Ritardo Degli Orologi in Moto (Italian, Time Dilation for Moving Clocks)
| Scientific Paper | |
|---|---|
| Title | Ritardo Degli Orologi in Moto (Italian, Time Dilation for Moving Clocks) |
| Read in full | Link to paper |
| Author(s) | Michele Barone |
| Keywords | Time Dilation |
| Published | 2002 |
| No. of pages | 11 |
Read the full paper here
Abstract
From La Natura del Tempo: Propagazioni super-luminali, paradosso dei gemelli, teletrasporto (The Nature of Time), edited by Dr. Franco Selleri.
Overview
The paper is written in Italian; its title on the PDF is simply "Ritardo degli orologi in moto" ("Retardation of moving clocks"), and it is bylined M. Barone of the Istituto di Fisica Nucleare at the "Demokritos" National Centre for Scientific Research in Aghia Paraskevi, Athens. It is a chapter contributed to Franco Selleri's collection La Natura del Tempo.
Its structure is that of a critical review rather than a new theory. Barone first sets out, accurately and without editorial comment, the standard experimental case for Time Dilation — cosmic-ray muons, secondary beams at accelerators, the CERN muon storage ring, flying atomic clocks and the GPS — and then, in a section headed "Convenzione o Proprietà della Natura?" ("Convention or property of nature?"), collects the published objections to each of them. A short closing section surveys proposals for detecting violations of Lorentz invariance. The author does not adjudicate; he sets the two bodies of literature side by side and lets the question stand, in keeping with the sceptical tradition of the volume in which it appears.
The standard case, as Barone sets it out
From Aristotle to Einstein
The opening frames the historical shift: "Il tempo è movimento" for Aristotle; for Newton absolute, true, mathematical time flowing uniformly of itself; for Einstein a time no longer absolute but dependent on the observer's velocity, such that an observer reaching the speed of light would find "his" time stopped. Barone derives the effect in the usual way from the Lorentz Transformation: for two frames S and S′, cΔt = γ(cΔt′ + βΔx′) with γ = 1/√(1 − β2) and β = v/c; for two events at the same place in S′ (Δx′ = 0) this reduces to Δt = γΔt′.
Cosmic-ray muons
The first confirmation cited is the muon lifetime in cosmic rays (Rossi and Hoag 1940; Rossi and Hall 1941). A primary proton striking an atmospheric nucleus produces a shower — pions, then muons and neutrinos, with π0 → γγ and pair conversion — sketched in Figure 1. With a laboratory mean life of 2.2 μs, fast Muons "should travel only a few hundred metres", yet many are detected at sea level; the accepted explanation is that fast muons live longer than slow ones. The same reasoning, Barone notes, underlies the practical operation of accelerator facilities: unstable particles cannot themselves be accelerated, so stable protons and electrons are fired at fixed targets to produce secondary beams of unstable particles that then travel hundreds of metres down evacuated transfer lines to experimental halls — distances that without dilation would be of the order of a centimetre.
The CERN muon storage ring
The most precise measurement he cites is the g−2 muon storage ring at CERN in the 1970s (Bailey et al., Nucl. Phys. B150, 1–75, 1979), a ring of radius 7 m built from 40 magnets, whose engineering drawing is reproduced as Figure 2. For muons at 0.9994c the quoted mean lives are
- τriposo = 2.197 μs τvolo = 64.4 μs
giving τvolo/τriposo = 29.3. Barone offers the memorable gloss that all these are measurements made with microscopic clocks: an unstable particle "goes 'tick' when it is born and 'tock' when it decays", and the relation between the flight time Δt and the rest-frame lifetime Δt0 is Δt = γΔt0.
Macroscopic clocks: Hafele–Keating and GPS
Caesium atomic clocks — the best of them accurate to one part in 1015 — provide the macroscopic tests. In October 1971 Hafele and Keating flew four caesium clocks around the world on commercial flights, eastward and westward, against reference clocks at the U.S. Naval Observatory: the eastward clocks lost 59 ± 10 ns and the westward clocks gained 273 ± 7 ns, which the authors took as further confirmation.
The GPS is treated at length as the same experiment on a larger scale: 24 satellites in near-circular orbits above 20,000 km, at four Earth radii, moving at 3.9 km/s with respect to a non-rotating geocentric frame; four satellites define four spheres intersecting in two points, one inside the Earth or far in space and the other the receiver's position, with differential corrections from ground stations bringing the fix to a few centimetres. Barone reports the correction as 38,700 ns per day, obtained as the difference between 45,900 ns/day from the weaker gravitational potential at satellite altitude and 7,200 ns/day from the satellites' orbital speed — "this would be a further proof of the validity of Special Relativity". Figure 3, redrawn from T. Herring's Pour la Science article, shows the uncorrected position spheres failing to meet in a point and the corrected ones meeting.
Transverse Doppler and SS433
The Doppler Effect vanishes classically for transverse motion but does not relativistically, because of the slowing of clocks fixed to the source. Ives and Stilwell performed the first such measurement with moving atoms in the 1930s (J. Opt. Soc. Am. 28, 215–226, 1938), confirmed repeatedly since. Barone adds an astrophysical case: the galactic object SS433, whose emission line shifts periodically to the red and the blue, understood as a binary emitting two diametrically opposed jets at 0.26c from an accretion disc around a compact object (possibly a Black Hole). Because the jets emerge at about a quarter of c, they suffer "a slowing of about 3 % of their velocity" — that is, the transverse-Doppler shift shows up as a systematic offset of the hydrogen line.
The objections
Particle experiments
Barone opens the critical section by noting flatly that "there is no unanimous agreement in the interpretation of the results presented above."
Harold Aspden argued (Lett. Nuovo Cimento 37, 307, 1983) that the flight lifetimes of mesons in inertial systems would differ from the measured values had the beam energies been lower than those reported, and that even at high energies a discrepancy with the predictions of Special Relativity would be masked by the precision of the measurements; he offers an alternative model in which mesons are continuously absorbed and re-emitted by the zero-point vacuum state pervading the universe, and reproduces the experimental values.
On cosmic rays, Barone points out that the measurements depend on the medium traversed — shower intensity is attenuated far more by a layer of air than by an equivalent thickness of dense matter such as iron — and records that Euler and Heisenberg gave the first relativistic-dilation interpretation only in 1938, on the basis of momentum-spectrum estimates and intensity-versus-altitude data, at a time when the muon was still being mistaken for a pion and called the "mesotron". He also relays Lobkowicz, Melissinos et al. on how delicate an in-flight lifetime measurement really is: momentum precision, the exact decay path length, beam solid angle and collimation, background subtraction and beam–detector interaction all enter, and "in general there exists a discrepancy between the number of particles at their creation and the number detected after the flight time, hidden by the statistics"; the invariance of the beam spectra is a point on which, he says, the literature is not clear.
Against the g−2 ring he raises two points. First, the authors themselves admit that the muons were subject to a transverse acceleration of 1021 cm s−2. Second, D. I. Blokhintsev (Phys. Lett. 13, 272, 1964) argued that a storage ring is not an inertial frame because the geo-gravitational potential acts on the beam, an effect that would show up for electron beams of 100 GeV and above — to which Barone replies in the paper's own voice that the g−2 muon beam was at 3 GeV, not the 50 MeV minimum required by that author's calculations. He adds that Bailey and collaborators supported their result by citing Mössbauer-effect and maser measurements of dilation, "but these last have been much criticised for their inconsistency".
Clock experiments and the meaning of the corrections
Herbert Dingle, in Nature of 8 September 1962, held that the arguments supporting retardation of moving clocks could equally well justify an acceleration of their rate, something he claimed to derive from Einstein's 1905 paper — leaving a contradiction in which two opposite solutions are both true, so that a reason must be given for choosing one. The Ives–Stilwell experiments, Barone notes, "are considered by some more a proof in favour of an absolute reference frame than in favour of clock retardation."
The macroscopic-clock experiments are criticised by Al Kelly (Electronics World, September 2000, p. 722), who holds that Hafele and Keating did not account for the accelerations and decelerations the airborne clocks underwent at the intermediate refuelling stops. On GPS, Kelly's point is that the daily correction on the orbiting clocks is computed from the satellite's absolute velocity compared with the absolute velocity of the terrestrial reference — which is tied to the Earth's centre in its revolution about the Sun — and not from the relative velocity between the satellite clocks and the ground clocks. If light is allowed to take values greater than c, the relevant speed becomes c plus or minus the Earth's rotational velocity, and the daily retardation is explained that way too; in short, Kelly holds that the Sagnac Effect is not a relativistic effect.
M. Bonizzoni and G. Giuliani assert that the experimental evidence from the 1940s to the 1970s made use of additional hypotheses that were unnecessary and entirely foreign to the theory they were meant to demonstrate; of the whole body of work, these authors salvage only the experiments done with particle beams in flight. Finally A. A. Tyapkin (Lett. Nuovo Cimento 7, 760, 1973) argued for the impossibility of first-order tests of Special Relativity using the phase shift of laser beams, as various authors had proposed.
Looking for violations of Lorentz invariance
The closing section reports Alan Kostelecký's proposal in Physical Review Letters for an experiment aboard the International Space Station using improved caesium clocks, cooled and launched upward so as to reduce motional broadening and be interrogated by microwaves at the apex of their trajectory, pushing the uncertainty to one part in 1027; the measurement could run for a long time because in the absence of gravity the atoms do not fall. Barone also notes reports in Physical Review Letters by Mugnai, Ranfagni and Ruggeri of the CNR in Florence, and by L. Wang at Princeton, of laboratory superluminal signals — the first 25 % faster than c, the second 300 times — which if sustained would be "falsification in the Popperian sense" of Special Relativity, fulfilling what "Einstein himself thought: that his theory would not survive very long."
Assessment
The paper's value is as a compact, well-referenced map of a controversy, written by someone who works inside experimental particle physics and who reports the standard results correctly before reporting the objections to them. The numbers he quotes for the mainstream case are right and check out: 64.4/2.197 = 29.3 for the CERN storage-ring dilation factor, which matches γ = 1/√(1 − 0.99942) ≈ 28.9 to the accuracy of the quoted velocity; and 45,900 − 7,200 = 38,700 ns/day for GPS. He is scrupulous in attributing each criticism to its author rather than asserting it himself, and in one place he answers a critic against the critic's own interest, pointing out that Blokhintsev's objection to the g−2 ring requires beam energies well below the 3 GeV actually used. The bibliography — Rossi and Hoag, Rossi and Hall, Lobkowicz, Bailey, Hafele and Keating, Van Flandern, Ives and Stilwell, Aspden, Euler and Heisenberg, Blokhintsev, Kelly, Bonizzoni and Giuliani, Tyapkin — is a genuinely useful reading list for anyone wanting to work through the question from both sides.
The difficulties are those of a survey that does not adjudicate. Several of the objections, laid side by side as they are here, are mutually incompatible: Aspden's vacuum absorption–re-emission model, Kelly's preferred-frame reading with superluminal light, Dingle's logical contradiction and Bonizzoni and Giuliani's "salvage only the in-flight beam experiments" cannot all be right, and the paper does not say which if any it favours. Some are also answerable in ways the paper does not record. The g−2 acceleration objection — 1021 cm s−2 transverse — is the clock hypothesis, and it has been tested directly: the muon lifetime in the ring is found to depend on γ alone and not on the acceleration, which is precisely the result the storage-ring geometry is designed to isolate. Kelly's Hafele–Keating objection about refuelling stops is a criticism of a 1971 experiment that has since been superseded by clock comparisons with no stops at all and far higher precision. And the Bonizzoni–Giuliani position, which keeps the in-flight beam results, keeps exactly the class of measurement that gives the γ-factor most directly.
Two smaller problems are internal. The paper quotes the GPS velocity correction as 7,200 ns/day in the exposition and then, reporting Kelly, as "the correction of 7,500 ns/day on the orbiting clocks" — the same quantity with two different values a few pages apart, without comment. And the superluminal reports adduced at the close have not held up as violations of relativistic causality: the Florence microwave and the Princeton anomalous-dispersion experiments both concern group and phase velocities in situations where no information is transmitted faster than c, which is why neither has come to be regarded, in the twenty-plus years since, as the Popperian falsification the paper anticipated. Kostelecký's Standard-Model-Extension programme, by contrast, has produced a large body of null results, tightening Lorentz-violation bounds rather than finding violations.
Read for what it is — a chapter in a sceptical volume, meant to show that a body of evidence usually presented as closed has a dissenting literature attached to it — the paper does its job accurately and without overclaiming. Barone nowhere asserts that time dilation is false; his question, in the section title, is whether it is a convention or a property of nature, and he leaves it open.