Harold Aspden's modified electrodynamics and vacuum lattice: a primer

Project folder: Researchers/Aspden-Hearld. It holds two documents by Harold Aspden (1927-2011 [memory, medium]; a Cambridge PhD and a long career as a patent manager at IBM UK [memory, medium]):

• A Problem in Plasma Science, a two-page web essay signed 30 October 2005 (the PDF is a 2019 printout from aetherometry.com) [read].
• Physics Unified (Sabberton Publications, Southampton, c.1980), a 212-page book [read: Step 1 facts].

Source gap (as revised in arbiter.md, QE revision). Physics Unified is a scan with no text layer, but the full text of all 212 pages is available through machine OCR (optical character recognition: software that turns a page picture into text), and its quality has been checked against page images (printed page number = PDF page minus 7) [arbiter, QE revision]. The book has been deep-read (read line by line, with equations checked against page images) in eight sections: Chapters 1-2 (PDF pp.7-36), Chapter 3 on aether experiments (pp.54-80), Chapters 5-6 on Planck's law, the Schroedinger equation, the electron g-factor and the lattice sum (pp.94-119), the graviton, decay table and psi states (pp.119-129), Chapter 7 on particle masses (pp.130-162), Chapter 9 on geomagnetism, planets, reversals and the cosmic background (pp.163-200), and Appendix III (p.211) [read: deep/Unified-Physics-8f6841.md]. The remaining pages (front matter, pp.37-53, Chapter 4 at about pp.81-93, and the Epilogue and Appendices I-II at about pp.201-210) were read only through page-by-page digests and OCR sampling. The real remaining gap is outside the book: every experiment the essay cites as support (Kobel 1930; Graneau 1983 and 1985; Roth 1978; Sethian, Hammer and Wharton 1978), Aspden's own journal papers (1969, 1977, 1985, 1986), the three Correa patents and Aspden's 1996 report Power from Space: The Correa Invention were not obtained. Statements about what those papers found are Aspden's description unless tagged [web]. To close the gap, obtain Aspden, J. Franklin Inst. 287, 179 (1969), the Graneau, Roth and Sethian papers, the Correa patents and the 1996 report. A second limit: web search was unavailable for the deep reads, so the modern particle values in section 6 are recalled CODATA/PDG values [memory, high unless stated], not web-checked.

Source tags: [read] = from the documents; [web] = Internet source with URL; [memory] = recalled from training, with confidence; [computed] = calculated for this primer (run example.py).

---

1. The idea in one paragraph

Everything we know about magnetic forces between electric currents was first learned from currents flowing round complete wire loops. James Clerk Maxwell noticed in the 1870s that such experiments cannot pin down the force between two single moving charges: you can add a certain extra term to the point-charge force law and, when you add it up around any closed loop, it vanishes, so no loop experiment can see it. Maxwell chose a version of that term for convenience. Harold Aspden argued he chose wrongly. Aspden's version contains the ratio of the two particles' masses, so it is tiny between two electrons but large when a heavy ion meets a light electron. He concluded that in a hot ionised gas (a plasma) the heavy ions should steal energy and become much hotter than the electrons, which he offered as the explanation for the million-degree solar corona and for odd ion heating seen in fusion experiments. His force law does not balance (the push on one particle is not matched by an equal and opposite push on the other), so he needed a medium, an "aether", to take up the difference; he then saw that aether as a possible energy source, and backed the Correa plasma-discharge device as a machine that taps it. In his book the same aether, pictured as a lattice of charged particles filling space, is used to calculate the strength of gravity, the fine-structure constant, the proton-to-electron mass ratio and the 2.7 K cosmic background temperature. This primer shows that Maxwell's loophole is real, that Aspden's own argument for ion heating cancels out when you do the calculation, and that his numerical "derivations" were close to the measurements of 1980 but are now clearly excluded.

---

2. What you need to know first

Vectors, the dot product and "BAC-CAB". For vectors a and b at angle theta, a.b = |a||b| cos(theta), a single number. The cross product a x b is a vector at right angles to both, of size |a||b| sin(theta). The identity a x (b x c) = b(a.c) - c(a.b) (read "BAC minus CAB") is used to rewrite the magnetic force. Read: Griffiths, Introduction to Electrodynamics, Ch. 1.

Exact differentials and closed loops. If a quantity is the rate of change of some function f along a path (df), adding it up along the path gives f(end) - f(start). Around a closed loop, end = start, so the total is zero. The same idea in time: if a power P(t) equals the time derivative of some function, the total energy delivered between two moments where that function has the same value is zero. This one idea is the key to the whole primer. Read: Griffiths Ch. 1 (the gradient theorem).

The magnetic force between moving charges. A charge moving with velocity v creates a magnetic field B; another charge Q moving with velocity V in that field feels the Lorentz force Q V x B. For slow charges (much slower than light) the field of a moving point charge is given by the Biot-Savart law. Read: Griffiths Ch. 5.

Newton's third law and field momentum. Newton's third law says the force of A on B is equal and opposite to the force of B on A; it is what makes the total momentum of A and B constant. The magnetic forces between two single moving charges do not obey it in general. Maxwell's theory balances the books by giving the electromagnetic field its own momentum. Read: Griffiths Ch. 8 (conservation laws); Taylor, Classical Mechanics, Ch. 1 and Ch. 3.

Temperature, kinetic energy and equipartition. In a gas in equilibrium, each particle has on average kinetic energy (3/2) k_B T, where k_B = 1.381 x 10^-23 J/K is Boltzmann's constant and T the absolute temperature, regardless of the particle's mass. Heavy particles therefore move more slowly: the root-mean-square speed is sqrt(3 k_B T / m). Read: Schroeder, An Introduction to Thermal Physics, Ch. 1.

Plasmas. A plasma is a gas hot enough that electrons are stripped from atoms, leaving a mixture of free electrons and positive ions. Electrons and ions can have different temperatures for a long time, because an electron bouncing off a much heavier ion hands over only a tiny fraction (about 2 m_e/M) of its energy per collision [memory, high]. So "ions hotter than electrons" is not by itself a paradox. Read: Chen, Introduction to Plasma Physics and Controlled Fusion (early chapters).

Gravitational potential. The gravitational potential phi at distance R from a mass M is -G M / R (energy per unit mass), where G is Newton's constant. Only differences of potential have physical effects; the zero can be put anywhere. Read: Taylor, Classical Mechanics, Ch. 4 (energy) or any first-year mechanics text.

---

3. The textbook view

Symbols used throughout (SI units unless stated): - q, m, v: charge, mass and velocity of the source particle (in the examples, an electron: q = -e, m = m_e). - Q, M, V: charge, mass and velocity of the particle that feels the force (an ion). - r: vector from q to Q; r = |r|. - e = 1.602 x 10^-19 C (elementary charge); m_e = 9.109 x 10^-31 kg; c = 2.998 x 10^8 m/s. - epsilon0 = 8.854 x 10^-12 F/m (vacuum permittivity), mu0 = 1/(epsilon0 c^2) (vacuum permeability). - All velocities are measured in one inertial (non-accelerating) frame.

Coulomb's law. F_C = (1/(4 pi epsilon0)) q Q r / r^3, size qQ/(4 pi epsilon0 r^2).

Magnetic force between two slow point charges. The Biot-Savart field of q at Q is B = (mu0/4 pi) q v x r / r^3, and the force on Q is Q V x B. With BAC-CAB:

F_mag = (mu0 qQ / (4 pi r^3)) V x (v x r) = (mu0 qQ / (4 pi r^3)) [ (V.r) v - (v.V) r ] ... (T1)

Its size is (v V / c^2) times the Coulomb force at most, so for everyday speeds it is a small correction to Coulomb.

Two features of (T1) matter here. 1. It is not equal and opposite: swap the roles of the particles and you generally get a force that is not minus this one. Mainstream physics accepts this and puts the missing momentum in the field (momentum density epsilon0 E x B) [memory, high]. Total momentum of particles plus field is conserved. 2. It is only established in this form for slow charges and as part of the full Maxwell-Lorentz theory, which is tested in accelerators, storage rings and plasma devices [memory, high for the general statement; medium for any claim that a specific experiment would have revealed Aspden's term, see section 6].

Maxwell's undetermined term. Maxwell (Treatise on Electricity and Magnetism, 1873, Vol. 2) observed that a term of the form

k (qQ / r^3) (v.r) V ... (T2)

can be added to the point-charge law with any constant k, because when q is one of many charges flowing steadily around a closed wire, (v.r)/r^3 summed around the loop is an exact differential and gives zero. Aspden's book quotes Maxwell's own words that one may take "any value of Q which appears to us to simplify the formulae" [read: book p.12]. This is real history and is correct [memory, high; arbiter: Established].

Plasma temperatures. In a plasma, ions and electrons exchange energy slowly (see section 2), and many processes (waves, magnetic reconnection, instabilities) heat one species more than the other. Ion temperatures above electron temperatures are observed in laboratory devices and in the solar corona [memory, medium]. Sethian, Hammer and Wharton (1978) saw electrons cool and ions heat, with the total perpendicular energy staying constant, about 1000 times faster than simple collisions predict, which they linked to current-driven instabilities [web: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.40.451]. That is faster sharing of energy, not new energy.

The Sun. The Sun's surface (the photosphere) radiates like a body at about 5,800 K. The corona, the thin outer atmosphere, is at about a million kelvin; its electrons are that hot too, not 6,000 K [web: summary of https://arxiv.org/pdf/1206.6097, via mathematician.md]. Why the corona is so hot is not fully settled [memory, medium]. The core is powered by hydrogen fusion; the neutrinos produced by specific fusion reactions (the pp chain and, since 2020, the CNO cycle) are detected directly [web: https://www.nature.com/articles/s41586-020-2934-0; https://arxiv.org/pdf/2006.15115].

The cosmic microwave background (CMB). Microwaves arrive from every direction with a near-perfect blackbody spectrum at T0 = 2.7255 +/- 0.0009 K [web: https://lambda.gsfc.nasa.gov/product/cobe/about_firas.html]. In the Big Bang picture it is light from the early universe, cooled by expansion, so at redshift z (looking back in time) it should be hotter by a factor (1 + z). Measurements in distant gas clouds agree: T(z) = T0 (1+z)^(1-beta) with beta = 0.010 +/- 0.013 [web: https://arxiv.org/abs/2106.00119].

The constants. The fine-structure constant alpha = e^2/(4 pi epsilon0 hbar c) (hbar is Planck's constant over 2 pi) has 1/alpha = 137.035999177 with relative uncertainty 1.6 x 10^-10; the proton-electron mass ratio is 1836.152673426 [web: https://physics.nist.gov/cgi-bin/cuu/Value?alph; https://physics.nist.gov/cgi-bin/cuu/Value?mpsme]. Mainstream physics measures these; it does not derive them. G = 6.67430 x 10^-11 m^3 kg^-1 s^-2 [web: https://physics.nist.gov/cgi-bin/cuu/Value?bg].

---

4. Where Aspden departs

The force law. Aspden's equation 14 (book, written with c = 1) is

F_on Q = (qQ / r^3) [ (V.r) v - (M/m) (v.r) V - (v.V) r ] [read: both documents]

In SI units put mu0/(4 pi) in front (equivalently 1/(4 pi epsilon0 c^2)). Compare with (T1): the first and last terms are exactly the textbook magnetic force. The only new piece is

F_extra = -(mu0 qQ / (4 pi r^3)) (M/m) (v.r) V,

which is Maxwell's term (T2) with k = -(M/m) instead of a constant. It pushes the ion along its own direction of motion, so it speeds it up or slows it down. Because it has the (v.r)/r^3 structure, it still vanishes around closed loops (when the source charges are all electrons, so m is fixed). Aspden is therefore right that no closed-circuit experiment can exclude it [arbiter: Established].

Aspden's reasons for this choice [read: essay; book Ch. 1 per reviewers]: (i) the minus sign avoids a "twisting" (torque) problem; (ii) for two equal charges with equal velocities the first two terms cancel and the force is a pure inverse-square attraction along the line joining them, of size (v/c)^2 times Coulomb, which he wanted as a bridge to gravity; (iii) a balance argument with reaction forces on "reference frame" masses introduces M/m. The mathematician found that the derivation assumes Newton's third law at one step and drops it at another, and never shows the result is unique [arbiter: Internally inconsistent as a proof].

The plasma argument. The essay's case for ion heating is four sentences [read]: (1) a slow ion with an electron approaching gains speed; (2) with the electron receding it loses speed; (3) and (4) the same for a fast ion, with bigger effects. From these Aspden concludes "the net effect ... must therefore be to cause each positive heavy ion on average to have kinetic energy far in excess of that of the average electron", and leaves the actual calculation to "some enthusiastic mathematician". Section 5 does that calculation for the simplest case.

The constants. The book's formulas reproduce 1/alpha = 137.035915 and m_p/m_e = 1836.15232 [computed; read: page image p.112]. The integer 1843 (the volume ratio of an electron to a lattice particle) is "uniquely determined" by an odd-integer rule. The mathematician first objected that the book's lattice sum gives 1844.6, closer to 1845 (which would give 137.011); the round-2 deep read corrected this: under the book's own rule (the ratio must rise to the first odd integer with a non-negative energy), 1845 gives a negative energy and is excluded, so 1843 is uniquely selected given the premises [arbiter Q4]. The premises are where the freedom lies: the odd-integer rule, the factor 1/2 in the mass, and the way the lattice sum is added up. That sum converges only conditionally (its value depends on the order of summation); the book sums in cubic shells, and the standard Ewald convention changes the lattice sum by exactly pi/6 and gives 1/alpha of about 152 instead of 137 [deep read; arbiter Q4: Internally inconsistent]. Appendix III, added after the main text, revises eq. 157 for the lattice moving through space at 390 km/s (the 1977 U-2 measurement of our motion relative to the CMB) and gives 1/alpha = 137.035953 [read: OCR p.211]: that is 0.7 standard uncertainties from the Williams-Olsen value 137.035963(15) that the book itself quotes (the digits in brackets are the uncertainty in the last two digits), but still 4.6 x 10^-5 (about 0.34 parts per million, ppm; roughly 2,100 standard uncertainties) from today's CODATA 137.035999177 [computed; arbiter Q3]. The size of the correction follows from the model and the measured speed, but it was added after the measurement it moves toward, it reverses the main text's statement that the effect is negligible, and it is applied to alpha alone (not to m_p/m_e or G); an after-the-fact adjustment of this kind is itself a lesson about fitted formulas (section 7). G comes from eq. 163, G = (e/m_e)^2 (4 pi)^2 (1/(108 pi))^6 (1/g)^8 in cgs units, with g = 5063 the graviton mass in electron masses [read: page image p.115]. Because G depends on g^-8, a 0.017% change of g (to about 5062.1) gives the measured G exactly [computed]; and the book says the graviton mass is "supported by the derivation of G" [read: p.151 per reviewers], so the agreement is partly built in.

Mercury's perihelion. Mercury's elliptical orbit slowly turns (its perihelion, the point nearest the Sun, advances); after the pull of the other planets is subtracted, about 43 arc-seconds per century remain, which general relativity (GR) gives as 6 pi G M_sun / [c^2 a (1 - e^2)] per orbit (a = semi-major axis, e = eccentricity) [memory, high]. In Chapter 2 Aspden lets the gravitational interaction energy reach the planet with a delay (retardation), argues that this multiplies G by 1 + (v/c)^2 and the force by 1 + 3(v/c)^2 (v = the planet's orbital speed), and arrives at an orbit equation (eq. 36) identical to GR's, which would give 42.98"/century [read: page image p.34-35; computed in the deep read]. The book never computes the 43" itself. The coefficient comes from a chain of choices (a linear energy profile inside the orbit, root-mean-square rather than mean distance, a round trip, the sign): flat instead of linear gives 2/3 of the answer (28.7"/century), a one-way trip 1/4, the Coulomb-type distribution twice the answer. The book picks its distribution because "had we used ... Fig. 13 ... we would have obtained double the last term", i.e. by agreement with GR [read: page image p.35]. Paul Gerber did the same thing in 1898 with a retarded potential tuned to Mercury; Seeliger's objection that the formula "is not the consequence of his premises" applies in kind, and Gerber's theory gave the wrong bending of light [web, secondary: https://en.wikipedia.org/wiki/Paul_Gerber]. Aspden offers no light-bending, radar-delay or binary-pulsar test in those pages [arbiter Q2].

---

5. Worked example: does one electron fly-by heat an ion?

We test Aspden's four-case argument with real numbers. All of it is reproduced in example.py (Parts A-C).

Setup. A plasma at T = 10^6 K (solar-corona scale). An electron passes a proton at closest distance (impact parameter) b = 10 nm, moving in a straight line. We treat the proton as nearly stationary during the pass but give it its thermal speed for the size of the force. (The pass lasts about b/v = 1.5 x 10^-15 s, during which the proton moves 0.2 nm, 2% of b.)

Step 1: speeds. v = sqrt(3 k_B T / m_e) = sqrt(3 x 1.381e-23 x 1e6 / 9.109e-31) = 6.74 x 10^6 m/s. For the proton, V = sqrt(3 k_B T / m_p) = 1.57 x 10^5 m/s. [computed]

Step 2: is the extra term big enough to matter? Its size relative to the Coulomb force is (M/m)(v V / c^2), because mu0 = 1/(epsilon0 c^2):

1836 x (6.74e6 x 1.57e5) / (9.0e16) = 0.022.

For an iron ion (M/m = 101,800, V = 2.1 x 10^4 m/s) it is 0.16 [computed; agrees with mathematician.md]. So this is not a negligible correction; Aspden is right to take it seriously. The question is the sign of the total.

Step 3: the power delivered to the ion. The extra force points along V, so the power (rate of doing work on the ion) is

P = F_extra . V = -(mu0 qQ / (4 pi)) (M/m) V^2 (v.r) / r^3.

For an electron and a proton qQ = -e^2, so

P = K0 V^2 (v.r) / r^3, with K0 = (mu0 e^2 / 4 pi)(M/m).

v.r is positive while the electron approaches (it moves toward the ion, and r points from electron to ion) and negative while it recedes. So case (1) really is a gain and case (2) really is a loss. Aspden's signs are right.

Step 4: the key identity. With the ion fixed, r = R_ion - x_electron, so dr/dt = -v. Then

d(r^2)/dt = 2 r.(dr/dt) = -2 v.r, so d(1/r)/dt = -(1/r^2)(dr/dt) = -(1/r^2)(-v.r/r) = (v.r)/r^3.

The power is therefore an exact time derivative:

P = K0 V^2 d(1/r)/dt.

Step 5: energy on the way in and on the way out. On the approach, 1/r goes from 0 (far away) to 1/b; on the way out, from 1/b back to 0. So

W_in = K0 V^2 / b, W_out = -K0 V^2 / b, W_net = 0.

Put in numbers. Rewrite K0 V^2 / b = [e^2/(4 pi epsilon0 b)] x [M V^2 / (m_e c^2)]: - e^2/(4 pi epsilon0 b) = 1.44 eV nm / 10 nm = 0.144 eV (the Coulomb energy at distance b). - M V^2 / (m_e c^2) = 3 k_B T / (m_e c^2) = (3 x 86.2 eV) / 511,000 eV = 5.06 x 10^-4. (This factor is the same for every kind of ion at the same temperature, because M V^2 = 3 k_B T.) - W_in = 0.144 x 5.06e-4 = +7.28 x 10^-5 eV, W_out = -7.28 x 10^-5 eV, net 0.

The numerical integration in example.py gives +7.2849e-5 eV, -7.2849e-5 eV and a net of about 10^-20 eV (rounding error, 6 x 10^-17 of the total work done) [computed]. For comparison, the proton's average kinetic energy is (3/2) k_B T = 129 eV.

Step 6: let the ion move. If the ion moves during the pass, d(1/r)/dt = ((v - V).r)/r^3, so (v.r)/r^3 = d(1/r)/dt + (V.r)/r^3. The first piece still totals zero. The second gives a leftover of about 2V/v (here 4.7%) of the half-pass swing, i.e. up to +/-3.4 x 10^-6 eV. Its sign depends on whether the ion is moving toward or away from the electron's path: +3.4e-6 eV at 90 degrees, -3.4e-6 eV at 270 degrees. Averaged over all directions of the ion's motion it is zero (the script gets 3 x 10^-21 eV) [computed].

What the example shows and does not show. - Aspden's own argument fails at first order: approach and recession cancel exactly, because the extra power is the time derivative of the electrons' electric potential at the ion (the mathematician's identity; arbiter: Refuted by calculation for that argument). - It does not prove the term has no effect in any plasma. We used straight-line paths and uncorrelated directions. Bent (Coulomb-attracted) paths, a steady electron drift (a current, as in a discharge tube) or other correlations between the ion's speed and the electron's motion were not included. A net effect, if any, would have to come from those, and nobody (Aspden included) has calculated it. That is a genuinely open, well-posed calculation for a reader with a computer (arbiter's "What would settle it", claim 2). - Even the half-pass swing is about 10^-4 times the Coulomb energy for a thermal ion, so any surviving effect would need a strong correlation to matter.

A second, shorter check: the cosmic background formula (example.py Part D). The book's eq. 230 near Earth reduces to T = phi m/k, with m = 0.0408 m_e (the lattice-particle mass) and k Boltzmann's constant, in cgs units: m/k = 3.716e-29 g / 1.381e-16 erg/K = 2.69 x 10^-13 K per (erg/g). - Sun's potential at 1 AU: G M_sun / AU = 6.674e-8 x 1.989e33 / 1.496e13 = 8.87 x 10^12 erg/g. Earth's at its surface: 6.26 x 10^11. Sum 9.50 x 10^12, so T = 2.56 K. The book rounds to 2.6 K; measured 2.7255 K [computed; read: book p.177 via reviewers]. - Apply the same rule to the Milky Way, whose potential relative to infinity is about v_esc^2/2 with local escape speed v_esc = 445 to 580 km/s [web: https://arxiv.org/pdf/1807.04565; https://iopscience.iop.org/article/10.3847/1538-4357/ac4244]: T = 267 to 453 K [computed]. - The Galaxy's contribution is 100 times larger than the Sun's, and leaving it out has no justification. And because the zero of potential is arbitrary (section 2), a temperature that depends on the value of the potential is not well defined. That is why the arbiter rates this part "Refuted by calculation". The same formula also predicts a +/-0.040 K annual swing as Earth's distance from the Sun changes; nobody seems to have checked it against satellite data.

---

6. Evidence table

On how the claims were received: Aspden's plasma papers appeared in refereed journals (J. Franklin Inst. 1969; IEEE Trans. Plasma Sci. 1977 and 1986; Phys. Lett. A 1985 [read: essay citations, not independently checked]). The record in these materials supports "ignored" (his own word), not "suppressed": no blocked funding, retraction or omitted data is documented [arbiter].

---

7. What a learner should take away

Solid. - Maxwell's loophole is real. Closed-loop experiments only test the integrated force, and terms of the form (v.r)/r^3 integrate to zero around a loop. This is worth understanding properly; the same point drives the Ampere-versus-Lorentz debate (see the review's ../Ampere/primer.md). - The force law is dimensionally consistent and equals the textbook magnetic force plus one extra term, which you can check yourself with BAC-CAB. - The extra term is not small for heavy ions: 2% of Coulomb for protons and 16% for iron at coronal temperatures. If it existed, it would matter. - Most of Aspden's arithmetic recomputes: alpha, m_p/m_e, G, the 2.56 K, the deuteron, neutron-decay, pion, muon g and lifetime steps all come out as printed, so the work is not careless [arbiter Q3]. But the round-2 deep reads found several printed numbers that do not follow from the book's own equations: the muon mass at its last digit (206.7690-206.7692, not 206.7688), the Earth/Moon mass ratio (1/94, not 1/83), the vacuum domain size (about 1,520, not 480 light years), the 336.9 MeV "quark" and the 38 keV lattice quantum (41.7 keV) [deep read; arbiter, Round 2].

Wrong, and why the mistakes are instructive. - Signs of individual cases are not a total. Aspden showed the ion gains on approach and loses on recession, then asserted a net gain. Because the power is an exact time derivative, the gains and losses cancel exactly. Lesson: before concluding a "net" effect, check whether the quantity you are adding up is the derivative of something that returns to its starting value. - Comparing temperatures in different places. The "factor 160" divides the corona's temperature by the photosphere's and calls it ions versus electrons. Lesson: check that the two numbers in a ratio describe the same thing. - Fits presented as derivations. A formula whose answer swings with one integer (1841, 1843, 1845 give 137.06, 137.036, 137.01) will hit its target once the rule that picks the integer is chosen; a quantity raised to the eighth power (g^8 in G) can be tuned to any value with a tiny shift. Lesson: count the choices before being impressed by agreement, and look at what happens when better data arrive. The book's own footnote value of 1/alpha (Williams-Olsen, 137.035963(15)) already sat 3.2 standard uncertainties from 137.035915 in 1980; Appendix III then added a lattice-motion correction that moved the answer to 137.035953, 0.7 standard uncertainties away. Today both are thousands of standard uncertainties off (3,800 and 2,100). A correction introduced after the measurement, in the direction of the measurement, and applied to one constant only, is exactly how a fitted formula keeps "agreeing" until the data become too precise. - Many precise matches with several chosen parameters. Chapter 7 matches seven particle numbers to 5-7 digits. Count the freedom in one of them, the proton's magnetic moment, 2.792846 against the 2.7928456 Aspden compared with [read: page image p.149; arbiter Q3]. It is built on the muon mass 206.7688, which matched the 1977 value 206.76859(29) to within 1 standard uncertainty. The inputs: 1. Shared with every match: the integer 1843 and the rule that picks it, the lattice-sum convention, and the structural constants 108 pi, 1/6, 8 and sqrt(3/2), which give alpha and m_p/m_e = 1836.152. 2. For the muon: k = 3/2 (a factor the book itself found as 1.49 in the deuteron and rounded), and a reaction cycle with "+alpha" and "-1" corrections (model choice). 3. For the moment: a pictured spinning electron-positron pair, giving the form factor (3^2 - 1)/(3^2 + 1) = 0.8; an extra 1/(1 - 2 alpha), introduced because "experimental data could, conceivably, have overestimated" the moment (without it the formula gives 2.7521, 1.5% low [computed]); and the muon mass entered as 206.7689 instead of the theory's 206.7688, because "the last digit of the muon mass is critical to this agreement". That is at least seven choices made with the target in view, on top of a fitted integer, to reproduce two numbers (the muon mass and the proton moment). Every comparison value predates the book, and where the measurement later moved, Aspden's number stayed with the old value [arbiter Q3]. A genuine prediction would fix the choices first and then hit a number not yet measured. Check yourself (optional), using the deuteron row of section 6 (2.22464 MeV): How many free choices went into this match, and how many independent numbers does it reproduce? (Answer at the end of the file.) - Choosing between options by the answer. The Mercury derivation (section 4) reaches GR's orbit equation only after picking, among distributions that give 2/3, 1/4 or 2 times the answer, the one that gives exactly GR, and says so. Reproducing a known result this way is a reconstruction, not a derivation; Gerber's 1898 version shows the same pattern and the same failure on light bending. - A potential is not a temperature. Only differences of potential are physical, so T = phi m/k depends on where you put zero, and including the Galaxy changes the answer by a factor of 100. - Asserting against direct evidence. "I am sure it is not [fusion]" ignores that neutrino detectors measure the specific fusion reactions, not just a temperature.

Genuinely open. - Does Aspden's term give a net ion energy gain at second order, or with correlated motion (a current-carrying discharge)? Nobody has done the kinetic calculation. It is a good project: a Monte Carlo of many encounters with bent paths and a drifting electron population. - Has any beam-ion or trap experiment already measured a force along the ion's velocity of size (M/m)(v V/c^2) times Coulomb? A literature search would settle claim 1 cheaply. - What does the Correa discharge device actually put out under neutral calorimetry (measuring heat in and out), with true power measurement of spiky waveforms? - Would Aspden's magnetic-moment formula (eq. 229), which reaches the right order of magnitude for the Earth with one tuned radius, survive a second body (the Sun, Jupiter) with no new tuning? The book never tries; it is a calculation a reader can do [arbiter Q4]. - Coronal heating itself is not fully settled in mainstream physics [memory, medium], though that does not make Aspden's mechanism the answer. - The Graneau wire-fragmentation experiments are real and their interpretation is contested [web: https://www.sciencedirect.com/science/article/abs/pii/0375960185905912], but they concern Ampere's law, not Aspden's.

---

8. Check yourself

1. Show, using BAC-CAB, that (V.r)v - (v.V)r equals V x (v x r). Which physical force is this?
2. Why can no experiment with steady currents in closed wire loops measure Aspden's extra term?
3. Redo section 5, Step 5, for b = 1 nm. What are W_in, W_out and the net?
4. Two equal charges move side by side with the same velocity v, perpendicular to r. What does the textbook law (T1) give for the force? What does Aspden's law give if instead v points along r?
5. Aspden's formula gives 2.56 K from the Sun and Earth. Give two independent reasons why this is not evidence that the CMB is a local effect.

---

9. Further reading

Mainstream. - D. J. Griffiths, Introduction to Electrodynamics (any edition from the 3rd): Ch. 1 (vectors), Ch. 5 (magnetostatics), Ch. 8 (conservation laws and field momentum). - J. R. Taylor, Classical Mechanics: Ch. 1 and Ch. 3 (Newton's third law, momentum). - D. V. Schroeder, An Introduction to Thermal Physics: Ch. 1 (equipartition). - F. F. Chen, Introduction to Plasma Physics and Controlled Fusion (electron and ion temperatures, collisions). - L. Spitzer, Physics of Fully Ionized Gases (electron-ion energy exchange) [memory, high]. - E. T. Whittaker, A History of the Theories of Aether and Electricity (1951), the source Aspden used for Maxwell's term. - J. C. Maxwell, A Treatise on Electricity and Magnetism, Vol. 2 (1873), the chapters comparing electrodynamic formulas. - J. D. Sethian, D. A. Hammer, C. B. Wharton, Phys. Rev. Lett. 40, 451 (1978) [web: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.40.451]. - Borexino Collaboration, CNO-cycle neutrinos, Nature 587, 577 (2020) [web: https://www.nature.com/articles/s41586-020-2934-0]. - NIST CODATA values: https://physics.nist.gov/cuu/Constants/ - P. Gerber, "Die raeumliche und zeitliche Ausbreitung der Gravitation", Zeitschrift f. Math. u. Phys. 43, 93 (1898) [read: cited in the book, p.35-36]; background at https://en.wikipedia.org/wiki/Paul_Gerber [web, secondary]. - In this review: ../Ampere/primer.md (closed-circuit equivalence of force laws) and ../Maxwell/primer.md.

Aspden's own key works (only the first two are in the folder). - A Problem in Plasma Science, web essay, 30 October 2005 [read]. - Physics Unified, Sabberton Publications, Southampton, c.1980 [read via OCR]. - "The law of electrodynamics", J. Franklin Inst. 287, 179 (1969) [cited in essay; not obtained]. - IEEE Trans. Plasma Sci. PS-5, 159 (1977) and PS-14, 282 (1986); Phys. Lett. A 111, 22 (1985) [cited in essay; not obtained]. - Power from Space: The Correa Invention, report (1996), at www.aspden.org [cited in essay; not obtained]. - Correa patents US 5,416,391; 5,449,989; 5,502,354 [https://patents.google.com/patent/US5449989A/].

---

Answers

1. V x (v x r) = v(V.r) - r(V.v) by BAC-CAB with a = V, b = v, c = r. Times mu0 qQ/(4 pi r^3), it is the Lorentz force Q V x B in the Biot-Savart field of q: the ordinary magnetic force.
2. For steady current, each carrier's contribution has the factor (v.r)/r^3 dt = d(1/r) along the wire (with v dt = ds). Summed around a closed loop, an exact differential gives f(end) - f(start) = 0. The extra term adds nothing to the total force, so loop experiments cannot see it, whatever its coefficient.
3. Everything scales as 1/b: the Coulomb energy is 1.44 eV, so W_in = 1.44 x 5.06e-4 = +7.28 x 10^-4 eV, W_out = -7.28 x 10^-4 eV, net 0.
4. Textbook, v = V perpendicular to r: (V.r) = 0, so F = -(mu0 q^2 / 4 pi r^3) v^2 r: an attraction of size (v/c)^2 times the Coulomb repulsion. Aspden with v = V along r, M = m: the first two terms are (v.r)v - (v.r)v = 0 and the force is again -(mu0 q^2 / 4 pi r^3) v^2 r (Aspden writes -(q^2/r^3) v^2 r with c = 1), the same attraction along the line. The textbook law gives zero in this in-line case (v(v.r) - r v^2 = 0 when v is parallel to r). This "always attractive along the line" property is what Aspden wanted for gravity.
5. Any two of: (a) the same rule applied to the Galaxy's potential gives 267-453 K, and a potential has no fixed zero, so the rule is not well defined; (b) the CMB temperature measured in distant gas clouds rises as (1+z), which a local potential near the Sun cannot produce; (c) 2.56 K is 0.17 K off the measured 2.7255 K, far outside the 0.001 K uncertainty, and the fix ("one electron per 600 lattice particles") was added after the fact; (d) the formula says nothing about the blackbody shape or the anisotropy pattern.

Section 7 (optional question). Five choices, all made with the measured 2.22464 MeV in view: model C chosen from four candidate structures; k = 3/2 imposed where the fit wanted 1.49; the 1/1836 finite-size factor; the 2r ground-state separation, adopted because "it happens to improve the agreement"; and the six-charge array (with its "mysterious sixth charge") [arbiter Q3; read: deep read of p.131-135]. They reproduce one number. On top of that sit the shared inputs (1843, alpha), which were themselves fitted. Five choices for one number is a fit, not a test.