The so-called “twin paradox” occurs when two clocks are synchronized, separated, and rejoined. If one clock remains in an inertial frame, then the other must be accelerated sometime during its journey, and it displays less elapsed proper time than the inertial clock. This is a “paradox” only in that it appears to be inconsistent but is not.

  • Hafele and Keating, Nature 227 (1970), pg 270 (proposal).Science Vol. 177 pg 166–170 (1972) (experiment).: They flew atomic clocks on commercial airliners around the world in both directions, and compared the time elapsed on the airborne clocks with the time elapsed on an earthbound clock (USNO). Their eastbound clock lost 59 ns on the USNO clock; their westbound clock gained 273 ns; these agree with GR predictions to well within their experimental resolution and uncertainties (which total about 25 ns). By using four cesium-beam atomic clocks they greatly reduced their systematic errors due to clock drift.
Criticised in: A. G. Kelly, “Reliability of Relativistic Effect Tests on Airborne Clocks”, Inst. Engineers Ireland Monograph No. 3 (February 1996), His criticism does not stand up, as he does not understand the properties of the atomic clocks and the way the four clocks were reduced to a single “paper” clock. The simple averages he advocates are not nearly as accurate as the paper clock used in the final paper—that was the whole point of flying four clocks (they call this “correlated rate change”; this technique is used by all standards organizations today to minimize the deficiencies of atomic clocks).
Also commented on in Schlegel, AJP 42, pg 183 (1974). He identifies the East–West time difference as the Sagnac effect, notes that this is independent of the clock's velocity relative to the (rotating) Earth, and proposes a coordinate system in which it is treated just like the international date line (for use in highly accurate time transfer around the world); while correct, this has been superceded by the ECI coordinate system of the GPS.
Here is a brief description of a repetition in the UK (2005): (Page 2)
  • Vessot et al., “A Test of the Equivalence Principle Using a Space-borne Clock”, Gel. Rel. Grav., 10, (1979) 181–204.”Test of Relativistic Gravitation with a Space borne Hydrogen Maser”, Phys. Rev. Lett. 45 2081–2084.: They flew a hydrogen maser in a Scout rocket up into space and back (not recovered). Gravitational effects are important, as are the velocity effects of SR. This experiment is also known as “Gravity Probe A”.
  • C. Alley, “Proper Time Experiments in Gravitational Fields with Atomic Clocks, Aircraft, and Laser Light Pulses,” in Quantum Optics, Experimental Gravity, and Measurement Theory, eds. Pierre Meystre and Marlan O. Scully, Proceedings Conf. Bad Windsheim 1981, 1983 Plenum Press New York, ISBN 0-306-41354-X, pg 363–427.: They flew atomic clocks in airplanes that remained localized over Chesapeake Bay, and also which flew to Greenland and back.
  • Bailey et al., “Measurements of relativistic time dilation for positive and negative muons in a circular orbit,” Nature 268 (July 28, 1977) pg 301.Bailey et al., Nuclear Physics B 150 pg 1–79 (1979).: They stored muons in a storage ring and measured their lifetime. When combined with measurements of the muon lifetime at rest this becomes a highly relativistic twin scenario (v ~0.9994 c), for which the stored muons are the traveling twin and return to a given point in the lab every few microseconds. Muon lifetime at rest: Meyer et al., Physical Review 132, pg 2693; Balandin et al., JETP 40, pg 811 (1974); Bardin et al., Physics Letters 137B, pg 135 (1984). Also a test of the clock hypotheses (below).

The Clock Hypothesis

The clock hypothesis states that the tick rate of a clock when measured in an inertial frame depends only upon its velocity relative to that frame, and is independent of its acceleration or higher derivatives. The experiment of Bailey et al. referenced above stored muons in a magnetic storage ring and measured their lifetime. While being stored in the ring they were subject to a proper acceleration of approximately 1018 g (1 g = 9.8 m/s2). The observed agreement between the lifetime of the stored muons with that of muons with the same energy moving inertially confirms the clock hypothesis for accelerations of that magnitude.

  • Sherwin, “Some Recent Experimental Tests of the 'Clock Paradox'“, Phys. Rev. 129 no. 1 (1960), pg 17.: He discusses some Mцssbauer experiments that show that the rate of a clock is independent of acceleration (~1016 g) and depends only upon velocity.

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