How does Gravity slow the Rates of Atomic Clocks?
It is the intrinsic motion of the earth’s surface velocity that causes an atomic clock to slow its rate at Earth’s surface.
One positive “proof” of General Relativity is based on the fact that clocks run at faster or slower rates when placed at different locations within the earth’s gravitational potential. For example, an atomic clock on Mount Everest will run faster than it will at the Dead Sea. This so called time dilation has often been portrayed as being the result of different amounts of gravitational potential energy mysteriously affecting the workings of the clock.
If we discard the metaphysical idea of gravitational potential then there is no mystery or need for General Relativity to explain the gravitational changes of clock rates. The cause of gravitational time dilation can only be attributed to a simple Lorentz Transformation of mass resulting from the different escape velocities of these locations. The higher escape velocity at the Dead Sea causes an increase in the mass of that clock’s internal mechanism and this slows the clock’s rate through the conservation of angular momentum.
A second smaller factor in this Lorentz mass transformation is the rotational velocity of the earth’s rotation at the similar latitude of these two places. To calculate a clock’s rate at the top of Mount Everest we need only determine the velocity of the vector produced by combining the vertical escape velocity with the horizontal rotational velocity. The Lorentz Transformation at this velocity increases the clock’s mass and decreases its rate of ticking by an equal amount. However, the greater escape velocity at the Dead Sea causes that clock to run even slower. This is true even though the rotational velocity at this lower elevation is slightly less.
The same, but more symmetrical process occurs to clocks aboard orbiting spacecraft. Clocks in the lowest of orbits, like space shuttle orbits, run slower even than clocks on the surface due to their much greater orbital velocity and only slightly less escape velocity. Clocks speed up at higher and higher orbits until at about 1.5 radii from the earth’s center they run at the same rate as surface clocks. Clocks in higher orbits yet, such as GPS orbits and geosynchronous Comsat orbits, continue to run faster and faster in higher and higher orbits due to decreases in both escape velocity and orbital velocity. Clock will run at a maximum rate at a position of rest relative to the 2.7 CBR photons. Any acceleration away from this point of rest will cause a clock to slow down. At .87 C the clock will run at one half because the mass of its inter workings has doubled.
There is no measurable intrinsic difference between a fourth vector gravitational “escape” velocity for a position in space and the velocity of a body moving through inertial space. Both motions effect the orbiting clock’s rate. The real difference is that inertial bodies move in three vectors and gravitating bodies move along a non-intuitive imaginary fourth vector.
The difference between an escape velocity vector for a position in space and its gravitational potential’s acceleration vector is that escape velocity is just a geometrical location within space and gravitational potential is usually depicted as a part of the physical structure of space.
An orbiting body is moving with two separate velocities that are at right angles to one another. Both velocities produce a Lorentz mass transformation that changes a clock’s rate through the conversation of angular momentum. The true absolute motion of the satellite is obtained by combining these two velocities into a single velocity vector. This combining of velocities can be verified precisely by the changing rates of GPS clocks as they are moved to different orbits.
The Earth’s Rotational Clock
A simple example of the time dilation mechanism is the day and night clock of the earth’s rotation. If the earth could be accelerated to a much higher velocity, its mass would be increased by an amount proportional to its increased kinetic energy (E=MC2). In order to conserve angular momentum, this increased mass would slow the earth’s rotation and “dilate” the day to a greater length. This increased length in the day could not be measured with earthbound atomic clocks because the same accelerated motion that increased the mass of the earth would also increase the mass of the clocks and slow their rates by the same amount. However, these changes in clock rates could be detected by monitoring the rates of non-local clocks such as pulsars both before and after the acceleration.
This same process of mass increase that would slow the earth’s rotation also slows the vibrational processes of the cesium atoms in atomic clocks. Time dilation does not change “time”. It merely represents physical changes in the parameters that are used to measure time.
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