# Is Light a Spinning Cube? Testing Harold Aspden's Photon **Doug Westmoreland** (project lead: direction and review) and **Claude, Anthropic** (research and analysis) Version 1.0, 1 November 2026. Written for readers without a physics background; the technical details are in the companion papers linked at the end. --- ## In short - **Who and what.** Harold Aspden (1927–2011) was a British engineer and physicist who spent five decades on a theory in which space is filled with a fine grid of tiny charged particles. In that theory, each photon (each particle of light) is a tiny cube of 27 of those particles, set turning when an atom gives off light. - **Why it matters.** Aspden's best-known result is built on this cube. It is his calculated value of the **fine-structure constant**, a pure number of about 1/137 that sets how strongly light and electric charge act on each other. His value matches measurement to 0.6 parts per million, like measuring a kilometre to within 0.6 millimetres. - **What the cube gets right.** It is an ingenious attempt to get Planck's constant, the number that links a photon's energy to its frequency, out of the structure of space instead of putting it in by hand. Very few theories even try. - **What it gets wrong.** Tested against measurements of real light, it fails four checks. One is partly a check of Aspden's own bookkeeping, and one rests on an assumption he questioned (that nothing in space moves faster than light): - it gives a photon far too little spin: about 1/200,000 of the measured amount for visible light; - by Aspden's own rules, it cannot carry off the one unit of spin an atom gives up when it sends out circularly polarized light; - it is far too weak a source: it would take at least a day or two to give off one ultraviolet photon (far longer than the age of the universe if only the cube itself counts), where a hydrogen atom takes about a billionth of a second; - to make gamma rays we measure every day, its parts would have to move faster than light. - **The electron.** Aspden's account of the electron's spin would make every electron in the universe spin the same way. Experiments rule that out. - **His own prediction.** Aspden suggested the cube would make two ways of measuring Planck's constant disagree slightly. Around 2011 the data seemed to lean his way, but the gap has since shrunk to about a tenth of the size he suggested (section 5). - **What it means.** The 1/137 match still stands as a number, but the cube cannot be what explains it. The checks also give three rules that any future model of space carrying light must obey (section 7). --- ## 1. What a photon is, as measured Each check in section 4 compares Aspden's cube with one of these measured facts. - **Light comes in lumps.** Each lump, a photon, carries energy in proportion to its frequency (how many waves pass per second): energy = h × frequency. The number h is Planck's constant. A blue photon carries more energy than a red one; an X-ray photon carries thousands of times more. Physicists measure photon energy in electron-volts (eV), or thousands of them (keV). Visible light is about 2.5 eV per photon. - **Photons come in every energy.** They range from radio waves to gamma rays, the most energetic light, given off by atomic nuclei and by violent events in space. Gamma rays have been seen with hundreds of trillions of times the energy of visible light. *(Used in check 4.4.)* - **Light can carry spin.** Spin here means an amount of turning motion, like the motion stored in a spinning flywheel. It can be handed from one object to another, but the total never changes. In "circularly polarized" light the electric field at each point turns round like the hand of a clock, once for every wave, and such light carries spin. In 1936 Richard Beth hung a thin crystal plate from a fine fibre, shone circularly polarized light through it, and measured the twist the light gave it. - **Every photon carries the same spin.** That amount is written ħ ("h-bar", Planck's constant divided by 2π). It is the same for a radio photon and an ultraviolet photon. An atom that absorbs one photon from an ordinary circularly polarized beam changes its spin around the beam's direction by exactly one ħ. *(Used in checks 4.1 and 4.2.)* - **Atoms give off light by sloshing charge back and forth.** When an atom gives off light, its electron's charge sloshes from side to side, so the atom is briefly lopsided, more negative on one side. Physicists call this lopsidedness a "dipole" (two poles). It sets how quickly an atom gives off its light and in which directions. An energized hydrogen atom gives off its main ultraviolet light within about 1.6 billionths of a second. *(Used in check 4.3.)* --- ## 2. Aspden's idea: a turning cube of space **His vacuum.** In Aspden's theory, empty space is not empty. It holds a regular grid, or lattice, of tiny charged particles he called **quons**, set in an even sea of the opposite charge. The quons sit a distance **d** apart, about 0.64 trillionths of a metre: less than a hundredth of the width of a hydrogen atom. Every quon circles in its own tiny orbit, all in step, about 120 billion billion times a second (1.2 × 10²⁰). That is some 200,000 times faster than visible light vibrates. Aspden calls this rhythm **Ω** (omega); strictly, his Ω counts turning as an angle per second, which makes it 2π times this number (section 4.1 explains the 2π). It is the frequency that, by energy = h × frequency, matches the energy locked up in an electron's mass, 511 keV. **His photon.** When an atom gives off or takes in light, Aspden says, it sets a small block of the lattice turning: a cube of 3 × 3 × 3 = 27 quons (Figure 1). He took it to be the smallest symmetrical block that can stir its neighbours, and the largest that can turn freely without bumping into them. So his picture has two motions: every quon's own tiny circling, which goes on everywhere all the time, and the far slower turning of a whole 27-quon cube, which is the photon. **How the energy gets from one atom to another.** In Aspden's account, the atom sheds its energy into the vacuum, and the cube's turning is the vacuum's reaction to it. What crosses space is a ripple in the lattice that, far from any matter, carries no energy itself: "in free space remote from matter and a radiating source, electromagnetic waves therefore travel without conveying energy" (Research Note 4/98). In 1969 he put it this way: "A photon is an event in which momentum is exchanged between matter and space-time"; the ripple "primes space at the disturbance frequency and encourages atomic systems elsewhere" to respond (*Physics without Einstein*, pp. 75–76). In our reading, then, a receiving atom draws a matching lump of energy from the vacuum where the ripple arrives. **Two versions.** Aspden described the cube in 1969 and again, differently, in 1997 and 2003. This page tests the later version, which underlies his fine-structure value, and notes where the 1969 one differs. ![Aspden's photon unit](https://aetherscience.org/aspden-analysis-files/fig-photon-cube.png) **Figure 1.** Aspden's photon unit. (a) The 27 quons of the cube and the axis it turns about. The dashed rings are the paths the quons follow as the cube turns. (b) One layer, seen from above. The quon on the axis doesn't move; 4 circle at distance d and 4 at 1.41 d (1.41 is the square root of 2). The black circle is the boundary Aspden drew (his figure 7.1), 1.9 d from the centre. The cube's farthest quons are 1.73 d from its centre and the next quons out are 2 d away, so it can turn without hitting them. From this cube, Aspden takes three steps. 1. **Frequency: four nudges per turn.** A cube looks exactly the same after a quarter turn. So as it turns, each corner swings past the neighbouring quons, and they get four nudges for every turn (Figure 2, and the animation below). In Aspden's picture, the light's frequency is four times the cube's turning rate. 2. **Inertia: how hard the cube is to set turning.** This resistance (the "moment of inertia") adds up each quon's mass times the square of its distance from the axis. Twelve quons at d give 12 d². Twelve at 1.41 d give 12 × 2 d² = 24 d², because 1.41 × 1.41 = 2. In total that is 36 d², times a quon's mass m₀. The cube resists turning equally about any axis through its centre. 3. **Spin bookkeeping.** Aspden says that adding energy E to the vacuum adds spin E/Ω: the energy divided by the vacuum's rhythm. **Chaining the steps.** The cube's spin is its inertia times its turning rate (step 2). By step 3, that spin is also the energy divided by Ω. By step 1, the turning rate is a quarter of the light's frequency. So the energy rises in step with the frequency, which is energy = h × frequency. And h comes out of the cube's inertia, its four nudges and Ω. This is why the cube matters: its 36, its four nudges per turn and the balance of forces that holds each quon in its orbit together give the number 144 in Aspden's formula for the fine-structure constant. ![Four nudges per turn](https://aetherscience.org/aspden-analysis-files/fig-photon-nudges.png) **Figure 2.** Why the cube nudges its neighbours four times per turn. (a) The middle layer at the start, after 45° and after 90°. After a quarter turn it looks the same as at the start. (b) The push on the nearest quon outside the cube, worked out from all 27 quons as the cube makes one full turn. There are four identical nudges, one as each corner swings past.
**Animation.** The cube's middle layer seen from above, turning (left), and the push felt by the neighbouring quon marked with a black ring (right). A real cube making visible light would turn about 150 trillion times a second; here it turns once every 4 seconds. Three turns give twelve nudges. --- ## 3. What the idea has going for it - **It tries to explain h.** Planck's constant is normally put into physics by hand, from measurement. Aspden tries to get it from the structure of space. Few theories attempt anything like this. - **No special direction.** The cube resists turning equally about every axis through its centre. That matters, because light behaves the same whichever way it is polarized: space has no special direction. - **The electron's energy is special.** Aspden singles out one cube, his "standard" unit, which goes with light of 511 keV, the energy locked up in an electron's mass. The real vacuum does behave specially there: light with at least twice that energy (1,022 keV) can turn into an electron and its antimatter twin, the positron. --- ## 4. Four checks against measurement ### 4.1 How much spin does a photon carry? **The measurement:** one ħ per photon, at every frequency that has been tested, from radio waves through microwaves and visible light to ultraviolet. **Why it comes out the same at every frequency.** Think of a drive shaft. A shaft carrying a given power delivers more twisting force (torque) the slower it turns: torque = power ÷ turning speed. Add up over time: torque adds up to spin delivered, and power adds up to energy delivered. So the same rule holds for the totals: spin = energy ÷ turning speed. In light, the field makes one full turn per wave, so its turning speed is set by the frequency. Physicists measure turning speed as an angle per second, and one full turn counts as 2π in their units; that is where the 2π comes from. A photon's energy is h × frequency, so its spin is (h × frequency) ÷ (2π × frequency). The frequency cancels, leaving h ÷ 2π = ħ, the same for every photon. **Aspden's photon.** His rule books the spin as energy divided by Ω, as if every photon's "shaft" turned at the vacuum's rhythm. For visible light, Ω turns about 200,000 times faster than the light does, so his photon carries about 1/200,000 of the measured spin. For the 21 cm radio waves that hydrogen gas gives off, it carries one part in 90 billion. Those radio waves are given off when the electron in a hydrogen atom flips over, so each must carry away exactly one ħ. The two rules agree only for light whose own frequency equals Ω: gamma rays of 511 keV (Figure 3). Aspden knew this. He wrote that "something in conventional physics does not make sense here in the declaration that a photon is a 'spin-1' particle" (Tutorial Note 8, 1997); "spin-1" is physicists' shorthand for "carries one ħ". It was a fair doubt to raise, but the one-ħ figure is not only theory: Beth's twisting plate and atoms absorbing light measure it directly. The 1969 version does no better. There, every cube already turns at a steady base rate, a quarter of Ω, and holds one ħ; light comes from a small speeding-up or slowing-down of that turning. But the one-ħ cube stays with the atom, and the extra turning that makes the light again carries only energy ÷ Ω (*Physics without Einstein*, eq. 4.9). That book also says space "can accept energy without changing its angular momentum" (p. 62), the opposite of the later rule. ![Spin carried by one photon](https://aetherscience.org/aspden-analysis-files/fig-photon-spin.png) **Figure 3.** Spin carried by one photon, for each kind of light. Blue: measured, one ħ per photon. The circles mark direct measurements of the twist light gives (Carrara 1949 with centimetre microwaves; Beth 1936 with light); at other frequencies it shows in how atoms and nuclei emit and absorb. Orange: Aspden's rule of 1997 and 2003. The vertical scale shrinks by a factor of 1,000 at each step, so the orange line falls far below the blue one for all ordinary light. ### 4.2 The cube can't carry off one unit of spin When an atom gives off or takes in circularly polarized light, its spin about the beam changes by exactly one unit (ħ). That spin can't vanish, so it must go into the cube, the lattice or the wave. Whichever way the cube's axis points, part of that one unit lies along the axis, in a form that only a one-unit step can carry. - **Not the cube.** By Aspden's own rule, a cube making visible light holds only about 1/200,000 of ħ. - **The wave and the lattice only take spin in steps of four.** Because the cube looks the same after every quarter turn, it stirs the lattice like a paddle with four blades. What it sends out is a four-lobed pattern that turns with the cube. A fixed point feels four pushes per turn, so the light's frequency is four times the cube's turning rate. But the pattern itself turns only at the cube's rate, so by the shaft rule it carries four units of spin per photon. The lattice also looks the same after a quarter turn about that axis, so it can soak up spin only in steps of four units too; if it does, the wave carries none. Either way, along the cube's axis the wave carries 0, 4 or 8 units, never one. One unit can't be made out of steps of four, so the cube cannot carry off the spin the atom gives up. Aspden's own answer, that the cube's spin is balanced by energy shifting from circling to straight-line jiggling in the vacuum (Lecture 22), supplies by his own rule only energy ÷ Ω: the same tiny amount. ### 4.3 Far too weak to give off light Think of the cube as a radio antenna. An antenna much smaller than its wave is a poor transmitter, and the cube is 50,000 to 100,000 times smaller than the ultraviolet wave it would have to send. A hydrogen atom is small too, about 1,000 times smaller than its wave, but it has a dipole: its charge sloshes from side to side, which is the best way for a small object to send out light. The cube is so symmetrical that it has no dipole, and the next two simplest kinds of lopsidedness cancel too. All that is left is a faint four-cornered one. But the turning cube also pushes on the quons around it, and because those sit at fixed points of the grid, their response can be lopsided in a simpler way: a stretch along one direction (a "quadrupole"), which sends out light much more easily. How much depends on how freely those neighbours can move, which Aspden's theory doesn't pin down, so we worked out both ends. We assumed only that the ripple spreads as a wave with the light's measured wavelength, as Aspden's own waves do. - **The cube alone:** about 10³³ times weaker than a hydrogen atom as a source (a 1 followed by 33 zeros). It would take over a million times the age of the universe to give off one ultraviolet photon. - **The cube with its neighbours responding freely:** about 10¹⁴ times weaker, taking a day or two per photon. A hydrogen atom takes 1.6 billionths of a second. Either way, the cube is at least ten trillion times too slow (Figure 4). Aspden held that light waves don't carry energy across space at all, but only "prime" it so that atoms elsewhere respond (section 2). That doesn't rescue the cube: what matters for a trigger is the size of the ripple, and even at best the cube's ripple is about 10 million times weaker than an atom's. ![How long it takes to emit one photon](https://aetherscience.org/aspden-analysis-files/fig-photon-emission.png) **Figure 4.** Time to give off one photon of hydrogen's main ultraviolet light (wavelength 122 nanometres): a hydrogen atom against Aspden's turning cube. The orange bar runs from the cube with its neighbouring quons responding freely (about 2 days) to the cube alone (over a million times the age of the universe). Each labelled tick is a million times the one before. Both ends are rough estimates. ### 4.4 It can't turn fast enough for gamma rays To make light of higher energy, the cube must turn faster. At 511 keV its outer quons already move at 58% of the speed of light. They would reach the speed of light at 876 keV, and the inner quons at 1,238 keV (Figure 5). But gamma rays above those energies exist, and they obey energy = h × frequency. - **Cobalt-60** gives off gamma rays of 1,173 and 1,332 keV, used every day in hospitals and industry. - **Pair creation:** light above 1,022 keV is seen routinely turning into electron–positron pairs. NASA's Fermi gamma-ray telescope detects gamma rays this way. - **A precision check:** in 2005 a team measured gamma rays of 841 to 5,421 keV, given off when silicon and sulphur nuclei capture neutrons, by bouncing them off a crystal (Rainville et al.). The total energy of each cascade matched the mass the atoms lost, weighed in a trap and converted by E = mc², to 0.4 parts per million: a joint test of energy = h × frequency and E = mc². Four of those gamma rays lie above 1,238 keV. **The assumption behind this check.** It assumes that nothing in the vacuum can move faster than light. Aspden did not accept Einstein's relativity, and he said the quons' locked-together motion leaves them at their rest mass (Tutorial Note 8). But the limits above don't depend on mass at all: they come only from the cube's size and how fast it must turn. And these speeds are measured against the grid around the cube. Measured against the still frame about which Aspden's grid circles, the grid itself moves at half the speed of light, so at moments the outer quons of even his 511 keV cube would pass light speed (0.5 + 0.58). In the 1969 version an atom uses a pair of cubes, one turning faster than the base rate and one slower (*Physics without Einstein*, pp. 71–72). The faster one reaches light speed at 365 keV. ![Speed of the cube's quons](https://aetherscience.org/aspden-analysis-files/fig-photon-speed.png) **Figure 5.** How fast the cube's quons must move, relative to the grid around them, to make light of a given energy. Orange: the 12 outer quons; blue: the 12 inner ones. Above the black line they would outrun light. Green arrow: gamma rays from the 2005 test, off the right of the scale, whose cascade totals matched E = mc² to 0.4 parts per million. Visible light, at about 0.0025 keV, sits right against the left edge, where the cube barely turns. --- ## 5. Aspden's own prediction: Planck's constant measured two ways In 1986 Aspden wrote that his theory "gives reason for suspecting" a small effect of the cube. When an atom gives off light, a little of its energy might go into setting the cube turning. Then Planck's constant worked out from the light of atoms would come out "larger by a few parts in ten million" than the value from two electrical methods (the Josephson and quantum Hall effects). He added that precise measurements of the fine-structure constant "may eventually clarify this issue" (paper 1987m). **The comparison he named.** One way to get Planck's constant, by counting the atoms in a near-perfect silicon sphere, leans on the light of hydrogen atoms (through the Rydberg constant). The other, the Kibble (or watt) balance, uses exactly the two electrical methods he named. - **For a while the data leaned his way.** In 2007 the balance at NIST, the US standards laboratory, gave 6.62606891 × 10⁻³⁴ joule-seconds; in 2011 the silicon sphere gave 6.62607014 × 10⁻³⁴. That is about 2 parts in 10 million higher, his predicted sign and size. - **Then the gap shrank.** Canada's balance soon came out higher than the sphere, and by 2017, when the values were combined to fix Planck's constant for the new SI units, all the methods agreed to within about 5 parts in 100 million. Even then the silicon sphere sat about 3 parts in 100 million high: his sign, but about a tenth of his size. **Fine-structure constant.** Today two very different measurements of that constant agree to about one part in a billion: one uses light kicking atoms, the other the electron's magnetism. Whether that comparison catches his effect depends on a detail of his photon. If the light's push on an atom keeps its usual size, as he wrote in 1969 ("The lost momentum will be simply h/c times the radiation frequency", *Physics without Einstein*, p. 76), his effect would show as a mismatch of 1 to 2.5 parts in 10 million, at least a hundred times more than is seen. If the push shrinks along with the energy, the effect cancels in this comparison. --- ## 6. The electron Electrons carry spin too, measured at half a photon's: ħ/2. They also act as tiny magnets. Aspden makes two claims about the electron that use the same ideas. ### 6.1 Spin from the vacuum's circling **The claim.** In 2003 Aspden wrote that an electron is carried round by the circling of the vacuum's quons. Adding an equal share from the vacuum's balancing motion, its spin comes out at ħ/2, "the well known quantity associated with so-called 'electron spin'" (*Physics of Creation*, ch. 6). In 1969 he gave the electron its own spin s, equal and opposite to that circling, and wrote: "The spin s has a set direction in space but the photon unit spins, though all parallel or anti-parallel, can be in any orientation" (*Physics without Einstein*, p. 67). **The size is built in.** Aspden chose the size of the orbit using ħ in the first place, so getting ħ/2 back restates that choice; it is not a separate success. **The direction is the problem.** In both versions the electron's spin is tied to the axis of the vacuum's circling. Within a region of space light-years across, that axis points one fixed way; he put it roughly at right angles to the plane of the planets' orbits. Aspden added that this direction has no effect on how atoms behave ("The aether behaves as an isotropic medium in its quantum mechanical interactions with the atom", *Physics of Creation*, ch. 6), but he gave no mechanism by which spins locked to one axis could behave that way. Measurement says electron spins are not tied to any fixed direction (Figure 6): - **Stern and Gerlach (1922)** sent a beam of silver atoms, whose magnetism comes from one electron's spin, through an uneven magnetic field, and the beam split in two. If every electron's spin pointed one fixed way, the whole beam would be pushed one way and land as a single spot, which would move as the magnet was turned. Instead, in this and countless later experiments, the beam splits into two equal spots lined up with the magnet, whichever way it points. - **A direct test.** In 2006 a University of Washington team hung a twisting pendulum containing about 10²³ lined-up electron spins and watched for any pull toward a fixed direction in space as the Earth turned. They found no energy difference larger than 5 × 10⁻²¹ electron-volts per electron between spins pointing along or against any fixed direction in space (Heckel et al.). - **Helium:** the two electrons in a helium atom pair up with opposite spins, so helium is not magnetic: magnets weakly repel it. Two spins locked the same way would make it attracted. His picture also gives the electron about a quarter of its measured magnetism. Aspden treated the electron's magnetism separately (*Physics without Einstein*, ch. 7, and later papers), and we have not yet checked that account. ![Electron spin](https://aetherscience.org/aspden-analysis-files/fig-electron-spin.png) **Figure 6.** The Stern–Gerlach experiment (top) and what lands on the screen as the magnet is turned. Middle: what spins locked to one fixed direction would give, one spot. Bottom: what is measured, always two spots lined up with the magnet's field (dashed line). ### 6.2 Electron waves from four photon units (not yet testable) Aspden proposed that a moving electron travels with "an entourage of four such photon spin units" that make it behave as a wave (his own summary of a 1986 *Physics Letters A* paper). We have only his summaries, not the working, so it can't be tested yet. To pass, it must give the wavelength set by a particle's whole mass. That is measured for electrons, neutrons, atoms and even molecules 25,000 times as heavy as a hydrogen atom; for atoms it is measured to about a part in ten billion and confirmed independently to about a part in a billion. --- ## 7. What we keep, and what any model of space carrying light must do **What we keep.** - Light is given off through an exchange with the vacuum. - The vacuum behaves specially at the electron's energy, 511 keV. - Aspden's value of the fine-structure constant still matches measurement to 0.6 parts per million, and that remains striking. The cube does not explain it physically, so the match still needs an explanation, or may be a coincidence. **Three rules for any working model.** These checks, and one more experiment, give three rules that any model of space carrying light must obey: 1. **One ħ of spin per photon, at every frequency.** A circularly polarized wave's field must turn at the wave's own frequency, not at some fixed inner rhythm of space. Ordinary waves in a springy (elastic) solid already do this; Aspden's spin rule does not. 2. **Atoms send and receive light mainly as dipoles.** Their strong lines change the atom's spin by at most one unit per photon. Rare lines that change it by two or three units do exist, and they are far slower (seconds to years instead of billionths of a second), for the size-against-wavelength reason in check 4.3. 3. **One photon, one detector.** In 1986 Grangier, Roger and Aspect sent single photons, one at a time, at a half-silvered mirror (a mirror that lets half the light through and reflects the other half), with a detector behind each path. In Aspden's picture the wave carries no energy itself and only sets off a release of energy from the vacuum wherever it arrives, so both detectors could fire. In the experiment, both fired together about five times less often than any picture of independent detectors allows. So either the energy travels with the wave as one lump, or the two detectors are linked instantly. Aspden did suggest that photon events are coordinated instantly through the vacuum's rigid structure (Lecture 22); his picture needs that instant link. The same rules guide our own models of a light-carrying vacuum. Earlier tests of the cube's mechanics, such as how its quons would behave at nearly the speed of light, are in [Part 1](/aspden-aether-units/) and the [test register](/aspden-test-register/). --- ## 8. Words used on this page | Word | Meaning | |---|---| | Photon | One lump of light. Its energy is h × frequency. | | Frequency | How many waves pass each second. | | h, ħ | Planck's constant, the number that links a photon's energy to its frequency; ħ ("h-bar") is h divided by 2π, the measured spin of every photon. | | Spin | An amount of turning motion that a particle carries and can hand on. The total never changes. | | Turning rate | How fast something turns, in turns per second. | | Fine-structure constant | A pure number, about 1/137, that sets how strongly light and electric charge act on each other. | | Quon | Aspden's name for the charged particles that, in his theory, fill space in a regular grid. | | d | The spacing between neighbouring quons, about 0.64 trillionths of a metre. | | Ω (omega) | The rhythm at which Aspden's quons circle: about 120 billion billion turns a second (counted as an angle per second, 2π times that). | | Moment of inertia | How hard something is to set turning: each part's mass times the square of its distance from the axis, added up. | | eV, keV | Electron-volt and thousand electron-volts, units of energy. Visible light is about 2.5 eV (0.0025 keV) per photon; the electron's mass is worth 511 keV, about 200,000 times more. | | Dipole | A lopsided spread of charge, more negative on one side, the way atoms send out light. | | Gamma ray | Light of very high energy, from atomic nuclei and from space. | | Positron | The electron's antimatter twin: same mass, opposite charge. | --- ## Sources **Aspden's texts** (copies in the archive on this site): - *Physics without Einstein* (1969), [chapter 4](https://aetherscience.org/book-physics-without-einstein/book-physics-without-einstein-pwech4/): the photon unit and the 1969 version of its frequency rule (pp. 64–67, eq. 4.3; eq. 4.9 on p. 73), space accepting energy "without changing its angular momentum" (p. 62), the pair of units in an atom (pp. 71–72), the photon as an "event" and waves that need not convey energy (pp. 73–76), and the electron's spin with "a set direction in space" (p. 67). - *Physics of Creation*, 2nd ed. (2003), [chapter 6](https://aetherscience.org/2edpocch6/) and [chapter 7](https://aetherscience.org/2edpocch7/): the 3 × 3 × 3 cube, four nudges per turn, the moment of inertia 36 m₀d², and the electron's spin. - [Tutorial Note 8, "The Nature of the Photon"](https://aetherscience.org/www-energyscience-org-uk-tu-tu08/) (1997): the spin rule E/Ω and the doubt about a "spin-1" photon. - [Research Note 4/98, "Maxwell's Equations"](https://aetherscience.org/www-energyscience-org-uk-notes-rn9804/): waves in free space "travel without conveying energy". - [Paper 1987m](https://aetherscience.org/aspden-www-aspden-org-papers-bib-1987m/), "The theoretical nature of the photon in a lattice vacuum" (NATO workshop, 1986; published 1987): the prediction in section 5. - [Paper 1986k](https://aetherscience.org/aspden-www-aspden-org-papers-bib-1986k/), "A causal theory for neutron diffraction", *Physics Letters A* 119, 105 (1986), and [Lecture 22](https://aetherscience.org/www-energyscience-org-uk-le-le22/): the four photon spin units. **Measurements:** - R. A. Beth, "Mechanical detection and measurement of the angular momentum of light", *Physical Review* 50, 115 (1936). - W. Gerlach and O. Stern, *Zeitschrift für Physik* 9, 349 (1922). - S. Rainville et al., "A direct test of E = mc²", *Nature* 438, 1096 (2005); summary from [NIST](https://www.nist.gov/node/399321). - N. Carrara, "Torque and angular momentum of centimetre electromagnetic waves", *Nature* 164, 882 (1949). - P. Grangier, G. Roger and A. Aspect, *Europhysics Letters* 1, 173 (1986). - M. S. Dewey et al., the gamma-ray lines behind the 2005 test ([arXiv:nucl-ex/0507011](https://arxiv.org/abs/nucl-ex/0507011)). - B. R. Heckel et al., "New CP-violation and preferred-frame tests with polarized electrons", *Physical Review Letters* 97, 021603 (2006) ([arXiv:hep-ph/0606218](https://arxiv.org/abs/hep-ph/0606218)). - Planck-constant values from Kibble balances and silicon spheres to 2014: review, [arXiv:1409.7597](https://arxiv.org/abs/1409.7597); the 2017 combined value: D. B. Newell et al., *Metrologia* 55, L13 (2018). **Our calculations:** the scripts photon_unit_checks.py (the numbers on this page), induced_check.py (the neighbouring quons' response in check 4.3), fig_photon.py (Figures 1–6) and anim_photon.py (the animation) are in [analysis-scripts.zip](/aspden-analysis-files/analysis-scripts.zip).