A NEW INTERPRETATION OF THE HAFELE-KEATING EXPERIMENT Domina Eberle Spencer, University of Connecticut, Storrs, Connecticut, 06268, U.S.A. and Uma Shama, Bridgewater State College, Bridgewater, Massachusetts, 02325, U.S.A.

A NEW INTERPRETATION OF THE HAFELE-KEATING EXPERIMENT

Domina Eberle Spencer,

University of Connecticut, Storrs, Connecticut, 06268, U.S.A

Uma Shama,

Bridgewater State College, Bridgewater, Massachusetts, 02325, U.S.A.

It is generally considered that one of the most crucial experiments in support of the special theory of relativity is the Hafele-Keating experiment¹. Four atomic clocks were flown around the world and then compared with the master clock in Washington, D.C. However, the original paper did not publish the raw data. Dr. Keating has been kind enough to permit us to analyze the raw data. We have found that an entirely different interpretation of the experimental data, which supports the universal time postulate on the velocity of light², is perfectly consistent with the experimental data obtained by Hafele and Keating. Thus, one of the essential experimental supports of the relativistic theory of time dilation is shown to be invalid. Instead, the original data provide additional strongsupport³ of the reality of the universal time postulate on the velocity of light.

Introduction

Two very important papers^1,2 were published in 1971 by J.C. Hafele of the Department of Physics, Washington University, St. Louis, Missouri, U.S.A. and R.E. Keating of the Time Service Division, U.S. Naval Observatory, Washington, D.C., U.S.A. In October, 1971, four cesium beam clocks were flown around the world twice on regularly scheduled commercial airlines: once in each direction. The purpose of the experiment was to test Einstein’s theory of relativity with macroscopic clocks. As the experimental data were analyzed by Hafele and Keating, the confirmation of Einstein’s data appeared to be convincing.

Dr. Keating has been kind enough to provide us with the raw experimental data. In this paper it will be shown that an analysis of the raw data yields very different results which are in agreement with the universal time postulate⁶.

The Raw Data

According to Hafele and Keating, “The fundamental unit of time interval, the second is now by definition equal to 9,192,631,770 accumulated periods of the frequency of the atomic transitions of an “ideal” cesium beam frequency standard.” They say that, “No two “real” cesium beam clocks keep precisely the same time, even when located together in the laboratory, but generally show systematic rate (or frequency) differences which in extreme cases may amount to time differences as large as 1 _sec per day.” Short term fluctuations in rate are caused mainly by shot noise in the beam tubes. Cesium beam clocks also exhibit small but more or less well defined quasi-permanent changes in rate. “Because of the random and independent character of these rate changes, the long-term average rate of an ensemble of clocks is more stable than the rate of any individual member.”

The actual experimental data are the time difference measurements between the traveling clocks and the AT(USNO) master clock BEFORE, BETWEEN and AFTER the travel made by each traveling clock, as shown in Fig. 1. There are four wiggly sinusoidal curves, one for each clock. These curves have two gaps: one to the left of center when the clocks were on the airplane flying eastward and one to the right of center when the clocks were on the airplane flying westward. We have drawn a smooth curve through the experimental data in Fig. 1. For each clock there is a roughly sinusoidal curve with very small local variations. The smooth curves interpolated during flight appear to be entirely unaffected by the motion of the airplane.

The way in which the data are presented in the published¹ paper of Hefele and Keating is shown in Fig. 2. Here it is apparent that the data if Fig. 1 have been subjected to a major smoothing process. The data period of the entire experiment lasted 636 hours. Time difference in nanoseconds relative to the MEAN(USNO) is plotted versus time in hours from the beginning of the experiment. Again, there are no data during the 65.4 hours required for the eastward trip and the 80.3 hours required for the westward trip. Data are shown for each of the four clocks and for their average. We have modified the Hafele-Keating figure by drawing smooth curves through the data. In this way we have interpolated data on the behavior of the clocks during the eastward and westward airplane flights. Smooth curves are necessary in every case, but these are not straight lines. Even the average curve is not a straight line. There appears to be no significant difference between the interpolated curves during the airplane flights and the measured portions when the clocks were on the ground. A smooth curve passes through all of the data points and there is no indication of any significant difference in the behavior of the clocks when in motion.

2. Linearity in Flight?

In order to obtain the time changes predicted by Einstein’s theory of relativity, Hafele and Keating² do something which is very surprising. They assume that, although the data of Fig. 1 and Fig. 2 are never linear, somehow when the airplane is in motion the curves become linear! And they assume that the slope of this straight line is the average of the data for the 25 hours before the trip. Has the clock a foreknowledge that it is about to travel on an airplane around the world? Using this straight line there is a difference between the experimental data after the trip and the extrapolation along the straight line which they call Dt and attribute to relativistic time dilation. But why should a curve for the discrepancy between the four traveling clocks and the standard clock suddenly become linear when the clocks are traveling in an airplane? An example taken from the Hafele-Keating paper² is shown in Fig. 3. We have added the smooth curves, which have no resemblance to the extrapolated straight lines. Thus, we would conclude that the relativistic time dilation confirmation claimed by Hafele and Keating is based on strange and unfounded assumptions. Curves which are never linear when they can be measured do not suddenly become linear when they cannot be measured!

Another interesting feature of the assumption that the discrepancies become linear when the clocks are flying is that the time dilitation is sometimes positive and sometimes negative for individual clocks for both eastward and westward flight. Only the linear analysis of the average of the four clocks gives the time dilitations predicted by Einstein’s theory of relativity.

3.The Universal Time Postulate

Einstein³was the first to formally state a postulate on the velocity of light in 1905 By 1907 he⁴ had found it necessary to modify this postulate to the form:

Postulate I*: The velocity of light in free space is a constant c irrespective of the velocity of source or receiver in any coordinate system which is not in rotation.

This means that in free space a light signal moves outward in a spherical wave. The radius of this sphere is always

(1)

where r_I is the radius of the sphere, Fig.4., c is the velocity of light in free space, t is the time of emission of the light signal and t is the instant of reception. The radius r_I is the distance from the point x(t), h(t), z(t) where the source was at the instant of emission to the point x,y,z where the receiver is at the instant t of reception,

(2)

Note that the center of the spherical wavefront is always at the point where the source was when the light signal was emitted. It is assumed to be entirely independent of the motion of the light source. From this deceptively simple postulate follow the necessity for contractions of length, time dilitation and variation of mass with velocity.

The universal time postulate was first suggested by Moon and Spencer⁵ in 1956, as the only postulate which would permit synchronization of clocks between accelerated observers moving in a straight line. It was generalized to 3-dimensional motion by Moon, Spencer and Moon⁶ in 1989:

Postulate III* In a coordinate system that is not moving with respect to the source and which is not in rotation, the velocity of light in free space is a constant c.

Here the radius of the spherical wavefront is

(3)

The difference is that r_III is defined differently, Fig.5. It is the distance from the point x(t), h(t). z(t) where the source is at the instant t of reception to the point x,y,z where the receiver is at the instant of reception t:

(4)

This means that the center of the spherical wavefront is always at the source and that there is no time dilitation. Consequently, in a coordinate system in which the source is in motion, the velocity of light is not a constant c but is c + v, where v is the instantaneous velocity of the source. Only in a coordinate system in which the source is stationary is the velocity of light equal to c.

4. Conclusions

Previous research has compared the predictions of Postulates I* and III* with a number of experiments. The data on the binary stars⁷ were studied by Moon and Spencer in 1953 and by Moon, Spencer and Moon in 1989. Both Postulates I* and III* were found to be in agreement with the binary star data even in Euclidean space.

The Michelson-Morley experiment was analyzed by E.E. Moon⁸ in 1993. He found that the null result could be explained by Postulate I* in a stationary coordinate system, but that a contraction of length which was a function of velocity was required in a reference frame which moved at a constant velocity with respect to the laboratory and that a contraction which was a function of both velocity and acceleration was required in an accelerated coordinate system. This is a generalization of the Fitzgerald contraction. On the other hand with Postulate III* a null fringe shift was predicted in stationary coordinate systems as well as coordinate systems moving at a constant velocity relative to the laboratory and also in accelerated coordinate systems, without any neeed for a Fitzgerald contraction of length.

The Michelson-Gale experiment was analyzed by Moon, Spencer and Moon⁹ in 1990. The correct fringe shift is predicted by both Postulates I* and III*, if analyzed in a non-rotating coordinate system attached to the axis of the Earth and also in a non-rotating coordinate system attached to the light source. However, the fringe shift originates in different parts of the rectangular path according to Postulates I* and III*.

The Sagnac effect was analyzed by Spencer and Shama¹⁰ in 1991. Here again the correct fringe shift was predicted by both Postulates I* and III* but was predicted to originate in different portions of the path.

It was not until Spencer and Shama¹¹ analyzed stellar aberration in 1996 that they found an experiment which discriminated between Postulates I* and III*. In a coordinate system in which the star is stationary, both Postulate I* and Postulate III* predict the correct stellar aberration first observed by Bradley in 1728. But in a coordinate system in which the star is moving and the telescope is stationary, Postulate I* predicts no stellar aberration while Postulate III* predicts the correct result. This is the first proof of the validity of Postulate III* and the failure of Postulate I*.

The present analysis of the Hafele-Keating experiment provides the second experimental proof of the validity of Postulate III* and the failure of Postulate I*.

Thus, we can conclude that the only postulate on the velocity of light which correctly predicts all of the experimental results hitherto analyzed is Postulate III*, the universal time postulate on the velocity of light.

References

J.C. Hafele and R.E. Keating, “Around-the-world atomic clocks: predicted relativistic time gains”, Science, Vol.177, p.166, 1972.
J.C. Hafele and R.E. Keating, “Around-the-world atomic clocks: observed relativistic time gains”, Science, Vol.177, p.168, 1972.
A. Einstein, “Zur Elektrodynamik bewegter Korper”, Ann. der Phys., 17, 1905, p.891.
A. Einstein, “Uber das Relativitatsprinzip und die aus demselben gezogenen Folgerungen”, Jahrbuch der Radioaktivitat, IV, p.422-462, V, p. 98-99 (Berichtigungen), 1907.

P. Moon and D.E. Spencer, “On the establishment of universal time”, Phil. Sci., Vol. 23, p.216, 1956.

P. Moon, D.E. Spencer and E.E. Moon, “Universal time and the velocity of light”, Physics Essays, Vol.2, p.268, 1989.

P. Moon and D.E. Spencer, “Binary stars and the velocity of light”, J. Opt. Soc. Am., Vol. 43, p. 635, 1953. P. Moon, D.E. Spencer and E.E. Moon, “Binary stars from three viewpoints, Physics Essays, Vol.2, p. 275, 1989.

E.E. Moon, “A postulational formulation of the Michelson-Morley experiment”, Physics Essays, Vol. 6, p. 487, 1993.

P. Moon, D.E. Spencer and E.E. Moon, “The Michelson-Gale experiment and its effect on the postulates on the velocity of light”, Physics Essays, Vol. 3, p.431, 1990.