The Changing Rates of Falling Clocks

A clear example of how the principle Absolute Motion differs from General Relativity Theory is the case of the slowing rate of time recorded by clocks that fall from high above the earth. Both Absolute Motion and General Relativity predict the same rates of ticking for clocks in deep space, clocks in orbit and clocks at the surface of the earth. However, for falling clocks, the rate of change in time produced by the dynamics of Absolute Motion is far different than that predicted by General Relativity Theory.
Consider a thought experiment in which a clock and an accelerometer are attached to a ball of high strength metal foam. Each cell of the foam contains a high vacuum so that the density of the ball is the same as air at sea level, thus making it weightless at standard atmospheric pressure. When the falling ball collides with the atmosphere, air resistance and its buoyancy will gradually slow it to a stop as it reaches the ground.
In the experiment, the clock-ball is dropped from a point of rest 8 radii above the center of the earth. At the moment that its released, it has no relative velocity with the earth. However, both are moving at 375 km/s relative to the 2.7 degree cosmic background radiation (CBR) in the direction of Leo. This motion gives the clock a background time dilation so that if one tick of the clock has duration of one at CBR rest, it has duration of 1.000000782 at this velocity. The Earth’s escape velocity at 8 radii is 3,954 m/s. This is the velocity that a body falling from deep space will attain when it reaches a point 8 radii above the earth. It is also the upward velocity that a body 8 radii above the earth must attain in order to escape the earth’s gravity. This additional velocity slows the duration of each tick to 1.000000799. The earth’s escape velocity at sea level is 11,179 m/s and the equatorial velocity is 448 m/s. These velocities further increase the duration of each tick to 1.000000830 at sea level. Both Absolute Motion and General Relativity predict that the ticking of clocks will slow from 1.000000799 at 8 radii to 1.000000830 at sea level, but they are completely opposite in their descriptions of the physical dynamics by which the clocks slow their rate of time.
The principle of Absolute Motion treats the gravitational time dilation exactly the same as a relativistic time dilation created by a measured velocity. As the clock “falls” to Earth, it experiences no acceleration and maintains a constant rate of ticking until it collides with the atmosphere. By the time it reaches the ground its accelerometer registers an upward acceleration to a velocity of 7,225 m/s and a transverse easterly acceleration to a velocity of 448 m/s. The slowing of the clock is in direct response to this change in motion and it occurs as the accelerometer records it. The direct cause of the clock slowing is the increase in kinetic mass caused by this measured velocity. The rotational velocities within the atoms of the clock must slow with the increase in their mass in order to conserve angular momentum. This decrease in rotational motion slows cyclical motion at all levels of the clock’s structure and thus slows its measure of time. It must be emphasized that the principle of Absolute Motion is not a theory because it offers no metaphysical assumptions susceptible to falsification. It is simply a description of the measured dynamics of gravitational and inertial motion. These actual physical measurements do not allow for another interpretation. Any other explanation must introduce a hidden variable that can void actual measurements and that can itself not be measured. The principle of Absolute Motion interprets all measurements at face value and does not postulate causes or effects that can’t be measured.
All measured acceleration produces change in motion and all changes in motion produce measured acceleration. All acceleration relative to CBR photon rest increases mass and all deceleration relative to CBR photon rest decreases mass.
The theory of General Relativity treats gravitational clock slowing as a metaphysical phenomenon in which the clock slowing is in response to a non-dynamical and non-local occult influence called a gravitational field. It is said that this field “curves” space and time in such a way that it produces change in motion that is not accessible to physical measurement and that can only be described with complex mathematical equations. In this theory, the clock gradually slows as the space between it and the earth’s center is decreased by a “curvature” of the gravitational field. Its rate of ticking slows from the time that it begins its fall until it reaches the ground. As it falls, each tick is just slightly longer than the one before it. The rapid acceleration experienced when the clock enters the atmosphere has no effect on its rate of ticking other than to slow the clock’s decent to the ground. This is a very paradoxical explanation of an effect that has no measurable cause and a cause without a measurable effect. It even seems to contradict the Equivalence Principle that states that a free falling body in a gravitational field will experience the same dynamics as a body floating in deep space. If a deep space clock and a free falling orbital clock maintain constant rates of ticking, how can a non-orbiting clock in free fall slow its rate? I do not see how a relativity enthusiast can answer this question without first invoking the Equivalence Principle and then overriding it. The standard answer to such questions is that the Equivalence Principle demands a non-intuitive four-dimensional space-time that is not accessible to physical measurement or the logic and philosophical reasoning of the human mind.
Once the clock comes to rest on the surface of the earth, the predicted rate of ticking is the same for both the principle of Absolute Motion and the theory of General Relativity. However, the predicted rates of ticking diverge again when the thought experiment is extended and the clock is allowed to fall into a hole drilled to the center of the earth. The principle of Absolute Motion predicts that a clock floating weightlessly at the center of the earth will not be effected by the dynamics of gravitational expansion and will run at the CBR background time dilation rate of 1.000000782 ticks. General Relativity predicts that the clock will continue to slow its ticking rate until it reaches the earth’s center. This prediction seems to contradict the idea of curved space upon which the dynamics of General Relativity are based. If clock slowing results from the curvature of the surrounding space, how can clock slowing occur at the center of the earth where the geometry of gravitational space is virtually flat just as it is in deep space?
It is also claimed that it is the gravitational potential that slows clocks. The gravitational potential of the earth is zero in deep space, increases to a maximum at sea level and then decreases back to zero at the earth’s center. By what mechanism does a clock determine whether it is in the zero gravity of deep space or in the zero gravity at the center of the earth?

Falling Clocks

The Orbiting Clock Paradox

A clock resting on the earth’s surface has an upward velocity along the fourth vector of 11,179 m/s. This upward surface velocity is caused by the gravitational expansion of the Earth. A body falling to earth from deep space will strike its surface at this velocity. In gravitational attraction theories this is called escape velocity because at sea level an upward moving body must move at this velocity or it will eventually fall back to earth. Motion along this gravitational fourth vector is absolute to the position of the earth’s center but is independent of the three Euclidean vectors. At points above the earth’s surface both escape velocity and surface velocity have the same value and are calculated by the formula (eV or sV = 2gR). The surface velocity or escape velocity at any point above the earth’s surface is equal to the square root of 2 times the acceleration of gravity (g) times the distance to the earth’s center (R). Motion at right angles to surface velocity is called orbital velocity and is calculated by the similar formula (oV = gR). Orbital velocity (oV) is equal to the square root of the acceleration of gravity (g) times the distance to the earth’s center (R).
Clocks moving along the forth vector of gravitational motion are slowed by an amount that is in addition to their background slowing as a result of their motion relative the 2.7o CBR rest. The clock slowing caused by forth vector gravitational motion results from its intrinsic velocity relative to the center of the earth.
Consider a thought experiment in which one atomic clock is placed at sea level and an identical second clock is accelerated along the earth’s surface into a sea level orbit at a velocity of 7905 m/s. Because of this increase in velocity, the orbiting clock would run at a slower rate than the clock at the earth’s surface. If this second clock’s orbit were increased from sea level to a synchronous Comsat orbit of 6.61538 earth radii, it would be necessary to slow its orbital velocity to 3,076 m/s and reduce its escape velocity to 4,346 m/s. Both of these changes in velocity would cause the clock to run faster than it did in a low earth orbit and slightly faster than the clock at the earth’s surface.

Next, consider the case of a clock carried up a ladder from the Equator to the height of a synchronous Comsat orbit. Both the orbiting clock and the clock atop the ladder would have no relative velocity between them. They would have the same values for kinetic energy and gravitational potential energy and would keep the same time. The only difference between them is that it took far less energy to carry the clock up the latter than to put the other one in orbit. The orbiting clock must be accelerated into a low earth orbit and then decelerated into the much higher Comsat orbit.

Now consider a third clock that is in the same orbit but traveling in the opposite direction. This third clock is the same distance from the earth’s center as the other two clocks and its orbital velocity of 3,076 m/s is identical to the velocities of the other clocks. When they pass twice a day, the third clock is moving relative to the first two at a velocity of 6,152 m/s. Since the dynamics of all three clocks are identical then they must all keep the same time. How is this possible with so much relative motion between them? An absolute velocity of 6,152 m/s should cause a clock to increase the length of its measured time intervals to 1.00000000021. Then 6 hours later, when the orbiting clocks are on opposite sides of the earth, they are both moving in the same direction with no relative velocity between them. How can both clocks run at a constant rate when the relative velocity between them is constantly changing?

This paradox is particularly difficult for relativity enthusiasts to answer because any explanation directly contradicts the fundamental tenants of relativity theory. If they claim that the clocks constantly change their rates in relation to the relative velocity between them, then all motion is absolute and the very idea of relative motion must be discarded. If during each orbit, the clocks undergo a cycle of speeding up and then slowing down, then the clocks must be changing their rates in relation to, not each other, but rather to an absolute preferred inertial reference frame. Each clock must monitor its changes in velocity relative to the 2.7o CBR photon rest and then change its rate of ticking according to its vector of motion within this frame. This must be done without the clocks experiencing any measurable inertial acceleration. If, to the contrary, it is claimed that both clocks maintain the same constant rate then, the principle of relative motion is still violated. In order to put two identical clocks into opposite synchronous orbits, it is necessary to accelerate each to velocities of 3,076 m/s in opposite directions. If relative motion changes the rates of clocks, how is it possible for synchronous clocks to maintain identical rates when they are then accelerated to a relative velocity of 6,152 m/s?

A possible way to measure this effect would be to synchronize two identical clocks in Equador and then transport one clock halfway around the world to Borneo. These clocks could then be monitored for a number of years to see if their elapsed times remained the same despite their constant motion in opposite directions at the relative velocity of 896 m/s. If the clocks did loose their synchronicity over time it would show that it is relative motion and not absolute motion that changes the rate of clocks. However, relativity theory has no means for predicting which clock will slow down or speed up. If we expand this experiment from two clocks to a great many clocks located at equal distances along the equator, it would seem impossible to determine how the rates would change for each clock.

The most likely result of such an experiment would be that clocks at sea level maintain constant rates of elapsed time while at any point on the equator. There are two possible explanations that could explain this result. While present day atomic clocks are not accurate enough to measure such an effect, one possibility is that each clock speeds up and then slows down during each orbit as its velocity changes within the 2.7o CBR photon rest. In this case all clocks would be running at a different and changing rate during any interval of time but their average rate would be the same and they would record exactly the same number of time intervals for each rotation of the earth. The other possibility is that each clock maintains the same exact rate throughout the day and year after year.

Orbiting clocks

Neither of these two possibilities is compatible with the principle of relative motion. The first requires the preferred reference frame of absolute rest and the second completely refutes the relativist’s claim that clocks in different states of motion must run at different rates. At this point in the paradox the relativity buff must drag out his old faithful four dimensional non-Euclidean geometry equations and try to show that space and time can be curved in a non-intuitive way that is not possible to visualize. When clocks are in the presence of such a curvature they can maintain constant rates regardless of their changing states of motion. It is explained that the equations can describe what is happening even though the rational mind is unable to visualize it. It is a metaphysical occurrence the dynamics of which can neither be measured nor rationalized. It can only be described with equations.

The changing rate of clocks caused by changes in both velocity and gravity are well documented and have been determined to a high degree of accuracy. Measuring the rates of orbiting atomic clocks is a highly developed science necessitated by the need to maintain the accuracy of the constellation of Global Positioning Satellites (GPS). The clocks in many different satellites must be designed to run as synchronously as possible with clocks on earth. This is difficult because a clock’s rate is influenced by both the kinetic time dilation of its orbital velocity and the gravitational escape velocity at the orbit’s distance from the earth’s center. The clocks in the lowest orbits run the slowest because both their orbital velocities and escape velocities are greater than those of the higher orbits. Clocks speed up as they are placed in higher and higher orbits because they must be decelerated to both lower orbital velocities and lower escape velocities.

In order to synchronize the clocks in the GPS constellation, technicians must first synchronize the cesium clock to be put in orbit with a cesium clock on Earth. They must then calculate the rate at which the clock will run when it is placed in its desired orbit and then calibrate it to run faster or slower than the earth clock so that it will run at the same rate when in orbit. The reason the clock’s rate changes is because the rate at which cesium atoms vibrate decreases when they are accelerated to higher velocities and increases when they are decelerated to lower velocities. The clock’s recording mechanism must be calibrated to make up for the changed vibration rate of its cesium atoms when in orbit. The ideal orbit for GPS clocks is 2.694 Earth radii. At this orbit the sum of its orbital and escape velocities is the same as the sum of these velocities at the earth’s surface. Clocks placed in this orbit would be synchronous with clocks on the earth’s surface without the need of any special calibration. Higher orbiting clocks would run faster and clocks in lower orbits would run slower.

Since the process of gravitational expansion changes the absolute values of mass, space and time, gravitational motion, such as an orbit, occurs along a forth vector that is independent of the first three vectors of Euclidean space. When two clocks are accelerated into the same orbit in opposite directions, they remain in sync with one another because they both slow by the same amount due to the same increase in motion along the forth vector.


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