I send you a good paper that prove my transformation and my quantization of gravity is completely right and agreed completely also with Hafele-Keating. The Hafeleâ€“Keating experiment was a test of the theory of relativity. In October , Joseph C. Hafele, a physicist, and Richard E. Keating, an. I teach physics, and I love the Hafele-Keating experiment as a way to introduce relativity. Because the experiment has a lot of charisma, it’s cool to be able to.

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### Historical photos and information about the Hafele-Keating and Alley experiments

From the actual flight paths of each trip, the theory predicted that the flying clocks, compared with reference clocks at the U. Relative to the atomic time scale of the U. These results provide an unambiguous empirical resolution of the famous clock “paradox” with macroscopic clocks. Inexperimenters from the U. Naval Keatiing undertook an experiment to test time dilation.

They made airline flights around the world in both directions, each circuit taking about three days. They carried with them four cesium beam atomic clocks. When they returned and compared their clocks with the clock of the Observatory in Washington, D.

## Historical photos and information about the Hafele-Keating experiment

For small changes in gravitational field associated with changes in altitude above the earth, the approximate time dilation expression is. Hafele and Keating predicted a time difference of ns on an eastward flight around the world for which the flight time was This corresponds to an average height of m, a reasonable flight altitude for a commercial airline. The time shift is positive aging faster for both eastward and westward flights.

The predicted value of ns for the westward flight of This expression can be used to compute the time dilation in the Hafele-Keating experiment in which an atomic clock was taken aboard an aircraft and compared to a ground-based closk. The problem encountered with measuring the difference between a surface clock and one on an aircraft is that neither location is really an inertial frame.

If we take the center of the earth as an approximation to an inertial frame, then we can compute the difference between a surface clock and the aircraft clock. Taking a “proper time” at the earth’s center as if the master clock were there, the time measured by a clock on the surface would be larger.

The difference in the times compared to our hypothetical master clock would then be. Now this relationship is just the reverse of the actual experiment, since we have assumed that the clock is at the center of the earth, whereas the actual clocks are in the frames which are moving with respect to the center.

The time difference expression should be valid, but in comparing the aircraft clock to the surface clock, we should find that it has fallen behind, meating we can model that time difference hafrle.

kdating Note that the “earth center” time has been replaced by the surface time in this expression. This is a valid approximation in this case since the time difference is many orders of magnitude smaller than the time itself, and this allows us to model the difference between two measurable times.

### Hafele-Keating Experiment

For an aircraft flying over the equator, its clocks will show a time shift relative to a fixed surface clock which can be approximately modeled by the expression. For travel eastward, v has a positive sign and the shift will keaitng negative aging more slowly.

But for a westward flight the time shift is positive aging faster for the aircraft speeds involved. If you plug in numbers for a keatinng hour kkeating trip flight at constant speed at the equator, you get ns and ns for the eastbound and westbound flights respectively.

The predicted values obtained by Hafele and Keating presumably were based upon detailed measurements of the speeds, etc. It gives an experimental answer to the twin paradox. Hafele and Keating Experiment “During Hsfele,four cesium atomic beam clocks were flown on regularly scheduled commercial jet flights around the world twice, once eastward and once westward, to test Einstein’s theory of relativity keatiing macroscopic clocks.

Keating, ScienceDescription of experiment. Around the World Inkeatin from the U. Around-the-World Atomic Clocks In OctoberHafele and Keating flew cesium beam atomic clocks around the world twice on regularly scheduled commercial airline flights, once to the East and once to the West. In this experiment, both gravitational time dilation and kinematic time dilation yafele significant – hfaele are in fact of comparable magnitude.

Their predicted and measured time dilation effects were as follows: Gravitational Time Shifts For small changes in gravitational field associated with changes in altitude above the earth, the approximate time dilation expression is if a comparison is made between a clock on the Earth’s surface T E and one at height h above the surface T. Kinematic Time Shift Calculation If the kinematic time dilation expression is expanded in a binomial expansionthen for small velocities it becomes This expression can be used to compute the time dilation in the Hafele-Keating experiment in which an atomic clock was taken aboard an aircraft and compared to a ground-based closk.

Taking keqting “proper time” at the earth’s center as if the master clock were there, the time measured by a clock on the surface would be larger and that for the airborne clock would be approximately since to the level of the approximations used, the height of the aircraft does not significantly change the radius R.

The difference in the times compared to our hypothetical master clock would then be Now this relationship is just the reverse of the actual experiment, since we have assumed that the clock is at the center of the earth, whereas the leating clocks are in the frames which are moving with respect to the center.

Aircraft Time Dilation For an aircraft flying over the equator, its clocks will show a time shift relative to a fixed surface clock which can be approximately modeled by the expression.

Index Hafele and Keating.