton. A neutrino is emitted to conserve angular momentum, and the result is a neutron. A neutron with a charge distribution. A neutron with a “negatively charged exterior, a positively charged middle, and a negative core”. After that you realise why the nuclear force has the profile that it does:
Nuclear force plot from the Dux college HSC physics course, neutron charge distribution image by Dru Renner, inverted by me
All that stuff about pion exchange was just one long drawn out nuclear disaster. John Baez and John Huerta wrote about the nuclear force in The Algebra of Grand Unified Theories. They said in 1932 Heisenberg proposed that the proton and the neutron were two states of the same particle. That’s garbage. Baez and Huerta also tell how in the 1930s Hideki Yukawa “predicted the existence of a particle that mediates the strong force, much as the photon mediates the electromagnetic force”. That’s garbage too. The photon doesn’t mediate the electromagnetic force. Hydrogen atoms don’t twinkle, and magnets don’t shine. In similar vein the pion doesn’t mediate the nuclear force. The screw nature of electromagnetism is responsible for both, because the nuclear force is electromagnetic.
That’s the paper that isn’t a model of leptons at all
That tells you all you need to know about electroweak theory, and the fabulous W-boson that was conjured up in Steven Weinberg’s 1967 paper a model of leptons. That’s the paper which started by saying “leptons interact only with photons”, which isn’t true. That’s the paper that isn’t a model of leptons at all. That’s the paper that led to the development of the Standard Model, which doesn’t know that electron capture does what it says on the tin. Or that beta decay is just the flip side of electron capture. A 939 MeV neutron doesn’t decay because an 80 GeV W-boson pops out of a quark, then decays into an electron and an antineutrino with a combined mass-energy of circa 1 MeV. It decays because the electron works its way out. It takes circa 15 minutes for a free neutron, where the electron isn’t tied down tight by the surrounding protons. You’ve seen something like this before. Beta decay is the jumping popper of particle physics.
The intermediate vector bosons don’t really exist
I am reminded of the end of Fight Club, where the skyscrapers go down one by one. Once you know that beta decay isn’t caused by the fabulous W-boson, you know that the intermediate vector bosons don’t really exist. So you know that the symmetry-breaking Higgs mechanism by which they get their mass is a load of old cobblers. Which isn’t surprising, because the Higgs mechanism doesn’t just contradict E=mc². It contradicts the bleeding obvious. Like I was saying, the electron has mass because a wave in a closed path has a resistance to change-in-motion. That’s why the inertia of a body depends upon its energy-content, not on its interaction with cosmic treacle. So how come all these ephemeral bump-on-a-graph particles were “discovered” in billion-dollar colliders, then set in stone by Nobel prizes?
There may be trouble ahead
When you know about electromagnetism and gravity, and about the photon and pair production and the electron and the positron, you can work things out for the other particles too. Then you can solve the mystery of the missing antimatter, and understand black holes. Then you know that there is no information paradox, but there are gamma ray bursters. Then you know what dark matter is, and dark energy and energy too. You won’t care that quantum gravity is a castle in the air or that Hawking radiation has no foundation, or that inflation is a solution to problems that don’t exist. Not when the mysteries of physics lie at your feet. You won’t care that the particle zoo is as useless as trying to understand gunpowder via the study of incandescent patterns in the air on New Year’s Eve. What you will care about is why Big Science is bad science, and why Alfred Nobel’s prizes did more harm than his dynamite. That’s the price for knowing the Theory of Everything. The certain knowledge that scientific knowledge has been held back for decades, and that this is the trouble with physics. The certain knowledge that there may be trouble ahead.