Recovering the Lorentz Ether: Difference between revisions
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The description of natural phenomena by observers in motion is a problem that many consider solved once and for all by the Lorentz transformations of the Theory of Special Relativity (TSR), though it was actually was left open. Consequences of my alternative transformations of the space and time variables are: (i) an explanation of the empirical data better than provided by the TSR; (ii) the elimination of those features of the TSR which give rise to paradoxes. This is obtained thanks to the recovery of a preferred inertial frame in which the Lorentz ether is at rest. In the present paper I expound the basic ideas of the research, leaving aside mathematical detail. | The description of natural phenomena by observers in motion is a problem that many consider solved once and for all by the Lorentz transformations of the Theory of Special Relativity (TSR), though it was actually was left open. Consequences of my alternative transformations of the space and time variables are: (i) an explanation of the empirical data better than provided by the TSR; (ii) the elimination of those features of the TSR which give rise to paradoxes. This is obtained thanks to the recovery of a preferred inertial frame in which the Lorentz ether is at rest. In the present paper I expound the basic ideas of the research, leaving aside mathematical detail. | ||
==Overview== | |||
Franco Selleri, of the University of Bari and INFN, wrote this 2004 ''[[Apeiron]]'' article as a non-technical exposition of a research programme he had pursued for a decade in ''Foundations of Physics'' and elsewhere. His target is not the mathematics of [[Special Relativity]] but its interpretation. Selleri argues that the Lorentz transformations contain a term that is purely conventional — a free synchronisation parameter that Einstein fixed by decree rather than by measurement — and that setting it to a different value yields a family of "equivalent transformations", every member of which except the Lorentz case presupposes a preferred inertial frame. Choosing the particular member with parameter ''e''<sub>1</sub> = 0 gives what he calls the '''inertial transformations''', in which time is entirely freed from the geometrical role Minkowski assigned it and the [[Aether]] at rest in the preferred frame is restored. | |||
The essay is deliberately philosophical in tone. Selleri opens by quoting Einstein's own late admissions — the 1949 letter to Solovine ("There is not a single concept of which I am convinced that it will resist firmly") and the April 1955 preface, his last written work, ending "how far in my opinion we still are from possessing a conceptual basis of physics, on which we can somehow rely" — and reads them as a warning against treating relativity as final. He then lists what he takes to be the theory's paradoxes: the invariance of light speed for a pursuer at 0.99''c'', the conventional character of distant simultaneity, the absence of an objective description of contraction and clock retardation, the asymmetric ageing of the twins in a theory "that carries the flag of relativism", the hyperdeterministic block universe, the loss of an objective value for energy, and the discontinuity between inertial frames and frames with arbitrarily small acceleration. His claim is that all of these dissolve once relativism — the doctrine that all inertial observers are strictly equivalent — is abandoned, while every empirical success of the theory is retained, and that in one case, the [[Sagnac Effect]], the alternative succeeds where relativity fails outright. | |||
==The argument== | |||
===The conventionality of simultaneity=== | |||
Selleri grounds his case in Einstein's own words. From the 1905 paper: "the latter cannot be defined at all unless we establish by definition that the 'time' required by light to travel from A to B equals the 'time' it requires to travel from B to A." From 1916, on the midpoint M of AB: this "is in reality neither a supposition nor a hypothesis about the physical nature of light, but a stipulation which I can make of my own free will." Reichenbach's 1925 analysis then generalises the stipulation: where relativity sets ''t''<sub>2</sub> − ''t''<sub>1</sub> = ½(''t''<sub>3</sub> − ''t''<sub>1</sub>), any rule ''t''<sub>2</sub> − ''t''<sub>1</sub> = ε(''t''<sub>3</sub> − ''t''<sub>1</sub>) with 0 < ε < 1 "would likewise be adequate and could not be considered false". Jammer's 1979 statement of the thesis of the conventionality of intrasystemic distant simultaneity — that ε "may be any number in the open interval between 0 and 1, i.e. 0 < ε < 1, without ever leading to any conflict with experience" — is the logical opening Selleri exploits: "there is an important logical space for different values of ε, i.e., in the final analysis, for alternative theories to the TSR!" | |||
===Two empirical facts=== | |||
Rather than assume a transformation, Selleri derives one from what he takes to be securely measured. The first is the invariance of the ''two-way'' speed of light. The 1978 British measurement gave ''c''<sub>ar</sub> = 299,792.4588 ± 0.0002 km/s, a precision of 10<sup>−9</sup>, a thousand times finer than needed to detect the ''u''<sup>2</sup>/''c''<sup>2</sup> ≈ 10<sup>−6</sup> variation classical physics would predict from the Earth's ~300 km/s galactic motion; no such variation was seen. He is careful that this says nothing about the ''one-way'' speed, quoting Poincaré (1898): "It will always be impossible to verify this postulate directly with experiments." | |||
The second is clock retardation by the factor ''R'' = √(1 − ''u''<sup>2</sup>/''c''<sup>2</sup>). Selleri cites the 1977 CERN muon storage ring, where muons at 0.9994''c'' with centripetal acceleration 10<sup>18</sup>''g'' lived 29.33 times longer than at rest, exactly as ''t'' = ''t''<sub>0</sub>/''R'' requires; the 1972 Hafele–Keating flights (westbound clocks losing 59 ± 10 ns, eastbound gaining 273 ± 7 ns); and the [[GPS]] constellation, whose onboard clocks are pre-slowed by 38,700 ns/day to compensate the combined gravitational (+45,900) and velocity (−7,200) effects. | |||
===The equivalent and inertial transformations=== | |||
From four standard assumptions (homogeneity and isotropy of space in S<sub>0</sub>; isotropic light speed ''c'' in S<sub>0</sub>; S moving at υ along +''x''<sub>0</sub>; axes coinciding at ''t'' = ''t''<sub>0</sub> = 0) plus the two empirical facts, Selleri shows the transformation from S<sub>0</sub> to S must take the form | |||
: ''x'' = (''x''<sub>0</sub> − υ''t''<sub>0</sub>)/''R'', ''y'' = ''y''<sub>0</sub>, ''z'' = ''z''<sub>0</sub>, ''t'' = ''Rt''<sub>0</sub> + ''e''<sub>1</sub>(''x''<sub>0</sub> − υ''t''<sub>0</sub>), | |||
with a single undetermined coefficient ''e''<sub>1</sub> — the synchronisation parameter, following Mansouri and Sexl's observation that the coefficient of ''x'' in the time transformation is purely conventional. The Lorentz transformations are the special case ''e''<sub>1</sub> = −υ/''Rc''<sup>2</sup>, the value that produces the space–time symmetry of Minkowski's "union of the two". Setting ''e''<sub>1</sub> = 0 gives the inertial transformations, in which the delay ''t'' − ''t''<sub>0</sub> depends only on ''t''<sub>0</sub> and not on position, so time is absolute; the price is that the one-way speed of light in S is anisotropic. Selleri reports having checked explicitly that Römer, Bradley, Fizeau, Michelson–Morley, Doppler and International Atomic Time data are all insensitive to ''e''<sub>1</sub>, and observes pointedly that "all such theories are based on the existence of a preferred frame, the only exception being the TSR." He claims that linear accelerations, rotating platforms and superluminal signals do single out ''e''<sub>1</sub> = 0, referring the argument to his earlier technical papers. | |||
===The objectivity of energy=== | |||
Selleri's most philosophical section attacks relativism through the [[Energy]] concept. Since every inertial observer assigns a particle a different velocity and hence a different ''E'' = ''mc''<sup>2</sup>/√(1 − ''u''<sup>2</sup>/''c''<sup>2</sup>), and none is privileged, "one is forced to conclude that a real energy value does not exist". He traces the same move in James Jeans (1943), who argued that because forces are apprehended differently by differently moving observers, "the forces cannot have a real objective existence; they are mere mental concepts" — and who followed the argument all the way to idealism: "The universe begins to look more like a great thought than like a great machine." For Selleri this is a ''reductio''. The escape is the non-equivalence of frames: with a preferred system, energy has a true value, the one relative to S<sub>0</sub>. | |||
===Einstein's ether=== | |||
A section of quotations documents Einstein's own return to the ether. The 1919 letter to Lorentz: "It would have been more correct if I had limited myself, in my earlier publications, to emphasizing only the non-existence of an ether velocity, instead of arguing the total non-existence of the ether." The 1920 Leiden address: "To deny the existence of the ether means, in the last analysis, denying all physical properties to empty space. But such a view is inconsistent with the fundamental facts of mechanics." Selleri accepts the relativistic ether as far as it goes — "a space endowed with physical properties can very well be called ether" — but finds it "strange and unpleasant to deprive the ether of all states of motion". The inertial transformations restore its immobility in S<sub>0</sub>, and with it the Lorentz ether entire. | |||
===Twins, aberration, Sagnac, cosmology=== | |||
Four applications close the argument. On the '''twins''', Selleri does not dispute the numbers (a 0.99''c'' round trip to Mira Ceti, 32 light years away, takes 64.6 years for the stay-at-home and about 9 for the traveller) but the interpretation: in Hafele–Keating the eastward and westward results differ only because velocities were added to and subtracted from the Earth's rotation "with respect to the surrounding space", which relativism forbids; treating the results as relativistic successes "means forgetting the relativism of the theory, and thoughtlessly calculating with respect to the inertial frame in which the Earth's center is instantaneously at rest." With a preferred frame, "the twin ageing less is always the one who feels the effects of larger absolute velocities." | |||
On '''aberration''', Selleri proves that every equivalent transformation yields the identical formula tan θ = ''R'' sin θ<sub>0</sub>/(cos θ<sub>0</sub> − υ/''c''), with all right-hand quantities referred to S<sub>0</sub>. Because the absolute aberration angle is the same for all S, the angle observed between any two frames is the same too. This, he argues, resolves a real difficulty: Einstein derived the formula with υ the relative star–Earth velocity, but stars move randomly, so the relative velocity differs from star to star while the observed aberration does not. Ives (1950) sharpened the point using spectroscopic binaries whose components have orbital velocities comparable to the Earth's yet show identical aberration. On the inertial transformations, υ is simply the Earth's absolute velocity, and the annual variation of aberration follows from the Earth's orbital motion. | |||
On the '''[[Sagnac Effect]]''', Selleri holds that relativity has no genuine derivation. Langevin's 1921 treatment claims general relativity but is "really 100% Galilean"; his 1937 paper offers two mutually independent treatments, the first assuming the platform everywhere uses the time of the motionless centre. Post's influential 1963 review likewise gives two proofs, one arbitrarily using ''t''′ = ''tR'', the other starting from the Lorentz transformation and then choosing '''r''' perpendicular to '''u''' so that the offending term vanishes. Hasselbach and Nicklaus list about twenty published "explanations", noting that "this great variety (if not disparity) in the derivation of the Sagnac phase shift constitutes one of the several controversies... that have been surrounding the Sagnac effect since the earliest days." Selleri's point is that Langevin's and Post's common tactic — eliminating ''x'' from the transformation of time — is precisely what ''e''<sub>1</sub> = 0 does honestly. | |||
On '''cosmology''', Selleri argues that the [[Big Bang]] rests on an unstable chain: the four-dimensional space of general relativity rests on Minkowski space, which rests entirely on the fourth Lorentz transformation. Remove that and no fourth dimension remains in which to embed and curve a three-dimensional universe. A genuine three-dimensional explosion would leave "an empty central region, the 'crater of the explosion,'" surrounded by galaxies and then by radiation alone — nothing like the isotropic sky the telescopes show. His conclusion is blunt: "The big bang never happened!" | |||
==Assessment== | |||
The strongest part of this paper is its foundational core, and it is not a fringe position. That the one-way speed of light is not directly measurable without a prior synchronisation convention, and that the Reichenbach parameter ε is genuinely free within the interval (0,1), is standard in the philosophy of physics literature — Reichenbach, Grünbaum, Jammer and (in physics) Mansouri and Sexl all say so. Selleri's derivation of the equivalent transformations from four geometric assumptions plus two measured facts (two-way light-speed invariance and the ''R'' factor for clocks) is clean, and the resulting one-parameter family with the Lorentz case at ''e''<sub>1</sub> = −υ/''Rc''<sup>2</sup> is correct. His observation that every member of the family except one requires a preferred frame is a real structural insight. The aberration argument is the sharpest empirical point in the essay: the Ives binary-star objection is a genuine puzzle for the naive "relative velocity" reading of Einstein's derivation, and Selleri's resolution — that υ is the observer's absolute velocity, so all stars aberrate alike — is economical. He is also right that the Hafele–Keating and GPS analyses are performed in the Earth-centred non-rotating frame, and that this is rarely remarked upon. | |||
The central difficulty is that the paper's own logic works against its conclusion. If, as Selleri establishes at length, all values of ''e''<sub>1</sub> are empirically equivalent for the great body of optical and clock experiments, then ''e''<sub>1</sub> = 0 cannot be "an explanation of the empirical data better than provided by the TSR" — it is, by construction, an equally good one with a different convention. The claim that certain experiments do single out ''e''<sub>1</sub> = 0 is the load-bearing assertion of the whole programme, and it is exactly the point at which the reader is referred elsewhere: "we cannot discuss it here for reasons of space." A reader of this paper alone therefore has no way to evaluate the decisive step. That is a legitimate choice for an expository article, but it means the article's title claim is not established within it. | |||
The Sagnac argument overstates its case. That published derivations of the Sagnac shift are numerous and disparate is true and well documented; that special relativity ''cannot'' produce one is a much stronger claim, and the standard modern treatment — integrating the light travel time around a closed path in the rotating frame, where the metric is non-diagonal and no global synchronisation exists — is neither Galilean nor arbitrary. The Sagnac shift, being first order in Ωrc and independent of the medium's refractive index, is what one expects for a rotating (hence non-inertial) frame in any theory that gets the round-trip light time right; Selleri's own point that a rotating frame cannot be globally synchronised is precisely the mainstream explanation, restated as a discontinuity objection. Similarly, on the twins, the appeal to "the surrounding space" in Hafele–Keating is not evidence for a preferred frame: the calculation is done in the Earth-centred inertial frame because that frame is inertial, and would give the same proper times computed in any other inertial frame. Selleri's argument would have force only if the results distinguished the Earth-centred frame from all other inertial frames, and they do not. | |||
The energy section is philosophy, not physics, and it slips between two claims. That ''E'' is frame-dependent is a theorem, not an interpretation; that a frame-dependent quantity is thereby unreal is Jeans's inference, not relativity's, and one can perfectly well hold energy to be an objective relational quantity — as objective as a velocity, which no one thinks unreal for having different values in different frames. Invariants exist in the theory (rest mass, the interval, proper time) and are exactly the objective quantities Selleri wants; he does not address them. Positing an unobservable preferred frame in order to designate one of the many frame values "the true one" purchases metaphysical comfort at the cost of a quantity that cannot in principle be determined — Selleri concedes "we are presently unable to identify S<sub>0</sub>." | |||
The cosmological section is the weakest, and the errors are substantive rather than interpretive. The "crater of the explosion" picture attacks a misconception rather than the theory: the [[Big Bang]] in standard cosmology is not an explosion into pre-existing space and has no centre, and the isotropy Selleri says a three-dimensional explosion could not produce is a straightforward consequence of homogeneous expansion, not of embedding in a fourth spatial dimension. The FLRW models do not require an extra ''spatial'' dimension at all — spatial curvature is intrinsic, and the observationally favoured case is spatially flat. Set against this, the model's quantitative successes go unmentioned: the blackbody spectrum of the cosmic microwave background and its acoustic-peak structure, the primordial abundances of deuterium and helium-4, and the (1+''z'') time dilation of Type Ia supernova light curves, which is a direct measurement of cosmic expansion and not a matter of interpretation. To assert "the big bang never happened" on the strength of an argument about the fourth coordinate of the Lorentz transformation is not commensurate with that body of measurement. | |||
Judged on its own terms, then, the paper is best read as two things at once. As an argument that the conventionality of simultaneity leaves genuine logical room for a preferred-frame theory empirically equivalent to relativity, it is careful, well sourced and worth taking seriously. As an argument that such a theory is empirically ''superior'', it defers its decisive evidence to other papers; and as cosmology, it substitutes a structural objection for engagement with the data. | |||
==See also== | |||
* [[Franco Selleri]] | |||
* [[Apeiron]] | |||
* [[Special Relativity]] | |||
* [[Aether]] | |||
* [[Sagnac Effect]] | |||
* [[Aberration]] | |||
* [[Hendrik Lorentz]] | |||
* [[Albert Einstein]] | |||
* [[Big Bang]] | |||
* [[Time]] | |||
[[Category:Scientific Paper|recovering lorentz ether]] | [[Category:Scientific Paper|recovering lorentz ether]] | ||
[[Category:Relativity|recovering lorentz ether]] | [[Category:Relativity|recovering lorentz ether]] | ||
[[Category:Aether|recovering lorentz ether]] | |||
[[Category:Time|recovering lorentz ether]] | |||
[[Category:Light|recovering lorentz ether]] | |||
[[Category:Philosophy of Science|recovering lorentz ether]] | |||
Revision as of 08:51, 21 July 2026
| Scientific Paper | |
|---|---|
| Title | Recovering the Lorentz Ether |
| Read in full | Link to paper |
| Author(s) | Franco Selleri |
| Keywords | Lorentz transformations, Special Relativity, preferred inertial frame |
| Published | 2004 |
| Journal | Apeiron |
| Volume | 11 |
| Number | 1 |
| No. of pages | 6 |
| Pages | 246-281 |
Read the full paper here
Abstract
The description of natural phenomena by observers in motion is a problem that many consider solved once and for all by the Lorentz transformations of the Theory of Special Relativity (TSR), though it was actually was left open. Consequences of my alternative transformations of the space and time variables are: (i) an explanation of the empirical data better than provided by the TSR; (ii) the elimination of those features of the TSR which give rise to paradoxes. This is obtained thanks to the recovery of a preferred inertial frame in which the Lorentz ether is at rest. In the present paper I expound the basic ideas of the research, leaving aside mathematical detail.
Overview
Franco Selleri, of the University of Bari and INFN, wrote this 2004 Apeiron article as a non-technical exposition of a research programme he had pursued for a decade in Foundations of Physics and elsewhere. His target is not the mathematics of Special Relativity but its interpretation. Selleri argues that the Lorentz transformations contain a term that is purely conventional — a free synchronisation parameter that Einstein fixed by decree rather than by measurement — and that setting it to a different value yields a family of "equivalent transformations", every member of which except the Lorentz case presupposes a preferred inertial frame. Choosing the particular member with parameter e1 = 0 gives what he calls the inertial transformations, in which time is entirely freed from the geometrical role Minkowski assigned it and the Aether at rest in the preferred frame is restored.
The essay is deliberately philosophical in tone. Selleri opens by quoting Einstein's own late admissions — the 1949 letter to Solovine ("There is not a single concept of which I am convinced that it will resist firmly") and the April 1955 preface, his last written work, ending "how far in my opinion we still are from possessing a conceptual basis of physics, on which we can somehow rely" — and reads them as a warning against treating relativity as final. He then lists what he takes to be the theory's paradoxes: the invariance of light speed for a pursuer at 0.99c, the conventional character of distant simultaneity, the absence of an objective description of contraction and clock retardation, the asymmetric ageing of the twins in a theory "that carries the flag of relativism", the hyperdeterministic block universe, the loss of an objective value for energy, and the discontinuity between inertial frames and frames with arbitrarily small acceleration. His claim is that all of these dissolve once relativism — the doctrine that all inertial observers are strictly equivalent — is abandoned, while every empirical success of the theory is retained, and that in one case, the Sagnac Effect, the alternative succeeds where relativity fails outright.
The argument
The conventionality of simultaneity
Selleri grounds his case in Einstein's own words. From the 1905 paper: "the latter cannot be defined at all unless we establish by definition that the 'time' required by light to travel from A to B equals the 'time' it requires to travel from B to A." From 1916, on the midpoint M of AB: this "is in reality neither a supposition nor a hypothesis about the physical nature of light, but a stipulation which I can make of my own free will." Reichenbach's 1925 analysis then generalises the stipulation: where relativity sets t2 − t1 = ½(t3 − t1), any rule t2 − t1 = ε(t3 − t1) with 0 < ε < 1 "would likewise be adequate and could not be considered false". Jammer's 1979 statement of the thesis of the conventionality of intrasystemic distant simultaneity — that ε "may be any number in the open interval between 0 and 1, i.e. 0 < ε < 1, without ever leading to any conflict with experience" — is the logical opening Selleri exploits: "there is an important logical space for different values of ε, i.e., in the final analysis, for alternative theories to the TSR!"
Two empirical facts
Rather than assume a transformation, Selleri derives one from what he takes to be securely measured. The first is the invariance of the two-way speed of light. The 1978 British measurement gave car = 299,792.4588 ± 0.0002 km/s, a precision of 10−9, a thousand times finer than needed to detect the u2/c2 ≈ 10−6 variation classical physics would predict from the Earth's ~300 km/s galactic motion; no such variation was seen. He is careful that this says nothing about the one-way speed, quoting Poincaré (1898): "It will always be impossible to verify this postulate directly with experiments."
The second is clock retardation by the factor R = √(1 − u2/c2). Selleri cites the 1977 CERN muon storage ring, where muons at 0.9994c with centripetal acceleration 1018g lived 29.33 times longer than at rest, exactly as t = t0/R requires; the 1972 Hafele–Keating flights (westbound clocks losing 59 ± 10 ns, eastbound gaining 273 ± 7 ns); and the GPS constellation, whose onboard clocks are pre-slowed by 38,700 ns/day to compensate the combined gravitational (+45,900) and velocity (−7,200) effects.
The equivalent and inertial transformations
From four standard assumptions (homogeneity and isotropy of space in S0; isotropic light speed c in S0; S moving at υ along +x0; axes coinciding at t = t0 = 0) plus the two empirical facts, Selleri shows the transformation from S0 to S must take the form
- x = (x0 − υt0)/R, y = y0, z = z0, t = Rt0 + e1(x0 − υt0),
with a single undetermined coefficient e1 — the synchronisation parameter, following Mansouri and Sexl's observation that the coefficient of x in the time transformation is purely conventional. The Lorentz transformations are the special case e1 = −υ/Rc2, the value that produces the space–time symmetry of Minkowski's "union of the two". Setting e1 = 0 gives the inertial transformations, in which the delay t − t0 depends only on t0 and not on position, so time is absolute; the price is that the one-way speed of light in S is anisotropic. Selleri reports having checked explicitly that Römer, Bradley, Fizeau, Michelson–Morley, Doppler and International Atomic Time data are all insensitive to e1, and observes pointedly that "all such theories are based on the existence of a preferred frame, the only exception being the TSR." He claims that linear accelerations, rotating platforms and superluminal signals do single out e1 = 0, referring the argument to his earlier technical papers.
The objectivity of energy
Selleri's most philosophical section attacks relativism through the Energy concept. Since every inertial observer assigns a particle a different velocity and hence a different E = mc2/√(1 − u2/c2), and none is privileged, "one is forced to conclude that a real energy value does not exist". He traces the same move in James Jeans (1943), who argued that because forces are apprehended differently by differently moving observers, "the forces cannot have a real objective existence; they are mere mental concepts" — and who followed the argument all the way to idealism: "The universe begins to look more like a great thought than like a great machine." For Selleri this is a reductio. The escape is the non-equivalence of frames: with a preferred system, energy has a true value, the one relative to S0.
Einstein's ether
A section of quotations documents Einstein's own return to the ether. The 1919 letter to Lorentz: "It would have been more correct if I had limited myself, in my earlier publications, to emphasizing only the non-existence of an ether velocity, instead of arguing the total non-existence of the ether." The 1920 Leiden address: "To deny the existence of the ether means, in the last analysis, denying all physical properties to empty space. But such a view is inconsistent with the fundamental facts of mechanics." Selleri accepts the relativistic ether as far as it goes — "a space endowed with physical properties can very well be called ether" — but finds it "strange and unpleasant to deprive the ether of all states of motion". The inertial transformations restore its immobility in S0, and with it the Lorentz ether entire.
Twins, aberration, Sagnac, cosmology
Four applications close the argument. On the twins, Selleri does not dispute the numbers (a 0.99c round trip to Mira Ceti, 32 light years away, takes 64.6 years for the stay-at-home and about 9 for the traveller) but the interpretation: in Hafele–Keating the eastward and westward results differ only because velocities were added to and subtracted from the Earth's rotation "with respect to the surrounding space", which relativism forbids; treating the results as relativistic successes "means forgetting the relativism of the theory, and thoughtlessly calculating with respect to the inertial frame in which the Earth's center is instantaneously at rest." With a preferred frame, "the twin ageing less is always the one who feels the effects of larger absolute velocities."
On aberration, Selleri proves that every equivalent transformation yields the identical formula tan θ = R sin θ0/(cos θ0 − υ/c), with all right-hand quantities referred to S0. Because the absolute aberration angle is the same for all S, the angle observed between any two frames is the same too. This, he argues, resolves a real difficulty: Einstein derived the formula with υ the relative star–Earth velocity, but stars move randomly, so the relative velocity differs from star to star while the observed aberration does not. Ives (1950) sharpened the point using spectroscopic binaries whose components have orbital velocities comparable to the Earth's yet show identical aberration. On the inertial transformations, υ is simply the Earth's absolute velocity, and the annual variation of aberration follows from the Earth's orbital motion.
On the Sagnac Effect, Selleri holds that relativity has no genuine derivation. Langevin's 1921 treatment claims general relativity but is "really 100% Galilean"; his 1937 paper offers two mutually independent treatments, the first assuming the platform everywhere uses the time of the motionless centre. Post's influential 1963 review likewise gives two proofs, one arbitrarily using t′ = tR, the other starting from the Lorentz transformation and then choosing r perpendicular to u so that the offending term vanishes. Hasselbach and Nicklaus list about twenty published "explanations", noting that "this great variety (if not disparity) in the derivation of the Sagnac phase shift constitutes one of the several controversies... that have been surrounding the Sagnac effect since the earliest days." Selleri's point is that Langevin's and Post's common tactic — eliminating x from the transformation of time — is precisely what e1 = 0 does honestly.
On cosmology, Selleri argues that the Big Bang rests on an unstable chain: the four-dimensional space of general relativity rests on Minkowski space, which rests entirely on the fourth Lorentz transformation. Remove that and no fourth dimension remains in which to embed and curve a three-dimensional universe. A genuine three-dimensional explosion would leave "an empty central region, the 'crater of the explosion,'" surrounded by galaxies and then by radiation alone — nothing like the isotropic sky the telescopes show. His conclusion is blunt: "The big bang never happened!"
Assessment
The strongest part of this paper is its foundational core, and it is not a fringe position. That the one-way speed of light is not directly measurable without a prior synchronisation convention, and that the Reichenbach parameter ε is genuinely free within the interval (0,1), is standard in the philosophy of physics literature — Reichenbach, Grünbaum, Jammer and (in physics) Mansouri and Sexl all say so. Selleri's derivation of the equivalent transformations from four geometric assumptions plus two measured facts (two-way light-speed invariance and the R factor for clocks) is clean, and the resulting one-parameter family with the Lorentz case at e1 = −υ/Rc2 is correct. His observation that every member of the family except one requires a preferred frame is a real structural insight. The aberration argument is the sharpest empirical point in the essay: the Ives binary-star objection is a genuine puzzle for the naive "relative velocity" reading of Einstein's derivation, and Selleri's resolution — that υ is the observer's absolute velocity, so all stars aberrate alike — is economical. He is also right that the Hafele–Keating and GPS analyses are performed in the Earth-centred non-rotating frame, and that this is rarely remarked upon.
The central difficulty is that the paper's own logic works against its conclusion. If, as Selleri establishes at length, all values of e1 are empirically equivalent for the great body of optical and clock experiments, then e1 = 0 cannot be "an explanation of the empirical data better than provided by the TSR" — it is, by construction, an equally good one with a different convention. The claim that certain experiments do single out e1 = 0 is the load-bearing assertion of the whole programme, and it is exactly the point at which the reader is referred elsewhere: "we cannot discuss it here for reasons of space." A reader of this paper alone therefore has no way to evaluate the decisive step. That is a legitimate choice for an expository article, but it means the article's title claim is not established within it.
The Sagnac argument overstates its case. That published derivations of the Sagnac shift are numerous and disparate is true and well documented; that special relativity cannot produce one is a much stronger claim, and the standard modern treatment — integrating the light travel time around a closed path in the rotating frame, where the metric is non-diagonal and no global synchronisation exists — is neither Galilean nor arbitrary. The Sagnac shift, being first order in Ωrc and independent of the medium's refractive index, is what one expects for a rotating (hence non-inertial) frame in any theory that gets the round-trip light time right; Selleri's own point that a rotating frame cannot be globally synchronised is precisely the mainstream explanation, restated as a discontinuity objection. Similarly, on the twins, the appeal to "the surrounding space" in Hafele–Keating is not evidence for a preferred frame: the calculation is done in the Earth-centred inertial frame because that frame is inertial, and would give the same proper times computed in any other inertial frame. Selleri's argument would have force only if the results distinguished the Earth-centred frame from all other inertial frames, and they do not.
The energy section is philosophy, not physics, and it slips between two claims. That E is frame-dependent is a theorem, not an interpretation; that a frame-dependent quantity is thereby unreal is Jeans's inference, not relativity's, and one can perfectly well hold energy to be an objective relational quantity — as objective as a velocity, which no one thinks unreal for having different values in different frames. Invariants exist in the theory (rest mass, the interval, proper time) and are exactly the objective quantities Selleri wants; he does not address them. Positing an unobservable preferred frame in order to designate one of the many frame values "the true one" purchases metaphysical comfort at the cost of a quantity that cannot in principle be determined — Selleri concedes "we are presently unable to identify S0."
The cosmological section is the weakest, and the errors are substantive rather than interpretive. The "crater of the explosion" picture attacks a misconception rather than the theory: the Big Bang in standard cosmology is not an explosion into pre-existing space and has no centre, and the isotropy Selleri says a three-dimensional explosion could not produce is a straightforward consequence of homogeneous expansion, not of embedding in a fourth spatial dimension. The FLRW models do not require an extra spatial dimension at all — spatial curvature is intrinsic, and the observationally favoured case is spatially flat. Set against this, the model's quantitative successes go unmentioned: the blackbody spectrum of the cosmic microwave background and its acoustic-peak structure, the primordial abundances of deuterium and helium-4, and the (1+z) time dilation of Type Ia supernova light curves, which is a direct measurement of cosmic expansion and not a matter of interpretation. To assert "the big bang never happened" on the strength of an argument about the fourth coordinate of the Lorentz transformation is not commensurate with that body of measurement.
Judged on its own terms, then, the paper is best read as two things at once. As an argument that the conventionality of simultaneity leaves genuine logical room for a preferred-frame theory empirically equivalent to relativity, it is careful, well sourced and worth taking seriously. As an argument that such a theory is empirically superior, it defers its decisive evidence to other papers; and as cosmology, it substitutes a structural objection for engagement with the data.