A Modified Lorentz Ether and Sherwin's Experiment

Scientific Paper
Title	A Modified Lorentz Ether and Sherwin's Experiment
Read in full	Link to paper
Author(s)	Ronald R Hatch
Keywords	Lorentz Ether, Sherwin Experiment, Tangherlini transformation, length contraction, mass increase
Published	1996
No. of pages	13

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Abstract

Chalmers W. Sherwin conducted an experiment which he reported in Physical Review A, Vol. 35, No.9, May 1987. The experiment was ingeniously designed to detect the Lorentzian stress induced by the Fitzgerald contraction of macroscopic matter moving at a velocity, v. Briefly, an accelerometer was spun on the end of a spring. If Fitzgerald contraction was real, Sherwin expected the accelerometer to display a signal at twice the rotation frequency, due to the galactic velocity of the solar system. The author's proposed modified Lorentz ether is described, including the increase of mass with velocity through the ether. Next, it is shown that the fault with Sherwin's expected results was, in fact, that he ignored the increase of mass with velocity. It is shown that the increase of mass, together with conservation of momentum, causes an elliptic orbit about the center flattened precisely in agreement with the Fitzgerald contraction. Thus, Sherwin's null result says: If the increase of mass with velocity is real, Fitzgerald contraction is real.

Overview

Ronald Hatch — a GPS engineer by trade, and one of the few relativity critics whose day job depended on getting relativistic corrections right — presented this paper to the Southwestern and Rocky Mountain Division of the AAAS at Northern Arizona University in June 1996. It is a rescue operation. Chalmers Sherwin's 1987 Physical Review A experiment spun a balanced pair of masses, one an accelerometer, on springs about a common centre, and looked for a signal at twice the rotation frequency that the Lorentz-Fitzgerald contraction of the rotating apparatus should produce as the solar system moves through the ether. Sherwin found nothing. Hatch, who believes in "a solid ether, which is a modified form of a Lorentz ether", takes that null result as a direct challenge to his own position, and sets out to show why it was inevitable.

His answer is a single omission: Sherwin left the relativistic increase of mass with velocity out of his analysis. Restore it, Hatch argues, and conservation of angular momentum forces the spinning mass into an orbit flattened in the direction of translation by exactly the Lorentz-Fitzgerald factor — so the attaching rod and the trajectory shorten together, the accelerometer feels nothing, and no signal can appear. The conclusion is turned around and offered as a positive result: "Sherwin's null result says: If the increase of mass with velocity is real, Fitzgerald contraction is real."

The argument

A modified Lorentz ether

Hatch begins by restating Sherwin's four Lorentz postulates from The Theory of Electrons (1909) — a preferred frame S in which light is isotropic at c; physical contraction of moving rods by √(1 − v²/c²); physical retardation of moving clocks by the same factor; and contraction caused by electron-mediated bonds — and then amends the last and adds a fifth. His postulate (4) becomes: "All fields and potentials whose sources are moving are flattened in the direction of motion by the Lorentz-Fitzgerald contraction factor." His postulate (5) supplies what Sherwin left out: the mass of a particle moving at speed v relative to S is increased by (1 − v²/c²)^−1/2. He stresses that these postulates are not foundational but derived from "the standing-wave structure of material particles in an elastic solid ether."

He also amends Henri Poincaré's relativity principle by inserting one word into Whittaker's translation: the local laws of physical phenomena must be the same for a fixed observer as for one in uniform translation. The insertion is deliberate — it exempts long-distance phenomena such as the cosmic background radiation, which Hatch takes to define the absolute frame while conceding "there is no way to prove such a claim."

Lorentz versus Tangherlini

The paper's framework is the Tangherlini (Mansouri-Sexl) transformation, in which light is isotropic only in the absolute frame. Its space equation is identical to the Lorentz one, x_b = γ(x_a − vt_a), as is its mass equation; only the time equation differs, t_a = γt_b, and the transformation is reciprocal rather than symmetric — clocks at rest in the absolute frame genuinely run faster, lengths there are genuinely longer, "as logic demands." The difference between the two transformations is a position-dependent clock bias, τ = −v'x_b/c², which Hatch traces to Einstein's convention of splitting round-trip light time equally between the outbound and inbound legs.

This yields the paper's sharpest observation about the standard formalism: "The Lorentz transformation achieves a slower running clock by actually increasing the clock rate, but then more than counteracting that effect with a changing clock bias as a function of position." On his reading the Lorentz Transformation remains "a useful fiction to simplify computations" with "no real physical effects associated with it" — from which he draws the consequence that Thomas precession cannot be explained by Lorentz boosts, and that "it is clearly invalid to use the Lorentz transformation to change frames in the middle of an experiment."

He then works the Michelson-Morley Experiment through both routes with a concrete numerical example: a 300 m arm at v = 0.6c, γ = 1.25. Transversely the light travels 375 m in the absolute frame, giving 2.5 μs there and 2.0 μs on the moving clock. Longitudinally the arm contracts to 240 m, the outbound leg takes 1.6 μs and the inbound 0.4 μs on moving clocks, summing to the same 2.0 μs; adding the clock bias of equation (22) makes each leg read 1.0 μs and restores an apparently isotropic c.

Why Sherwin saw nothing

Now the experiment. A mass on a rod of length r spins at v_s about a centre that translates at v_t along x. The squared x-velocity becomes v_t² + 2v_tv_scos θ + v_s²cos²θ while the y component is unchanged. Hatch separates the terms. The constant v_t² raises the mass by γ, and holding angular momentum fixed then lowers the spin speed to v_s/γ — so "a spinning mass can act the same as a clock", running slow by exactly the moving-clock factor.

The cross term 2v_tv_scos θ is the cyclical part, and it is the heart of the paper. It modulates the mass around the cycle and hence, again through angular momentum, the spin speed. Integrated over a full turn the modulation cancels, so the period is unaffected; but quadrant by quadrant it does not. The first and fourth quadrants run long and the second and third short, by ±(P/4)(v_tr/c²) in Hatch's low-velocity approximation. Two consequences follow. First, adding the Poincaré clock bias of equation (12) makes the spin appear perfectly uniform to a co-moving observer. Second — the physical point — during the slow quadrant the translating centre runs ahead by an extra Δx = r(v_t²/c²), so the separation at quadrant end is r(1 − v_t²/c²) rather than r. Folding in the apparent translational velocity increase of equation (28) leaves a trajectory flattened along the translation direction by precisely the factor by which the rod itself is contracted. Rod and orbit shorten in step, so no differential stress reaches the accelerometer, and Sherwin's null result is what the theory requires.

Extensions

Hatch adds several observations. A camera taking instantaneous snapshots at quarter periods would catch the mass short of 90° and past 270°, but real light's finite transit time exactly compensates, so a real camera sees uniform rotation. If the spin axis is tilted at φ to the translation, the cyclical effect scales with cos φ while the constant clock-slowing does not — which he uses to fault Andrew Dring's 1996 Galilean Electrodynamics torque analysis of a relativistic gyroscope, which likewise omitted the mass increase. A spinning rim flattens without stress, because the extra length contraction of the rim where it aligns with the translation exactly matches the variation in element spin speed.

Most substantially, he notes that nothing requires the restoring force to be a rod: if gravitational potential arises from an ether density excess around a particle, it too should flatten with velocity. He offers two places to look. VLBI quasar astrometry in 1976 was achieving about 50 milliarcseconds against an expected 1 mas, and his computation gives ±2–3 mas of unmodelled baseline variation from the Earth's orbital flattening of station potentials. And the 1967 Ash-Shapiro-Smith radar-plus-optical planetary fits, which predicted positions six weeks ahead with larger errors than expected, might in his view be improved by including velocity-induced potential flattening.

Assessment

Hatch is doing something more disciplined than most ether papers. He starts from a null result that hurts his position, says so plainly, and does the calculation rather than explaining the experiment away. The calculation itself is a real piece of work: identifying the cross term 2v_tv_scos θ as the source of a quadrant-dependent spin modulation, and showing that it flattens the orbit by exactly the contraction factor of the rod, is a specific and checkable mechanical claim, not hand-waving. His remark on how the Lorentz Transformation manufactures time dilation — by raising the clock rate and then overcompensating with a position-dependent bias — is a genuine insight into the Einstein synchronisation convention, and is the kind of thing that gets obscured in textbook presentations. The Tangherlini/Mansouri-Sexl framework he works in is a respectable test theory, and his honesty about the CMB identification ("there is no way to prove such a claim") is characteristic.

The central difficulty is that the result was guaranteed before the calculation began. Hatch's postulates (1)–(5) are, by construction, the Lorentzian reading of a theory empirically equivalent to special relativity; the Tangherlini transformation differs from the Lorentz transformation by a synchronisation convention alone. Any local experiment in such a theory must return a null, and Sherwin's did. So the paper does not distinguish its ether from relativity; it demonstrates, at length and in one particular apparatus, that it cannot be distinguished. Hatch feels this himself in his closing paragraph, where the systematic conspiracy of cancellations moves him to speak of "evidence for design". Read in the other direction the same cancellations are what a symmetry looks like from inside — which is precisely the relativity principle he has modified but not abandoned.

Two steps are asserted rather than derived. The first is that a translational velocity can be imparted "without changing the angular momentum of the spinning mass": angular momentum is not a boost invariant, and its transformation is exactly what a careful treatment of this problem turns on, yet the paper simply stipulates constancy. The second is the velocity composition in equation (25), which adds v_t and v_s galileanly and then inserts the result into a relativistic mass formula. To the order Hatch works at, the cross term he needs is what survives either way, but the mixing is not justified in the text, and the whole quadrant asymmetry rests on it. The reliance on "increase of mass with velocity" as a physical fact rather than a frame-dependent bookkeeping device is also worth flagging: modern practice keeps the mass invariant and puts the γ in the momentum, and Hatch's argument would need restating — though probably not overturning — in those terms.

The two observational proposals have not aged well, and they are the only places where the paper reaches beyond empirical equivalence. VLBI astrometry did not stay at 50 milliarcseconds: the ICRF3 catalogue now places thousands of extragalactic radio sources at the tens-of-microarcsecond level, roughly two orders of magnitude below Hatch's predicted ±2–3 mas annual systematic, and no such signal appears in the residuals. Similarly, the six-week extrapolation errors in the 1967 planetary fits reflected the ephemeris state of that era; modern ephemerides such as the JPL DE and INPOP series fit interplanetary ranging at the metre level over decades without any velocity-flattening term. Neither result refutes a Lorentzian ether — nothing local can — but both remove the specific effects Hatch offered as its signature.

A note on the source: this PDF is a scan and its OCR is imperfect. "Sherwin" is frequently rendered "Shenvin", and several exponents have been lost — equation (26) as extracted reads m_t = m_s(1 − v_t²/c²) where the context requires the −1/2 power. Readers checking the algebra should assume dropped superscripts rather than errors by the author.

See also

• Ronald R Hatch
• Aether
• Lorentz Transformation
• Length Contraction
• Time Dilation
• Michelson-Morley Experiment
• Simultaneity
• Hendrik Lorentz
• Henri Poincaré
• Special Relativity
• Mass
• Inertia
• Speed of Light
• Cosmic Microwave Background