View source for Eight Proofs of Absolute Simultaneity

{{Infobox paper
| title = Eight Proofs of Absolute Simultaneity
| url = [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_5335.pdf Link to paper]
| author = [[Franco Selleri]]
| keywords = simultaneity, absolute, principle of relativity, Lorentz transformations, Sagnac effect
| published = 2010
| journal = [[Proceedings of the NPA]]
| volume = 7
| num_pages = 10
| pages = 504-512
}}

'''Read the full paper''' [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_5335.pdf 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 e<sub>1</sub> - 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 e<sub>1</sub>, 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  e<sub>1</sub> = 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: ''e''<sub>1</sub>, 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 &mdash; homogeneity and isotropy of space in a privileged frame ''S''<sub>0</sub>, isotropic light propagation in ''S''<sub>0</sub>, standard axis geometry, the constancy of the ''two-way'' speed of light in every frame, and clock retardation by the factor ''R'' = &radic;(1 &minus; ''v''<sup>2</sup>/''c''<sup>2</sup>) &mdash; do not fix the theory uniquely. They leave a one-parameter family, the "Equivalent Transformations" (ET), indexed by ''e''<sub>1</sub>. Setting ''e''<sub>1</sub> = &minus;''v''/(''Rc''<sup>2</sup>) recovers the [[Lorentz Transformation|Lorentz transformation]]; setting ''e''<sub>1</sub> = 0 gives what Selleri calls the "inertial transformations" (IT), in which ''t'' = ''Rt''<sub>0</sub> everywhere, so that events simultaneous in the privileged frame are simultaneous in every frame.

Reichenbach and Jammer held that ''e''<sub>1</sub> is a free convention &mdash; 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 ''e''<sub>1</sub> = 0. If he is right, [[Simultaneity|simultaneity]] is a fact about the world rather than a stipulation, a privileged frame exists, and the [[Aether|ether]] returns as the seat of clock retardation and rod contraction &mdash; "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|special relativity]] exactly, but in what the theory says about the one-way propagation of [[Light|light]] and about the reality of the present moment.

==The arguments==

===Sagnac effect on the rotating disc===

The centrepiece. A disc of circumference ''L''<sub>0</sub> (laboratory) and ''L'' (on the rim) rotates with rim speed ''v''; the laboratory is taken to be at rest in ''S''<sub>0</sub>. In the laboratory the counter-rotating pulse closes on the source at ''c'' + ''v'' and the co-rotating pulse at ''c'' &minus; ''v'', giving &Delta;''t''<sub>0</sub> = 2''L''<sub>0</sub>''v''/(''c''<sup>2</sup>''R''<sup>2</sup>), essentially the [[Sagnac Effect|Sagnac]] formula. On the rim, the one-way light speed of the ET, ''c''<sub>&plusmn;</sub>(&theta;) = ''c''/(1 + &beta;&#771; cos&theta;) with &beta;&#771; = ''v''/''c'' &minus; ''e''<sub>1</sub>''Rc'', gives &Delta;''t'' = 2''L''&beta;&#771;/''c''. Requiring these to describe the same phenomenon through the clock-retardation relation &Delta;''t'' = ''R''&Delta;''t''<sub>0</sub>, and using ''L''<sub>0</sub> = ''LR'', forces &beta;&#771; = ''v''/''c'' and hence ''e''<sub>1</sub> = 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 ''v''<sup>2</sup>/2''c''<sup>2</sup>, a gravitational term in ''g''(&phi;)''h''/''c''<sup>2</sup>, and a "Sagnac correction" 2&Omega;''A''<sub>E</sub>/''c''<sup>2</sup>, where ''A''<sub>E</sub> 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&ndash;satellite and satellite&ndash;Tokyo transit times with the anisotropic speeds ''c''<sub>WS</sub>, ''c''<sub>ST</sub> instead of ''c'', the residual is exactly 2&Omega;''A''<sub>E</sub>/''c''<sup>2</sup>. The test case is the 1976 Saburi transatlantic comparison: a flown clock made Tokyo 9.42 &micro;s fast on Washington, 9.50 &micro;s after the velocity and gravitational corrections, while the satellite link gave 9.11 &micro;s &mdash; a 0.39 &micro;s 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''<sub>&minus;</sub>/''c''<sub>+</sub> = (1 + &beta;)/(1 &minus; &beta;), is independent of the unknown clock function ''F''(''v'', &hellip;) 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 + &beta;)/(1 &minus; &beta;), 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 &Delta;''t'' = 2''vL''/''c''<sup>2</sup> 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|Lorentz transformation]] the line ''t''&prime; = 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 ''e''<sub>1</sub> &ne; 0 but ''not'' for ''e''<sub>1</sub> = 0, where ''t''&prime; = ''Rt''<sub>0</sub> 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 ''S''<sub>0</sub> simultaneous in ''S'', so ''e''<sub>1</sub> = 0. The seventh proof is [[Ronald R Hatch|Ron Hatch]]'s: millisecond-pulsar and VLBI comparisons show terrestrial clocks biased with position along the Earth's orbital velocity, &Delta;&tau; = &minus;'''v'''&middot;'''x'''/''c''<sup>2</sup>, so that the noon second runs about 300 ps short of the midnight second &mdash; 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&ndash;Eisner&ndash;Hayden objection that if aberration were due to ''relative'' velocity, spectroscopic binaries such as Mizar A should show apparent separations of order 1&prime;10&Prime;, whereas the observed value is under 0.01&Prime;.

==Assessment==

The algebra of the central Sagnac derivation is correct. Working it through independently: &Delta;''t''<sub>0</sub> = ''L''<sub>0</sub>[1/(''c''&minus;''v'') &minus; 1/(''c''+''v'')] = 2''L''<sub>0</sub>''v''/(''c''<sup>2</sup>''R''<sup>2</sup>) as in Eq. (7); the rim result 2''L''&beta;&#771;/''c'' follows from Eq. (4); the ratio with Eq. (9) does give &beta;&#771; = ''v''/''c'' and so ''e''<sub>1</sub> = 0. Selleri's inertial transformation likewise reproduces its own advertised consequences: light chasing an observer with ''v'' &rarr; ''c'' does approach at ''c''/2, the "50% reduction" he quotes. Hatch's 300 ps is also arithmetically sound on its own terms &mdash; the diurnal rate variation implied by &Delta;&tau; = &minus;''vx''/''c''<sup>2</sup> is 2''v''&omega;''R''<sub>E</sub>/''c''<sup>2</sup> &asymp; 3.1 &times; 10<sup>&minus;10</sup>, 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 (&asymp; 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 &minus; 9.11 = 0.39 &micro;s), and 0.39 &micro;s is the right size for 2&Omega;''A''<sub>E</sub>/''c''<sup>2</sup> with a geostationary relay, requiring ''A''<sub>E</sub> &asymp; 2.4 &times; 10<sup>14</sup> m<sup>2</sup> &mdash; about what the quadrangle O&ndash;W&ndash;S&ndash;T&ndash;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 2&Omega;''A''<sub>E</sub>/''c''<sup>2</sup> 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 &#8750;'''v'''&middot;''d'''''l'''/''c''<sup>2</sup>, which reduces to 2''vL''/''c''<sup>2</sup> 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 &mdash; Eq. (6), &Delta;''t'' = ''R''&Delta;''t''<sub>0</sub> &mdash; 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 2&Omega;''A''/''c''<sup>2</sup> 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 S''<sub>0</sub> is agreed by everyone; the inference "therefore two events simultaneous in ''S''<sub>0</sub> 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&ndash;Eisner&ndash;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 &mdash; every fringe count, every clock comparison at a meeting point &mdash; 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.

==See also==

* [[Franco Selleri]]
* [[Simultaneity]]
* [[Sagnac Effect]]
* [[Lorentz Transformation]]
* [[Speed of Light]]
* [[Ronald R Hatch]]
* [[Ruyong Wang]]
* [[Aether]]
* [[Time Dilation]]
* [[Length Contraction]]
* [[GPS]]
* [[Michelson–Morley experiment]]
* [[Kennedy-Thorndike experiment]]
* [[Hendrik Lorentz]]

[[Category:Scientific Paper|proofs absolute simultaneity]]

[[Category:Relativity|proofs absolute simultaneity]]

[[Category:Aether|proofs absolute simultaneity]]

[[Category:Time|proofs absolute simultaneity]]

[[Category:Light|proofs absolute simultaneity]]