Special relativity

Scientific Theory
Name	Special relativity
Type	Theory of space, time, and motion
Author(s)	Albert Einstein
Keywords	Relativity, special relativity, simultaneity, time dilation, length contraction, Lorentz transformation, E = mc2
Year	1905

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Wikipedia Dispute: wikipedia:Special relativity

This Natural Philosophy wiki page disputes content found on Wikipedia page wikipedia:Special relativity

Special relativity is the physical theory published by Albert Einstein in 1905 in the paper On the Electrodynamics of Moving Bodies. It describes the relationship between space and time for observers moving uniformly relative to one another, and it replaced the Galilean transformations of classical mechanics with the Lorentz transformations. In mainstream physics it is regarded as extensively confirmed by experiment.

Special relativity is also the single most-discussed subject on this wiki. It is the keyword of more papers catalogued here than any other concept in physics, and the literature indexed under it — several hundred papers, together with dozens of books — is overwhelmingly critical. The critics are not a single school. They disagree with each other about what is wrong, about what should replace the theory, and about whether anything need replace it at all. What they share is the conviction that the theory's two postulates, its derivation, its treatment of time and simultaneity, or its claimed experimental support will not survive careful examination. This article states the theory briefly and then presents that body of work, author by author and argument by argument.

The general theory is treated separately at General relativity; particular topics have their own pages at Time Dilation, Twin paradox, Lorentz transformation, Michelson–Morley experiment, Sagnac Effect, Speed of Light, Aether and Preferred frame.

The theory in outline

Postulates

The theory is conventionally built on two postulates:

Principle of relativity — the laws of physics take the same form in all inertial (non-accelerating) frames of reference.
Constancy of the speed of light — light propagates in vacuum at the same speed c for all observers, regardless of the motion of the source or of the observer.

The Lorentz transformation

From the postulates Einstein derived the coordinate transformation between two inertial frames in relative motion along a common x axis with speed v:

x′ = γ(x − vt), t′ = γ(t − vx/c²), y′ = y, z′ = z

with γ = 1/√(1 − v²/c²). The same equations had been written earlier by Hendrik Lorentz and Henri Poincaré in the context of an aether theory; Einstein's contribution was to derive them from the two postulates alone, without an aether, and to read them as statements about space and time themselves rather than about the behaviour of matter moving through a medium.

Principal consequences

Relativity of simultaneity — events judged simultaneous in one inertial frame need not be simultaneous in another. This is carried by the vx/c² term in the time transformation.
Time dilation — a moving clock is observed to run slow by the factor γ.
Length contraction — a moving object is observed to be shortened along its direction of motion by the factor 1/γ.
Velocity addition — velocities combine as (u + v)/(1 + uv/c²) rather than additively, so that c cannot be exceeded by composition.
Relativistic mass and momentum — inertia increases with speed by the factor γ.
Mass–energy equivalence — expressed by E = mc².
Minkowski space-time — the invariance of the interval s² = c²t² − x² − y² − z², the geometrical form given to the theory by Hermann Minkowski in 1908.

The results usually cited in support of the theory are the null result of the Michelson–Morley experiment, the extended lifetimes of fast muons, the transverse Doppler effect, the energy–momentum relations used in particle accelerators, and the clock corrections applied in GPS. Every one of these is contested somewhere in the literature that follows.

The critical literature on this wiki

The community of the John Chappell Natural Philosophy Society and its predecessor the Natural Philosophy Alliance, together with the journal Galilean Electrodynamics founded by Petr Beckmann in 1989, has produced a critical literature on special relativity spanning more than a century. Much of it is gathered here. Chapter 2 - Catalogue of Errors for Both Theories of Relativity (2012), translated from the documentation of G O Mueller, surveys "95 years of criticism (1908–2003)" and identifies some 3,789 critical works. Zifeng Li's The Essence of Special Relativity and its Influence on Science, Philosophy and Society (2006) attempts a census of the other side of the ledger: the journals, meetings and networks devoted to questioning the theory, three distinguishable academic positions on it, four attitudes among the general public, and the recorded misgivings of well-known scientists.

The sections below group the arguments by idea rather than by author. Many authors appear in several sections, because the objections are connected: a critic who rejects the second postulate usually also rejects relative simultaneity, and one who accepts absolute simultaneity usually ends with a preferred frame.

Challenges to the two postulates

The first postulate: does an inertial frame exist?

Several authors argue that the relativity principle, as Einstein stated it, cannot be applied to the world we actually inhabit, because the strictly inertial frame it presupposes is nowhere realised.

Neil E Munch makes the point most bluntly in Boundaries of Applicability of Special Relativity (1999). Einstein's theory assumes kinematics (no forces), rectilinear motion at constant velocity, light-speed constancy, compliance with the Lorentz transformation, and agreement with the Michelson–Morley, Doppler and electrodynamic data. But kinematics presumes no gravity, and rectilinear constant-velocity motion precludes rotation and acceleration of any kind. Such an environment, Munch argues, is found nowhere in the universe, so the theory is applicable nowhere.

Antonis Agathangelidis argues the same way in Experimental Disproof of Special Relativity (1998): the condition of constant relative translation "is never fulfilled in nature, where curved paths and accelerations are everywhere present," and any answer to the questions this raises is fatal to the theory and to the Lorentz transformations it implies. Constantin I Mocanu draws a constructive conclusion from the same observation. In Hertz's Speciasl Relativity and Physical Reality (1994) he notes that it is hard to accept that launching a rocket is a succession of inertial motions, or that a re-entering satellite with continuously decaying angular momentum respects the Lorentz–Poincaré symmetries; kinematics, as the science of pure motion, must cover the non-inertial case too. Mocanu's answer is a companion transformation: in Co-Lorentz Coordinate Transformations; Co-Einstein Special Relativity: Part I (1998) and Co-Lorentz Coordinate Transformations; Co-Einstein Special Relativity - Part II (1999) he derives, from the reciprocity principle itself, a non-reciprocal "Co-Lorentz" transformation valid for non-uniform motion, so that relativistic kinematics becomes "a double-faced theory" using the Lorentz transformation for inertial motion and the Co-Lorentz transformation otherwise. His Hertz's Relativity: A Complimentary Theory to Einstein's SR (1995) extends Maxwell–Hertz electrodynamics to relativistic speeds in a coordinate-free formulation that needs no postulates at all.

Roland L Hron pushes the argument into gravity in Inertial Systems, Reference Frames and the Lorentz Transformations in a Gravitational Field (1999): if two frames near the same mass move in a straight line relative to each other, at least one must be accelerating relative to that mass, so Lorentz transformations cannot be applied to "non-accelerating reference frames" anywhere in a universe defined by its masses. He adds that the transformations are not covariant but one-way relationships. Jeff Alford examines what the first postulate actually asserts about mechanics in The Mechanical Part of Einstein's First Postulate in SRT (2001), and gives a compact statement of the postulates and their five consequences in Chapter 1: A Brief Overview of SRT (2008).

Georg Galeczki attacks the postulate from the side of what a physical law is. In Physical Laws and the Theory of Special Relativity (1994) he distinguishes specific laws from fundamental conservation principles and concludes that physical laws pertain to closed systems, are formulated in inertial frames determined by the centre of mass of the closed system, that a unique global inertial frame exists, and that physical laws need not be Lorentz covariant. With Peter Marquardt in A Non-Expanding, Non-Relativistic Universe (1996) he generalises the claim to cosmology: all relativities — Galilean, Machian, Einsteinian — are ruled out on principle and on observation, from atoms up to galaxies, and electromagnetic waves propagate isotropically in the fundamental frame defined by the mass–energy distribution of the universe.

The second postulate: is light-speed constancy forced by the evidence?

The second postulate draws the heaviest fire, on the ground that the experiments cited for it establish something weaker than what the postulate asserts.

Zifeng Li states the distinction directly in Special Relativity Arising from a Misunderstanding of Experimental Results on the Constant Speed of Light (2008): all experiments show that the speed of light relative to its source measured in vacuum is constant, whereas Einstein read this as light moving at fixed velocity c in the "stationary" system whether emitted by a stationary or a moving body. On Li's account the whole theory rests on the substitution of the second statement for the first.

Ludek Nerad's A Critical Analysis of Special Relativity Theory (1997) lists the same objection first among several: the second postulate is not a necessary consequence of the experimental data; rejecting Newtonian velocity addition contradicts either the definition of velocity, or the addition of distances, or the notion of time as an absolute independent variable; a multiplicative factor and two new variables are introduced arbitrarily; and the asymmetry of the Galilean transformation with respect to time is sacrificed without justification.

Curtis E Renshaw argues in The Restoration of Space and Time from a Galilean Approach to Relativity's Second Postulate (1998) that Maxwell's equations do not in fact deliver the postulate. Dimensional analysis of a planar electromagnetic wave gives a propagation speed c = (ε₀μ₀)^−1/2, but says nothing about the values of ε₀ and μ₀ in any particular frame, and therefore nothing about the speed of propagation with respect to a given source; the frame-invariance of c is an extra assumption, not a deduction.

Thomas E Phipps shows that even granting both postulates does not give the usual theory. Logical Insufficiency of the "Two Postulates" of Special Relativity (1993) exhibits an alternative kinematics in which the Lorentz contraction does not occur but which is fully compatible with the two postulates, so that the breaking of space-time symmetry is not a logical consequence of them.

Milo M Wolff removes the postulate from two of the theory's best-attested results. Derivation of the Relativistic Doppler Shift and Mass-Increase Formulas Without Assuming Special Relativity (1997) and Relativistic Mass Increase and Doppler Shift Without Special Relativity (1998) derive both formulae from the conservation laws plus the assumption of symmetry between a wave source and a wave receiver with no preferred frame of motion, using no Lorentz transformation at all. Wolff draws the philosophical moral himself: the experimentally proven Doppler and mass-increase effects are thereby separated cleanly from the controversial length and time changes, and the result adds evidence for the wave structure of matter.

Erich Wanek locates a paradox inside the postulate's own algebra. In Challenging Special Relativity: A New Train Paradox (2006) he observes that in c′ = x′/t′ the length contraction and the time dilation carry the same factor and cancel, so that constancy of c in every system forces the clocks to alter their pace according to the direction of motion — the "train paradox" of his title.

Irving C Laucks made an early version of this argument in Was Newton Right After All? (1959). Einstein's proof that motion affects time was a thought experiment with clocks synchronised by light, and Einstein said the kind of signal was immaterial; later interpreters said sound would serve as well. But, Laucks notes, any airline passenger's watch refutes the sound version, and Lorentz–Einstein transformation equations written with the speed of sound are unthinkable — and if they do not hold with sound as the signal, the argument for holding them with light must be something other than the one given.

The derivation of the Lorentz transformation

A large group of papers argues that the trouble is not in the postulates but in the algebra that Einstein used to get from them to the transformation equations.

Francisco J Müller's Fourteen Arguments Against Einstein's Theory of Special Relativity (1998) opens with the observation that neither Einstein nor anyone else ever used his 1905 "proof" of the Lorentz transformations again, and asks why. Among the fourteen: sloppiness in the use of symbols; the integration of a purely numerical equation; the commission of a "dualistic sin" in Einstein's own words, the theory really requiring three postulates; length contraction having the same ad hoc character as the earlier Lorentz–FitzGerald contraction; and logical flaws invalidating the claim of relative simultaneity. Müller charges the theory with the "fallacy of misplaced concreteness" — treating space and time as substantive things — and with holding that one object can have different real lengths or ages for different observers, in violation of its objective identity.

Thomas Smid gives two detailed technical readings. Mathematical Flaws in Einstein's "On the Electrodynamics of Moving Bodies" (2007) argues that the 1905 derivation first treats the speed of light as an additive quantity in the same sense as the speeds of material objects — in contradiction to the invariance it is supposed to be establishing — and then compensates with a faulty application of the chain rule for differentiation. Mathematical Inconsistencies in Einstein's Algebraic Derivation of the Lorentz Transformation (2005) treats the simpler derivation in Einstein's 1920 popular book, where two sets of equations each valid only for a positive or a negative value of x are suddenly assumed to hold for both; on Smid's reading only that sign error yields the transformation.

Aleksandar Vukelja reaches the same verdict by a different route. Mathematical Invalidity of the Lorentz Transformation in Relativity Theory (2005) reproduces Einstein's derivation step by step and identifies the transformation as "an imaginary solution to a set of equations which evaluate to zero throughout the derivation process." Triangle of Velocities and Mathematical Invalidity of the Lorentz Transformation in Special Relativity (2007) offers a general-case proof of invalidity independent of the derivation procedure, together with his own "Triangle of Velocities" reading of what the equations do describe.

Diego José Arturo Sa argues in On Lorentz Transformation (2005) and Frequent Errors in Special Relativity (2006) that an error preserved since Lorentz, Minkowski and Einstein is the writing of the transformations as if they referred to finite magnitudes when they should refer to infinitesimals — and that most of the paradoxes pervading the theory can be traced to it. He adds that reading the transformations as applying to coordinates rather than to intervals may be incorrect, and that the contraction factor cannot keep its accepted form if it is taken to equal a quotient of time differentials.

Wallace Kantor approached the transformation as a postulate in its own right. Lorentz Transformations Reconsidered (1989) is a review of the equations taken as postulates and of their prevailing derivations, reporting "past subtle oversights and kinematics anomalies," in particular an ignored dual synchroneity; Lorentz Transformations Reconsidered: 2 (1991) answers a rebuttal by showing it to rest on logically invalid assertions.

Boris I Peshchevitsky's The Lorentz Transformation and Its Reference Frames (1991) investigates the connection between linear space-time transformations and the character of the frames they connect, and concludes that the Lorentz transformation describes a system in which the time is decreed — "local time" — so that relativistic effects are consequences of that decreed reference time rather than effects in nature.

Zbigniew Oziewicz attacks the uniqueness of the boost itself. The Lorentz Boost-Link is Not Unique: Relative Velocity as a Morphism in a Connected Groupoid Category of Null Objects (2006) solves the isometry-link problem in general and proves that the solution is not unique; Ternary Relative Velocity (2007) shows that the Lorentz boost entails a ternary relative velocity — the velocity of a body relative to an interior observer as seen by a preferred exterior observer — with a non-associative addition law, so that a theory founded on the axiom that every pair of frames is related by a Lorentz isometry needs a preferred observer after all.

Sidney Bertram takes the opposite tack, deriving the transformation rather than refuting it. Wave-Particle Interactions and the Lorentz Transform (1997) and The Lorentz Transform (2008) obtain the x′ and t′ coordinates from Huygens' sources generated in a local medium by a moving particle, the momentum increase over the Newtonian value following from the growth of the particle's "surrogate" in the target's field. Alex Ceapa likewise seeks to supply the missing physics rather than discard the result: Einstein's Special Relativity as Practical Theory (2004) argues that Einstein tacitly omitted the physical justification of the manipulations leading to the transformation, so that the classical principle of physical determination of equations was never implemented in the resulting theory; Lorentz Transformation as a Complementary Time-Dependent Coordinate Transformation (2005) and Consequences of Founding SRT on the Whole Einstein's 1905 Paper on Relativity (2005) supply that derivation by tracing radius vectors of moving geometrical points with light.

Claimed internal contradictions

Reciprocity: each clock slower than the other

The oldest and most-repeated charge on this wiki is that the theory's symmetry between frames is self-contradictory: each of two observers in uniform relative motion must find the other's clock running slow and the other's rod shortened, and this, the critics hold, is not a perspective effect but a flat contradiction.

The argument is Herbert Dingle's. The Origin and Present Status of the Special Relativity Theory (1960) reviews the circumstances in which the theory arose, in the light of recent difficulties and of the revival of Ritz's alternative; The Twins Paradox of Special Relativity, published posthumously in October 1980, restates his reciprocity argument in its final form. The paper as catalogued here also carries an obituary of Dingle and a sidebar by Ian McCausland entitled "Why Not Discuss Relativity?". McCausland's own An Inconsistency in Special Relativity (1990) presents the argument from Einstein's original paper: the theory requires that each of two clocks in uniform relative motion actually runs slower than the other, which is an internal inconsistency. His Problems in Special Relativity (1983) makes the broader complaint that the arguments used to defend the theory against criticism contain many inconsistencies, and that these should be examined thoroughly and objectively by scientists and philosophers.

John Philip Claybourne devoted a full-length analysis to the point in The Reciprocity of Einstein's Special Relativity Theory (1992), observing that in all the supporting literature there is not a single comprehensive analysis investigating whether the reciprocity or symmetry features are physically possible, and that in the absence of such an analysis most physicists simply believe that the theory contains no contradiction. Allen D Allen framed the same difficulty as a question about what the derivative dx/dt refers to, in his 1988 paper on time dilation and the spatial interval for which dx/dt is a speed.

Louis Essen, whose caesium clock defined the second, summarised his criticism in a few lines in a letter to Carl Zapffe, transcribed here as Letter from Louis Essen to Carl A Zapffe: Harry Ricker Commentary (1984) with a commentary by Harry Hamlin Ricker. Its most memorable statement is that relativity is "not a theory."

Robert L Henderson's The Fundamental Fault with Special Relativity (1997) traces the whole family of "bizarre concepts" to a misunderstanding of the FitzGerald and Lorentz contraction; Lee Coe's Galilean-Newtonian Relativity versus Einsteinian Relativity (1991) holds that the theory's postulates, physics, mathematics and logic are all dubious and that the crop of paradoxes they generate cannot be reconciled with Galilean–Newtonian relativity or with any other part of classical physics.

Shifting assumptions

Neil E Munch contributed the most sustained single-author programme on this wiki — eleven papers catalogued here — devoted to one diagnosis: that the theory is worked with assumptions that are dropped and re-assumed at will, so that its derivations and its applications do not use the same premises.

Examples of Conflicts in Special Relativity Resulting from Shifting Assumptions (1997) and Conflicts in Special Relativity Resulting from Assumption Shifts (1999) identify five or six such assumptions and the conflicts each produces: contradictory provisions for the orientations of v and c; contradictory interpretations of x, x′, t, t′; an inappropriate assumption of linearity; and incompatible resulting equations. If light-use and all orientations of c and v are assumed, Munch argues, contraction is required in some orientations and dilation in others — contradicting the linearity that the derivation also assumes.

The consequence he presses hardest is that the theory's lengths and times are light-travel lengths and times, not arbitrary lengths and clock rates. Consequences of Relativity's Failure To Control Assumptions (2005) puts it this way: because the light-wave equations are the assumed basis of the theory, the time terms must be the elapsed time of light travel along the length term, "not clock time or clock rates or the age of twins as often assumed" — and with that, he holds, the Einstein–Lorentz transformation is critically flawed. Simple (but Critical) Flaws in Special Relativity Discussed in Everyday Language (2006) restates the point without algebra, and Ten Reasons Why We Need to Continue Discussing Special Relativity's Flaws (2006) answers the objection that the subject is closed, citing among other things the theory's requirement that a moving length contract and lengthen at the same instant.

The Doppler equations are Munch's test case. Clarified Relationships of Special Relativity and Doppler Equations (1997) and Conflicting Relationships in Special Relativity and its Doppler Equations (1998) show that when the light-use assumption is held constant the relativistic and Doppler equations become identical, and develop a generalised three-ratio expression whose solutions, tested with the standard equations, all produce serious conflicts. What Exactly Are the Problems (If Any) with Special Relativity Theory and Tests (1997) argues that most critical papers propose solutions without working through the problem, and that the experimental constraints have never been assembled in a form useful for testing proposed corrections. Some Questions Raised by the 'Three Reference Frames' (2006) sets out his positive proposal: the light-wave discontinuities visible when spherical waves from a single moving source are drawn over two frames are corrected only by replacing the two principles with a third frame — an aether — relative to which light speed is constant, together with a universal time.

Logic and the fallacy of misplaced concreteness

John E Chappell, founder of the Natural Philosophy Alliance, argued that the decisive faults are logical. Logical Analysis of Special Relativity (1998) holds that the theory is "a construct of the subculture of physics, not a certain reflection of reality," inferior to other theories that explain the same evidence because its two postulates contradict each other and each commits the fallacy of misplaced concreteness, and that the simultaneity thought experiment violates the law of non-contradiction. The Fallacy of Misplaced Concreteness as Revealed in Special Relativity (1999) develops the charge of reification on its own: a controlling influence over the velocity of light can logically be attributed only to something able to exert force, and a coordinate system, being an abstract set of points and lines, cannot. Simultaneity Cannot Possibly be Relative to Motion (1999) presents a modified version of Melbourne Evans's 1962 critique, arguing that Einstein reached relative simultaneity in the moving-train thought experiment only by contradicting himself within one chain of reasoning, and that avoiding the contradiction leads inevitably to absolute simultaneity whatever velocity is attributed to light. Related critiques of the theory's logical structure appear in Chappell's Crucial Flaws in Special Relativity: Logic and Simultaneity (1996) and Joseph F Cuny's A Refutation of Special Relativity (2002), and the mathematical objections are collected in Are there Mathematical Errors in Einstein's 1905 Derivation of Special Relativity (SRT)?.

Georg Galeczki adds two arguments of a different kind. Special Relativity's Heel of Achilles: the Units of Measurements (2000, revised 2004 as Special Relativity's Heel of Achilles) argues that the treatment of measurement units is the origin of the theory's contradictory interpretations, and grounds for rejecting it as irrelevant to physics. Minkowski's Scalar Invariant Incompatible with any Equation of Motion (2000) offers what Galeczki calls the first purely mathematical proof of the incompatibility of Minkowski space with particle dynamics, diagnosing the theory as "a tragic confusion" between the independent Eulerian coordinates x, y, z, t and the Lagrangian coordinates x(t), y(t), z(t) of a particle moving under forces — only continuous field theories being describable in the Eulerian manner.

Clocks, the twin paradox and time dilation

The twin paradox is treated on this wiki not as a resolved feature of the theory but as the point at which its treatment of time becomes visibly incoherent.

Thomas E Phipps's Twin Paradoxes (2007) reviews several paradoxical aspects of the twin problem and concludes that none has been permanently resolved. Sadanand S. Savarkar's A Requiem for the Misconceived Twins (2005) and A Reformulation and Vindication of Einstein's Experimentum Crucis (2005) revisit the problem and the crucial experiment attached to it. Nick Percival's A Very Doable Experiment For NASA To Look Inside The Twin Paradox (2006) notes that there is wide disagreement about how the net proper-time difference accumulates even among those who insist there is no paradox, and proposes an experiment to settle it.

Alexander L Kholmetskii analyses the paradox comparatively in The Twin Paradox in Special Relativity and in Lorentz Ether Theory (2003), confirming the standard relativistic result but then constructing a variant with symmetrical causal chains of events, in which the two twins' trajectories are realised with some probability. That probabilistic presentation, he argues, destroys the conception of equivalence among all inertial observers; the problem is then re-worked inside Lorentz ether theory.

Cynthia Kolb Whitney's The Twins, the Mesons, and the Paradox (1997) connects the paradox to the evidence usually taken to settle it: time dilation appears well validated by the slow decay of fast unstable particles, yet the same prediction produces a paradox that confounds ordinary logic.

That meson evidence is itself contested. Donald T MacRoberts's The "Time Dilation" of Mesons Re-Examined (1992) accepts that the CERN high-velocity experiments demonstrate a functional relationship between meson lifetime and velocity with respect to the Earth, but denies that this has anything to do with the time dilation of special relativity; on his reading the experiments are one more aether-drift investigation, returning the usual answer that the Earth's velocity with respect to a fundamental frame is zero.

Simon J Prokhovnik arrives at a preferred frame from the clock paradox while defending the theory rather than attacking it. The Mathematical and Physical Self-Consistence of Special Relativity (1987) shows that the usual resolution of the clock paradox leads to a second, physical paradox — a bona fide absolute effect emerging as a consequence of purely relative uniform motion — and that the resolution of that second paradox, due to G. Builder, yields an interpretation in which the theory's results are the necessary and unique consequence of the existence of a fundamental frame.

Joseph Levy makes the distinction that much of the aether-based literature turns on. Aether-Theory Clock Retardation vs Special Relativity Time Dilation (2008) assumes an aether not entrained by the motion of celestial bodies and argues that, contrary to special relativity, time itself is not affected by motion: the reading of a moving clock is the compound of two facts — that it ticks slower because it moves through the aether, and that the usual synchronisation procedures introduce a synchronism discrepancy. Torgny Sjödin's Real and Apparent Effects in Special Relativity (1989) makes the same separation formally, showing that the observed slowing of clocks and shortening of rods each decompose into a real part due to motion with respect to the privileged frame and an apparent part due to the chosen synchronisation — and that the measurability of the one-way velocity of light is a meaningless question in the Einsteinian interpretation but a meaningful one in the Lorentzian.

Ronald R Hatch argues in Clock Behavior and the Search for an Underlying Mechanism for Relativistic Phenomena (2002) that special and general relativity sometimes produce clock effects of equal magnitude that cancel and sometimes effects of equal magnitude that add, which cannot be coincidence; the effects appear to be related to energy, yet nothing in the two disjoint theories suggests the underlying mechanism. With Michael Brill, Thomas E Phipps and Tom Van Flandern he set out the associated timekeeping puzzle in Properties of Geodesics: Resolving an Apparent Conflict of Global Positioning System Evidence with General Relativity (2008).

Further material is gathered at Time Dilation and Twin paradox.

Simultaneity and the one-way speed of light

If simultaneity is not relative, the theory loses its distinctive content. A large part of the literature here is accordingly devoted to Einstein's definition of distant simultaneity and to the fact that the one-way speed of light is fixed by convention rather than measured.

Andrew R Dring's The Definition of Simultaneity (1996) argues that Einstein's definition has remained unchallenged despite being logically circular, introduces a manifestly frame-independent replacement, and derives from it a proof that the postulates of relativity are inconsistent. Harry E Mongold's The Concept of Simultaneity (1978) distinguishes the two operationalist senses in which the word is used in expositions of the theory and argues that neither is tenable in a strict sense.

Robert S Neiswander locates the trouble in a single term. Simultaneity, Absolutely (1996) traces non-simultaneity to the position-sensitive term in the Lorentz time transformation and argues that this term is not supportable by properly designed experiments, by the construction of the Lorentz equations, or by the established behaviour of satellite clocks. The Domain of Special Relativity (1997) makes the complementary point with an image: a unicorn may be defined as a horse plus a horn, but the abundance of horses does not establish the existence of unicorns; a relativistic system may be defined as one exhibiting motion-sensitive time dilation plus position-sensitive time offset, and the abundance of time-dilation effects does not by itself establish that any such system exists.

John Philip Claybourne's Experimental Data and Simultaneity (1990) argues that satellite-clock data contradict the predictions about simultaneity and demonstrate the need to revise accepted views of simultaneity and synchronisation. Thomas E Phipps's Absolute Simultaneity With and Without Light Signals (1996) demonstrates, first by an example built on Einstein's train and then by a general argument, that absolute synchronicity of clocks permanently at rest in various inertial systems is attainable without transporting clocks and without light signals at all, provided one assumes that relative clock rates are determined by relative states of motion rather than by position.

Joseph Levy's Is Simultaneity Relative or Absolute? (1997) criticises the criteria offered for the relativity of simultaneity from a logical viewpoint and proposes replacements under which relative simultaneity is called into question. W Vincent Coon's Simultaneity Interpretations (1996) shows that in inertial-frame scenarios the Einstein interpretation of the Lorentz transformation competes with rival transformations, obtainable by re-evaluating its simultaneity, which do not support light-speed invariance. Ronald R Hatch's Symmetry or Simultaneity (1999) frames the whole question as a choice Einstein made and Lorentz and Poincaré refused: absolute equivalence of all inertial frames with non-simultaneity, versus a single absolute frame with simultaneity. Einstein chose the first, Hatch argues, on positivist grounds — treating absence of proof as proof of absence — because no measurement could provide a criterion of simultaneity giving the same result for all observers.

R G Zaripov works the conventionality out mathematically in a series of papers: Convention in the General Definition of Simultaneity (1998) derives a general definition of the simultaneity of distant events covering both isotropic and anisotropic descriptions, obtains new two-dimensional space-time transformations, and shows that the special cases include Euclidean, pseudo-Euclidean and Galilean kinematics, all of equal validity with relativistic mechanics for describing the phenomena. Convention in Defining Simultaneity by Slow Clock Transport (1999) does the same for synchronisation by slow clock transport, Convention in the General Definition of Distance (2000) for distance, and Clock Synchronization and Finsler Structure of a Flat Anisotropic Space-Time (2001) shows the resulting space-time to have the structure of a flat anisotropic Finsler space.

Curtis E Renshaw proposes experimental tests. A Test of Relativistic Simultaneity (1997) points out that the theory was born from a thought experiment about the relative simultaneity of distant events, that this is the aspect most troubling to intuition, and that the theory is in any case only mathematically equivalent to most problems it is applied to; The Experiment of Fizeau as a Test of Relativistic Simultaneity (2008) turns the Fizeau experiment into such a test. Dan Wagner's Experiment Proposed to Resolve Simultaneity and One-Way Light-Speed Issues (1998) proposes a feasible experiment with two separated atomic clocks in solar orbit to answer the question whether clocks synchronised by light signal still measure one-way light speeds of c after being uniformly accelerated to a new velocity, with expected results differing from those of relativity theory and error sources shown to be negligible.

Thomas E Phipps's Testing Relativity Theory for One-way Light Propagation (2005) makes the general methodological point: most existing verifications of the theory rest implicitly on two-way light-speed averaging, whereas Bradley stellar aberration is a genuinely one-way propagation phenomenon, and Very Long Baseline Interferometry now offers resolution enough to look for the never-verified second-order departure the theory predicts.

Aether, preferred frames and equivalent theories

A recurring conclusion is that the empirical content of special relativity is reproduced exactly by a theory with a preferred frame and a physical aether, and that the choice between them is therefore not made by experiment.

Franco Selleri is the most systematic exponent of this position; seven of his papers are catalogued here. Theories Equivalent to Special Relativity (1994) sets out to find the complete set of theories empirically equivalent to special relativity on the assumption that the one-way velocity of light is not measurable, and reaches a result Selleri emphasised for the rest of his career: any modification of the coefficients of the Lorentz transformation, however small, gives rise to an aether theory. Space, Time, and Their Transformations (1995) constructs the set T of transformations equivalent for explaining the evidence from two empirical assumptions only — that the two-way velocity of light is c in all inertial systems and all directions, and that time dilation occurs with the usual factor. Noninvariant One-Way Velocity of Light and Particle Collisions (1996) defines energy and momentum consistently with the new transformations, which formally equal the relativistic expressions only in the privileged frame but numerically do so in all frames, and shows that the precise data on inelastic thresholds and particle masses are explained equally well.

Selleri's best-known argument is the rotating-platform limit. Noninvariant One-Way Speed of Light and Locally Equivalent Reference Frames (1997) calculates the velocity of light relative to the rim of a uniformly rotating platform of radius R in an isotropic inertial frame, finds values necessarily different from c, and observes that these do not change as R increases with the peripheral velocity held constant — so that any small piece of the rim can be considered better and better at rest in an inertial frame, while the anisotropy persists. The Zero Acceleration Discontinuity and Absolute Simultaneity (2005) sharpens this into a discontinuity at zero acceleration: agreement between the inertial and rotating cases requires the synchronisation coefficient e₁ to vanish, that is, requires replacing the Lorentz transformation by the "inertial" transformations based on absolute simultaneity. The Inertial Transformations and the Relativity Principle (2005) shows that clocks in all inertial systems can be re-synchronised so as to make a different, arbitrarily chosen system the isotropic one without changing any empirical consequence, so that the theory is compatible with a relativity principle weaker than Einstein's. Recovering the Lorentz Ether (2004) states the programme plainly: the alternative transformations explain the data better and eliminate the features that give rise to paradoxes, at the price of recovering a preferred inertial frame in which the Lorentz aether is at rest.

Stephane Baune denies the standard claim that the two frameworks cannot be told apart. Theory of Special Relativity vs. Preferred Reference Frame Theory: A Theoretical Distinction (2005) and its 2006 update describe a simple experiment whose predicted outcome differs between the two, using in the updated version only logical arguments and no Lorentz equations.

Mogens True Wegener's A Classical Alternative to STR (1995), dedicated to Phipps, argues for rejecting the theory in favour of a classical alternative based on the invariance of proper time, modifying the second postulate so that the one-way light speed may vary while its average remains invariant. Alexander L Kholmetskii's On Relativistic Kinematics in the Galilean Space (1995) describes complete space-time by two four-dimensional orthogonal subspaces, one with Galilean and one with Lorentz transformation laws, corresponding to two non-equivalent ways of building an inertial frame, and argues that this explains the physical sense of Lorentz's "world ether" hypothesis.

S Richard Hazelett's Special Relativity: The Experiments Equally Support Various Aether Theories (1998) argues that the successes of special relativity are equally the successes of aether theory as developed by Stokes, FitzGerald, Lorentz, Michelson, Herbert Ives and Petr Beckmann, together with the implications of Ronald R Hatch's work on light aberration, and that the differing physical implications of the competing theories deserve wider attention. Stephan J G Gift answered a standing challenge of the Natural Philosophy Alliance to produce a replacement theory in A Theory of Space and Time: Answering the Challenge of the President of the NPA (2005), pointing to the semi-classical aether-based theory derived from Maxwell, Lorentz, FitzGerald, Larmor and Ives, which agrees with special relativity over its full range of correct predictions; Experimental Detection of the Ether (2006) sets out his empirical case for the medium, explaining the null results of Michelson–Morley and Kennedy–Thorndike by the experimentally established contraction.

John Philip Claybourne argues in Why an Ether is Positively Necessary and a Candidate for the Job (1993) that although the mathematics of electrodynamics and of special relativity operates without reference to a medium, the aether concept is not thereby contradicted — merely not addressed — and that examining how energy and momentum pass between charged bodies shows the electric field must be their source. A P Bredimas's Schrodinger's "Aether" Unifies Quantum Mechanics and Relativistic Theories (1997) proposes Schrödinger's aether, ruled by transformation-isometries, as the bridge between quantum mechanics and the relativistic theories, beginning from a reminder of "contradictions in special relativity."

Koshun Suto returns the aether question to experiment. Thought Experiments whose Results do not Agree with the Prediction of Special Relativity (2001) and Thought Experiment to Offer a Definitive Answer to the Michelson-Morley Experiment (2006) argue that Einstein changed the aether question from whether it exists to whether it is needed as a concept, and that an experiment deciding whether light propagation is isotropic or anisotropic relative to its source — long thought not to exist — does exist. His New Transformation Equations which Replace Lorentz–Einstein Transformations to be Applied inside an Atom (2001) derives, from the relation E_ab² + c²p_n² = E₀² for an electron in a hydrogen atom, the conclusion that the electron's mass decreases as its velocity increases inside the atom.

Further material is gathered at Aether and Preferred frame.

The Sagnac effect and ring laser gyroscopes

The Sagnac effect — the travel-time difference between light beams sent in opposite directions around a rotating loop — is treated on this wiki as among the most direct experimental difficulties for special relativity, because the effect is real, first-order in v/c, and manufactured commercially. The orthodox reply, due to Paul Langevin, is that the rotating apparatus is non-inertial and that special relativity accounts for the effect exactly; critics reply that the effect nonetheless exhibits an anisotropic one-way speed of light, and that appeals to non-inertiality do not dispose of the problem.

The most striking testimony collected here comes from Cynthia Kolb Whitney, and carries unusual weight because she began as a defender of the theory with the credentials to defend it. Whitney took her MIT Ph.D. in mathematical physics in September 1967 with a thesis on special relativity itself — Pauli Algebra Techniques in Special Relativity, written under Laszlo Tisza — and in that same year joined the Charles Stark Draper Laboratory, where she was assigned to the ring laser gyroscope, an instrument whose entire operating principle is the Sagnac effect. It was the first application of her doctoral subject to a working device. In her 2013 John Chappell Memorial Lecture she recorded the result:

The engineers did not believe in SRT. Some of them, including myself, were dealing with ring laser gyroscopes, which are based on the Sagnac effect. For SRT, the Sagnac effect is a very inconvenient physical truth. But I argued with those engineers for quite a while. In fact, I argued for a whole decade. And I lost.

Whitney subsequently became Editor of Galilean Electrodynamics and developed a revised model of light-signal propagation intended to yield the mathematics the Sagnac effect requires without the second postulate. She has also reported that Tisza later told her of MIT physics faculty voicing private doubts about the substance of special relativity at a departmental tea, one of them remarking that it would take decades to correct all of Einstein's mistakes. Her Special Relativity Theory Aberrated (1994) and the three-part series Finding Absolution for Special Relativity Theory (Part II, Part III, 1996–97) work through the Sagnac effect and Galilean relativity together with absolute space and Doppler shifts; On What Optical Systems Can See (2006) examines the dictum that strictly inertial motion cannot be detected without an external reference, and argues that the optical results usually proclaimed "null" have often in fact been ambiguous. Her monograph Essentials on Special Relativity Theory (2006) collects the mature statement of her position.

Related arguments on this wiki include Ruyong Wang's report of a Sagnac-type travel-time difference in a uniformly moving fibre — published in the mainstream literature as Physics Letters A 312 (2003), pp. 7–10 — which removes rotation from the phenomenon altogether, and his phase-conjugate interferometer proposal for a first-order test of the isotropy of the one-way speed of light in a uniformly moving system; Franco Selleri's argument that the infinite-radius limit of a rotating frame is locally inertial yet retains light-speed anisotropy; Alphonsus G Kelly's work on clock synchronization around a rotating Earth; and the question posed by Howard C Hayden and Whitney in If Sagnac and Michelson-Gale, Why Not Michelson-Morley? (1990) — if rotation is optically detectable, why is translation not? The full literature is gathered at Sagnac Effect.

Electrodynamics without special relativity

Einstein's 1905 paper opens with the asymmetry in the description of a moving magnet and a moving conductor. A substantial body of work here argues that electrodynamics neither needs the theory nor is consistently described by it.

Unipolar induction

In An Experimental Disproof of Special Relativity Theory (Unipolar Induction) (2003) and a series of related papers, Francisco J Müller argues that experiments on unipolar induction — the effect of Faraday's 1832 unipolar inductor, or homopolar generator — directly falsify relativistic electrodynamics. Modifying the apparatus so that the whole circuit except one radial conductor is magnetically shielded, Müller reports electromotive force and motor action across field-free regions, where the local magnetic field is zero and a purely local field theory should predict nothing. By building a continuous magnet system that avoids all transversal magnet edges (his "edge effect"), he obtains induction where special relativity predicts none, and concludes that neither special nor general relativity can account for this "edge effect at a distance." Because Einstein's 1905 paper opens precisely with the magnet-and-conductor problem, Müller presents unipolar induction as a disproof at the theory's own starting point. His Some Remarks About Newton's Third Law and Special Relativity (1998) presses a related conflict: Ampère's law complies with Newton's third law and the Lorentz force does not, yet it is the Lorentz force that harmonises with special relativity.

The status of the Lorentz force

Georg Galeczki made that conflict a programme. What Does the Lorentz Force Have to do with Special Relativity? (1997, with Peter Marquardt) and What Does the Lorentz Force Have to do with Maxwell's Equations? (1998) argue that F = q(E + v × B) is independent of Maxwell's field equations and is not derivable as a "Lorentz-transformed Coulomb law"; its resemblance to the transformed normal component of E is misleading, because the Lorentz force is a phenomenological expression describing a charge moving in external fields originating in independent, decoupled systems. Electrodynamics, on this reading, can be built without the transformation. Dynamic Gamma Factor: Yes; Lorentz Transformation: No (1999) accepts the empirical γ while rejecting its kinematic interpretation: mass increase and the slowing of physical processes are non-reciprocal, absolute effects depending on Newtonian absolute velocity, as confirmed in the Bertozzi experiment, while the definition of uniform velocity excludes all non-Galilean transformations, so the kinematic gamma factor equals one and the mass increase is a consequence of kinetic energy possessing inertia.

Reformulating relativistic electrodynamics

Nizar Hamdan pursues the opposite strategy — keeping the relativity principle while discarding the Lorentz transformation. Abandoning the Idea of Relativistic Length Contraction in Relativistic Electrodynamics (2004) derives the fundamental relativistic equations for a charged particle, and the relativistic charge density, from the three-vector Lorentz force law without the transformation, making the kinematic length contraction useless as a basis for any dynamical variable. On the Invariance of Maxwell's Field Equations under Lorentz Transformations (2006) reformulates the theory by applying the relativity principle directly to Maxwell's equations; On the Interpretation of the Doppler Effect in Special Relativity Theory (2006) obtains the relativistic Doppler effect from the Lorentz force law and the relativity principle alone; Derivation of de Broglie's Relations from Newton's Second Law (2007) addresses the never-resolved inconsistency between special relativity and the de Broglie wave by expanding Newton's second law to all particle velocities; and Derivation of Einstein's Equation, E = mc2, from the Classical Force Laws (2007, with A. K. Hariri and José Luis López-Bonilla) obtains E = mc² from the Lorentz force law and Newton's second law without thought experiments or conservation arguments.

Victor N Barykin built a five-part generalisation of Maxwell's electrodynamics for moving media that does not resort to special relativity at all, basing its calculations on Newton's space, incorporating superluminal velocities, and describing the classical Bradley, Fizeau, Michelson and Doppler experiments in a unified way: Part I (2002), Part II (2003), Part III (2004), Part IV (2007) and Part V (2007).

Alexander L Kholmetskii reports internal difficulties in the standard field transformations. The Faraday Induction Law and Field Transformations in Special Relativity (2003) analyses the non-invariance of the Faraday induction law for integration over a conducting circuit, distinguishing the cases in which the internal fields of rearranged conduction electrons do and do not contribute; Do We Understand the Field Transformations in Classical Electrodynamics? (2004) traces the relationship between transformed non-radiating fields and their sources through the laws of electrostatics and magnetostatics.

Oleg D Jefimenko's Derivation of Relativistic Transformations for Gravitational Fields from Retarded Field Integrals (1995) derives transformation equations for gravitational fields analogous to the Lorentz–Einstein transformations of relativistic electrodynamics from retarded field integrals, showing that Newtonian gravitation extended to time-dependent fields is fully compatible with the relativity principle and admits a covariant formulation — and thus that the classical theory of retardation can support a relativity theory equivalent to Einstein's in its practical aspects but free of its controversial elements. D E McLennan's Maxwell Equations: A New Approach (1989) obtains Maxwell's equations from a hypothetical subatomic particle, the "emon," whose magnetic property appears only in motion.

Stefan Marinov's Propulsive and Rotating Ampère Bridges and the Principle of Relativity (1991) reports that the historical Ampère bridge experiment and his own rotational variant appear to violate the principle of relativity: the rotating bridge is an electromotor without a stator, rotating under internal forces, yet back-tension is induced in contradiction to the relativistic requirement that tension appear only when there is relative motion of magnet and wire.

Howard C Hayden's Einsteinian and Quantum-Mechanical Observers (1993) points to a different kind of gap: Maxwell's equations are automatically consistent with the Lorentz transformation, and quantum electrodynamics rests on Maxwell's equations, yet there is no successful theory incorporating the features of both special relativity and QED — and the two carry inherently inconsistent notions of the observer.

Mass, energy and the neutrino

E = mc² and the relativistic mass formula have their own critical literature here.

Ricardo L Carezani's Autodynamics is the most radical position: the concept of two or more reference frames is redundant, both mathematically and physically, and special relativity should be replaced by a single-frame formulation. The consequence Carezani pressed hardest is the elimination of the neutrino. A New Experiment With RaE (1988) revisits the classic discrepancy between the calorimetric measurement of the total decay energy of RaE (²¹⁰₈₃Bi) and the kinetic energy that special relativity calculates to be available from the beta-decay velocity spectrum — the discrepancy that led Pauli to postulate the neutrino — and proposes a new calorimetric test. Nucleus-Nucleus Collision (1998) applies autodynamic equations to the smaller-than-expected linear momentum transfer in nucleus–nucleus collisions and argues that the "missing mass" and "missing momentum" of RaE, ²³⁸U, muon decay, anomalous mean paths and electron–electron and proton–proton annihilation all have in common a failure produced by applying special-relativistic equations. Super-Kamiokande: Super-Proof for Neutrino Non-existence (1998) and Neutrinos at Fermi Lab (1998) extend the argument to the great detectors, treating background events and shielding in detail.

Zifeng Li's The Essential Relationship Between Mass and Energy (2007) analyses the mass–velocity relationships of the competing theories and rejects both the mass–velocity and the mass–energy equations of special relativity, offering an alternative account of the source of the energy released in nuclear processes. Müller and others likewise argue that Einstein's derivation of E = mc² begs the question, and dispute the popular beliefs that the equation was the essential basis for the atomic bomb and that atomic energy arises from the transmutation of mass into energy.

Steven Dinowitz's Super-Relativistic Dynamics (1991) proposes a different mass equation in which motion relative to the locally dominant gravitational field is the critical factor: a body at the Earth's surface moving at the velocity of light relative to the Earth's gravitational field, along or against the Earth's orbital velocity, would have a mass 120,000 times its rest mass.

Vyacheslav N Streltsov argues in Elongation of Moving Bodies (2003) that the theory associates a four-component quantity with a material rod, and that since the space-like interval is a Lorentz scalar equal to the rest length, the space part of it — the length of the rod in motion — is because of the pseudo-Euclidean sign always greater than the interval: moving bodies elongate rather than contract. His "Einstein Reconsidered" commentary argues that the theory should properly be named the Lorentz–Poincaré–Einstein–Minkowski relativity theory.

Experimental tests said to fail or to admit other explanations

Neil E Munch's Five Sets of Experimental Evidence Which Contradict Special Relativity (2000) assembles the case in one place: that proper lengths on Earth do not reduce to zero when viewed by passing photons at speed c, though the theory requires it; that the Michelson–Morley tests are now conceded by at least one establishment physicist (Mermin) to have been inconclusive, and that the frequency "locking" of contra-flowing light beams raises further questions about their efficacy; and that forces such as gravity are present everywhere the theory is applied.

Theodore D Mitsopoulos treats the Michelson–Morley result as misinterpreted rather than null. The Interpretation of the Michelson-Morley Experiment and the Replacement of Classical Physics by Special Relativity (1987) and Disproof of Special Relativity and Restoration of Classical Physics (1989) propose that the physical environment is the real carrier of light propagation, that the kinematics of radiation depends on the mutual states of motion of environment, frame and apparatus, and that a classical explanation of the null result is available — whereupon the Lorentz transformation becomes disputable.

Chalmers W Sherwin's An Analysis of the Silvertooth Experiment (1989) is an instructive counter-example within the critical literature: examining Silvertooth's claim to have detected an ether wind with counter-propagating optical beams, Sherwin confirms Phipps's conclusion that the observed antinodes cannot be affected by the phase of the light at the photocathode, and traces the reported profiles to ac-coupling between photodetector and oscilloscope. The wiki catalogues both this and B. A. Manning's preliminary analysis of the same experiment.

Tom Van Flandern's The Speed of Gravity: An Experimental Contradiction of Einstein's Special Relativity (1998) observes that of the ten independent classes of experiment testing the theory, half at first appeared to contradict its frame-reciprocity prediction in favour of the earlier non-reciprocal Lorentzian theory, and were subsequently reconciled by new interpretations and are now cited as corroboration — GPS among them, since GPS shows that clocks in many different frames can be simultaneously synchronised.

Curtis E Renshaw built a series of papers around the Pioneer 10 and 11 anomaly, arguing that the constant skewing between predicted and observed Doppler shifts — an apparent sunward acceleration of about 8×10⁻⁸ cm/s² — equals the difference between the Newtonian and special-relativistic Doppler expressions, and that using Galilean Doppler equations without the time-dilation component in the data reduction makes the "anomaly," including its physically baseless Earth-year periodicity, disappear. His Apparent Super-luminal Jets as a Test of Special Relativity (1996) argues that certain orientations of astrophysical jets require, under the theory's own assumptions, velocities relative to the source exceeding c, whereas other models do not.

Elsewhere on the wiki, Peter Ripota's Einstein's Time Dilation Experimentally Refuted (2009) cites a 1996 entangled-photon experiment by Antoine Suarez and Valerio Scarani at CERN in which a rapidly rotating detector produced no expected phase shift, and Nick Percival's Data That Allegedly Proves Special Relativity Disproves It (2013) re-analyses the GPS, Hafele–Keating and muon-decay data and argues that they do not support — and in places contradict — the theory. The preferred-frame and asymmetry arguments are collected in Critical Flaws in Special Relativity and Its Possible Replacement by Doppler Concepts, which holds that the Doppler effect, the Sagnac effect, GPS timing, stellar aberration and unipolar induction are all asymmetric between observers and therefore require an absolute frame.

Rival kinematics and replacement theories

Much of this literature is constructive. The theories proposed here to replace or supersede special relativity fall into several families.

Galilean and classical restorations. Walter Babin's A Classical Replacement for Special Relativity (2008) argues that all the formulas and physical effects of the theory devolve to those of classical mechanics and electrodynamics, relativistic effects being Doppler modifications of wavelength, frequency and energy arising naturally from the finite velocity of light in the observer's frame; Hoek, Fizeau, and Einstein's Special Relativity (2008) works the historical aether-drag experiments through the same lens. Adolphe Martin's Reception of Light Signals in Galilean Space-Time (1997) argues that the time of light reception by an observer moving relative to a source is a different event from reception of the same light by an observer at rest, and that treating them as the same event is what introduces the paradoxes; using Einstein's own coordinates but reasoning as a Galilean, he obtains light speeds c′ relative to the moving observer. Roger J Anderton's Special Relativity is Galilean Relativity (2008) argues that once the mathematical errors are corrected the two theories coincide, and asks how many corrections a theory can absorb and still be the same theory; Light Waves and Special Relativity (2008) argues that the illusory character of waves as presented in elementary texts has not been properly appreciated in relativistic contexts.

Anisotropic and Finslerian kinematics. Jian-Miin Liu keeps both postulates but changes the geometry. A New Test Theory of Special Relativity: Testing its Structures in Gravity-free Space and Time (1997) assumes generalised Finslerian structures for gravity-free space and time in the usual inertial coordinate system without losing flatness, so that the Lorentz transformation becomes localised between inertial systems and gravity-free space-time matches the Fock velocity-space; Generalized Finsler Geometry and its Cartan Connection in Modification of Special Relativity (2002) supplies the mathematical apparatus. His An Inconsistency in the Theory of Special Relativity and its Resolution (1997) locates the motivation in a boundless velocity-space implied by the flat metric structures, and Motivations to Modify Special Relativity (2002) lists the wider reasons: the point-like or string-like particles the theory forces, and hence the divergences of quantum field and string theory; the non-uniformity of momentum space, which frustrates Lorentz-invariant statistical mechanics; and unexplained observations. R G Zaripov's anisotropic Finsler space-time, described above, belongs to the same family.

Emission and medium theories. Herbert Dingle already noted in 1960 that Ritz's emission theory, long thought disproved, had again become a distinct possibility. Milo M Wolff's derivations without the transformation belong to his wave structure of matter. Lorenzo Mencherini's On the Concept of Integrality in the Theory of Special Relativity (1989) starts from the notion of a body "integral" in a frame — one whose points have constant coordinates in time — and asks what kinematic relationship two bodies can then have.

Observation-based theories. Zifeng Li's Moving Objects Observation Theory in Place of Special Relativity (2007) introduces a "visual space-time" and derives the relations among the real space-time of moving coordinate systems, the visual space-time and the observer; Rejecting Einstein Relativity & Developing Newton Physics (2008) sets the programme in its wider context. James P Siepmann's "Laws of Space and Observation" treat Space as an entity in its own right and time as non-relative: The Laws of Space and Observation (1999) presents the Relative Space Density and Relative Space Warp equations, and The Light Clock: A New Method of Measuring True Time (1999) argues that current interval measurements record a periodic occurrence rather than true time, which can be measured only against the objective speed of light.

Reconstructions from classical clocks and fields. John Byl's Special Relativity via Electromagnetic Clocks (1999) and Deriving Special Relativity Theory from Electromagnetic Clocks (2003) derive length contraction, time dilation and mass increase from classical mechanics and electromagnetism plus the assumptions that an aether exists and that time dilation is the same for all electromagnetic clocks — the later paper proving, rather than assuming, that clock periods are orientation-independent. Giuseppe Antoni's Special Relativity as an Evolution of Classical Physics (1989) presents the theory as continuous with the classical tradition, noting that the Lorentz formulae had already been obtained by Poincaré in the fixed-ether theory; with Umberto Bartocci, A Simple Classical Interpretation of Fizeau's Experiment (2001) defends Stokes's dragged-aether theory against the two phenomena usually held to refute it, Bradley aberration and the speed of light in moving water, by a simple time-delay model. Lawrence M Stephenson's The Significance of Precursor Electromagnetic Waves in Special and General Relativity (1998) accepts the mathematics while holding that its interpretation, especially in relation to quantum theory, is far from complete, and offers precursor electromagnetic waves as a new route into it. John R Warfield's A New SRT Based on the Higgs Field (2006) makes the Higgs field determine the value of mass and the rate of time, allowing both to differ between frames, and Consequences of Relativity (2005) draws out eight consequences of his flowing-space picture.

History, priority and reception

A separate strand holds that the mathematics of the theory was in place before 1905 and that the historical account taught to students is a reconstruction.

Alexei A Tyapkin's On the History of the Special Relativity Concept (1997) supplements what he calls a one-sided image of this stage in the history of science by recalling the forgotten approaches that show relativity's close relation to classical concepts, emphasising particular statements of Poincaré and Lorentz. Michele Barone's Some Almost Unknown Aspects of Special Relativity Theory (1997) applies Thomas Kuhn's observation that the textbook tradition in which scientists feel themselves participants is one that never existed. The priority argument is stated on this wiki in Errors Before Einstein; Vyacheslav N Streltsov makes the same case in naming the theory after four men rather than one.

Jozef S Wilczynski's Comment on 'The Einstein-Lorentz Transformation...' by J. A. Morales (1990), published in the Toth-Maatian Review, belongs to the same critical current, as does Joe Alexander Nahhas's early Special Relativity Theory: Based on Two Erroneous Principles (1977), which reads the length contraction as a visual effect of projected light aberration.

Zifeng Li's survey work, G O Mueller's catalogue of 3,789 critical works, and Ian McCausland's complaint that the defences of the theory are never subjected to the scrutiny the theory itself demands together document the reception history that this wiki exists in part to preserve.