Eight Proofs of Absolute Simultaneity
| Scientific Paper | |
|---|---|
| Title | Eight Proofs of Absolute Simultaneity |
| Read in full | Link to paper |
| Author(s) | Franco Selleri |
| Keywords | simultaneity, absolute, principle of relativity, Lorentz transformations, Sagnac effect |
| Published | 2010 |
| Journal | Proceedings of the NPA |
| Volume | 7 |
| No. of pages | 10 |
| Pages | 504-512 |
Read the full paper here
Abstract
The conviction that relativistic simultaneity has a conventional nature is shared by many authors, but it will be shown that simultaneity exists in the physical reality and therefore cannot be conventional. If the coefficient - we call it e1 - of the space variable x in the Lorentz, or other, transformation of time had a conventional nature it should be possible to modify it without touching the empirical predictions of the theory: this expectation can be called Reichenbach-Jammer conjecture ("RJ conjecture"). Given that Einstein's principle of relativity leads necessarily to the Lorentz transformations, and thus also to a fixed nonzero value of e1, the modification would imply a reformulation of the relativistic idea itself. With respect to the idealized expectation, based on the RJ conjecture, the concrete development of physics produces some exciting novelties. Several phenomena, in particular those taking place in accelerating frames (Sagnac effect, and all that), converge in a strong indication of e1 = 0. This implies absolute simultaneity and a new type of space and time transformations, which we call "inertial". We give eight proofs of absolute simultaneity, deduced from essentially independent normally accepted premises.
Overview
This is Selleri's summary statement of a programme he pursued from the mid-1990s until his death. Its subject is one number: e1, the coefficient of the space coordinate in the transformation of time between two frames. Following Mansouri and Sexl (1977), Selleri shows that six assumptions much weaker than Einstein's two postulates — homogeneity and isotropy of space in a privileged frame S0, isotropic light propagation in S0, standard axis geometry, the constancy of the two-way speed of light in every frame, and clock retardation by the factor R = √(1 − v2/c2) — do not fix the theory uniquely. They leave a one-parameter family, the "Equivalent Transformations" (ET), indexed by e1. Setting e1 = −v/(Rc2) recovers the Lorentz transformation; setting e1 = 0 gives what Selleri calls the "inertial transformations" (IT), in which t = Rt0 everywhere, so that events simultaneous in the privileged frame are simultaneous in every frame.
Reichenbach and Jammer held that e1 is a free convention — a matter of how one chooses to set clocks, with no empirical consequence. Selleri's claim is the opposite: eight arguments, drawn from what he presents as mutually independent and individually uncontroversial premises, converge on e1 = 0. If he is right, simultaneity is a fact about the world rather than a stipulation, a privileged frame exists, and the ether returns as the seat of clock retardation and rod contraction — "very much in the realistic line of thought of Hendrik Lorentz." The departure from the mainstream is therefore not in the ET's predictions for two-way experiments, which reproduce those of special relativity exactly, but in what the theory says about the one-way propagation of light and about the reality of the present moment.
The arguments
Sagnac effect on the rotating disc
The centrepiece. A disc of circumference L0 (laboratory) and L (on the rim) rotates with rim speed v; the laboratory is taken to be at rest in S0. In the laboratory the counter-rotating pulse closes on the source at c + v and the co-rotating pulse at c − v, giving Δt0 = 2L0v/(c2R2), essentially the Sagnac formula. On the rim, the one-way light speed of the ET, c±(θ) = c/(1 + β̃ cosθ) with β̃ = v/c − e1Rc, gives Δt = 2Lβ̃/c. Requiring these to describe the same phenomenon through the clock-retardation relation Δt = RΔt0, and using L0 = LR, forces β̃ = v/c and hence e1 = 0. Selleri's charge against relativity here is stark: applied consistently through the "acceleration hypothesis", it makes the one-way speed on the rim equal to c in both senses, so "the Sagnac effect goes to zero, contrary to empirical evidence."
The "Sagnac correction" of terrestrial timekeeping
The CCDS and CCIR rules of 1980 prescribe three corrections when clocks at different sites are compared: a velocity term in v2/2c2, a gravitational term in g(φ)h/c2, and a "Sagnac correction" 2ΩAE/c2, where AE is the equatorial projection of the area swept by the signal path and the two Earth radii. Selleri, following A. G. Kelly, calls the third "unconvincing" unless the eastward and westward speeds of light relative to the Earth differ. He recovers it from Eq. (4): writing the Washington–satellite and satellite–Tokyo transit times with the anisotropic speeds cWS, cST instead of c, the residual is exactly 2ΩAE/c2. The test case is the 1976 Saburi Washington–Tokyo comparison: a flown clock made Tokyo 9.42 µs fast on Washington, 9.50 µs after the velocity and gravitational corrections, while the satellite link gave 9.11 µs — a 0.39 µs discrepancy which the Sagnac term removes.
The rotating platform revisited, and Wang's fibre-optic conveyor
By symmetry, the ratio of the two rim light speeds, c−/c+ = (1 + β)/(1 − β), is independent of the unknown clock function F(v, …) and of both circumference lengths, and equals the ratio of the instantaneous speeds at any point of the rim. A short arc AB is for a short time indistinguishable from a piece of a co-moving inertial frame; therefore the one-way speed in that inertial frame cannot be c. Selleri presses this as a discontinuity: experiments are always done where the acceleration is small but nonzero, and there the ratio is (1 + β)/(1 − β), while the theory insists that at exactly zero acceleration it jumps to 1. R. Wang's fibre-optic conveyor, in which straight moving fibre segments contribute Δt = 2vL/c2 exactly as circular ones do, is offered as direct evidence that the local light speed is the same in an accelerated frame and in the locally co-moving inertial frame.
Block universe, Bell's spaceships, Hatch's clocks, aberration
Three further arguments are less quantitative. From the Lorentz transformation the line t′ = 0 has slope v/c in a Minkowski diagram, so every moving observer's "reality" includes events in another's future; iterating, relativity yields "a hyper-deterministic universe in which the whole future is completely pre-established in the minutest details", and Selleri notes that the same follows for every ET with e1 ≠ 0 but not for e1 = 0, where t′ = Rt0 makes the reality line unique. In the Bell's-spaceships configuration, two identically accelerated ships whose clocks accumulate identical delay must, he argues, keep events simultaneous in S0 simultaneous in S, so e1 = 0. The seventh proof is Ron Hatch's: millisecond-pulsar and VLBI comparisons show terrestrial clocks biased with position along the Earth's orbital velocity, Δτ = −v·x/c2, so that the noon second runs about 300 ps short of the midnight second — the bias that makes light appear isotropic in an Earth-centred frame. On aberration, Selleri concedes that every ET predicts the same angle, and uses the section instead to press the Ives–Eisner–Hayden objection that if aberration were due to relative velocity, spectroscopic binaries such as Mizar A should show apparent separations of order 1′10″, whereas the observed value is under 0.01″.
Assessment
The algebra of the central Sagnac derivation is correct. Working it through independently: Δt0 = L0[1/(c−v) − 1/(c+v)] = 2L0v/(c2R2) as in Eq. (7); the rim result 2Lβ̃/c follows from Eq. (4); the ratio with Eq. (9) does give β̃ = v/c and so e1 = 0. Selleri's inertial transformation likewise reproduces its own advertised consequences: light chasing an observer with v → c does approach at c/2, the "50% reduction" he quotes. Hatch's 300 ps is also arithmetically sound on its own terms — the diurnal rate variation implied by Δτ = −vx/c2 is 2vωRE/c2 ≈ 3.1 × 10−10, i.e. about 310 ps per second peak-to-peak, and it is some 360 times larger than the direct solar-potential term across an Earth diameter (≈ 0.84 ps/s), which is why the "noon/midnight problem" cannot be a gravitational effect misplaced. The Saburi figures are consistent (9.42 + 0.08 = 9.50; 9.50 − 9.11 = 0.39 µs), and 0.39 µs is the right size for 2ΩAE/c2 with a geostationary relay, requiring AE ≈ 2.4 × 1014 m2 — about what the quadrangle O–W–S–T–O subtends when S sits at 42,000 km. Nothing in the paper's numbers is wrong.
The difficulties are elsewhere. First, two of the eight "proofs" recover results that standard theory already gives. The 2ΩAE/c2 correction is derived routinely in the Earth-centred inertial frame, where light moves at c and the receiving station moves during transit; obtaining the same formula from an anisotropic c in the rotating frame is a re-parameterisation of the same geometry, not a discriminating test. The same holds for Wang's conveyor: the closed-loop delay ∮v·dl/c2, which reduces to 2vL/c2 for straight segments, is what special relativity predicts for a co-moving source and detector on a moving loop. Agreement here is agreement with everybody.
Second, the load-bearing step is the "acceleration hypothesis", and it is used in two different strengths without the difference being marked. Applied to proper time — Eq. (6), Δt = RΔt0 — it is a local statement with excellent support (Selleri rightly cites the CERN muon lifetime measurements). Applied to Eq. (4) around the whole rim it becomes a global claim: that a single synchronisation can be propagated all the way round a rotating loop. It cannot. The standard account of the Sagnac effect is precisely that Einstein synchronisation on a rotating rim fails to close, leaving a gap of 2ΩA/c2 at the seam. Selleri's "discontinuity at zero acceleration" is that non-closure stated in other words; it is a topological property of rotating coordinates, not a defect in the local physics, and relativity does not in fact predict a null Sagnac effect on the platform.
Third, the Bell's-spaceships argument assumes what it sets out to prove. That the two clocks accumulate equal delay as reckoned in S0 is agreed by everyone; the inference "therefore two events simultaneous in S0 will be such also in S" is the relativity of simultaneity being denied, not refuted. Fourth, the aberration section, on the author's own showing, discriminates nothing, and the Ives–Eisner–Hayden binary-star objection targets Einstein's loose phrase "velocity of the observer relatively to an infinitely distant source" rather than the theory: in special relativity the aberration angle depends on the change in the observer's velocity and on the direction of the incoming ray at the observer, not on the source's motion, so no differential aberration between binary components is predicted. That is why the paper announces eight proofs but labels Hatch's as "the seventh" and never quite delivers a discriminating eighth.
The deepest problem is the one Selleri half-concedes when he quotes Hatch approvingly: the Lorentz transformations are "inertial transformations combined with clock biases." If the two differ only by a re-setting of clocks, they agree on every coincidence — every fringe count, every clock comparison at a meeting point — and the choice between them is exactly the convention Reichenbach described. Selleri's arguments do not exhibit a measurement that separates them; they exhibit a synchronisation that he finds more natural, and a privileged frame which, as he admits in the aberration section, "we are presently unable to identify." The programme is internally consistent and its arithmetic is clean, but it does not escape the conventionality thesis it sets out to refute.