Lorentz ether theory

What is now often called Lorentz ether theory (LET) has its roots in Hendrik Lorentz's "theory of electrons", which was the final point in the development of the classical aether theories at the end of the 19th and at the beginning of the 20th century.

Lorentz's initial theory was created between 1892 and 1895 and was based on a completely motionless aether. It explained the failure of the negative aether drift experiments to first order in v/c by introducing an auxiliary variable called "local time" for connecting systems at rest and in motion in the aether. In addition, the negative result of the Michelson–Morley experiment led to the introduction of the hypothesis of length contraction in 1892. However, other experiments also produced negative results and (guided by Henri Poincaré's principle of relativity) Lorentz tried in 1899 and 1904 to expand his theory to all orders in v/c by introducing the Lorentz transformation. In addition, he assumed that also non-electromagnetic forces (if they exist) transform like electric forces. However, Lorentz's expression for charge density and current were incorrect, so his theory did not fully exclude the possibility of detecting the aether. Eventually, it was Henri Poincaré who in 1905 corrected the errors in Lorentz's paper and actually incorporated non-electromagnetic forces (including gravitation) within the theory, which he called "The New Mechanics". Many aspects of Lorentz's theory were incorporated into special relativity (SR) with the works of Albert Einstein and Hermann Minkowski.

Today LET is often treated as some sort of "Lorentzian" or "neo-Lorentzian" interpretation of special relativity. The introduction of length contraction and time dilation for all phenomena in a "preferred" frame of reference, which plays the role of Lorentz's immobile aether, leads to the complete Lorentz transformation (see the Robertson–Mansouri–Sexl test theory as an example). Because the same mathematical formalism occurs in both, it is not possible to distinguish between LET and SR by experiment. However, in LET the existence of an undetectable aether is assumed and the validity of the relativity principle seems to be only coincidental, which is one reason why SR is commonly preferred over LET.

Whereas mainstream physics regards LET and special relativity as experimentally indistinguishable and prefers the latter on grounds of parsimony — an undetectable aether being, on that view, an idle hypothesis — many researchers documented on this wiki take the opposite position. For them a real preferred frame is not surplus metaphysics but the physically preferable interpretation: length contraction, time dilation and the slowing of clocks are real dynamical effects of motion through a physical medium, not the symmetric appearances of a four-dimensional geometry. On this reading the two theories are not merely notational variants of one another. They agree on the second-order predictions tested so far, but they part company over whether simultaneity is absolute, whether the one-way speed of light is truly isotropic, and whether laboratory and astronomical data already show a small but genuine anisotropy. The section below gathers this work as it appears in papers archived on this wiki, organised by the ideas that recur across it.

Historical development

Lorentz ether theory (LET) was developed mainly between 1892 and 1906 by Hendrik Lorentz and Henri Poincaré, building on Fresnel's aether, Maxwell's equations, and the electron theory of Clausius. Lorentz drew a strict separation between matter (electrons) and the aether: in his model the aether is completely motionless and is not dragged along by moving bodies. It was natural, though not logically required, to identify this stationary aether with Newton's absolute space. The aether's condition was described purely by the electric and magnetic fields, replacing older mechanical models with an abstract electromagnetic aether that mediated between electrons and propagated changes at the speed of light. Lorentz explained the Zeeman effect on this basis, earning the 1902 Nobel Prize. A central element of his 1895 theory was the "theorem of corresponding states," which held that an observer moving through the aether could, to first order in v/c, use the same electrodynamic equations as an observer at rest, and so make the same observations.

The Michelson–Morley experiment (1887) posed a major challenge, since the expected motion relative to the aether was not detected. To reconcile the immobile aether with this null result, FitzGerald (1889, qualitatively) and Lorentz (1892, quantitatively) proposed that a body's dimension along the direction of motion is slightly reduced; because measuring instruments contract in the same ratio, a co-moving observer would not notice it. This length contraction was widely regarded as an ad hoc hypothesis. The precise relativistic form, with no perpendicular expansion, was given by Larmor (1897) and Lorentz (1904), who also argued that the electrons themselves contract.

Equally important was "local time," t' = t − vx/c², the time coordinate Lorentz assigned to an observer moving through the aether (an expression Voigt had used earlier). With it Lorentz explained aberration, the Doppler effect, and the Fizeau experiment. For Lorentz, length contraction was a real physical effect but local time was only a convenient mathematical device. Poincaré saw more in it: in 1900 he interpreted local time as the result of moving observers synchronizing clocks by light signals while unaware of their own motion, treating it as a genuine physical effect—though he still held that clocks at rest in the aether showed the true time. It was not initially recognized that local time already contained what is now called time dilation, first noticed by Larmor (1897) and Lorentz (1899).

Because first-order results were insufficient—other null experiments such as Trouton–Noble probed second-order effects—the theory was extended into the full Lorentz transformation, given in algebraically modern form by Larmor (1897) and Lorentz (1899), and completed in Lorentz's 1904 paper, in which all molecular forces transform like electrostatic ones so that motion relative to the aether becomes undetectable. Abraham (1904) noted that a purely electromagnetic contracted electron would be unstable, requiring non-electromagnetic forces. In June 1905 Poincaré supplied the "Poincaré stresses" to stabilize the electron, corrected Lorentz's transformation formulae, demonstrated the Lorentz covariance of the Maxwell–Lorentz equations and the group character of the transformation (naming it the Lorentz transformation and the Lorentz group), and sketched a compatible theory of gravitation, including gravitational waves. In his extended 1906 "Palermo paper" he showed the invariance of x² + y² + z² − c²t² and treated the transformation as a rotation in a four-dimensional space with an imaginary time coordinate, anticipating four-vectors, though he judged the geometric reformulation not worth the effort.

Related work on electromagnetic mass held that a charged body's electromagnetic energy contributes to its mass, increasing with velocity; Lorentz (1899, 1904) derived distinct longitudinal and transverse masses, and many hoped all mass might prove electromagnetic. That program was abandoned, since all mass—not just its electromagnetic part—is proportional to energy, as explained by mass–energy equivalence. Lorentz (1900) and Poincaré (1905–06) also attempted Lorentz-compatible theories of gravitation propagating at the speed of light, but these were superseded by general relativity.

From Lorentz ether theory to special relativity

In 1905 Albert Einstein published special relativity. By re-examining the meaning of space and time coordinates, he showed that the "effective" coordinates of the Lorentz transformation are simply the inertial coordinates of moving frames. All observable consequences of LET followed from two principles—the principle of relativity and the constancy of the speed of light—without postulating an undetectable aether. Lorentz and Poincaré had used these principles but had not recognized that they were sufficient, making the earlier auxiliary assumptions unnecessary. In 1907 Hermann Minkowski recast the theory in a unified four-dimensional spacetime, and the naturalness of the Einstein–Minkowski formulation drove rapid acceptance of special relativity and a corresponding loss of interest in the aether.

LET and special relativity are experimentally equivalent; their only difference is LET's postulate of a unique but undetectable absolute rest frame, which plays no role in predictions. Mainstream physics came to prefer special relativity on grounds of parsimony, since it dispenses with an unobservable aether. The question of priority—whether Poincaré and Lorentz should be counted as founders of the theory alongside Einstein—remains disputed and is treated neutrally in the literature. Lorentz himself never fully abandoned the aether: throughout his life he retained a preference for a preferred frame in which clocks show the "real" time, while granting that if the relativity principle holds this frame cannot be found by experiment, and that the choice between the two views is largely a matter of taste.

The neo-Lorentzian tradition on this wiki

The historical account above ends where the mainstream story usually does: with Lorentz's own admission that, once the relativity principle is granted, the choice between his ether and Einstein's interpretation is "a matter of taste". Many researchers whose work is archived on this wiki do not grant that the question is settled. They belong to a continuing neo-Lorentzian tradition — the label itself was already being debated by Simon J. Prokhovnik and Victor Clube in their 1980 exchange Does Neo-Lorentzian Relativity Exist? — which holds that a physical aether at rest in a preferred inertial frame is not only viable but preferable to Einstein's interpretation. The papers below are grouped by the ideas they develop rather than by author.

Why a preferred frame is preferred

The starting point for most of these authors is a distinction the mainstream account tends to blur: between saying that absolute space does not exist and saying that it is superfluous. In Relativity and Absolute Space (1989) Phillip Scribner argues that Einstein's 1905 paper established only the latter — that the notion of absolute space is dispensable — and that every phenomenon covered by special relativity can be explained, and even predicted, on the assumption that absolute space does exist, provided one follows Lorentz in postulating that motion through it causes real temporal and spatial distortions in the moving object. On this view what Einstein called "relativity" is explained as the appearance of a symmetry between observers, not as evidence that no preferred frame exists.

Horst E Wilhelm, in From Relativistic Paradoxes to Absolute Space and Time Physics (1994), presses the same point historically. He notes that Voigt (1887), Lorentz (1904) and Einstein (1905) introduced the hypothesis that Maxwell's equations retain their form in every inertial frame, and he treats this as physically equivalent to the questionable assumptions that no electromagnetic carrier exists and that a light signal has the same one-way speed in all frames. Reinstating a substratum at absolute rest, he argues, dissolves the paradoxes that follow from denying it.

Constantin Antonopoulos approaches the question through logic and semantics rather than electrodynamics. In The Semantics of Absolute Space (1994) he argues that motion and growth in space presuppose space, and that Einstein's length-contraction relation, far from contradicting the existence of absolute space, actually presupposes it. A parallel realist case is made by Peter F Erickson in Absolute Space, Absolute Time, & Absolute Motion (2006), who defends the reality of all three from an analysis of the nature of infinitesimals and the number line, treating non-Euclidean geometry as a manipulation of symbols rather than a description of physical space.

The most systematic realist programme in this group is that of Ronald R Hatch, whose A Modified Lorentzian Ether Theory (2000) — which he also called an "Ether Gauge Theory" — presents a step-by-step alternative to both special and general relativity, each step constrained by experiment, and offers in the bargain a concrete mechanism for both gravitation and inertia. The recurring claim across all these papers is that the aether earns its keep: it supplies a physical cause for effects that Einstein's interpretation can only postulate.

Absolute simultaneity and the one-way speed of light

The technical heart of the wiki's neo-Lorentzian work is the claim that distant simultaneity is a physical fact rather than a convention, and that this shows up in the one-way speed of light. Here the central figure is Franco Selleri. In Recovering the Lorentz Ether (2004) he replaces the Lorentz transformation with a family of alternative "inertial" transformations that single out a preferred frame in which the Lorentz ether is at rest; he argues that these transformations describe the empirical data better than the theory of special relativity and eliminate the features of it that give rise to paradoxes. In the companion paper Space and Time Physics with the Lorentz Ether: The Clock Paradox (2004) he applies the scheme to the clock paradox and claims a complete resolution in the privileged frame.

Selleri's argument turns on a single coefficient. In the transformation of time between frames, the coefficient of the space variable — he calls it e₁ — encodes the choice of clock synchronisation. In The Zero Acceleration Discontinuity and Absolute Simultaneity (2005) he shows that the velocity of light relative to inertial frames agrees with the zero-acceleration limit of the velocity of light relative to rotating platforms only if e₁ = 0 — that is, only if the Lorentz transformation is replaced by his inertial transformation, which yields an anisotropic one-way speed of light while preserving the measured two-way average. Setting e₁ = 0 makes simultaneity absolute. In Eight Proofs of Absolute Simultaneity (2010) he argues directly against what he calls the Reichenbach–Jammer conjecture, the view that e₁ is merely conventional: if it were conventional it could be altered without touching any empirical prediction, and Selleri contends that it cannot, so simultaneity belongs to physical reality.

The same theme recurs in the work of others. Thomas E Phipps, in Absolute Simultaneity With and Without Light Signals (1996), demonstrates that clocks permanently at rest in different inertial systems can be given an absolute synchronisation without transporting them and without exchanging light signals at all, on the assumption that relative clock rates are fixed by relative states of motion rather than by position. Ramon Risco-Delgado reaches Selleri-like transformations from a different premise in Inertial Transformations from the Homogeneity of Absolute Space (1997): assuming a privileged frame and the homogeneity of absolute space, he derives a transformation law that, he stresses, no experiment performed to date can distinguish from the Lorentz transformation. And Dennis J McCarthy, in The Orbiting Clock Paradox: Should the Lorentzian View Be Preferred? (1999), analyses a circling observer who sees a central inertial clock run fast and argues that the Lorentzian reading of the situation is the one to be preferred.

Experiments read as favouring a preferred frame

A second strand rereads the classic and modern optical experiments as showing small but real effects rather than perfect nulls. Jean Pierre Vigier set the tone in his 1997 Relativistic Interpretation (with Non-Zero Photon Mass) of the Small Ether Drift Velocity Detected by Michelson, Morley and Miller, arguing that the small drifts seen from 1887 to 1926 are not compatible with the classical addition of velocities and that introducing a very small photon mass implies a slight anisotropy in the velocity of light. Hector A Munera extended this in An Absolute Space Interpretation (with Non-Zero Photon Mass) of the Non-Null Results of Michelson-Morley and imilar Experiments: An Extension of Vigier's Proposal (1997), taking the residual drifts as compatible with absolute space once a small photon rest mass is admitted.

Munera also reworked the experimental record itself. In Michelson-Morley Experiments Revisited: Systematic Errors, Consistency Among Different Experiments, and Compatibility with Absolute Space (1998) he argues that the original experiment and every repetition were never actually null, that an incorrect inter-session averaging made the non-null results look smaller than they were, and that Illingworth's and other repetitions were in fact consistent with Miller's positive results and with a preferred frame. His 2009 review Towards the Reinstatement of Absolute Space, and Some Possible Cosmological Implications gathers four different terrestrial experiments that, he argues, all point toward solar motion in a plane near right ascension 75°, contradicting the received principle that the Earth's motion cannot be detected on Earth.

Several independent measurements are read the same way. Reginald T. Cahill and Kirsty Kitto, in Michelson-Morley Experiments Revisited and the Cosmic Background Radiation Preferred Frame (2003), reanalyse gas-mode interferometer data — correcting the Illingworth run for the refractive index of the helium used — and recover an absolute speed of the Earth of order 369 km/s, comparable to the cosmic-microwave-background dipole. Eugene I Shtyrkov, in Observation of Ether Drift in Experiments with Geostationary Satellites (2005), reports an orbital component of the ether drift of about 29.4 km/s from satellite tracking, close to the Earth's known orbital velocity. Carlos Enrique Navia, in Amplified Doppler Shift Observed in Diffraction Images as Function of the COBE "Ether Drift" Direction (2006), reports a one-way laser-diffraction effect consistent with a speed-of-light anisotropy of amplitude c/Δc ≈ 0.00123, matching the COBE dipole. Ronald R Hatch frames the whole search in In Search of an Ether Drift (2002): the CBR dipole already shows the solar system moving through a unique frame at about one percent of the speed of light, in conflict with the equivalence of all inertial frames, and this motivates the direct search.

The tradition also connects these readings to earlier positive results. Paul Wesley, in Michelson-Morley Result, a Voigt-Doppler Effect in Absolute Space-Time (1987), revives Voigt's 1887 treatment of the Michelson–Morley result as a Doppler effect, distinguishing the phase velocity (which gives the null fringe shift) from the energy-propagation velocity (fixed relative to absolute space), and uses the latter to account for the results of Roemer, Bradley, the Sagnac experiment, Marinov, and the 2.7 K anisotropy. A broad survey of the modern situation is given by Doug Marett in On the Continuing Relevance of Lorentz Ether Theory in the Age of Relativity (2011), which stresses that virtually all optical experiments to date cannot distinguish the predicted outcomes of Lorentz ether theory from those of special relativity, and reviews modern attempts to detect motion relative to a preferred frame.

Lorentzian gravitation and cosmology

Where Lorentz and Poincaré left their attempts at a Lorentz-covariant gravitation unfinished, several wiki authors take up the thread. Paul Wesley, in A Scalar Gravitation Theory in Absolute Space-Time (1988), extends Poisson's equation to include the mass equivalent of the gravitational field energy itself as part of the source, and converts it to a wave equation with time retardation; he reports that the model recovers roughly forty percent of the otherwise unaccounted precession of the perihelion of Mercury, and that the gravitational redshift, the slowing of the speed of light, and light bending follow from Newtonian gravitation together with the behaviour of photons. Ronald R Hatch's modified Lorentzian ether theory (above) is likewise notable for deriving both gravitation and inertia from a single mechanism.

On the largest scales, J. Brandes offers a Lorentzian reinterpretation of general relativity in A Lorentzian Approach to General Relativity: Einstein's Closed Universe Reinterpreted (1997), in which curvilinear space is not reality itself but is projected onto an underlying Euclidean space; on this reading, he argues, black holes disappear. Hector A Munera draws cosmological consequences from the preferred frame in Redshift in Absolute Space: Periodicity of Quasars and Other Cosmological Implications (1998), decomposing observed redshift into gravitational and velocity components and connecting the scheme to the reported periodicity of quasar redshifts.

Replacement kinematics and electrodynamics developed here

Finally, a number of authors set out to rebuild mechanics and electrodynamics on an absolute foundation. Paul Wesley's Evidence for Newtonian Absolute Space and Time (1997) develops what he calls "neomechanics", in which momentum is defined using the absolute velocity and a cosmological limit velocity equal to c emerges naturally; he cites the Monstein–Wesley experiment as confirmation and treats the one-way energy velocity of light as physically fixed relative to absolute space. His Weber Electrodynamics with Fields, Waves, and Absolute Space (1987) reconstructs electrodynamics from Wilhelm Weber's force law — which satisfies Newton's third law and conservation of energy and reproduces Ampère's original law — and extends the resulting Weber field to radiation by introducing time retardation in absolute space.

Ronald R Hatch supplies the dynamical counterpart to this programme. In Lorentzian Dynamics (1999) he argues that any absolute-ether theory must replace the kinematic explanations of special relativity with real dynamic forces, and works through the experimental issues this raises, generalising Sherwin's experiment into a series of thought experiments; the same experiment is the direct stimulus of his earlier A Modified Lorentz Ether and Sherwin's Experiment (1996), which analyses the stress a real FitzGerald contraction would induce in moving matter.

Related contributions round out the picture. G E Ivanchenko, in Relativity of Absolute Space and Time True and False Indications of Measuring Devices (2001), argues that Einstein's principle of relativity is stated too imprecisely and leads to accepting false instrument readings as true, and proposes a reformulated principle free of that defect. Rodrigo de Abreu and Vasco Guerra, in Special Relativity in Absolute Space: from a contradiction in terms to an obviousness (2006), give an alternative derivation of the standard relativistic effects that starts from a privileged frame in the spirit of Lorentz and Poincaré, arguing that the principle of relativity is not incompatible with a preferred, absolute frame. And Edward Kapuscik, in Non-Lorentzian Gauge Fields in Maxwell Electrodynamics (2000), points out that standard Maxwell electrodynamics admits a wider class of gauge fields than is usually recognised, leaving room for structure that a strictly Lorentzian reading overlooks.

Taken together, these papers make the case that the wiki's owner-community has long regarded as the missing half of the Lorentz-ether story: that the preferred-frame interpretation is a live, developed research programme, not merely a historical predecessor of special relativity.

See also

• Special relativity
• Aether
• Preferred frame
• Speed of Light
• Michelson–Morley experiment
• Time dilation