Space

A lot of people are interested in space. It’s an interesting thing. Especially since it’s a something, not a nothing. Something that used to be called the aether¹. It was also called the fifth element or quintessence, and “was believed to fill the universe beyond the terrestrial sphere”:

Abell S1063 image taken by the JWST, see the Space.com article JWST peers through a cosmic lens in deepest gaze to date

People tend to think that Einstein dispensed with the aether, and that the Michelson-Morley experiment proved it didn’t exist. Try searching the internet on that. What you see goes something like this: “Yes, Einstein’s theory of special relativity, developed in 1905, showed that the concept of a luminiferous aether was unnecessary to explain the behavior of light and motion. This conclusion was supported by the results of the Michelson-Morley experiment, which failed to detect the aether”.

Einstein said space was the aether of general relativity

However it isn’t the whole truth, because in 1920 Einstein gave his Leyden Address. That’s where he said space was the aether of general relativity. He also said a gravitational field is a place where space is “neither homogeneous nor isotropic”. This spatial inhomogeneity is non-linear, so when you plot your measurements, the result is what’s called a curved metric. Or curved spacetime if you prefer. Note that light doesn’t curve because it follows the curvature of spacetime. That’s not how gravity works. It curves wherever there’s a spacetime gradient, the first derivative of gravitational potential. Spacetime curvature is the second derivative of potential, associated with the tidal force. Anyway, in his final paragraph Einstein said this: “Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether”.

According to the general theory of relativity space without aether is unthinkable

It’s cut and dried, from the man himself. However not enough people know about this. As to why, take a look at the Grokipedia article Criticism of Wikipedia. It says Wikipedia favours consensus over expert curation, and the goal is to reflect what sources report, not to determine truth. It’s true. Take a look at an old version of Wikipedia article on Aether Theories. It quotes the final paragraph of Einstein’s Leyden Address, giving what I gave above, along with things like this: “According to the general theory of relativity space without aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time”. It then goes on to quote Nobel Laureate Robert B Laughlin saying this: “It is ironic that Einstein’s most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium when his original premise [in special relativity] was that no such medium existed”. Laughlin was talking about space itself, not the interstellar medium:

Interstellar medium image by NASA, see Interstellar: Crossing the Cosmic Void

He also said “space is more like a piece of window glass than ideal Newtonian emptiness”. He finished up with this: “The modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether. But we do not call it this because it is taboo”. It’s good stuff, and the takeaway is that yes, space is indeed an aether. But take a look at the current Wikipedia article. The Einstein quote is not there. Nor is the Robert B Laughlin quote. The article now dismisses the idea of space as an aether. And it’s not the only example. Check out an old Wikipedia article on the variable speed of light. It tells how Einstein repeatedly said the speed of light varies with gravitational potential, year after year². Compare and contrast with the current article. All references to Einstein have gone. It is but a short stop from favouring consensus to censoring the truth.

Inhomogeneous vacuum: an alternative interpretation of curved spacetime

Einstein’s 1920 Leyden Address was not some one-off. In 1924 he wrote an article called Concerning the Aether. That’s where he spoke of “the physical qualities of space”, and said elementary particles “are to be understood as fields of some kind or particular states of space”. He also referred to Newton. Newton’s Opticks dates from 1704. It includes query 20 where Newton asked if the aethereal medium grew “denser and denser by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curve lines”. That tallies with what Einstein said about a gravitational field being a place where space is neither homogeneous nor isotropic. And with what Einstein said about Huygens and the refraction of light by the gravitational field. And with modern papers such as Inhomogeneous Vacuum: An Alternative Interpretation of Curved Spacetime by Xing-Hao Ye and Qiang Lin:

Images from Gravitational Lensing Analyzed by Graded Refractive Index of Vacuum by Xing-Hao Ye, and Qiang Lin 

Yes, it’s good stuff. What’s not so good is that this was 1924, two years before the photon got its name, and two years before people like Schrödinger were talking about the electron as a wave in a closed path. See for example Charles Galton Darwin’s 1927 Nature paper on The electron as a vector wave, which talked about a spherical harmonic for the two directions of spin. Einstein had no clear concept of the electron. He also said electromagnetic theory could not give a satisfactory explanation of gravitation. Even though he knew about the speed of light varying with gravitational potential, and about c = 1/√(ε₀μ₀) where ε₀ is vacuum permittivity and μ₀ is vacuum permeability. He did however say the metric tensor and the electromagnetic tensor were “different expressions of the state of the aether”. He finished by saying this: “every theory of local action assumes continuous fields, and thus also the existence of an aether”. I just love reading Einstein talking about this stuff.

Einstein distanced himself from the luminiferous aether

What I don’t love is the way Einstein distanced himself from the luminiferous aether. He said, of the new aether, that “the idea of motion may not be applied to it”. I don’t know why. He must surely have read Maxwell saying light consists of “transverse undulations of the same medium which is the cause of electric and magnetic phenomena”. He had Maxwell’s picture on his wall. He admired Maxwell, He understood Maxwell’s unification of electricity and magnetism. He knew that electromagnetic waves do not consist of oscillating electric and magnetic fields inducing one another. People who say this, say it’s why electromagnetic waves don’t need a medium, but it isn’t true. See section 11.10 of John Jackson’s Classical Electrodynamics. That’s where you can read that “one should properly speak of the electromagnetic field F_µv rather than E or B separately”. Also see³ the Wikipedia electromagnetic radiation article where you can read this: “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”. The electric wave E is the spatial derivative of the sinusoidal F_µv electromagnetic wave, whilst the magnetic wave B is the time derivative. It’s something like the image below, where the upper portion depicts the F_µv electromagnetic wave and the lower portion depicts E and B:

Flat image drawn by the author, without the twist of circular polarization

This is why Hermann Minkowski referred to the time axis in Space and Time. It’s why we have Faraday’s law ∇ × E = − ∂B/∂t. It doesn’t mean that changing one field creates the other. The equals sign is an “is”. The curl of E is the time rate of change of B because they’re two aspects of the same thing: the electromagnetic wave. When an ocean wave travels through the sea, the sea waves When a seismic travels through the ground, the ground waves. When an electromagnetic wave travels through space, space waves. That’s what Maxwell was talking about with his transverse undulations.

Electromagnetism is like twist and turn

It’s not the only omission. Einstein must surely have read Maxwell saying linear electric motion is related to rotational magnetic motion via the screw nature of electromagnetism. Minkowski said something similar in Space and Time: “the two forces considered together can most vividly be described by a certain analogy to the force-screw in mechanics”. Electromagnetism is like twist and turn, related to the frame-dragging of gravitomagnetism. If space is twisted and you moved through it, you might think that space is turning. Somehow Einstein didn’t seem to know this, even though he knew that relative motion makes a magnetic field look like an electric field, and vice versa. Einstein knew that magnetism was all about rotation, because he knew that electron spin was real, because of the Einstein-de Haas effect. He knew about Kaluza-Klein theory. But as far as I can tell, he never talked about electromagnetism in terms of plain vanilla curved space⁴.

Attempts were made to represent the material particles as structures in the field

But that’s one for another day. For now it’s enough to know that in 1929 Einstein wrote an article on the history of field theory. That’s where he referred to gravitational fields and electromagnetic fields as states of space. He also said attempts were made to represent the material particles as structures in the field. He was on the right lines, because here we are a hundred years later, and Quantum Field Theory says particles are excitations of quantum fields. But don’t think space is some seething mass of vacuum fluctuations or virtual particles popping in and out of existence. Vacuum energy isn’t like that⁵. If it was we wouldn’t be able to see a distant galaxy:

Messier 77 Image from ESA/Webb

You wouldn’t even be able to see the Moon. Or your hand in front of your face. Or papers such as There are no particles, there are only fields by Art Hobson, and Does matter differ from vacuum? by Christoph Schiller.

Is the electron a photon with toroidal topology?

See Is the electron a photon with toroidal topology? by John G Williamson and Martin van der Mark. The answer is yes. This paper describes the electron as a 511keV photon wrapped and trapped as an electromagnetic field knot. It has a 720° twisted double-loop Möbius spinor topology with a displacement-current g-factor of 2. It is, in Maxwell’s words to Peter Guthrie Tait, a worble embracing itself:

 Flat image drawn by the author, without the the twist of circular polarization, or the chirality of the two directions of spin

It’s a trivial knot, akin to a clove hitch, whilst the proton is akin to a trefoil knot⁶. The proton g-factor of 5.585 is a dead giveaway. The quarks are merely the three double loops. That’s why you’ve never seen a free quark. It’s why mass is a measure of energy-content as per E=mc², and charge is topological. It’s why charged particles attract and repel like counter-rotating and co-rotating vortices. And get this: apart from electrons and protons and their antiparticles, there are no other stable matter particles. When you know that the electron is a photon with toroidal topology, you know that the neutrino, which always moves at the speed of light, is more like a photon than an electron. Which means it isn’t matter. So it doesn’t count. The neutron doesn’t count either because it isn’t stable.

Inhomogeneous space is what dark matter is

What about dark matter? Well, in 1916 Einstein said “the energy of the gravitational field shall act gravitationally in the same way as any other kind of energy”. Gravitational field energy causes gravity, and it isn’t made up of WIMPs. Or any kind of messenger particles such as gravitons. Messenger particles, which are also known as exchange particles, are virtual particles. As in not real. See Cathryn Carson’s two part paper on the peculiar notion of exchange forces. She tells us that the messenger-particle idea worked its way into QED from the mid-1930s, even though Heisenberg used a neutron model that was later retracted. It’s wrong. Hydrogen atoms don’t twinkle. Magnets don’t shine. The virtual photons of QED exist only in the mathematics of the model. It’s the same for other messenger particles, including gravitons. Instead, gravitational field energy is spatial energy. A gravitational field in itself causes gravity because it’s a place where there’s extra spatial energy. Because it’s a place where space “is neither homogeneous nor isotropic”. Unfortunately the FLRW metric assumes the homogeneity and isotropy of space. Talk about throwing the baby out with the bathwater. Unfortunately there aren’t many papers about inhomogeneous space. If there were, you would know that inhomogeneous space is what dark matter is.

At the fundamental level, space and energy are the same thing

There’s more. Have a read of the Science account of Einstein’s 1930 Nottingham address. It says Einstein wanted to derive elements of matter such as electrons and protons out of the metric structure of space. It also says this: “space will have to be regarded as a primary thing and that matter is derived from it, so to speak”. We normally say matter is made of energy, which is true. A photon is energy because it’s a wave. If you take energy out of a wave it’s diminished, and if you take all the energy out of a wave it’s not there any more. On top of that, we can make electrons and positrons out of photons:

GPT-generated image of gamma-gamma pair production

That means we can quite literally make electrons and positrons out of energy. We can do the same sort of thing with protons and antiprotons. So matter really is made of energy. For the cherry on top, if space is the primary thing, what Einstein was saying is matter is made of space. Like William Kingdon Clifford said in his 1876 Space Theory of Matter. This is why the energy of the gravitational field acts gravitationally in the same way as matter. Because at the fundamental level, space and energy are the same thing.

Dark energy is space itself

That ought to deliver a new perspective on the thing called dark energy. People usually say it’s responsible for the accelerating expansion of space, but see Is Hubble’s Expansion due to Dark Energy? by Ramesh Gupta and Anirudh Pradhan. They say dark energy is also responsible for the expansion of space too. I think they’re right. Because my take on general relativity is that space isn’t just some kind of gin-clear ghostly elastic solid. As per Erwin Schrödinger’s cosmic pressure⁷, it’s a compressed gin-clear ghostly elastic solid. This means dark energy isn‘t mysterious. This means dark energy is space itself.

Dark energy image from ScienceNotes.Org

It’s the thing the universe is made of. That’s the expanding universe, that was once the size of a grapefruit. Nowadays people tend to say the observable universe was once the size of a grapefruit, because WMAP showed that there was no overall curvature. What’s missing is the notion of the universe having an edge.

The edge of the universe

For myself, I like the hall of mirrors universe, but without the exotic topologies. I take my tip from Newton, who suggested the universe doesn’t collapse because it’s infinite. Flip that around, and the universe can’t expand if it’s infinite. So I like to think the universe is both finite and flat. The original title of Minkowski’s Space and Time was Raum und Zeit. The German word for space is raum. It also means room. So when you’re lying in bed tonight, think of a water droplet. A wave inside the droplet can’t get out of the droplet. If it encounters the edge it undergoes total internal reflection. Think of the universe as something like that. It’s like the room you’re in, but like a hall of mirrors, without any walls, and no outside. If a light wave reached the edge of the universe it would undergo total internal reflection. There is no eternal void beyond the edge of the universe, because there is no space beyond the edge of space. That’s the space from which the universe is made. It is the aether. The aether doesn’t fill space. It is space. The quintessence. The fifth element. Only in truth it’s the first element, the quintessential thing. Because at the fundamental level it’s the only element. Because it’s the thing from which all other things are made. You know how people say that atoms are 99% empty space? That isn’t true⁸. They’re 100% empty space. Because a subatomic particle is made of field, and a field is a state of space, be it undulating or twisted or turning or denser or frozen or whatever. So, since atoms are made of space, so are you. Sleep tight.

 

_{1  It’s also referred to as the æther, the aither, and the ether. Since the latter is also the name of a group of organic compounds, I prefer to use the word aether.}

_{2  For example in 1920 Einstein said this: “In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position”. The word velocity is given in this translation, it ought to be speed. Irwin Shapiro reiterated it in 1964., saying this: “Because, according to the general theory, the speed of a light wave depends on the strength of the gravitational potential along its path, these time delays should thereby be increased by almost 2×10⁻⁴ sec when the radar pulses pass near the sun”.}

_{3  Also see the Wikipedia article on Jefimenko’s equations where you can read this: “neither Maxwell’s equations nor their solutions indicate an existence of causal links between electric and magnetic fields. Therefore, we must conclude that an electromagnetic field is a dual entity always having an electric and a magnetic component”.}

_{4  There’s nothing in Jeroen van Dongen’s 2010 book Einstein’s Unification. Or in any of my other Einstein books. The situation is not helped by the Einstein digital papers being taken offline because they’re going to be paywalled. One wonders if money is the real motivation for that. Or whether Princeton favour consensus too.}

_{5  Vacuum energy isn’t like that because it’s quiescent. If it wasn’t, we wouldn’t have the vacuum catastrophe. Note that the Casimir effect is something different. It’s extremely weak, and is due to electromagnetic noise rather than the innate energy of space.}

_{6  Qiu-Hong Hu told me that the late Sir Michael Atiyah of TQFT fame knew about the trefoil proton way back in 2011. Find a picture of a trefoil knot and trace around it anticlockwise from the bottom left calling out the crossing-over directions: up, down, up. That’s no accident. Andras Kovacs told me about a guy called Giuliano Bettini who wrote a paper in 2010 called The Moebius Strip: a Biology of Elementary Particles. That features a trefoil proton too.}

_{7  Search the internet on cosmic pressure, and see the 2014 Cambridge companion to Einstein by Michel Janssen and ‎Christoph Lehner: “Schrödinger [1918] had pointed out another way of treating the cosmological constant: moving it from the left-hand side of Equation [7], where it represents a contribution to space-time curvature, to the right-hand side, where it represents a contribution to the energy-matter distribution. Then it would correspond physically to a kind of cosmic pressure”.}

_{8  Some people will tell you that you are not mostly empty space. but that isn’t true either. Because the electron’s field is what the electron is, because a field is a state of space, and because you are made of electrons. And other particles too, but the same applies to them.}