Herbert E. Ives: the moving atomic clock and the ether: a primer

Project folder: Researchers/Ives. Herbert Eugene Ives (1882-1953) was a physicist at Bell Telephone Laboratories, a pioneer of television and facsimile (sending pictures over telephone lines), and the son of the colour-photography inventor Frederic E. Ives [read: README]. He is best known for the Ives-Stilwell experiment of 1938, done with his Bell Labs colleague G. R. Stilwell, which measured the slowing of fast-moving hydrogen atoms used as clocks. From 1922 to 1938 his main research besides television was photoelectricity [read: NAS memoir p.19], which he explained in thin metal films by standing light waves (section 4.8). He is in this review because T. H. Moray's book The Sea of Energy in Which the Earth Floats (5th ed.) reprints, as its Appendix VI, M. Ruderfer's 1975 paper "Neutrino Structure of the Ether", which builds on Ives: it calls Ives's work "the most direct verification of the validity of a Lorentz ether" and says "the continued neglect of Ives' gravitational theory is unwarranted" [read: Moray 5th ed., printed pp.271-272, in review/Morray-TH/_text]. Section 4.10 explains in detail why Ives matters to Moray, and answers the owner's question whether a Lorentz ether adds any force beyond Lorentz and Einstein (short answer: no, for everything Ives himself derived; the energy reservoir is Ruderfer's and Moray's addition).

What changed in this version (2026-10-07, after QE round 2). Ives's own papers arrived (31 of them, 1924-1951, obtained legally under follow-up Q10) and the reviews were redone. The main changes for the reader: his gravitation theory turns out to be the Schwarzschild solution of general relativity, derived exactly and in ether language, with nothing fitted (section 4.4 is rewritten; the earlier "one matched number" argument was wrong and is withdrawn); Ives-Stilwell Part II (1941) answers the 1938 doublet caveat (section 4.1); his 1945 derivation from conservation laws and his 1949 transported-clock argument are now read (section 4.3); his separate physical claims (the photon, radiation pressure, a "dishing" disk) and his ripple-tank analogue of an ether are added (section 4.9); and section 4.10 is new.

The folder holds the 1956 National Academy of Sciences (NAS) memoir of Ives by O. E. Buckley and K. K. Darrow (with a long assessment by the relativist H. P. Robertson), two history-of-physics papers by I. Bonizzoni and G. Giuliani (2000) and Giuliani (2015), H. C. Ohanian's 2008 paper on Einstein's E = mc^2 derivations, the Wikipedia and Optica biographies, the project README, and (new) a folder Ives-papers/ with 31 of Ives's own papers: the photoelectric papers of 1924-26, the 1933 standing-wave paper with T. C. Fry, the relativity and ether papers of 1937-1951 in the Journal of the Optical Society of America (JOSA), Physical Review and the Philosophical Magazine, the two Ives-Stilwell clock papers (1938, 1941), the two moving-medium (ripple-tank) papers (1941, 1942) and the 1951 Rumford Medal lecture. The Investigator added the 1952-53 mass-energy papers and later work by others (research/files/, OCR in research/files/ocr/).

Source gap (repeated from claims.md and arbiter.md, updated after QE round 2). - Deep-read from text and page images (equations checked): Ives-Stilwell 1938 and Part II (1941); Ives 1937 (JOSA 27:263, 27:310, 27:305); 1938 (28:296); 1939 gravitation (29:183); 1945 (Phil. Mag. 36:392); 1947 (Phys. Rev. 72:229); 1948 (JOSA 38:413); 1949 (JOSA 39:757); Pobedonostsev-Parshin (6 pp.); Faraj; Lalli 2014; Preikschat's thesis passages; the 1952 and 1953 mass-energy papers. - Read by a reviewer or QE in the extracted text, not deep-read: the 1942 radiation-pressure and ripple-tank papers, the 1939 rotating-disk passage, the 1951 photon passage, the 1947 historical note, and Ruderfer's appendix in the Moray book (printed pp.271-275, read again for this primer). - Digest only: the 1924-26 photoelectric papers, Ives-Fry 1933, the 1937 papers 27:177 and 27:389, the 1939 chronotopic-interval and double-Fizeau-wheel papers, 1940, the 1943-44 wave-packet papers, JOSA 38:879 (1948), JOSA 40:185 (1950), "Revisions" (1951) and the Rumford lecture outside the photon passage. Statements resting on these are marked "digest". - Not obtained: JOSA 42:540 (1952; in copyright, cited by reference), the 1953 JOSA 43 notes (same), "Unsymmetrical Doppler Effect in Hydrogen Canal Rays" (Rev. Sci. Instr. 9:283, 1938), the 1951 clock-paradox letter (Nature 168:246), Proc. Roy. Dublin Soc. 26:9 (1952), the Hazelett and Turner collection The Einstein Myth and the Ives Papers (1979), Bridgman's 1959 memo and Lalli 2013 (known only through Lalli 2014 or an abstract), Robertson's referee report (only a historian's quotation), R. C. Jones's 1939 paper and Otting's (known only through Part II), the full Russian account of Pobedonostsev and Parshin (Zh. Tekh. Fiz. 1989, issue 3) and their later papers. - Known digest errors, not used here: "H-alpha" for H-beta (1938 digest); "He" for H2; the 1941 factor printed (1 - v/c^2)^(1/2); the 1942 ripple exponent; the 1948 digest's garbled mass formula and orbit equation (corrected from page images in the deep read). - No conclusion in this primer now rests on [memory] alone; where a point leans partly on [memory] it is marked.

Source tags: [read] = from a document in the folder or in research/files/ (page given where useful); [web] = Internet source, URL or the research/ note that holds it; [memory] = recalled from training, with confidence; [calc] = computed by a reviewer, the arbiter or for this primer, and reproduced in example.py.

Acronyms used throughout: SR = special relativity (Einstein, 1905); GR = general relativity (Einstein, 1915); MM = the Michelson-Morley experiment (1887); KT = the Kennedy-Thorndike experiment (1932); IS = the Ives-Stilwell experiment (1938); JOSA = Journal of the Optical Society of America; NAS = National Academy of Sciences; LoC = Library of Congress; NYT = New York Times; RSI = Review of Scientific Instruments (Rev. Sci. Instr.); SPIE = Society of Photo-Optical Instrumentation Engineers (a conference publisher); NRL = US Naval Research Laboratory; Phil. Mag. = Philosophical Magazine; Phys. Rev. = Physical Review; Proc. APS = Proceedings of the American Philosophical Society; PPN = parametrized post-Newtonian (a standard way of comparing gravity theories by a few numbers, section 3.5).

---

1. The idea in one paragraph

Einstein predicted in 1907 that an atom moving fast should give out light of a slightly lower frequency than the same atom at rest, because a moving clock runs slow and an atom's light is a kind of clock tick. The effect is tiny: for atoms moving at about 0.4 percent of the speed of light it changes the wavelength by about one part in a hundred thousand, and it is buried under the much larger ordinary Doppler shift (the change in pitch you hear when a siren passes). For thirty years nobody managed to measure it. In 1938 Ives and Stilwell found a clever way: look at the atoms coming toward you and going away from you at the same time, so that the large ordinary shifts cancel and only the small clock effect is left. They saw it, at the size Einstein's formula predicts. The twist is that Ives did not believe Einstein's account. He believed in a fixed ether, a medium filling space through which light travels, and he read his result as proof that clocks really do slow down when they move through that ether, as the older theories of Larmor and Lorentz said. Both sides claimed the result at once, and both were right about the numbers, because the two theories were built to give the same predictions. Ives spent the rest of his life rebuilding relativity inside an ether: he derived the shrinking of moving rods, the slowing of moving clocks and the growth of moving mass from old-fashioned conservation of energy and momentum, and he rederived Einstein's theory of gravity (Mercury's orbit, the bending of starlight, the slowing of clocks near the Sun) as ordinary forces acting in flat space, with the ether's properties changing near a mass. He said himself that this gives "no new law of gravitation" and that his force equations "are actually implicit in the general relativity solution". So, as the question supposed, Ives's ether adds no new force and no new prediction to what Lorentz and Einstein give: it is a different explanation of the same observations. That is exactly why it mattered to the Moray circle: a respected Bell Labs physicist had shown that believing in a physical ether is not ruled out by any relativity experiment. The further step, that this ether holds a store of energy that could be tapped, is M. Ruderfer's and Moray's, not Ives's. The measurement holds up and has been repeated to parts per billion; the ether reading cannot be tested against Einstein's; a few of Ives's side claims (that the photon would be abandoned, that special relativity contradicts itself) do not survive.

---

2. What you need to know first

2.1 Waves, wavelength and frequency. Light is a wave with wavelength lambda (lambda, the distance between crests) and frequency nu (nu, crests per second), with lambda * nu = c, where c = 2.998 x 10^8 m/s is the speed of light. A longer wavelength means a lower frequency (redder light); a shorter one means higher frequency (bluer light). Wavelengths here are in angstroms: 1 A = 10^-10 m. Hydrogen's blue-green line called H-beta has lambda0 = 4861.3 A when the atom is at rest. Read: any introductory physics text on waves, e.g. Halliday, Resnick and Walker, Fundamentals of Physics, the chapters on waves and on light.

2.2 The ordinary (first-order) Doppler effect. A source moving toward you at speed v squeezes its waves together: you see lambda0 (1 - v/c); moving away, lambda0 (1 + v/c). It is called "first order" because it is proportional to beta = v/c to the first power, and it changes sign with direction. Read: Hecht, Optics, the sections on the Doppler effect.

2.3 Time dilation and the factor gamma. In SR a clock moving at speed v, seen from the laboratory, ticks slower by the factor gamma = 1/sqrt(1 - beta^2). For small beta, gamma is about 1 + beta^2/2 (a Taylor series; the next term is (3/8) beta^4). The effect is "second order": proportional to beta^2, and the same whichever way the clock moves. Read: Taylor and Wheeler, Spacetime Physics; Griffiths, Introduction to Electrodynamics, Chapter 12 (Electrodynamics and Relativity); A. P. French, Special Relativity.

2.4 The relativistic Doppler effect. Put 2.2 and 2.3 together. An atom moving at speed v, whose light you view at angle theta to its motion, gives an observed wavelength lambda = lambda0 (1 - beta cos theta) gamma when approaching. The factor (1 - beta cos theta) is the squeezing of the waves; the factor gamma is the atom's slower clock. Viewed exactly side-on (theta = 90 degrees) only gamma is left: the "transverse Doppler effect". Read: French, Special Relativity; Griffiths Chapter 12.

2.5 The ether and the Lorentz-FitzGerald contraction. Nineteenth-century physics held that light is a wave in a medium, the ether, at rest in some absolute frame. The Earth moves through it, so the speed of light measured in a laboratory should depend on direction. The Michelson-Morley experiment (1887) found no such dependence. FitzGerald and Lorentz proposed that bodies moving through the ether shrink along their motion by sqrt(1 - beta^2), exactly enough to hide the effect. Larmor and Lorentz then found that clocks must also slow by gamma for every experiment to come out null. This "Lorentz ether theory" gives the same equations, the Lorentz transformations, as Einstein's 1905 SR. Einstein's step was to drop the ether: if no experiment can detect it, treat all uniformly moving frames as equal. Read: Whittaker, A History of the Theories of Aether and Electricity (a separate review project here); Rindler, Relativity: Special, General and Cosmological.

2.6 Clock synchronization. To measure a one-way speed you need two clocks, one at each end, set to the same time. Einstein defined "same time" by light signals: send a flash from A to B and back, and take the moment at B as halfway between departure and return. Another way is to set two clocks together and carry one to B; but a moving clock runs slow, so it arrives slightly behind, by an amount that shrinks as you carry it more slowly. Reichenbach (1928) argued that the choice of synchronization is a convention: no experiment can measure the one-way speed of light without first choosing one [memory: high]. Read: Taylor and Wheeler; Rindler.

2.7 Least-squares fit and chi-square. To test whether data follow y = k x, choose k to minimise the sum of squared misfits. Chi-square, the sum of (misfit / expected error)^2, should be about the number of points if the quoted errors are right; much smaller means the points agree "too well" (the errors were overestimated or the points are not independent). Read: Taylor, An Introduction to Error Analysis.

2.8 Mass, energy and momentum in SR. A body of rest mass m moving at speed v has momentum p = gamma m v and kinetic energy K = (gamma - 1) m c^2, which is (1/2) m v^2 at low speed. Light carrying energy E carries momentum E/c. E = m c^2 says a body that gives off energy L loses mass L/c^2. Read: Griffiths Chapter 12; French.

2.9 Standing light waves and the photoelectric effect (needed only for section 4.8). When a light wave meets a mirror, the incoming and reflected waves add. Where they arrive in step the field is strong (an antinode); half a wavelength's worth of path later they cancel (a node). The pattern does not travel; it is a "standing wave", with antinodes spaced lambda_m/2 apart, where lambda_m is the wavelength in the material (lambda divided by its refractive index n). For green light, lambda = 550 nm in vacuum, the antinodes in air are 275 nm apart [calc, this primer]. Lippmann's colour photography (1891) used this: a photographic film pressed against a mercury mirror records the standing-wave pattern as thin layers, which later reflect the same colour [memory: high; the memoir describes the process, read: NAS memoir pp.6-7]. In the photoelectric effect, light falling on a metal knocks electrons out, but only if each photon's energy h nu (h is Planck's constant) exceeds a threshold; the longest wavelength that still works is the "long-wave limit". In a film thinner than a wavelength lying on a mirror-like metal, how strongly the film emits depends on where the standing-wave antinodes fall inside it, and so on the film's thickness, the angle of the light and its polarization (the direction in which the light's electric field points). Read: Hecht, Optics, the sections on standing waves and on reflection from metals; any modern-physics text (e.g. Serway, Moses and Moyer, Modern Physics) on the photoelectric effect.

2.10 Rulers and clocks near a mass: the Schwarzschild "line element" (needed for sections 3.5 and 4.4; no tensors). General relativity (GR) is usually taught with tensors, but its one most-tested result can be stated with nothing beyond the Pythagorean theorem. In flat space, two nearby points separated by dx, dy, dz are a distance dl apart with dl^2 = dx^2 + dy^2 + dz^2. Special relativity adds time: for two nearby events separated by dt in time and dl in space, the quantity ds^2 = c^2 dt^2 - dl^2 is the same for every observer, and ds/c is the time a clock that travels between the two events actually records (its "proper time"). This formula is called a line element; it tells you how to turn coordinate differences into what real rulers and clocks read. In 1916 K. Schwarzschild found GR's line element outside a single, non-rotating, spherical mass M. In polar coordinates (r the distance from the centre, theta the angle), for motion in one plane:

ds^2 = c^2 y dt^2 - dr^2/y - r^2 dtheta^2, with y = 1 - 2GM/(r c^2).

Here G = 6.674 x 10^-11 m^3 kg^-1 s^-2 is Newton's constant and t is the time of a clock far from the mass. Read it term by term, as "how rulers and clocks behave near a mass" [memory: high; Ives's own 1939 reading, below]:

• Clocks. A clock at rest at distance r (dr = dtheta = 0) records ds/c = sqrt(y) dt: it runs slow by the factor sqrt(y). Light it emits arrives at a distant observer lowered in frequency by that factor: the gravitational red shift.
• Radial rulers. A short ruler pointing at the mass has proper length dr/sqrt(y): more ruler-lengths fit along the radius than flat-space geometry expects. Equivalently, if you insist on flat space, the ruler has shrunk by sqrt(y) along the radius. Rulers across the radius are unchanged.
• Light. Light has ds = 0. So, in the coordinates r and t, light moves at speed c y along the radius and c sqrt(y) across it: slower, and direction-dependent, near the mass. Any local observer, with local rulers and clocks, still measures c.
• Sizes. For the Sun's surface (G M = 1.327 x 10^20 m^3/s^2, R = 6.957 x 10^8 m), 2GM/(Rc^2) = 4.25 x 10^-6. Clocks there run slow by 2.12 x 10^-6 (a red shift equal to a Doppler speed of 0.636 km/s), and the coordinate light speeds fall short of c by 1,273 m/s radially and 636 m/s sideways [calc: example.py Part 7].

The key quantity 2GM/r is also the square of the Newtonian escape speed V (V^2 = 2GM/r; 617.8 km/s at the Sun's surface), so y = 1 - V^2/c^2: the same algebraic form as the special-relativity factor 1 - v^2/c^2 for a body moving at the escape speed. Ives built his gravitation on that coincidence (section 4.4). Read: Taylor, Wheeler and Bertschinger, Exploring Black Holes (written without tensors, built around this line element); Rindler, Relativity, the chapter on the Schwarzschild metric.

2.11 Orbits, perihelion precession, and the variable u = 1/r (needed for sections 3.5, 4.4 and the second worked example). A planet's closest point to the Sun is its perihelion. In Newton's theory the orbit is a closed ellipse and the perihelion stays put. Writing u = 1/r and using the angle theta as the variable, Newton's orbit obeys d^2u/dtheta^2 + u = K (K a constant), whose solution u = K + A cos(theta) repeats exactly every 2 pi radians. If a small effect changes the equation to d^2u/dtheta^2 + u(1 - epsilon) = K, the solution is u = K/(1 - epsilon) + A cos(sqrt(1 - epsilon) theta); the perihelion now comes back after 2 pi/sqrt(1 - epsilon), about 2 pi (1 + epsilon/2), so the ellipse turns by about pi epsilon per orbit. All the gravitation arithmetic in this primer is about the size of epsilon. Read: Goldstein, Classical Mechanics, the chapter on central forces; Rindler, the section on the perihelion of Mercury.

2.12 "Same predictions, different explanation": empirical equivalence (needed for sections 4.2, 4.10). Two theories are empirically equivalent when every experiment gives the same number in both. Then no experiment can choose between them, however strongly their pictures differ. The standard example is this project's: H. A. Lorentz's ether theory (1904-1909: a fixed ether, with real shrinking of moving rods and real slowing of moving clocks) and Einstein's special relativity (1905: no ether; the shrinking and slowing follow from the relativity of simultaneity). They share the same equations, the Lorentz transformations. A choice between empirically equivalent theories is made on other grounds, such as simplicity, fruitfulness or taste, and those choices can change. Read: Rindler, Relativity, the opening chapters; J. S. Bell, "How to teach special relativity" (1976), in Speakable and Unspeakable in Quantum Mechanics, a modern physicist's defence of teaching relativity Lorentz's way [memory: high].

---

3. The textbook view

3.1 The transverse Doppler effect and how to see it. With the symbols of section 2, light from atoms moving toward the spectrograph (the instrument that spreads light into wavelengths) at a small angle theta to the line of sight, and from atoms moving away, arrives at

lambda_blue = lambda0 (1 - beta cos theta) gamma, lambda_red = lambda0 (1 + beta cos theta) gamma.

Their average, the "centre of gravity" of the two displaced lines, is

lambda_centre = (lambda_blue + lambda_red)/2 = lambda0 gamma = lambda0 (1 + beta^2/2 + ...),

exactly, whatever theta is [calc: example.py Part 1]. The centre is shifted to the red by lambda0 beta^2/2, the time-dilation effect, while the large first-order shifts lambda0 beta cos theta sit symmetrically on each side. Einstein proposed the measurement in 1907 with hydrogen "canal rays" [read: Ives 1947 Note p.812; Giuliani 2015 p.3]. Canal rays are beams of positive ions (here H2+ and H3+, hydrogen molecules missing one electron) accelerated through a voltage V; an ion of mass M gets kinetic energy eV, so beta^2 = 2eV/(M c^2), where e is the electron charge. The ions break up into hydrogen atoms that keep the ion's speed and glow.

3.2 Three experiments fix the Lorentz transformation. H. P. Robertson (1949) and later R. Mansouri and R. Sexl (1977) wrote the most general transformation between a "preferred" frame and a moving one with free functions, and asked which experiments pin those functions down [memory: high; Robertson's summary in the NAS memoir, read: memoir p.23-24]. MM fixes the ratio of contraction along and across the motion. KT, an interferometer with unequal arms, fixes the clock rate relative to the lengths. An IS-type test fixes the remaining overall factor. With all three at their relativistic values, the theory is the Lorentz transformation; any leftover "preferred frame" makes no measurable difference, provided clocks are synchronized Einstein's way [web: https://en.wikipedia.org/wiki/Test_theories_of_special_relativity]. Robertson put it in the memoir: MM and KT alone give the transformations with "an unknown function k(v)", which "must be unity in the special theory of relativity but can differ from this value on any theory, such as that of Lorentz, based on the assumption of an aether"; IS "shows that k is in fact equal to unity within the observational error" [read: NAS memoir p.23-24].

3.3 Modern status. The second-order Doppler effect has been measured ever more precisely: Otting 1939; Mandelberg and Witten 1962 (exponent 0.498 +/- 0.025 against 0.5) [read: Giuliani 2015 p.10, second hand; existence confirmed, web: https://arxiv.org/pdf/physics/0008012]; laser and storage-ring tests on lithium ions, Saathoff 2003, Reinhardt 2007, and Botermann et al. 2014 at beta = 0.338, agreement within a few parts in 10^9 [read: research/files/Botermann-2014-arXiv-1409.7951; web: https://link.springer.com/article/10.1038/nphys778]. Time dilation of a real decaying clock: muons in the CERN storage ring at gamma = 29.3 [web: https://inspirehep.net/literature/124922].

3.4 SR and rotation. The Sagnac effect: light sent both ways around a rotating loop returns with a time difference 4 A Omega / c^2 (A the enclosed area, Omega the rotation rate), a phase shift 4 A Omega/(lambda c). SR derives it from an inertial (non-rotating) frame; von Laue (1920) and Langevin (1921) did so [web: https://en.wikipedia.org/wiki/Sagnac_effect]. A fixed-ether calculation gives the same first-order result.

3.5 Gravitation. GR describes gravity as curved spacetime; around one spherical mass, everything solar-system tests probe is in the Schwarzschild line element of section 2.10. Its classic results [calc: arbiter; example.py Part 7]: - Mercury's orbit turns (precesses) by an extra 6 pi G M/(c^2 a (1 - e^2)) radians per orbit, 42.98 arcsec per century (G M = 1.32712 x 10^20 m^3/s^2 for the Sun, a = 5.791 x 10^10 m the orbit's semi-major axis, e = 0.2056 its eccentricity). In the language of 2.11, epsilon = 6 G^2 M^2/(c^2 h^2), with h the planet's angular momentum per unit mass. - Light grazing the Sun bends by 4GM/(c^2 R) = 1.7512 arcsec. Half of this (0.8756 arcsec) comes from the slowing of clocks alone; the other half from the radial term dr^2/y, the "shrinking of radial rulers" [calc: 1939 deep read; example.py Part 7]. - Clocks lower in the field run slow (gravitational red shift; Pound-Rebka 1960 [memory: high]). Radar signals passing the Sun are delayed (Shapiro delay, proposed by I. Shapiro in 1964 and measured in the following years [memory: high]), because light is slower there in the coordinates of 2.10.

What flat-space alternatives give. A Newtonian force acting on the special-relativity moving mass m0/sqrt(1 - v^2/c^2) gives one sixth of Mercury's advance, 7.16 arcsec per century (Sommerfeld; epsilon = G^2 M^2/(c^2 h^2), 6 times too small) [web: https://arxiv.org/pdf/physics/9805032]. G. Nordström's scalar theory (1913) has the right Newtonian limit but bends light not at all [web: https://en.wikipedia.org/wiki/Scalar_theories_of_gravitation, via the arbiter]. So "Newton plus special relativity" is not enough for gravity: something must also depend on position in the field, not only on speed. G. D. Birkhoff's flat-space theory (1943-44) reproduced the classic tests with Newtonian time but drew objections: it admits only matter whose sound speed equals c, and its force law was a formal choice, not derived (medium confidence, summary-level web check by the arbiter: https://arxiv.org/pdf/gr-qc/9912003).

PPN numbers. Physicists compare gravity theories by a few numbers in the line element written for weak fields; the two that matter here are gamma_PPN (how much space is curved per unit mass; light bending is proportional to (1 + gamma_PPN)/2) and beta_PPN (how nonlinear the time part is). GR has gamma_PPN = beta_PPN = 1; the perihelion advance is GR's times (2 + 2 gamma_PPN - beta_PPN)/3. Measurements put both within small fractions of a percent of 1 [memory: high; not web-checked, no verdict rests on it alone]. Any theory that gets these two numbers equal to 1 agrees with every classic solar-system test.

3.6 E = mc^2. Einstein's 1905 note: a body at rest emits two equal light pulses of total energy L in opposite directions. Seen from a frame moving at v, the pulses carry total energy L gamma (one Doppler-boosted, one reduced). Call E the body's energy in its rest frame and H in the moving frame, before (0) and after (1). Energy conservation in both frames gives (H0 - E0) - (H1 - E1) = L (gamma - 1). Einstein says H - E is the body's kinetic energy K plus a constant, so the kinetic energy drops by L (gamma - 1), about L beta^2/2 = (1/2)(L/c^2) v^2. Comparing with K = (1/2) m v^2, the mass drops by L/c^2. Planck (1907) noted that the last comparison is valid "only as a first approximation"; von Laue (1911) and Klein (1918) gave fully general proofs [read: Ives 1952 p.542; Ohanian 2008 deep read]. The relation itself is confirmed to 4 parts in 10^7 (Rainville et al. 2005) [web: https://news.mit.edu/2005/emc2].

---

4. Where Ives departs, side by side with the textbook

The fair way to read Ives is to start from what he got right. His starting points are real physics: the Lorentz ether theory is empirically equivalent to SR (Robertson, Jones, Mansouri-Sexl all agree); MM really does leave the absolute contraction and clock rate open; synchronization really is a convention; Planck really did object to Einstein's 1905 step. Ives's departures are in what he inferred from those starting points.

4.1 What the 1938 experiment measured (claim 1)

Ives and Stilwell solved a real problem. Viewing exactly side-on, a tiny error in angle gives a first-order shift as big as the effect sought; "very small deviations from this direction would introduce shifts of the order of magnitude of the expected effect" [read: p.215, quoted by Giuliani]. So they viewed along the beam, directly and in a small concave mirror at about 7 degrees, and measured the centre of the two displaced lines against the undisplaced line from atoms at rest [read: p.217]. The algebra in 3.1 shows why the centre does not care about the angle.

One printed slip. Page 216 writes the centre shift as "lambda = lambda0 (1 - V^2/c^2)^(1/2)", a frequency factor attached to a wavelength; taken literally it would put the centre to the blue. Page 226 gives the correct frequency form and Table III uses lambda0 beta^2/2 [read: page images p.216, p.225-226, checked by the Investigator and the Mathematician]. The slip is in the original paper, not in the secondary authors who quoted it. Which way did the centre move? The QE deep read checked pp.215-226 on the page images: Ives and Stilwell never say "red" or "blue" for the centre shift and never give its sign; they speak only of "a shift of the center of gravity of the displaced lines with respect to the undisplaced line" [read: p.216]. The direction follows from their closing formula nu = nu0 (1 - V^2/c^2)^(1/2): a lower frequency means the centre lies on the red (long-wavelength) side [read: deep read of pp.217-226; the inference is the deep reader's and the arbiter's]. They tabulate only the mean of the direct and reflected displacements, so no asymmetry between the approaching and receding lines can be read from the paper, and they report none; they bound any difference in apparent speed between the direct and mirror views at 1/100 of 1 percent [read: p.217 footnote, p.222].

Ives and Stilwell's own caveats, kept: every measured shift (at most 0.047 A) is smaller than the 0.09 A separation of the two close components of H-beta, so "some of the observed shift could be due to a variation of relative intensity of these components"; this "could be excluded if voltages at least twice and preferably several times the highest here used could be employed" [read: p.225]. Other checks the paper reports: mirror symmetry (a tube with a mirror imaging the discharge on itself and a tube with a plane mirror "gave identical results"), the linearity of the spectrograph's scale (tested on three molecular hydrogen lines), faint molecular hydrogen lines that at first gave "very erratic and confusing displacements" (cured by choosing voltages that put the canal-ray lines in clear spaces), the orientation of the apparatus (Table II) and a stray magnetic field reversed at ten times its strength with no effect [read: pp.217-224, deep read]. The paper does not discuss the 3-4 percent mean deficit that a reviewer's arithmetic finds in Table III (section 5, Step 6).

Part II (1941) answers the caveat. Ives and Stilwell rebuilt the tube with three accelerating gaps (sparking had stopped them near 20,000 V) and ran it "up to about 43,000" volts. For H2 particles the centre shift reached "over 0.11 A as against the previous maximum of 0.047 A": observed 0.113 and 0.1145 A at 42,260 and 42,280 V, against 0.1098 and 0.1073 A computed, and "over this entire range the relationship previously observed is maintained" [read: JOSA 31:369, p.369 and Table I, page image, deep read]. That is about 1.25 times the 0.09 A doublet separation. The centre of two lines can never lie outside the interval between them, so a brightness change between the two components cannot by itself produce a shift larger than their separation: the 1938 caveat is answered on the authors' own numbers [calc: arbiter; example.py Part 6]. The limits, kept: the new points were taken on faster, coarser plates ("somewhat less precision"); the H2 points sit on average about 3 percent above the computed curve (the opposite sign to 1938), which the authors put down to a mirror reflecting less than 100 percent (the reviewers count six above against three at or below, or six, one and two; check Table I before quoting); one entry (H3O at 42,280 V, "computed" 0.0012) looks like a misprint for about 0.0118 [read: deep read]. Part II also answers two critics. R. C. Jones (1939) asked whether the "stationary" reference atoms could be pushed along the beam, shifting the reference line: with the mirror covered they found a reference-line displacement equal to about 750 m/s at 14,000 V, none within error with the mirror in. And a double-ended tube with the optics reversed gave 0.0744 A against 0.0717 A computed at 28,300 V (one point, no error bar), which they say "completely disposes of" an objection by G. Otting [read: deep read]. These are the authors answering their own critics: fair, but not independent. Part II never uses the words "ether" or "relativity"; it credits the prediction to Larmor and Lorentz [read: arbiter, from the deep read].

4.2 The ether reading (claim 2)

Ives's argument, in his words: null experiments like MM "could be equally well explained, and more simply" by an ether dragged along by the Earth or by light whose speed adds to its source's (ballistic or emission theory), so the positive clock-rate result "may hence be claimed to give more decisive evidence for the Larmor-Lorentz theory" [read: p.226]. His 1947 "Historical Note" makes the strongest version of this, and it is good physics. MM fixes only the ratio of contraction along and across the motion. A light clock (a pulse bouncing between two mirrors) shrunk in different absolute ways all pass MM but tick at different rates: Voigt's 1887 choice gives period T0/(1 - beta^2), Lorentz's (l = 1) T0/sqrt(1 - beta^2), an equal-volume shrinkage T0/(1 - beta^2)^(2/3), and a shrinkage in both directions gives no change at all. "These latter [the canal-ray data] decide unequivocally for l=1" [read: JOSA 37:810-812; calc: example.py Part 3].

Where the inference stops. Ives's own 1937 Doppler paper shows the point: if clocks did not slow, the centre shift would depend on the laboratory's velocity through the ether; with the Larmor-Lorentz clock factor, that dependence cancels and the result "depends only on the relative velocity between source and spectrograph" [read: JOSA 27:389-391, as summarised by the Mathematician and Bonizzoni-Giuliani]. So in Ives's own theory the experiment cannot see the ether. Jones said so in 1939: "The theoretical predictions we shall obtain here are identical with those obtained by Ives from electron theory" [read: Giuliani p.9]. On the day of the announcement both camps claimed the result: the NYT of 27 April 1938 reported Einstein calling it "the most direct proof yet brought forth in support of the theory of relativity", in an article that described it as verifying "the existence of ether in space" [web: research/2026-10-07-nytimes.md]. Bell Laboratories, Ives's employer and funder (an interested party), wrote in 1947 that it "furnished the first direct proof of the system of compensation for motion embodied in the theories of Larmor, Lorentz and Einstein" [read: Bell Laboratories Record Aug 1947].

Ives in his own words, before and after. In 1937 he showed that the Kennedy-Thorndike experiment "cannot by itself test the Larmor-Lorentz hypothesis" without knowing how much moving clocks slow, and proposed the canal-ray experiment to settle it, crediting "Einstein and Ritz" with seeing its crucial role thirty years before (JOSA 27:177, 27:389) [read: digests, QE round 2]. In his 1947 historical note he is fair to Einstein: Voigt offered no physical justification for his equations, Lorentz claimed no objective reality for his "local time", and Einstein alone "believed the equations' predictions" and named the canal-ray shift "as an experimentum crucis". He adds that the clock-rate test is the most conclusive one because Michelson-Morley can be explained by an entrained ether and the growth of mass by a change of charge [read: JOSA 37:810, extracted text, QE round 2]. So the man who read IS as evidence for the ether also gave Einstein full credit for predicting it.

Ives on rotation. In 1953 he argued that the Sagnac and Michelson-Gale experiments give "positive first-order results exactly in conformity with the idea that the light signals travel in a fixed ether", and that Einstein's scheme handles only uniform motion [read: JOSA 43 "Genesis", as reported by the Physicist]. His own 1938 analysis, "Light signals sent around a closed path" (JOSA 28:296), is more careful. There he derives the standard first-order Sagnac result himself, a time difference 4 A w/c^2 (w the rotation rate), says it "agrees with the result of the Sagnac experiment", and reproduces Langevin's result that transported clocks measure the speed c. He does not claim SR gives a different number. His objection is to interpretation: with transported clocks, two clocks at one place read different times, which he calls "a physical absurdity" [read: page images, deep read of JOSA 28:296]. The textbook answer (3.4): SR gets the same first-order result from an inertial frame, so rotation does not decide between them. The arbiter keeps "Refuted by calculation" for the claim that rotation shows a fixed ether and that SR cannot handle it, and adds that the narrower question "does Ives's reading of the Sagnac effect differ measurably from SR's?" is Not testable as stated (same first-order number) [arbiter].

4.3 Ives's rebuilt theory and transported clocks (claim 3)

Ives's programme (1937-1951) was to derive the Lorentz transformations from classical ether physics plus conservation of energy and momentum, with distant clocks set by carrying clocks across, not by Einstein's light-signal definition [read: JOSA 27:263; JOSA 37:812-813; JOSA 43 "Genesis"]. It ran along three routes, all now read: (a) transported rods and clocks (1937); (b) conservation laws applied to light striking matter (1943-45); (c) an operational vocabulary of "rod-clock-quotients" (1948-51). (The 1937 papers speak of "observed velocity"; the term "rod-clock-quotient" is first defined in JOSA 38:879, 1948, not in the 1953 papers as an earlier version of this primer said [read: digests 1948, 1949; deep read 1949].)

Route (a), 1937. A clock carried at its self-measured speed q runs slow during the trip, so the one-way light speed it measures depends on q; his transformations "approximate to the Lorentz-Poincare formulation when q is small" [read: JOSA 43 "Genesis"], becoming Lorentz's when the clocks "are moved infinitely slowly" [read: JOSA 27:391]. Robertson, Ives's referee and critic, wrote: "Originally I looked for errors in Ives' deductions ... in each case his deductions were in fact valid", and the theory is "completely equivalent in substance" to SR [read: NAS memoir p.24].

What the 1937 derivations show, now read from the page images (JOSA 27:263 and 27:310) with a 40-digit numerical check [read; calc: QE deep read]. Ives's results depend only on the observed transport speeds of his clocks and rods, not on the laboratory's speed v through the ether, and reduce exactly to the Lorentz transformation as those speeds go to zero. For a finite transport speed q they agree exactly with what SR predicts for the same transport procedure. They differ from the Lorentz formulas used with Einstein-synchronized clocks, at first order in q: the one-way light speed changes by the fraction q/(2c), 1.7 x 10^-9 for a clock walked at 1 m/s and 5 x 10^-7 for one flown at 300 m/s. That is a choice of synchronization, not a different physical prediction, which is Robertson's verdict. Ives himself names no experiment that would separate his theory from SR, and concedes the ether's "elusiveness by any measurements of the sort we have been considering" [read: JOSA 27 p.271]. The papers carry several misprints and algebra slips (in Eqs. 14, 25, 33, 34, 38-40) that do not change his conclusions. The older summary that his formulas "approach but never coincide" with Lorentz's is accurate for the formulas, not for the predictions [arbiter].

Route (b), 1945: relativity's effects from fifty-year-old physics. "Derivation of the Lorentz Transformations" (Phil. Mag. 36:392, 1945) is the paper Ruderfer cites first, and Ives called it "logically the first of the series" [read: deep read, note 8]. Its aim: to derive the transformations "by imposing the laws of conservation of energy and of momentum on radiation processes as developed by Maxwell's methods", while "the space and time concepts of Newton and Maxwell are retained without alteration" [read: p.1]. The chain, step by step [read: page images; calc: deep read, SymPy]:

1. A pulse of light of energy U reflecting off a mirror pushes it (classical radiation pressure; Maxwell, Poynting, Abraham). Light of energy U carries momentum U/c and so a "mass equivalent" U/c^2 (a pre-1905 result, Poincare 1900 [memory: high]).
2. Treat a particle struck by light. If total "mass" (matter plus the light's U/c^2) and momentum are both conserved, the reflected light carries away less mass-equivalent than the incident light brought, so the particle's mass must grow. Doing this in small steps and integrating gives M = M0/sqrt(1 - v^2/c^2), "where M0 is the mass when the particle is stationary with respect to the wave transmitting medium". Ives then shows that his "conservation of mass" assumption is the same as conservation of energy.
3. Repeat the experiment on a platform moving at V through the ether. Requiring the conservation laws still to hold, he gets the relativistic Doppler factor sqrt((1 + V/c)/(1 - V/c)) and, as a by-product, Einstein's velocity-addition law w = (V + v)/(1 + vV/c^2), "imposed here by the conservation of energy and momentum".
4. Maxwell's field of an oscillating charge on the moving platform does not give that factor unless the clock rate (D1), lengths along the motion (D2) and lengths across it (D3) change. One equation links them: D3^4 D1^3/D2^2 = sqrt(1 - V^2/c^2). Two light clocks (along and across the motion) give D1 D2 = 1 - V^2/c^2 and D1 D3 = sqrt(1 - V^2/c^2). The unique solution is D1 = D2 = sqrt(1 - V^2/c^2), D3 = 1: clocks slow, rods shrink along the motion, nothing changes across it.

Ives's conclusion: "The fact that the Lorentz transformations with all their consequences are deducible from these classes the 'Special Principle of Relativity' as a superfluous hypothesis" [read: p.11]. In context "superfluous" means "not needed as a separate axiom", not "false". The deep reader and the arbiter found the chain correct in its algebra and free of any special-relativity formula put in by hand, but not a derivation from conservation laws alone. Three premises do the extra work: the inertia of energy (step 2); an unexplained step in which an extra term "must drop out" (step 3; a counterexample with a nonzero term satisfies both conservation laws exactly and gives a different final speed, 0.709 instead of 0.696 in units of c); and the assumption that every clock, in every orientation, slows alike (step 4), which is what Michelson-Morley and Kennedy-Thorndike establish. The relativity principle is not removed; it is moved into those premises. Ives names no experiment whose result would differ from SR's; in note 11 he calls aberration and the Sagnac and Michelson-Gale experiments "direct proofs" of motion through the medium, but SR predicts all three [read: deep read; arbiter]. The arbiter rates "the relativity principle is superfluous" Not testable as stated (and not shown in logic), and calls the 1945 route the most instructive of the three, because it shows how little of SR is extra once you accept that energy has inertia. The same "dynamical" way of teaching relativity, where rods shrink and clocks slow because of the forces inside them, was later defended by J. S. Bell (1976) [memory: high].

Route (c), 1948-51: rod-clock-quotients and one-way light speed. In his last papers Ives kept the word "velocity" for speeds relative to the ether and called whatever moving, shrunken rods and slowed clocks measure a "rod-clock-quotient". His charges: Einstein's statement that c was "firmly established by experiment" was invalid, because only the out-and-back speed of light had ever been measured; the constant in his own revised transformations "is not equal to c and should not be called the velocity of light"; and SR "leads to an internal inconsistency if clocks are admitted for distant time setting", so that the Lorentz transformations are "an approximation, owing their simplicity of form to the exclusion of clocks in the determination of epoch" (JOSA 39:757, 1949) [read: deep read 1949; digests 1948, 1950, 1951]. The 1949 deep read checked his equations with SymPy. They are, term for term, the Lorentz transformation written with clocks that each lag Einstein's time by k r', where r' is the distance the setting clock was carried and k = (sqrt(1 + q^2/c^2) - 1)/q, about q/(2c^2), for a clock carried at self-measured speed q. SR predicts exactly Ives's one-way light speed c/(1 - c k), about c + q/2, for clocks set this way, and it tends to c as q goes to zero. The out-and-back speed is c for every k. Ives knew the limit and accepted it as a fact, but rejected it because a clock carried at zero speed "could not be performed" [read: deep read 1949, p.4]. Sizes: a clock walked 10 m at 1 m/s lags by 5.6 x 10^-17 s; one flown 10,000 km at 250 m/s by 14 ns [calc: example.py Part 8]. He names no experiment that separates his transformations from SR; the 1950 and 1951 papers cite only Michelson-Morley and Ives-Stilwell, which SR predicts identically [read: deep read]. What survives is a recognised point: the one-way speed of light depends on a choice of how distant clocks are set (Reichenbach's convention, 2.6).

The clock paradox (a side argument). In "The aberration of clocks and the clock paradox" (JOSA 27:305, 1937) Ives states the paradox as a symmetric slowing: if only relative motion matters, each of two clocks should be slow relative to the other, "a logical inconsistency". He resolves it with the ether as reference: on reunion, the clock that is fast is the one "which has moved least with respect to the motion of their point of coincidence through the ether" [read: p.307-308, page images]. His Eq. (17) gives the textbook lag at leading order, (1/2) T q^2/c^2 for a round trip of duration T. He does not discuss the standard SR resolution, in which the travelling clock changes inertial frame at the turn-around, so the situation is not symmetric and the lag is the difference of the two clocks' proper times (the time each clock itself records along its path) [read: absence in pp.305-309]. The arbiter rates the claim that the paradox shows SR to be logically contradictory as Refuted by calculation [arbiter; the proper-time argument is memory: high, see Taylor and Wheeler]. The US Naval Research Laboratory's 1959 bibliography of the clock paradox lists this paper as resolving it "through motion relative to the ether" [web: https://en.wikisource.org/wiki/The_clock_problem_(clock_paradox)_in_relativity].

To see how small the transport error is: carry a clock 1 km at 1 m/s. It runs slow by the fraction q^2/(2c^2) = 5.6 x 10^-18 for d/q = 1000 s, so it arrives 5.6 x 10^-15 s behind; at 0.5 m/s the lag halves [calc, this primer]. Because the lag falls in proportion to q, one can carry clocks at two speeds and extrapolate to zero; the "never" is an idealization, as frictionless planes are, not a contradiction. That is the reviewers' and arbiter's ground for calling the internal-contradiction charge refuted. P. W. Bridgman, the founder of operationalism (the view that a physical concept means no more than the operations used to measure it), was sympathetic to Ives and made the opposite objection in unpublished notes of 1959: Ives's view that absolute simultaneity was "real but indeterminable" was "a complete negation of the operational attitude which [Ives] correctly adopt[ed] in most other situations" [read: Lalli 2014 p.363; Bridgman's memo not read]. Ives saw himself as a "natural philosopher" seeking how nature works, against the attitude that "the sole object of physical theory is to predict the results of experiment" (Ives 1940, quoted by Lalli 2014 p.361) [read]; his case for the ether was a case about explanation, not prediction. A. I. Miller judged that the theory "was never developed to the point where it could be seriously considered as an alternative" (Miller's characterization, quoted by Giuliani p.8).

4.4 Gravitation (claim 4): the Schwarzschild solution as forces in an ether

Correction to the earlier version of this primer. It said that only the 1948 abstract had been read, that Ives's extra velocity terms had to "supply the rest" of Mercury's advance, and that "one matched number does not test a force law with that much freedom". It also said light bending and red shift were "not addressed in anything read", and gave Ives's low-speed mass as m0 (1 + v^2/(4c^2)). All of that was wrong. It was an inference from an abstract, and the 1/4 was an arithmetic slip by a reviewer. The full papers (1939, 1947, 1948) show that nothing was fitted: Ives's gravitation is GR's Schwarzschild solution, rederived exactly and described as forces in flat space [read: deep reads 1939, 1947, 1948; arbiter, "Changes after QE"].

The one postulate. Ives's starting point, in 1939 for light and in 1948 for mass: a body at rest in a gravitational field "assumes the dimensions, clock rate, and mass of a body at the same point in a Newtonian field, moving with the velocity acquired in falling from infinity under the Newtonian law of attraction" [read: JOSA 38:416, page image]. That speed is the escape speed V, with V^2 = 2GM/r. So a clock at rest at distance r runs slow by sqrt(1 - V^2/c^2) = sqrt(y), a rod pointing at the mass shrinks by sqrt(y), a rod across the radius is unchanged, and the mass grows by 1/sqrt(y), with y = 1 - 2GM/(r c^2) exactly as in section 2.10. In a footnote he says the falling speed is only bookkeeping: "the primarily significant quantity is the corresponding acceleration, which is equivalent to the upward push experienced in a true gravitational field" [read: 1948 fn.6]. Notation warning: Ives writes this y as "gamma"; it is not the special-relativity factor gamma of section 2.3.

1939, light (JOSA 29:183). Ives adds that an interferometer which reads null outside a field still reads null inside it (the gravitational version of Michelson-Morley), and that a moving interferometer shrinks along its motion relative to the local light speed. From these he gets light speeds through the ether of c y along the radius and c sqrt(y) across it, measured on ideal "stationary" rods and clocks that are unaffected by motion or field, and then:

ds^2 = c^2 y dT^2 - R^2 dtheta^2 - dR^2/y,

which he calls "the Schwarzschild formula of general relativity, ordinarily derived by means of the tensor calculus" [read: p.4]. The deep reader checked every step with SymPy: the result is exact Schwarzschild, not an approximation, for a small interferometer moving in one plane [calc]. Ives reads ds as the apparatus's own arm length (equivalently its own clock time), a concrete answer to Einstein's remark, quoted by Levi-Civita, that he knew no physical meaning for ds [read: p.5, fn.5]. Predictions: he states in words that clocks in a field run slow ("a 'red shift'") and that light passing a mass bends; he gives no numbers. His light-speed field gives the full GR deflection, 1.7512 arcsec at the Sun's edge; dropping the radial shrinking of rods would give only half, 0.8756 [calc: 1939 deep read; example.py Part 7]. He tests his own ether against the eclipse result: an ether with the same light speed in every direction would make clocks in the Sun run slow, "but stars seen near the sun would not be displaced in apparent position; the latter conclusion being in conflict with observation" [read: p.4]. So the one choice he makes between ether models is made by experiment, and the ether that survives is the one that mirrors GR. His own limits: the formula is "of purely optical significance"; "There is in it no non-Euclidean geometry, nor new law of gravitation. It calls for anisotropy of the ether due to the presence of a center of gravitational attraction, but makes no suggestion as to how this anisotropy affects other than optical phenomena" [read: pp.4-5]. "Anisotropy" means the direction-dependent light speeds above. With real rods and clocks, which shrink and slow, "the measured velocity in either direction ... is c" [read: p.2]. The one door he leaves ajar: if the null reading did not hold for large apparatus, "a sufficiently large and sensitive interferometer could be used to detect motion in a gravitational field"; he thought it "probable" that it does hold, which would mean no detection [read: p.4].

1947, the transverse force (Phys. Rev. 72:229). G. D. Birkhoff's flat-space gravity (1943-44) wrote its equations with the planet's own clock time and four-dimensional ("Minkowski") forces. Ives rewrote them with ordinary time and ordinary force (rate of change of momentum, with the moving mass m0/sqrt(1 - v^2/c^2)). Newton's pull on that moving mass gives only a fraction of Mercury's advance; Birkhoff's equations contain one more piece, which Ives states as a theorem: "A particle in motion in a gravitational field experiences an additional force, normal to the direction of motion, of value v^2/c^2 times the component of the gravitational force normal to the direction of motion" [read: p.3]. For Mercury v^2/c^2 is 2.5 x 10^-8 [calc: example.py Part 7]: tiny, but always in the same sense, so it adds up over centuries. Because it acts at right angles to the motion it does no work: the energy equation is unchanged, and Ives notes that "an infinite number of such additional terms could be set down" that would leave it unchanged [read: p.3]. He does not endorse Birkhoff's theory as physics: the force entered through "his choice for gravity of the third term of a formal expansion", and "an independent physical derivation of these transverse forces would be welcome" [read: p.4]. His one hint at an origin is an analogy: the force is "similar to the 'fundamental law' proposed in a posthumous note by Gauss" for moving charges, and "the occurrence of c^2 stems from the idea of the attraction being transmitted with the speed of light" [read: p.4]. That is a resemblance he points out, not a derivation.

1948, the orbit (JOSA 38:413). Ives extends the postulate from clocks and rods to mass. A body moving in the field has gravitational mass

m_g = m0 / (y - rdot^2/(c^2 y) - r^2 thetadot^2/c^2)^(1/2)

(rdot the radial speed, thetadot the angular speed, m0 the mass far from any field) [read: page image p.1]. The bracket is the rate of the planet's own clock compared with absolute time, so mass grows exactly as the clock slows. At low speed and weak field m_g is about m0 (1 + GM/(r c^2) + v^2/(2c^2)): the speed part is the ordinary special-relativity mass increase, and the new part depends on position [calc: 1948 deep read]. With force defined Newton's way, as rate of change of momentum, two choices (no sideways force on mass m_g, so its angular momentum is constant; and a split of the leftover force modelled on the 1947 paper) give the orbit equation

d^2u/dtheta^2 + u (1 - 6 G^2 M^2 b^2/(c^2 h^2)) = K-bar,

with u = 1/r, h the angular momentum per unit mass, b a constant within 10^-8 of 1, K-bar a constant [read: page image p.3]. By section 2.11 the orbit turns by 6 pi GM/(c^2 a (1 - e^2)) per orbit: 42.98 arcsec per century for Mercury, GR's value. Ives then quotes the comparison himself: Sommerfeld's special-relativity mass alone gives the same equation with 1 in place of 6, "an elliptic orbit with one sixth the advance of perihelion that has been observed for the planet Mercury. Consequently Eq. (25) gives the correct advance of perihelion" [read: pp.3-4; calc: example.py Part 7, including a numerical integration of the orbit equation]. And he says where it comes from: his starting relation "is a relation also obtained in the general relativity treatment", the value of y is the same, and "The force equations are actually implicit in the general relativity solution, which is commonly claimed to negate the concept of force" [read: page image p.4]. In the same paper he shows that Birkhoff's sideways force and his own position-dependent mass factor are the same thing written two ways: "the equivalence of a multiplying factor [sqrt(y)] in the denominator of the local mass to a force at right angles to the motion" [read: page image p.2]. His final footnote concedes that GR gives "no ground for favoring" his pair of force equations over Birkhoff's "simple and symmetrical" pair; the two give identical orbits [read: fn.9; calc].

Where Ives's result rests on a choice (the same rigour as for his critics). The arbiter and the Mathematician list four points [arbiter, claim 4; calc: Mathematician]:

1. The exact form of y, with no (GM/(r c^2))^2 term, is the real input. If y were 1 - 2m/r + kappa m^2/r^2 (m = GM/c^2), the perihelion advance would be (6 - kappa)/6 of GR's. Ives says such terms would enter only at order 1/c^4 and may be dropped; for forces that is not so. He states the exactness openly and it coincides with GR, so it is an input, not a fudge. "No free parameter" holds given kappa = 0. In PPN language (3.5), the postulate builds in gamma_PPN = beta_PPN = 1.
2. His "note added in proof" says his force equation is "also exact". That holds for the three relations that fix the orbit (y, constant angular momentum, constant energy), which are exactly Schwarzschild's; the printed radial force equation is correct only to first order in 1/c^2, and differs from the exact one by terms that give no perihelion advance (about 2.5 parts in 10^8 for Mercury, absorbed in the measured GM of the Sun) [calc: 1948 deep read].
3. The zero sideways force and the split of the leftover force into a pair are his choices; he concedes it (fn.9).
4. Eddington (1917, 1923) and H. B. Phillips (1922) had given the same relations; Ives cites them. It is a re-derivation, not a prediction made in advance.

Verdicts (arbiter, claim 4). Predictions for one static central mass (Mercury's 43 arcsec per century, light bending 1.75 arcsec, red shift): Established, because they are GR's own numbers, derived by Ives without fitting. The ether-and-forces reading, and the transverse force as a separate physical force: Not testable as stated (no measurable difference; Ives concedes it). As a complete, independent theory (many bodies, radiation, binary pulsars, gravitational waves, Shapiro delay as his own prediction), and the large-interferometer conjecture and the "also exact" claim: Never properly tested (never worked out; not dismissed). The earlier belief that the terms were fitted to 43: Refuted by calculation.

Reception. The papers were refereed and printed in Phys. Rev. and JOSA. H. P. Robertson's referee report on the 1947 paper called its "Lorentzian" framing "a bit (ca. 40 yrs) out of date", and it was published [web: https://pmc.ncbi.nlm.nih.gov/articles/PMC4856100/]. After 1948 the theory is barely cited except by Ruderfer and the neo-Lorentzians. Two readings are on file, both kept: Ruderfer's, that a useful and transparent derivation was overlooked ("the continued neglect of Ives' gravitational theory is unwarranted"); and the Contrarian reviewer's, that it adds no prediction and its author says so, so there was nothing to test or cite: neglect by irrelevance, not suppression [arbiter]. Citation indices for Phys. Rev. 72:229 and JOSA 38:413 would show which. What this means for the owner's question is in section 4.10.

4.5 E = mc^2 (claim 5)

Ives (1952) did not doubt E = mc^2. He credited a valid derivation to Poincare's radiation momentum (1900) plus the relativity principle, and to Pauli (1920) [read: JOSA 42:540-542]. His own derivation is correct: the two pulses' momenta in the moving frame differ by L v gamma / c^2, the body's momentum gamma m v must drop by the same amount at unchanged velocity, so m - m' = L/c^2 [calc: Mathematician]. (Poincare's own illustration, checked by the Physicist: 3 x 10^6 J of light carries momentum 0.01 kg m/s, enough to push a 1 kg apparatus back at 1 cm/s.)

His target was Einstein's 1905 step "H - E differs from K only by a constant".

The check: the factor L/((m - m')c^2) appears only because Ives added the relativistic particle formula, which Einstein deliberately did not use. Einstein's chain runs from energy conservation to L (gamma - 1) to L beta^2/2 to L/c^2 without ever using the result, so it is not circular (Stachel and Torretti 1982; Ohanian 2008; the Mathematician's calculation). Ives's Appendix remark that subtracting the two observers' equations gives only 0 = 0 is also wrong: it gives L (gamma - 1) [calc: Mathematician]. What survives is Planck's 1907 point, which Ives quoted: the comparison with (1/2) m v^2 assumes the body behaves like a simple particle, valid only "as a first approximation". Ohanian calls Planck's objection "perfectly correct" and gives a counterexample (a gas in a massless box) to show the 1905 argument is general only for slow internal motions [read: Ohanian deep read]. Jammer (1961), Arzelies (1966) and Miller (1981) sided with Ives (per Ohanian). In 1953, answering Riseman and Young, Ives narrowed his charge: his breakdown was algebraic, with "no commitment" to its physical meaning, and "something must be added ... from valid physical considerations, not by assumption" [read: JOSA 43:619]. A cross-link: Ives's own 1943-45 derivations (section 4.3, route b) take the mass equivalent E/c^2 of radiation as an input. That is a different starting point, not a contradiction of his 1952 charge [arbiter, claim 5].

4.6 "Atoms are not clocks" (claim 6, the secondary authors', not Ives's)

Bonizzoni and Giuliani (2000) and Giuliani (2015) point out that the IS formula also follows from conservation of energy and momentum when a moving atom emits a light quantum (Schroedinger 1922; Davisson 1938), with no talk of clocks; Giuliani holds that in quantum mechanics "atoms are not clocks" [read: Giuliani pp.4-6]. The two derivations give the same numbers; they differ only by a recoil term Delta E/(2 E1), with Delta E = 2.55 eV the H-beta photon energy and E1 = 938 MeV the atom's rest energy, about 1.4 x 10^-9 [calc: Mathematician]. A. I. Miller held the opposite view: IS is "the only positive proof" of time dilation [read: Bonizzoni-Giuliani p.23]. Giuliani does not endorse an ether.

4.7 The record around the work (kept whatever the verdicts)

• Reception. Ives's own account, in a letter of 24 October 1950, of a hostile reception at Princeton in 1938, with Pauli reporting that his "work didn't amount to anything": documented in one published source (Hazelett and Turner 1979, p.90, quoted by Bonizzoni and Giuliani); Ives is a party; no second source found yet. Beside it: Einstein's public praise (NYT, 27 April 1938), Ives's NAS membership from 1933 and his presidency of the Optical Society of America (1924-25). These concern different audiences and do not conflict.
• Robertson's stake. The memoir's verdict on Ives's relativity work is Robertson's; Robertson had refereed Ives's papers and disagreed with him [web: Lalli 2016, PMC4856100]. His technical finding (equivalence) is shared by Jones, Bridgman and Mansouri-Sexl, so it does not rest on his authority. The memoirists add: "So far as we know, Ives to the end remained faithful to his own interpretation" [read: memoir p.25].
• Ives's attitude. In a letter of 5 October 1951 to E. E. Butterfield (LoC MSS27508, Box 13), as the historian R. Lalli quotes it, Ives wrote of championing "the classical English school of physical thought ... against the paradox of the Semitic school". Lalli writes of "the implicit anti-Semitism that this sentence seems to imply", which he discusses in a longer 2013 paper (not read here) [read: Lalli 2014 p.361]. Only this one sentence of the letter has been seen by anyone in this review, through Lalli. It bears on Ives's motives and alliances, not on his equations. The phrases "progressive marginalization" and "hidden network of allies" are from the abstract of Lalli 2013, not from the 2014 chapter [web: abstract, research/2026-10-07-pure-mpg.md].
• The Butterfield letters. The Library of Congress finding aid for the Ives papers says letters from E. E. Butterfield in the late 1940s and early 1950s "describe the dissatisfaction in certain scientific circles with Einstein's theories. Einstein and his followers are castigated as left-wing radicals" (the archive's summary of Butterfield's letters, not Ives's words) [web: https://findingaids.loc.gov/repositories/19/resources/4117]. The box-level contents have not been examined.
• Later use. The Hazelett and Turner volume (1977/1979, revised 2005) preserved much of Ives's later correspondence; its editor R. Hazelett had a commercial profile (Hazelett Strip-Casting, per Martin Gardner, a critic), and Giuliani calls its preface "grossly anti-relativist" (his characterization). Robertson already worried in 1956 that Ives's work was "seized upon" as overthrowing relativity [read: memoir p.25]. Search results show that it was: the book or Ives is cited in Hans Nieper's free-energy book Revolution in Technik, Medizin, Gesellschaft (a direct link into the literature this archive collects), in the geocentrist book "Galileo Was Wrong", and by the Chinese Academy of Sciences "Relativity Criticism Group" during the Cultural Revolution (per a 2019 study) [web: search-result snippets only, pages not opened, research/2026-10-07-google-search.md]. This shows how Ives's work was used, not what he intended.
• The neo-Lorentzian line (related work). Others kept the Lorentz ether reading alive after Ives: G. Builder (Australian Journal of Physics, 1957-58), who extended Ives's 1948 one-way light-speed argument [read: Preikschat thesis p.53]; M. Ruderfer, who proposed a Mossbauer-effect ether-drift experiment in 1960 (Phys. Rev. Lett. 5) and later built a "neutrino structure of the ether" (1975) on Ives's gravitation papers [web: research/2026-10-07-semantic-scholar.md]; S. Prokhovnik; and the later dissenters H. Dingle and L. Janossy [web: research notes, sites.md]. Ruderfer is the link to Moray: his appendix in Moray's book is what brings Ives into this archive. None of this work changes a verdict here; it is the record of who took up the idea.
• Preikschat's rotor experiment. E. Preikschat's University of Birmingham PhD thesis (October 1968; the "1964" in the file name is the start of its copyright span) carried out Ruderfer's Mossbauer rotor experiment and set a limit of (2.0 +/- 5.2) cm/s on an ether drift [read: thesis pp.1, 54, 158]. Preikschat cites Ives 8 times (an earlier note's "27 times" was a counting error). He summarises Ives 1948 (JOSA 38:879): the one-way speed of light depends on how clocks are synchronized, not on the velocity through the ether, so SR and the Lorentz-FitzGerald contraction theory are locally equivalent. He also says, following Ruderfer (1961), that both theories predict a null in his own experiment [read: p.54]. So his limit is a null for the ether and for SR alike. The thesis is the experimenter's own account and calls the result "the most sensitive test of the theory" (his characterization).
• Dirac 1951. P. A. M. Dirac, a Nobel laureate, asked "Is there an aether?" (Nature 168:906, 1951), arguing that quantum mechanics might allow one [memory: high]. Ives's 1953 "Genesis" paper answers him [read: JOSA 43 "Genesis"; Dirac's paper not read]. It is context for claim 2: in 1951 the question was not closed for everyone.
• A government record of usage. The US Naval Research Laboratory's annotated bibliography on the clock paradox (M. Benton, May 1959) lists Ives and Stilwell 1938 ("Verifies the dependence of the passage of time upon motion") and 1941 ("Direct experimental verification of retardation using atomic clocks") as the experimental evidence, and Ives 1937 as resolving the paradox "through motion relative to the ether" [web: https://en.wikisource.org/wiki/The_clock_problem_(clock_paradox)_in_relativity].
• A dissenting repeat, now read from its table. L. A. Pobedonostsev (V. G. Khlopin Radium Institute, Leningrad) and P. F. Parshin, "New results in Ives experiment", SPIE Vol. 1121, Interferometry '89, pp.36-41 (1989) [read: page images]. (The earlier "1991-95" was the date range of other papers by the same authors.) They accelerated H2+ ions to 150-2,000 keV, viewed the H-alpha line (6563 A) at 77 and 257 degrees to the beam, and photographed it with a grating spectrograph. Their table: the observed second-order shift is 0.17 to 0.60 of the SR value at 150-300 keV (the "more than twice" deficit holds for 9 of the 10 low-energy points) and 0.9 to 1.1 of it at 1.5-2.0 MeV. In absolute terms the low-energy shortfall is 0.31-0.52 A [read: p.4]. Their only stated error is 0.04 A per line; there is no systematic-error budget. The arbiter's weighing, from the table [calc: deep reader and arbiter]: (1) the deficit jumps around from point to point (0.60, 0.69, 0.82, then 0.40...) by 0.1-0.4 A, several times the stated error, where a real effect of the kind they propose would vary smoothly with energy; (2) the two viewing directions are separate optical paths, one through a flexible fibre (Ives and Stilwell used one line of sight and a mirror precisely to avoid this), and an error of 0.5 degree from exactly opposite directions would shift the result by about 0.4 A at beta = 0.015, the size of the deficit; this shows a possible cause of the right size, not that it happened; (3) the classical model they propose (Marinov 1972) predicts about +5 percent at their angle, not a 40-80 percent deficit, and the authors themselves say "other factors unknown before" may act. No replication or rebuttal has been found. Claim 1 stays Established on the storage-ring tests at parts per billion. The dissent stays in the record; silence is not refutation, and the deciding record is their full Russian account (Zh. Tekh. Fiz. 1989, issue 3, pp.84-99) with its raw data.
• A reinterpretation of the 1938 data (Faraj). A. A. Faraj, "The Ives-Stilwell Experiment" (General Science Journal, after 2009), says Ives and Stilwell measured "only a slight asymmetry in the observed longitudinal Doppler effect for equal positive and negative velocities", not a clock effect [read: Faraj pp.2-3]. He does not derive this; he takes it from D. Y. Gezari (2009) and W. Kantor (1971). Faraj is an advocate of the emission (ballistic) theory of light. Weighing [calc: deep reader, from Faraj's own equations]: his step that makes the emission-theory and Larmor-Lorentz predictions "identical" multiplies a shift by a ratio of averages, which is invalid; corrected, his own equations give an emission-theory centre shift of lambda0 beta^2, twice the observed value (about 0.040 A where 0.0185 A was observed at 7,780 V). The asymmetry reading is not Ives's own: Ives and Stilwell read the centre shift as the clock effect. Ives did publish a 1938 paper titled "Unsymmetrical Doppler Effect in Hydrogen Canal Rays" (Rev. Sci. Instr. 9:283) [read: NAS memoir bibliography], which Faraj does not cite and nobody here has read; what it reports is an open question. Faraj's claim does not change claim 1 or 2B.
• Where the record goes dark. (a) No further canal-ray work by Ives after Part II (1941): settled in his mind; war work at Bell Labs [memory: low; nothing in the files states his wartime work]; or Stilwell moved on. The earlier reading that the higher voltages were out of reach is weakened: Part II reached 43 kV and met the goal Ives had set. (b) The Bell Laboratories Record says nothing on the experiment in its 1938 issues (text search) yet praises it in 1947. (c) The gravitation theory is barely cited after 1948 except by Ruderfer and the neo-Lorentzians, although it was published in Phys. Rev. and JOSA. Explanations on file: it adds no prediction beyond GR, so there was nothing to test or cite; Robertson's "ca. 40 yrs out of date"; GR's success after 1960; or Ives's reputation being tied to an ether position. Against suppression: it was refereed and printed (section 4.4). (d) The bibliography in the 1956 NAS memoir stops at 1951. It omits "Extrapolation from the Michelson-Morley experiment" (JOSA 40:185, 1950), the 1952 mass-energy paper, Proc. Roy. Dublin Soc. 26:9 (1952) and the 1953 papers [read: NAS memoir pp.43-44, checked by QE]. So the absence of an E = mc^2 paper from that list says nothing about the paper. Whether Robertson, who wrote the memoir's relativity assessment, had any hand in the list is not in the record. Deciding records: Bell Labs project files, the LoC container list for MSS27508, citation indices for Phys. Rev. 72:229 and JOSA 38:413.
• Dates and places. Death given as 13 November 1953 (NAS memoir, Wikipedia), 15 November (Optica) or 3 November (LoC); the place as the Century Club of New York, where he was stricken with a heart attack (NAS memoir pp.28-29), or Upper Montclair, New Jersey (Wikipedia). Birth 31 July (LoC) or 21 July (Chappell wiki) 1882. His television demonstration for Herbert Hoover is dated 7 April 1927 (NAS, Wikipedia) or 27 April 1927 (Optica); Wikipedia's "185-line" picture conflicts with the 50 scanning holes (NAS) and 50 lines (Optica) [read: all from the folder's biographies]. Unresolved, immaterial to the physics.

4.8 Ives's standing-wave photoelectric work (context for the Moray link, not a claim)

This is mainstream, uncontested physics, so it gets no verdict. It is here because Ives himself called it his most important work, and because it is his own work on two of Moray's central interests, standing waves and the conversion of light into electric current (follow-up Q10). Refresher: section 2.9.

• The puzzle. Thin films of the alkali metals (lithium, sodium, potassium, rubidium, caesium) give off photoelectrons under visible light. With polarized light at an angle (often 60 degrees), the emission can be "twenty or more times as great" when the light's electric field lies in the plane of incidence than when it is perpendicular to it. This was called the "selective" effect, the other the "normal" effect (terms Ives deprecated). It had been known since 1897 and "had remained a mystery" [read: NAS memoir pp.19-20]. Ives found that the ratio of the two passed through a maximum as a film thickened, and in sodium-potassium alloys showed sharp peaks (ratio 14 at 18 percent sodium, 16 at 50-50, 31 at about 90 percent sodium) [read: pp.20-21].
• The idea. Ives traced it to his 1908 doctoral thesis on Lippmann colour photography, where standing light waves imprint layers in a film. More than twenty years later he guessed that the curious photo-effects in his thin films "might be due to the standing-wave pattern formed in the film by interference between the incident beam and the beam reflected from the specular metallic surface on which the film had been deposited". To test it he re-measured the optical constants of sodium, potassium, rubidium and caesium. The result, in the memoirists' words: "the photoelectric emission, in a wide variety of cases, was proportional to the intensity of the standing waves in the alkali-metal film. Thus was resolved one of the major problems of photoelectricity!" [read: pp.21-22]. The memoir gives no numbers for the fit. Ives's own word: "I regard my work on the photoelectric effect as probably my most important contribution to science" [read: p.19].
• Related findings. As a film's thickness changes, its long-wave limit moves out to the resonance wavelength of the free atom and back, shown for all five alkali metals [read: p.22]. In 1933, with T. C. Fry, Ives repeated Otto Wiener's 1890 standing-wave experiment using a photoelectric probe surface (a quartz wedge) in place of a photographic film (JOSA 23:73) [read: digest]. His 1951 Rumford Medal lecture, "Adventures with Standing Light Waves" (Proc. Am. Acad. Arts Sci. 81:1-32), surveys this line of work [read: digest; photon passage read in the extracted text, section 4.9].
• Ives's own numbers (now in hand, digest level). Selective-to-normal emission ratios of 15-25, against at most about 4 that differences in absorption could explain (ApJ 60:209, 1924); a ratio of 70 at 70 degrees for sodium-potassium alloy, from Elster and Geitel (ApJ 60:231, 1924); photoemission peaking 5-10 times above its room-temperature value near 650 K (ApJ 64:128, 1926); and the commercial gas-filled potassium cells used for sending pictures over telephone lines (Bell System Tech. J. 5:320, 1926) [read: digests, QE round 2]. Ives's own judgement grew stronger with time. In 1933 he expected "only positional and qualitative agreement" between standing-wave intensity and emission and called the result "very satisfactory"; in 1951 the theory is "confirmed to fine detail" [read: digests]. The memoirists' "This 'hunch' was right" is their summary; Ives's 1933 wording is more guarded.
• What it does and does not say for Moray's interests. It shows that a standing-wave pattern of light inside a thin metal film sets how strongly the film emits electrons. The memoir gives no energy-conversion efficiency and nothing about electrical output beyond the remark that photocurrent is instantaneous and "rigorously proportional to the intensity of the light" (useful for television) [read: p.19]. His own papers give no efficiency either: they are about where in a film the light is strong, not about extracting power. Some of his 1930s papers (for example "Correlation of Optical Properties and Photoelectric Emission in Thin Films of Alkali Metals", with H. B. Briggs, JOSA 28:330, 1938) are listed in the memoir bibliography but are not in the folder.

4.9 Ives's separate physical claims, and a picture of what a Lorentz ether means (claim 7)

Most of Ives's work is a different explanation of results relativity already gives. A few items go further, and they are kept here whatever the verdicts. Each is marked "different prediction" or "different explanation".

The ripple-tank ether (Ives and Stilwell, JOSA 31:14, 1941; 32:25, 1942): the clearest picture in the record. This is the best way to see what Ives meant by a Lorentz ether, because here the "ether" is real and visible. Air jets, interrupted 30 times a second, make capillary ripples on a pool of mercury; the waves travel at c = 19.20 cm/s relative to the mercury. The jets and camera ride on a lathe bed, so the sources can move through the medium at v = 11.28 cm/s, v/c = 0.585, a speed at which "relativistic" factors are large (gamma = 1.23) [read: JOSA 32:25, extracted text; calc: example.py Part 9]. From the photographs, "on the assumption of the invariance of the phenomena with motion", they derive "the Fitzgerald contraction, the Larmor-Lorentz change of clock rate, and the Fresnel convection coefficient" [read: JOSA 31:14 p.1]: a pattern made by moving sources looks just like the stationary pattern if the source spacing is shrunk by the FitzGerald factor and the source periods are stretched by the Larmor-Lorentz factor; Fresnel drag and aberration appear too. Think of creatures built of ripples, whose rulers and clocks were themselves wave patterns: they could never detect their motion through the mercury, though an outsider can see it plainly. That is Lorentz's ether in one picture. The analogy is imperfect in a telling way: one measured wavelength ratio is 0.852 where the ideal medium gives (1 - v^2/c^2) = 0.658, a 30 percent miss that the authors put down to dispersion (ripple speed depends on wavelength), without quantifying it [read: JOSA 32:25; calc]. Mathematically, the result is the covariance of a non-dispersive wave equation under the Lorentz transformation built with that medium's wave speed [arbiter]. A demonstration, not a test of light. Verdict: Established as a classical-wave analogy; not a test of the ether for light.

The photon "will go the way of the caloric" (1951 Rumford lecture). A different prediction. "I venture to predict that this will be done, and that the photon will go the way of the 'caloric' that Rumford demolished", after conceding "the difficulty of arriving at an explanation of all optical phenomena, such for instance as the Compton effect" [read: extracted text of the 1951 lecture, via QE and two reviewers]. (Caloric was the fluid once thought to be heat, abandoned after Rumford's cannon-boring experiments.) His grounds: in a standing wave, photons would have to exist and not exist alternately at the antinodes and nodes; Lorentz's 1910 coherence objection; Poincare's view that the quantum belongs to the atom, not to the light; and bipartition-angle data of Beck and Sommerfeld (not examined here). Weighing: the standing-wave point is sound but does not discriminate, because quantum theory also predicts that a single photon in a standing-wave mode is detected with probability proportional to the wave's intensity, exactly what Ives measured [arbiter; memory: high]. In 1951 his view was held by serious physicists, and the photoelectric and Compton effects have semiclassical treatments (Lamb and Scully, 1969 [memory: medium]). What later experiments contradict is a purely classical light field: Grangier, Roger and Aspect (1986) found fewer coincidences behind a beam splitter than any classical wave allows, by 13 standard deviations [web: https://courses.physics.illinois.edu/phys513/sp2019/reading/week1/GrangierSinglePhoton1986.pdf, search summary via the arbiter]. Ives could not have known it. Verdict: Tested, not supported. His partial point, that waves explain more than the particle picture suggests, is mainstream-compatible. It bears on Moray, who wrote on "radiant energy".

Radiation pressure on a moving absorber (JOSA 32:32, 1942). A different explanation (a definition), not a different prediction. Ives finds the pressure on a perfect absorber moving at v toward a source to be P = E_a (c + v)/(c - v), and says Lorentz's P = E_i and Poynting and Abraham's P = E_i (1 + v/c) are wrong (E_i and E_a are energy densities; the OCR leaves E_a's exact definition unclear) [read: digest; extracted text]. Two reviewers and the arbiter worked it: the force needed to hold the absorber at constant speed, including the momentum carried by its growing mass, comes out as u(1 + b)/(1 - b) with b = v/c and u the incident energy density, which is Ives's formula and also the plane-wave energy density in the absorber's own frame [calc: arbiter, SymPy]. Poynting's u(1 + b) is the incident momentum rate alone. So Ives is right for the quantity he names, and the older values are a different quantity rather than wrong. Verdicts: the formula Established; "earlier values are wrong" Not testable as stated.

A spinning disk "dishes" (JOSA 29:472, 1939). A different prediction in a narrow sense. Ives argues that the "twist" Wood and Hackett saw in a double toothed-wheel (Fizeau) experiment follows from FitzGerald contraction, and that a rotating disk, whose rim contracts while its radius does not (the Ehrenfest paradox), bends out of its plane like a saw blade, with a paraboloidal profile at small spin rates [read: extracted text, via QE]. Mainstream: the Ehrenfest problem is a matter of elastic stresses, since no real body can be spun up while keeping every part rigid. The Physicist's size check: a 10 cm disk at 100 revolutions per second has rim speed v/c = 2.1 x 10^-7, a dish depth of about 18 nm and a contraction strain of about 2 x 10^-14, against an ordinary centrifugal strain of about 6 x 10^-5 [calc: Physicist, not re-run]. No experiment is on record. Verdict: Never properly tested (and far below the classical stress background).

Two more, in short. The 1948-51 "rod-clock-quotient" statements (section 4.3, route c): a different explanation, Not testable as stated. The 1939 large-interferometer conjecture (section 4.4): Never properly tested. Aberration of starlight as his "strongest evidence" for the ether (1937), evidence by "sheer weight of enormous probability", "not metric": Not testable as stated, since SR predicts aberration too [read: JOSA 27:263 p.10].

4.10 Why Ives matters to Moray, and what a Lorentz ether does and does not add

This section answers the owner's two questions directly. Everything in it is drawn from sections 4.2-4.9 and from the Moray book itself.

How Ives gets into the Moray story. No Ives paper mentions Moray [read: all 31 papers, digests and deep reads]. The link is M. Ruderfer (Dimensions, Inc., Hempstead, New York), whose "Neutrino Structure of the Ether" (Lettere al Nuovo Cimento 13:1, 1975) is reprinted "with permission" as Appendix VI of Moray's The Sea of Energy in Which the Earth Floats, 5th edition, printed pp.271-275 [read: review/Morray-TH/_text, Sea of Energy 5th ed.]. The book's own text points the reader there when it discusses "the modern hypothesis of the Neutrino sea" and suggests that J. A. Wheeler "and Henry Moray are talking about the same thing" [read: same file, printed pp.202-203]. Ruderfer's argument runs in four steps, in his words:

1. An ether is still allowed. After quoting Pauli (an ether "does not possess any mechanical properties"), Ruderfer says "the widespread rejection of an ether applies to a Galilean ether, but not to a Lorentz-invariant ether since its description of observation is necessarily identical to that of relativity" [read: p.271].
2. Ives is the proof. "The most direct verification of the validity of a Lorentz ether, and one which is independent of relativity, is found in the theoretical works of IVES. Building on the earlier theories of FITZGERALD, LORENTZ and LARMOR, he produced a classical derivation of the Lorentz transformations (5) [Phil. Mag. 1945], showed the consistency of the Lorentz ether with experiment (6) [JOSA 1937-1952] and extended Lorentz-ether theory to gravitational phenomena (7) [JOSA 1939, 1948] by a classical derivation of the Schwarzschild metric, hence to an identical explanation of the three famous tests of relativity. He further showed (8) [Phys. Rev. 1947] that the gravitational equivalence of the ether and relativity theories results from the proper correction of Newtonian gravitation, which has an infinite speed of propagation, for propagation at the speed of light. As a result, any Lorentz-ether theory of gravitation which provides the static Newtonian gravitational force is necessarily equivalent observationally to general relativity (9)." Note (9): "The continued neglect of Ives' gravitational theory is unwarranted" [read: pp.271-272].
3. So the ether has properties worth studying, and they are energy. "The admissibility of the Lorentz ether focuses attention on its properties." He defines the ether as "the totality of all the presently unobservable forms of energy that may exist in the microcosm", and proposes that a "vast sea of low-energy neutrinos (and antineutrinos)" is its main part: "the total unobservable energy in the neutrino sea may far exceed the total energy contained in matter, i.e. the vacuum is then a plenum rather than a void", and "since neutrinos are restricted to speed c, the neutrino sea is necessarily Lorentz invariant" [read: p.272].
4. Gravity, inertia and an energy source from the sea. He proposes a push theory of gravity after "the 200-year-old concept of LESAGE": a mass that absorbs a little of the neutrino flux from all sides is pushed toward other masses by the shadow each casts, giving an inverse-square force; "Correction for the finite velocity of neutrinos after IVES, as discussed above, provides the observational equivalent to the general-relativistic description." He suggests random fluctuations in the flux might explain 1/f electrical noise, play a part in radioactive decay and heat large bodies such as Jupiter, and he ends: "the existence of a vast store of energy in the Universe which can interact with matter may be directly pertinent to the urgent need for nonchemical forms of energy suitable for human use" [read: pp.274-275].

So Ives matters to Moray as a credential and a bridge. A respected experimenter (Bell Laboratories, NAS member from 1933, president of the Optical Society of America 1924-25) had shown that a physical ether can be kept without contradicting any relativity test, special or general. Ruderfer uses that to say an ether is "admissible", fills it with energy, and the Moray book uses Ruderfer to say that a "sea of energy" is not excluded by modern physics. Steps 1 and 2 are about Ives. Steps 3 and 4 are Ruderfer's own: none of the 31 Ives papers gives the ether an energy content, a flow or a force that could be tapped. In Ives's 1939, 1945 and 1948 papers the ether supplies a frame (absolute rest, absolute time) and a mechanism (why rods shrink and clocks slow), not a field, a force or an energy source [read: deep reads; arbiter]. Ruderfer is an interested party in the sense of the review's rules: he cites Ives as support for his own neutrino-sea model, and the 1960 rotor experiment Preikschat carried out was his proposal (section 4.7). A second, smaller bridge is Ives's standing-wave photoelectric work (section 4.8): mainstream physics on two of Moray's interests, standing waves and the conversion of light into current, but with no energy-conversion efficiency.

The reading in the question: "even if Ives is correct, the ether follows Lorentz and Einstein; a Lorentz ether contributes no new forces beyond those specified by Lorentz/Einstein, so it is only a difference of explanation." All three reviewers and the arbiter agree: this is correct for Ives's core theory, and it is Ives's own position [arbiter, owner's questions]. The evidence, in the sources' words:

• Special relativity: Robertson, Ives's referee, found his deductions valid and the theory "completely equivalent in substance to the special theory of relativity" [read: NAS memoir p.24]. Ives conceded the ether's "elusiveness by any measurements of the sort we have been considering" (1937) and in 1945 claimed "no suggestion of a new principle" [read].
• Gravity: "There is in it no non-Euclidean geometry, nor new law of gravitation" (1939); "The force equations are actually implicit in the general relativity solution" (1948) [read].
• Why it must be so: Lorentz's theory and Einstein's use the same equations; the ether adds a preferred frame on which no measurement depends. In the language of section 2.6, the two differ only in which clock-synchronisation convention is called "true"; the out-and-back speed of light is c whichever is chosen [arbiter; Mathematician].

Four qualifications make the summary exact [arbiter]:

1. The cost of the ether is an assumption, not a force. For Lorentz's picture to work, every force that holds matter together must itself behave like electromagnetism under motion (be "Lorentz-covariant"); otherwise rods of different materials would shrink by different amounts and Michelson-Morley and Kennedy-Thorndike would not be null. Einstein's postulate gives this automatically; Lorentz must assume it for each force. It has been tested to high precision by Hughes-Drever-type experiments [memory: high].
2. In gravity, something beyond special relativity is needed, but it is not a new force. Speed-dependent mass alone gives one sixth of Mercury's advance (section 4.4). The rest comes from making mass, clock rate and radial length depend on position in the field. GR puts that into curved spacetime; Ives puts it into the state of the ether at that point. His 1947 "transverse force" and his 1948 position-dependent mass are, by his own 1948 statement, the same effect seen two ways. So the reading in the question needs "Lorentz/Einstein" to include Einstein's gravity, not only special relativity.
3. Ruderfer's "any Lorentz-ether theory ... is necessarily equivalent" is not a theorem. Nordstrom's scalar theory has the right Newtonian force and bends no light (section 3.5). What gives Ives GR's numbers is his particular postulate with the exact y, which builds in GR's two PPN numbers, not the mere presence of an ether or a Newtonian force. Ives's own hedging is more accurate than Ruderfer's gloss. Likewise, Ives's paper only likens the transverse force to a light-speed correction of Newton (the Gauss analogy); it does not derive it from finite propagation speed, as Ruderfer's sentence implies.
4. Ives's separate claims (section 4.9) are not rewritings. The photon prediction was a different prediction and was not supported; the radiation-pressure formula is a definition; the dishing disk is untested.

The Mathematician adds a tension inside Ruderfer's step 3: a vacuum energy that is truly Lorentz-invariant has the same form in every frame and offers no gradient to extract work from, while a neutrino sea at rest in one frame is not Lorentz-invariant in that sense and could in principle be detected (Ruderfer's own 1960 rotor proposal; Preikschat's null of 2.0 +/- 5.2 cm/s) [arbiter]. So the two things Ruderfer wants from the ether, invisibility (to stay equivalent to relativity) and usable energy, pull in opposite directions. That is a question for the Moray review, not a verdict on Ives.

How to read Ives in one paragraph. Ives was a first-rate experimenter who preferred Lorentz's way of explaining relativity: rods and clocks really shrink and slow because they move through a medium, space and time stay Newton's, and force stays force. He showed, carefully and mostly correctly, that this way can reproduce everything special relativity and the one-mass tests of general relativity predict, starting from conservation laws and simple postulates. That is a real achievement in explanation, and his 1945 and 1948 derivations are good study material because they show which physical assumptions carry relativity's content. It is not a discovery of anything relativity misses, and he never claimed it was, except in his charges that Einstein's theory is inconsistent (which do not survive) and his prediction about the photon (which failed). The energy-filled ether comes from those who cited him, not from Ives.

---

5. Worked example: the size of the moving-clock shift, and what the 1938 plates show

Everything here is reproduced in example.py (run: .venv/bin/python review/Ives/example.py). Data are from Tables I and III of JOSA 28 [read: OCR in research/files/ocr/, checked against page images by the Mathematician and Contrarian].

Step 1. The speed of the atoms (plate 177). H2+ ions, mass M = 2 m_p (m_p the proton mass, rest energy m_p c^2 = 938.272 MeV), fall through V = 18,350 volts and gain kinetic energy eV = 18,350 eV. From (1/2) M v^2 = eV:

beta^2 = 2 eV/(M c^2) = 2 x 18,350 / (2 x 938.272 x 10^6) = 1.956 x 10^-5, beta = 0.00442,

so v = 1,326 km/s. (The exact relativistic energy formula changes beta^2 by 0.0015 percent: negligible.)

Step 2. The ordinary Doppler shift. lambda0 beta = 4861.3 x 0.00442 = 21.50 A. Seen at 7 degrees it is 21.50 x cos 7 = 21.34 A. Table I prints 21.55 A computed and 21.37 A observed (corrected for the 7-degree angle) [read]. So the blue and red lines sit about 21.5 A either side of 4861.3 A.

Step 3. The clock shift. The centre of the two lines moves by

lambda0 (gamma - 1) = 4861.3 x (1/sqrt(1 - 1.956 x 10^-5) - 1) = 0.0475 A.

Table III prints 0.0478 A (computed from voltage), 0.0469 A (computed from the measured line spacing) and observed 0.047 A [read]. The clock shift is 0.2 percent of the ordinary shift and 1 part in 100,000 of the wavelength: the experiment had to locate a line centre to a few thousandths of an angstrom. The probable error of each measured spacing was "about 0.0025 A" [read: p.220].

Step 4. What would no clock slowing give? With the classical Doppler formula (source moving through a medium at rest in the laboratory, no change in the atom's rate), lambda_blue = lambda0 (1 - beta cos theta) and lambda_red = lambda0 (1 + beta cos theta); their centre is exactly lambda0, a shift of zero [calc: example.py Part 1]. So the observed 0.047 A is the clock effect itself.

Step 5. Ives's four contractions. For a light clock with mirror spacing a at rest, period T0 = 2a/c. Moving at v through the light medium, a pulse across the motion over a distance b takes 2b/(c sqrt(1 - beta^2)) per round trip, and along the motion over a distance L takes 2L/(c (1 - beta^2)). MM requires the two equal, so L = b sqrt(1 - beta^2); the absolute size b = a s is free. Then T/T0 = s / sqrt(1 - beta^2), and the centre shift is lambda0 (T/T0 - 1). At 18,350 V [calc: example.py Part 3]:

Step 6. All eight plates. Recomputing lambda0 eV/(n m_p c^2) for each plate (n = 2 for H2+, 3 for H3+) reproduces the printed "computed" column to within 1.1 percent [calc]:

Mean ratio 0.964, sample standard deviation 0.040; seven of eight lie below 1. A straight line through the origin, observed = k x computed, with 0.0025 A per point, gives k = 0.972 +/- 0.031 (prediction k = 1). Voigt's k = 2 lies 33 standard errors away, equal volume (k = 4/3) 11.5, no clock change (k = 0) 31 [calc: example.py Part 4; matches the Mathematician and arbiter]. Chi-square about k = 1 is 1.7 for 8 points, where about 8 is expected: the points hug the line more closely than the quoted error allows. That agrees with Mandelberg and Witten's later judgement that the 1938 points "fit the curve with an accuracy of about 2 to 3%" but the real uncertainty was "more nearly 10-15%" [read: Giuliani p.10, second hand]. The orientation test (Table II: tube pointed N, N, S, E, W, W at 18,000 V) gave 0.036, 0.052, 0.050, 0.045, 0.051, 0.047 A, mean 0.0468 against 0.0472 computed; two north-pointing plates differ by 40 percent [read: page image p.224], which also fits a 10-15 percent real uncertainty.

Step 7. Part II (1941) and the doublet caveat. At 42,260 V an H2+ ion has beta^2 = 2 x 42,260/(2 x 938.272 x 10^6) = 4.504 x 10^-5, so the centre shift is lambda0 beta^2/2 = 4861.3 x 2.252 x 10^-5 = 0.1095 A (printed 0.1098; observed 0.113) [calc: example.py Part 6]. The two components of H-beta are about 0.09 A apart. A centre of gravity of two lines always lies between them, so no change in their relative brightness can move the centre by more than 0.09 A. The observed 0.113 A is about 1.25 times that: the effect cannot be a brightness artefact alone. This is the check Ives and Stilwell set themselves in 1938, and they met it.

What the example shows. The measured shift has the right size (within a few percent), scales with voltage, and scales with ion mass (H2+ and H3+ points have the same mean ratio, 0.960 and 0.969 [calc: Mathematician]), which an intensity artefact in the H-beta doublet would have no reason to do; Part II (Step 7) rules that artefact out as the whole explanation. It decisively excludes Voigt's, the equal-volume and the no-clock-change hypotheses: this is Ives's real contribution. It does not and cannot say whether the slowing is "relative to the ether" or "relative to the observer", because both theories put the same gamma in Step 3. And the 3-4 percent mean deficit, though small against a 10-15 percent real uncertainty, is not zero-mean and has no systematic-error budget in the paper; that remains an open detail.

5b. A second worked example: Mercury's orbit, with and without position-dependent mass

This is the calculation behind section 4.4 and the owner's question; it is in example.py Part 7.

Step 1. Mercury's numbers. G M = 1.32712 x 10^20 m^3/s^2 (Sun), a = 5.7909 x 10^10 m, e = 0.20563, period 87.969 days, so 36,525/87.969 = 415.2 orbits per century; c = 2.9979 x 10^8 m/s.

Step 2. The Ives/GR advance per orbit. 6 pi G M/(c^2 a (1 - e^2)) = 6 pi x 1.32712 x 10^20 / ((2.9979 x 10^8)^2 x 5.7909 x 10^10 x 0.95772) = 5.019 x 10^-7 radians.

Step 3. Per century, in arcseconds. 5.019 x 10^-7 x 415.2 = 2.084 x 10^-4 rad; times 206,265 arcsec per radian = 42.98 arcsec per century. The observed excess (after the pull of the other planets is removed) is about 43 [memory: high].

Step 4. Special-relativity mass alone. Sommerfeld's equation has epsilon one sixth as large, so 42.98/6 = 7.16 arcsec per century. Ives quotes this himself and says his equation, with 6 in place of 1, "gives the correct advance".

Step 5. Where the factor 6 comes from. In section 2.11 the turn per orbit is about pi epsilon. A Newtonian force on a mass that grows only with speed gives epsilon = G^2M^2/(c^2 h^2). Making the clock rate, the radial length and the mass also depend on position, through y = 1 - 2GM/(rc^2) (Ives's postulate, which is GR's Schwarzschild solution), multiplies epsilon by 6. example.py integrates the orbit equation numerically with an exaggerated epsilon (0.01) and recovers the predicted turn, 2 pi/sqrt(1 - epsilon) - 2 pi = 0.03165 rad, to five digits.

Step 6. The size of the 1947 "transverse force". Mercury's mean speed is 47.36 km/s, so v^2/c^2 = 2.5 x 10^-8: the sideways push is 2.5 x 10^-8 of the sideways part of the Sun's pull. Tiny, but always in the same sense, which is how it adds up to 36 extra arcseconds a century.

Step 7. Light, for comparison. At the Sun's edge (R = 6.957 x 10^8 m), 4 G M/(c^2 R) = 8.49 x 10^-6 rad = 1.7512 arcsec; with clock slowing alone (no radial shrinking of rulers), half of that, 0.8756 arcsec. The 1919 eclipse and later radio measurements favour the full value [memory: high]; Ives used exactly this fact to reject the isotropic ether (section 4.4).

What the example shows. Ives's numbers are GR's numbers, for the reason he gave: his postulate reproduces the Schwarzschild solution. Nothing was fitted to 43. The example also shows why "Newton plus special relativity" is not the whole of "Lorentz/Einstein": gravity needs the position-dependent factors as well, and Ives supplied them as properties of the ether rather than as curvature.

---

6. Evidence table

---

7. What a learner should take away

Solid. - The Ives-Stilwell design is a model of experimental thinking: when the effect you want (0.05 A) is buried under one about 450 times larger (21.5 A) that depends on an angle you cannot control, measure in two opposite directions and take the average. The large term cancels exactly (section 3.1). - A moving atom's light is shifted by the factor gamma, as Einstein predicted; confirmed in 1938 at the few-percent level and today at parts per billion. - Ives's 1947 point is correct and important: MM alone cannot tell you how fast a moving clock runs; a clock-rate experiment is needed, and it selects Lorentz's contraction over Voigt's and others. This is exactly the role IS plays in modern test theories. - Ives's own derivation of E = mc^2 from the momentum of light is correct, and Planck's caution about Einstein's 1905 step was a real point that took Laue and Klein to settle. - Ives's gravitation papers (1939, 1948) are a correct, tensor-free route to the Schwarzschild solution and to GR's three classic numbers (Mercury 43 arcsec per century, light bending 1.75 arcsec, the red shift), with nothing fitted. They are good study material: they show that GR's one-mass results amount to "clocks slow, radial rulers shrink and mass grows, by sqrt(y), near a mass", and that half the light bending comes from the rulers. - His 1945 derivation shows how much of special relativity follows once you accept that energy has inertia (E/c^2) and that all clocks slow alike; the lesson is in which premises carry the weight. - The ripple-tank experiments (1941-42) give a real, visible model of a Lorentz ether: a medium that is there, yet cannot be detected by observers whose rulers and clocks are made of its own waves.

Wrong, and why the mistake is instructive. - "The result is evidence for the ether over Einstein." Two theories that make the same predictions cannot be separated by any experiment. Ives's own algebra shows the laboratory's ether velocity cancels. The lesson: before claiming an experiment favours your theory, ask what the rival predicts for the same measurement. - "SR is internally contradictory because clocks must be moved infinitely slowly" (1937, 1949). Ives's own 1949 equations are the Lorentz transformation with transported clocks offset by a tiny, computable amount; SR predicts the same offset. The transport error shrinks in proportion to the transport speed; idealised limits are routine in physics. And SR defines synchronization by light; it does not need transported clocks at all. - "Any Lorentz-ether theory with a Newtonian force must agree with GR" (Ruderfer's gloss on Ives). Nordstrom's theory is a counterexample; what gives Ives GR's numbers is his specific postulate. The lesson: a successful derivation shows that its particular premises work, not that every theory of that kind would. - "The photon will go the way of the caloric." A clear prediction, and a failed one: later single-photon experiments rule out a purely classical light field. The lesson: a phenomenon both pictures explain (standing waves) cannot decide between them; look for one where they differ (photon coincidences). - "Einstein's derivation is circular." The circle appears only after a second formula for kinetic energy, one Einstein did not use, is added. The lesson: check whether a "hidden assumption" is in the original argument or in your reconstruction of it. - "Rotation proves a fixed ether." SR handles rotating apparatus from an inertial frame and gets the same first-order Sagnac result, as Ives's own 1938 calculation does. - "The clock paradox shows relativity is self-contradictory." The two clocks are not in symmetric situations: the travelling one changes inertial frame. The lesson: before calling a theory contradictory, state its own resolution of the puzzle and show where that fails.

Also solid, and less known. Ives's explanation of the "selective" photoelectric effect of thin alkali films by standing light waves in the film (section 4.8), which he regarded as his most important work.

The owner's question, in one line. A Lorentz ether, as Ives built it, adds no force and no measurable effect beyond special and general relativity; it is a different explanation of the same observations, bought at the price of assuming every force in matter behaves like electromagnetism under motion. The energy-filled ether of Ruderfer and the Moray book is a further hypothesis that Ives's work allows but does not support (section 4.10).

Genuinely open. - Can Ives's gravitation be extended beyond one static mass (two bodies, radiation, binary-pulsar decay), and does anything but his postulate fix the second-order term (kappa = 0)? - Is the 1945 "must drop out" step derivable from conservation laws alone, or does it need the relativity principle? (No one has shown either.) - Does the 1942 radiation-pressure paper define E_a as the energy density in the absorber's own frame, as the reviewers' derivations suggest (a clean copy would decide)? - Does a spinning disk dish as Ives says, once real elastic stresses are included? - Is a Ruderfer-type neutrino sea compatible with Lorentz invariance and with neutrino-detection limits? (A question for the Moray review.) - What lies behind Pobedonostsev and Parshin's reported deviation at 150-300 keV: viewing-angle alignment of their two optical arms, beam-energy calibration, line shapes, or something real? Their table is now read; the full Russian account (Zh. Tekh. Fiz. 1989) and raw data would decide. - Is the 3-4 percent mean deficit in Table III a systematic effect or noise? (The direction of the centre shift is settled: the paper never states it, and it follows from the formula as a red shift.) - What does Ives's own "Unsymmetrical Doppler Effect in Hydrogen Canal Rays" (Rev. Sci. Instr. 9:283, 1938) report, and does it bear on the asymmetry reading of Faraj, Gezari and Kantor? - Why the record of Ives's experimental work stops after 1941, and what the LoC correspondence shows about how his views were received. How the gravitation papers were cited (citation indices). - Part II's Table I: how many points lie above the computed curve (the reviewers' counts differ by one).

---

8. Check yourself

1. Atoms in a canal-ray beam are viewed at a small angle theta, toward and away from the spectrograph. Show that the average of the two observed wavelengths does not depend on theta. Why did that matter to Ives and Stilwell?
2. Mercury has a = 5.79 x 10^10 m, e = 0.206 and makes 415 orbits per century; for the Sun G M = 1.327 x 10^20 m^3/s^2. Compute the perihelion advance in arcsec per century from Ives's 1948 orbit equation (turn per orbit 6 pi GM/(c^2 a (1 - e^2))) and from special-relativity mass increase alone. What, in Ives's picture, supplies the extra factor, and is it a new force?
3. Using Ives's 1947 light-clock argument, what centre shift would Voigt's contraction predict at 18,350 V, and why does Michelson-Morley alone not rule Voigt out?
4. A colleague says: "Ives-Stilwell proves the ether exists, because Ives predicted it from ether theory and it came out right; and Ruderfer showed that this ether is a sea of usable energy." What is the strongest correct reply to each half?
5. In Ives's 1952 argument, where does the factor L/((m - m') c^2) come from, and why does its appearance not make Einstein's 1905 argument circular?

---

9. Further reading

Mainstream. - E. F. Taylor and J. A. Wheeler, Spacetime Physics (2nd ed., 1992): time dilation and clock synchronization from first principles. - D. J. Griffiths, Introduction to Electrodynamics, Chapter 12 (relativity, Doppler effect, relativistic momentum and energy). - A. P. French, Special Relativity (MIT Introductory Physics Series): the relativistic Doppler effect and photon-emission kinematics. - W. Rindler, Relativity: Special, General and Cosmological: synchronization, the Sagnac effect, Mercury. - J. R. Taylor, An Introduction to Error Analysis: least squares and chi-square for section 5. - R. Mansouri and R. U. Sexl, "A test theory of special relativity", Gen. Rel. Grav. 8 (1977) [memory: high]; summary at https://en.wikipedia.org/wiki/Test_theories_of_special_relativity. - B. Botermann et al., "Test of time dilation using stored Li+ ions as clocks at relativistic speed", Phys. Rev. Lett. 113:120405 (2014), arXiv 1409.7951 (saved in research/files/). - H. C. Ohanian, "Einstein's E = mc^2 mistakes", arXiv 0805.1400 (2008) (in the folder). - G. Giuliani, "Experiment and theory: the case of the Doppler effect for photons", arXiv 1502.05736 (2015); I. Bonizzoni and G. Giuliani, arXiv physics/0008012 (2000) (both in the folder): history of how IS was interpreted. - R. Lalli, "'Dirty work', but someone has to do it: Howard P. Robertson and the refereeing practices of Physical Review in the 1930s", Notes Rec. R. Soc. 70(2):151-174 (2016), https://pmc.ncbi.nlm.nih.gov/articles/PMC4856100/; Lalli 2014 ESHS chapter on Ives's revival of the Larmor-Lorentz ether (saved in research/files/). - P. A. M. Dirac, "Is there an aether?", Nature 168:906 (1951) (not obtained), the paper Ives answered in 1953. - E. Preikschat, "The Mossbauer Effect and Tests of Relativity", PhD thesis, University of Birmingham (October 1968) (saved in research/files/): Ruderfer's rotor ether-drift experiment and a survey of Ives's place in test theories. - M. Benton, "The Clock Problem (Clock Paradox) in Relativity", US Naval Research Laboratory annotated bibliography (1959), https://en.wikisource.org/wiki/The_clock_problem_(clock_paradox)_in_relativity.

Ives's own key works (in the folder's Ives-papers/ unless marked; read in this order for the story). - H. E. Ives, "The Doppler effect considered in relation to the Michelson-Morley experiment", JOSA 27:389 (1937), with JOSA 27:177 (1937): the proposal for the canal-ray experiment. - H. E. Ives and G. R. Stilwell, "An experimental study of the rate of a moving atomic clock", JOSA 28:215-226 (1938), and Part II, JOSA 31:369-374 (1941): the experiment and its extension to 43 kV. - H. E. Ives, "Light signals on moving bodies as measured by transported rods and clocks", JOSA 27:263 (1937), with 27:310; "The aberration of clocks and the clock paradox", JOSA 27:305 (1937); "Light signals sent around a closed path", JOSA 28:296 (1938): transported clocks, the clock paradox and the Sagnac effect. - H. E. Ives, "Behavior of an interferometer in a gravitational field", JOSA 29:183 (1939): the Schwarzschild line element from optics. The shortest and clearest of the gravitation papers; start here. - H. E. Ives and G. R. Stilwell, "Interference phenomena with a moving medium", I and II, JOSA 31:14 (1941) and JOSA 32:25 (1942): the ripple-tank ether. - H. E. Ives, "Derivation of the Lorentz transformations", Phil. Mag. (7) 36:392 (1945): relativity's effects from conservation laws; with "Impact of a wave-packet and a reflecting particle", JOSA 33:163 (1943), and JOSA 34:222 (1944). - H. E. Ives, "The physical significance of Birkhoff's gravitational equations", Phys. Rev. 72:229 (1947): the transverse force. - H. E. Ives, "Historical note on the rate of a moving atomic clock", JOSA 37:810-813 (1947): the four contractions, and credit to Einstein. - H. E. Ives, "The behavior of an interferometer in a gravitational field. II. Application to a planetary orbit", JOSA 38:413 (1948): Mercury from the postulate. - H. E. Ives, JOSA 38:879 (1948) on one-way light speed; "Lorentz-type transformations as derived from performable rod and clock operations", JOSA 39:757 (1949); "Extrapolation from the Michelson-Morley experiment", JOSA 40:185 (1950); "Revisions of the Lorentz transformations", Proc. APS 95:125 (1951): the rod-clock-quotient papers. - H. E. Ives, "Pressure of radiation in a moving system", JOSA 32:32 (1942); "Theory of the double Fizeau toothed wheel", JOSA 29:472 (1939): radiation pressure and the dishing disk. - H. E. Ives, "Adventures with Standing Light Waves", Proc. Am. Acad. Arts Sci. 81:1-32 (1951), Rumford Medal lecture; the photoelectric papers ApJ 60:209 and 60:231 (1924), ApJ 64:128 (1926), Bell System Tech. J. 5:320 (1926); H. E. Ives and T. C. Fry, JOSA 23:73 (1933): the standing-wave photoelectric work. - H. E. Ives, "Derivation of the mass-energy relation", JOSA 42:540-543 (1952), and "Note on the mass-energy relationship", JOSA 43:619 (1953); "Genesis of the query 'Is there an ether?'", JOSA 43 (1953), his reply to Dirac (still in copyright; cited by reference). - Not obtained: "Unsymmetrical Doppler effect in hydrogen canal rays", Rev. Sci. Instr. 9:283 (1938); the clock-paradox letter, Nature 168:246 (1951); Proc. Roy. Dublin Soc. 26:9 (1952); R. Hazelett and D. Turner (eds.), The Einstein Myth and the Ives Papers (1979).

The Moray link. - M. Ruderfer, "Neutrino Structure of the Ether", Lett. Nuovo Cimento 13:1 (1975), reprinted as Appendix VI of T. H. Moray, The Sea of Energy in Which the Earth Floats, 5th ed., printed pp.271-275 (text in review/Morray-TH/_text). Read pp.271-272 for the use of Ives, pp.272-275 for the neutrino sea. - For gravity theories compared with GR: C. M. Will, Theory and Experiment in Gravitational Physics (the PPN numbers), [memory: high]; and Will's article in Scientific American 231:24 (November 1974), which Ruderfer cites in his note (9) [read: Moray p.272; article not obtained]. - Mainstream reading of the "dynamical" (Lorentzian) way of teaching relativity: J. S. Bell, "How to teach special relativity" (1976), in Speakable and Unspeakable in Quantum Mechanics [memory: high]. - E. F. Taylor, J. A. Wheeler and E. Bertschinger, Exploring Black Holes: the Schwarzschild line element without tensors (section 2.10). - O. E. Buckley and K. K. Darrow, NAS Biographical Memoir of Herbert Eugene Ives (1956), with full bibliography (in the folder).

---

Answers

1. lambda_blue + lambda_red = lambda0 gamma [(1 - beta cos theta) + (1 + beta cos theta)] = 2 lambda0 gamma, so the average is lambda0 gamma: theta has cancelled. Side-on viewing would need theta = 90 degrees exactly; an error of a few arc-minutes there gives a first-order shift as big as the effect. Averaging the approaching and receding lines removes that sensitivity.
2. Turn per orbit: 6 pi x 1.327 x 10^20/((3.00 x 10^8)^2 x 5.79 x 10^10 x (1 - 0.206^2)) = 5.02 x 10^-7 rad; times 415 = 2.08 x 10^-4 rad = 43.0 arcsec per century. Special-relativity mass alone gives one sixth, 7.2 arcsec. In Ives's picture the extra comes from making the clock rate, the radial length and the mass of a body depend on its position in the field, by the factor y = 1 - 2GM/(rc^2), as if it were moving at the escape speed; the same thing can be written as the 1947 sideways force of size v^2/c^2 times the sideways part of gravity. It is not a new force beyond Einstein's: it is the content of GR's Schwarzschild solution, written as a force in flat space (Ives: the force equations "are actually implicit in the general relativity solution"). It is new only relative to special relativity alone.
3. Voigt's clock period is T0/(1 - beta^2), so the centre shift is about lambda0 beta^2 = 4861.3 x 1.956 x 10^-5 = 0.095 A, twice Lorentz's 0.0475 A. MM compares the two arms' travel times, so it is satisfied by any shrinkage that keeps the along/across ratio at sqrt(1 - beta^2); the overall size, and so the clock rate, is left free. Only a clock-rate measurement fixes it.
4. SR predicts exactly the same shift, by the same formula. Ives's own algebra shows the laboratory's velocity through the ether cancels from the result, and Jones (1939) showed the predictions are identical. An experiment that both theories predict equally cannot favour either; it does exclude Voigt-type contractions, entrained-ether and ballistic theories (the last two also fail other tests). On the second half: Ives's work shows only that a Lorentz ether is admissible, because it predicts the same as relativity; it gives the ether no energy content. Ruderfer's neutrino sea is his own addition. To be more than admissible it would have to predict something relativity does not: for a sea at rest in one frame, a frame-dependent effect (the kind Preikschat's rotor looked for and did not find, 2.0 +/- 5.2 cm/s), a detectable neutrino flux, or a measured transfer of energy from the sea to matter.
5. It appears when Ives writes the kinetic energy twice: once as Einstein's L (gamma - 1) from energy conservation, once as the particle formula (m - m') c^2 (gamma - 1). Einstein never used the second formula; he compared his result with (1/2) m v^2 at low speed and read off the mass change. So L = (m - m') c^2 is his output, not his input. The fair criticism (Planck 1907, Ohanian 2008) is that this comparison treats the body as a simple particle and is general only to first order.