Some have asked me why only the rotation of the earth is significant in the Einsteins thought experiment concerning the time dilation of a clock on the surface of the earth. This question is also relevant to the Hefele-Keating experiment. To put it another way,
Why ISN'T the orbital speed or the galactic speed of the earth significant in the Hefele-Keating experiment?
My answer has been that the proper acceleration of the earths surface relative to the center, and the airplanes that move parallel to the earths surface, is larger than the proper acceleration of the other components. The proper acceleration of each component is equivalent to the centripetal acceleration, which is basically the result of force.
The clocks in the HK experiment are desynchronized by the difference in proper acceleration, not the difference in 'relative motion'. If there was no proper acceleration, the three clocks would meet once and no more. The centripetal force on the clocks is what breaks the apparent symmetry.
So I calculated the proper acceleration, a, of each the different components of the proper acceleration for a clock at the equator of the earth using the formula for centripetal acceleration:
a=v^2/r
for circular motion where r is the distance to the center of the circle, v is the velocity relative to the center of the circle, and a is the proper acceleration.
a(earth's rotation)= 0.0337 m/s^2 = 3.37x10^-2 m/s^2
a(earth's solar system orbit) = 0.0059 m/s^2=5.9x10^-3 m/s^2
a(suns' galactic orbit)= 2.054x10^-9 m/s^2.
Obviously, the proper acceleration associated with the earth's rotation far exceeds the proper acceleration associated with the other components of motion.
There is another wrinkle in the Hefele Keating experiment. The three clocks in the Hefele Keating experiment had different values for proper acceleration. The centripetal acceleration of the airplanes were different from the centripetal acceleration of the earth's surface. I leave that as an exercise for the skeptical reader.
There is a erroneous rumor going about that acceleration is unimportant in special relativity. This is not true. The proper acceleration, meaning the acceleration associated with force interactions, is very important in special relativity. In the case of the HK experiment, the centripetal acceleration is an approximation for proper acceleration sufficient to resolve the conundrums often presented by nonscientists.
Why ISN'T the orbital speed or the galactic speed of the earth significant in the Hefele-Keating experiment?
My answer has been that the proper acceleration of the earths surface relative to the center, and the airplanes that move parallel to the earths surface, is larger than the proper acceleration of the other components. The proper acceleration of each component is equivalent to the centripetal acceleration, which is basically the result of force.
The clocks in the HK experiment are desynchronized by the difference in proper acceleration, not the difference in 'relative motion'. If there was no proper acceleration, the three clocks would meet once and no more. The centripetal force on the clocks is what breaks the apparent symmetry.
So I calculated the proper acceleration, a, of each the different components of the proper acceleration for a clock at the equator of the earth using the formula for centripetal acceleration:
a=v^2/r
for circular motion where r is the distance to the center of the circle, v is the velocity relative to the center of the circle, and a is the proper acceleration.
a(earth's rotation)= 0.0337 m/s^2 = 3.37x10^-2 m/s^2
a(earth's solar system orbit) = 0.0059 m/s^2=5.9x10^-3 m/s^2
a(suns' galactic orbit)= 2.054x10^-9 m/s^2.
Obviously, the proper acceleration associated with the earth's rotation far exceeds the proper acceleration associated with the other components of motion.
There is another wrinkle in the Hefele Keating experiment. The three clocks in the Hefele Keating experiment had different values for proper acceleration. The centripetal acceleration of the airplanes were different from the centripetal acceleration of the earth's surface. I leave that as an exercise for the skeptical reader.
There is a erroneous rumor going about that acceleration is unimportant in special relativity. This is not true. The proper acceleration, meaning the acceleration associated with force interactions, is very important in special relativity. In the case of the HK experiment, the centripetal acceleration is an approximation for proper acceleration sufficient to resolve the conundrums often presented by nonscientists.
via International Skeptics Forum http://ift.tt/1MTVCHK
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