I want to tell a story of two adventurous "scientists" that, allegedly,
proved SR and GR by using borrowed cesium atomic clocks, which they
carried along with them while traveling around the globe TWICE, using
commercial flights.
You can read the original publication here (1971):
http://www.personal.psu.edu/rq9/HOW/Atomic_Clocks_Predictions.pdfas well as the Wiki narrative here:
https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experimentIt's worthy to mention that this is THE CHEAPEST EXPERIMENT to prove SR
and GR simultaneously. It only costed $8,000 from a grant of the US
Naval Observatory. Of this amount, $7600 was spent on plane tickets,
including two seats on each flight for the atomic clocks. They performed
TWO ROUNDS around the world, each one on opposite directions.
ALERTS ABOUT THE HOAX:
1) Consider that each path flight, linearized, was composed by no less
than 5 segments (US, UK, Turkey, Philipines, Japan, US), and required
that both adventurers spend about 1 day of accomodations at each stage
(hotel, etc.).
2) With the help of EXPERTS in navegation, they APPROXIMATED the globe
circumvalation AS IF it was done following the Equator IN JUST ONE TRIP.
Here entered a lot of approximations in the calculations, to linearize
the travels. Nothing different than the ABUSE OF STATISTICAL CORRECTIONS
within the 1961 Pound-Rebka experiment.
3) No less than 10 take-off and landings existed. At each one, the
EFFECTS of acceleration, altitude change, geomagnetic and atmospheric
effects, humidity, presurization, heat, velocity changes, etc., WERE
IGNORED.
4) The couple used APPROXIMATIONS of relativity to generate these
formulae for calculations of time effects due to SR and GR:
FOR SPECIAL RELATIVITY
A clock that is stationary on the surface at the equator has a speed RΩ
relative to nonrotating space, and hence runs slow relative to
hypothetical coordinate clocks of this space in the ratio 1 - R² Ω²/2c²,
where R is the earth's radius and Ω its angular speed.
If τ and τ₀ are the respective times recorded by the flying and ground
reference clocks during a complete circumnavigation, their time
difference, to a first approximation, is given by
τ - τ₀ = -( 2RΩv + v²) τ₀/2c²
NOTE 1: OBSERVE THAT THIS IS A QUADRATIC EQUATION IN τ₀. THIS HAS NOT
BEEN ADDRESSED IN CALCULATIONS.
NOTE 2: v (the speed of the plane) is v>0 flying eastward. The opposite
is negative.
FOR GENERAL RELATIVITY
τ - τ₀ = [gh/c²-( 2RΩv + v²) /2c² ] τ₀
where h is the AVERAGE ALTITUDE OF THE PLANE, being h << R.
FINAL RESULTS, AS PUBLISHED IN 1972 IN SCIENCE MAGAZINE (values are in
nanoseconds)
Predicted for GR (eastward flight): +144 ± 14
Predicted for SR (eastward flight): -184 ± 18
THEORETICAL TOTAL EASTWARD FLIGHT: -40 ± 23
MEASURED TOTAL EASTWARD FLIGHT: -59 ± 10
NOTE 3: More than 70% error for SR (use values at extremes).
NOTE 4: Starting 4 October 1971, eastward flights lasted 65 hours, with
41 accumulated hours of flight.
Predicted for GR (westward flight): +179 ± 18
Predicted for SR (westward flight): +96 ± 10
THEORETICAL TOTAL WESTWARD FLIGHT: +275 ± 21
MEASURED TOTAL WESTWARD FLIGHT: +273 ± 7
NOTE 5: In this case, the error is lower than 1% (use values at
extremes).
NOTE 6: After a week of vacations, and starting 13 October 1971,
westward flights lasted 80.3 hours, with 48.6 accumulated hours of
flight.
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If after reading the brief resume, you still think that this IS REAL
SCIENCE, and that the results ARE NOT COOKED by two ambitious
relativists, then you deserve to be a gullible imbecile, like the ones
who supported this HOAX and made it public.
If you dig a little bit in the equations for SR and GR that were used by
these two, you'll find that are only A GROSS APPROXIMATION generated
using the 1915 Schwarzschild's solution, 56 years after he developed it.
It's the same shameful procedure that Pound and Rebka used on their 1961
experiment, devised to CHECK if the 1911 Einstein's equations were true
and, then, PHOTONS HAVE MASS.
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J. C. HAFELE - Department of Physics, Washington University, St. Louis,
Missouri
RICHARD E. KEATING - Time Service Division, U.S. Naval Observatory,
Washington, D.C.
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