Time Dilation and the Hafele and Keating Flight around the Earth

Another good one from Bill Howell:

Hello again Dr. Borchardt-

I re-read your Infinite Universe Theory paper and sure enough, it prompted another question to bother you with :-). This one’s about Relativity’s prediction of time dilation. I understand what you are saying in the paper that science should not be a slave to mathematics, about the ‘occupational hazard’ of mathematicians confusing their tools of analysis as representing actual reality, and the delusion of thinking of time as an actual dimension just because it can conveniently be represented by an axis on a plot. With that said, I’ve read that experiments with atomic clocks in aircraft and spacecraft have documented an actual time-lag in accordance with Einstein’s theory of Relativity when compared with a control clock that did not experience the acceleration. Assuming these results are true, that would constitute empirical evidence (versus the mathematical delusion issue mentioned above) of, well, … something. But whatever it is evidence of; it is consistent with the predictions of Relativity theory. Do you have an alternate (Univironmental Deterministic) explanation for such empirical results?

As you know, time is motion. Universal time is the motion of each microcosm with respect to all other microcosms. A clock measures the motion of a specific microcosm with respect to its macrocosm. Thus, an hourglass measures the flow of sand through a restriction under the effect of gravity. If I should take an hourglass with me into outer space, I would find that the rate of flow of sand would decrease. An “hour,” as measured by the hourglass would be much longer than it would be on Earth. I could interpret this in one of two ways: 1) via the old scientific world view, systems philosophy, or 2) via the new scientific worldview, univironmental determinism. In the first, I would adhere steadfastly to the systems point of view, seeing the hourglass as a “system” without an environment. In keeping with my other assumptions as an indeterminist, I might accept Einstein’s view that, in this case, time has somehow “dilated.” Of course, the adjustments I would use to get the correct time really would not be the relativistic equations that Einstein derived, but you get the idea. In the second, the correct analysis involves the proper inclusion of the macrocosm. The equation for the gravitational effect on hourglass flow would be a rather simple function of altitude. It certainly would not require relativity and its silly idea that motion was a thing, and therefore could dilate.

Among the most frequently cited proofs of relativity remains the Hafele and Keating (1972) experiment. This involved four supposedly precise atomic clocks on planes flying in opposite directions around the earth. There are two interpretations of the data. I will give both, and you can decide which one is correct.

Conventional: Hafele and Keating (1972) Proves Time Dilation

In the conventional interpretation, it is believed that Hafele and Keating proved that the east-bound clock slowed down by 59 nanoseconds and that the west-bound clock sped up by 273 nanoseconds relative to a clock in Washington. Even if true, this would be quite a shock. Einstein claimed that all moving clocks are supposed to run slow with respect to the observer. There should have been little difference between eastward and westward travel. After a bit of back-tracking by figuratively placing the reference clock at the non-rotating center of the earth and including gravity as a major contributor to the result, their calculations seemed to agree with relativity. Unfortunately for Einstein, this interpretation of the experiment indicated that the part about “motion with respect to the observer” had to be discarded. Hafele had to use “motion with respect to the underlying nonrotating inertial space” to get the math to agree with relativity predictions. This is a big step away from the solipsism that underpins relativity, but that is seldom noted in the many citations of Hafele and Keating as a proof of relativity. Some skeptics (e.g., Bethell, 2009, p. 133-41; Kehr, 2002) have tried to find a physical reason for the published results.

Skeptical: Hafele and Keating (1972) Proves Nothing

In the second interpretation, skeptics have considered the experiment to have been a total failure due to the erratic behavior of the clocks (e.g., Spencer and Shama, 1996; Kelly, 2000). Kelly (2000) was able to obtain the raw data (in bold characters), which looked like this:

Table 1. Original test results and the Hafele and Keating alterations (ns) (from Kelly, 2000, Table 3).

Of course, all clocks, even the relatively precise cesium beam clocks used in the experiment, fail to keep accurate time at some level. The clocks used in the experiment produced highly variable results as seen in Table 1. When compared to the ground-based clock some had gained and some had lost. Now, this is not necessarily a death knell for this type of experiment. The tendency for a clock to gain or lose time is called “drift.” If the drift occurs at a steady rate throughout the experiment we can subtract it to get an accurate time. For example, if my watch gains a second per day, I will have to subtract 7 seconds from the observed time to get the correct time next week. This is not what happened in the Hafele and Keating experiment. Drifts were highly irregular for each of the clocks (Fig. 1). The total range in drift during the course of the experiment was about 7000 ns (nanoseconds) for an experiment purporting to measure as little as 59 ns. Not only were the drifts for the four clocks highly variable, the drifts for each of the individual clocks changed throughout the experiment (changes in slope of the lines in Fig. 1).

Figure 1. Sketch of results given by Hafele and Keating (1972) (from Kelly, 2000). G = time gain; L = time loss.

Drifts determined when the clocks were on the ground in Washington were extrapolated across the time the clocks were in transit. Clock 408 was about the worst: it lost time (L) before the eastward flight and gained time (G) after the flight (Fig. 1). Clock 447 had the most consistent drift rate, but it showed no significant gain or loss during both flights (Fig. 1). On top of all this, Hafele and Keating had the temerity to average this mess (bold dashed line in the center of Fig. 1) before applying the adjustments and math (Table 1) that they ultimately anointed as being in “agreement with relativity.”

Lessons Learned

It seems that every time I evaluate one of the experiments said to confirm SRT or GRT either the data or the interpretations are poor. Hafele-Keating is no different. You might ask: “Aren’t all important experiments confirmed by others?” Actually, this is seldom the case—of my 320 publications, only one was repeated by others in any detail (see Wills and Borchardt, 1993 vs. Turner and others, 2008). Except for some refinement, the results were essentially the same. To go to the trouble of redoing an experiment, one must be a highly motivated skeptic. Being the second Einstein is not enough. The skeptics I referenced remain unpublished in ranking journals and they probably could not get funds to redo the experiment in any case. Apparently, slip-shod work in favor of relativity has a ready market among believers; those opposed present only a minor inconvenience to the conventional wisdom.

The upshot is that the “data” presented by Hafele and Keating are an embarrassment for science. If they actually had obtained data that supported Einstein’s idea that clocks are slowed simply by increases in velocity, the UD approach still would be necessary to provide a physical explanation. We would have to consider the microcosm (the cesium beam clock) and the macrocosm through which it travels. A hint for the necessity of this is found in the International System (SI) definition of a second as “the duration of 9,192,631,770 cycles of microwave light absorbed or emitted by the hyperfine transition of cesium-133 atoms in their ground state undisturbed by external fields (italics mine).” At minimum, cesium beam clocks have to be heavily shielded from magnetic effects—the Hafele clocks were triple shielded. The general appellation “external fields” is a bow to the possibility that there may be other fields to consider. Of course, there are all manner of particles in the Earth’s atmosphere and in the etherosphere (TSW, p. 202). How these would affect the clocks physically was and is still not well known. Clocks on the ground show less variability than the mobile clocks used on the planes, so the macrocosm evidently played an important part in the erratic results. A proper analysis would require an exploration of such effects.

By the way, I also re-read your explanation for the apparent stellar-shift (viz a viz the Eddington eclipse experiment) as being due to refraction in the ‘etherosphere’ and is not evidence for a gravity well or curved space-time around the sun. Such an elegant and simple explanation. Thank you.

You are welcome Bill. You might want to read Moody (2009), which is a similar analysis of the data that Eddington claimed to be the first experimental proof of GRT, catapulting Einstein into the limelight in 1919.


Bethell, Tom, 2009, Questioning Einstein: Is relativity necessary?: Pueblo West, CO, Vales Lake Publishing, 206 p.

Hafele, J.C., and Keating, R.E., 1972a, Around-the-World Atomic Clocks: Predicted Relativistic Time Gains: Science, v. 177, no. 4044, p. 166-168.

Hafele, J.C., and Keating, R.E., 1972b, Around-the-World Atomic Clocks: Observed Relativistic Time Gains: Science, v. 177, no. 4044, p. 168-170.

Kehr, R.W., 2002, The Detection of Ether (1st ed.): Overland Park, Kansas.

Moody, R.J., 2009, The eclipse data from 1919: The greatest hoax in 20th century science (http://www.worldnpa.org/pdf/abstracts/abstracts_1039.pdf), 16th Natural Philosophy Alliance Conference, Storrs, CT, United States, p. 26.

Spencer, D.E., and Shama, Uma, 1996, A new interpretation of the Hafele-Keating experiment (http://www.shaping.ru/congress/english/spenser1/spencer1.asp).

Turner, R., Koehler, R.D., Briggs, R.W., and Wesnousky, S.G., 2008, Paleoseismic and Slip-Rate Observations along the Honey Lake Fault Zone, Northeastern California, USA: Bulletin of the Seismological Society of America, v. 98, no. 4, p. 1730-1736.

Wills, C.J., and Borchardt, Glenn, 1993, Holocene slip rate and earthquake recurrence on the Honey Lake fault zone, northeastern California: Geology, v. 21, p. 853-856.

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