Just Which Equivalence Principle Do You Believe In?
The Pound-Rebka Experiment
The Pound-Rebka Experiment is quite complex in its technical details but in principle it is very simple. Photons of a precisely determined wavelength were emitted at the top and bottom of the 22.5-meter-high Jefferson Tower on the Harvard campus. When the photons from the top of the tower were measured at the bottom, their wavelengths were decreased (blue-shifted) by a small amount; and when photons from the bottom were measured at the top, their wavelengths were increased (red-shifted) by the same amount.
Proponents of the theory of General Relativity offer three different conflicting explanations of these results that are said to be equivalent to each other and therefore all equally correct. All make the claim that the results of the Pound-Rebka Experiment are proof of the Equivalence Principle even though nothing in these measurements suggests any need for the Equivalence Principle.
In the drawing of tower #1, the photons are emitted with a wavelength of exactly one (=1). As they travel through the proposed gravitational field at the constant velocity of C, they interact with it so that the descending photons acquire mass, momentum and energy from the field and the ascending photons transfer mass, momentum and energy to the field. Thus the intrinsic wavelengths of the photons gradually change as they move through the field.
The main problem with this explanation lies in the conceptualization of a physical process by which mass, momentum and energy could be either added to or subtracted from a photon without changing its velocity or angular momentum. Such a mechanism has never been proposed except for a mathematical description of a four-dimensional substance called a space-time continuum. This is a non-Doppler explanation of the shifts in which both source, observer and all photons are in the same inertial reference frame and the photons move at exactly C relative to both source and observer.
In the drawing of tower #2, the photons are emitted at a wavelength of exactly one (=1) that remains constant as they move through the gravitational field. However, as they move thorough this field, the photons fall toward the earth like any other material body, so that the descending photons move at speeds increasingly greater than C, and the ascending photons move at decreasing speeds of less than C. During their time of travel (t=22.5/C=7.5052x10-8s) the ascending photons slow their velocity by (v=gt=.000000736m/s) and the descending photons increase their velocity to C+.000000736m/s. The red and blue shifts are Doppler shifts in which both source and observer are in the same inertial reference frame and each photon is in a different inertial reference frame. The shifts occur because the ascending photons arrive at the observer at a relative velocity of less than C and the descending photons arrive at a velocity greater than C. This change in the photons velocity will produce shifts in their wavelengths of the measured value of 2.5x10-15.
The central problem with this explanation is that it violates the constancy of the speed of light because each of the 22 photons used in this drawing is moving at a different velocity and none are moving at C relative to either source or observer.
In the drawing of tower #3, it is proposed that gravity causes clocks at the bottom of the tower to run slower than clocks at the top. This causes the emitter to take more time to produce a photon and thus increase its wavelength by 2.5 x 10-15. The faster clock at the top of the tower makes the emitter produce its photons in shorter time intervals and with shorter wavelengths. While all photons move at exactly C in this example, the observer at the top of the tower would measure their velocity to be less than C and the observer at the bottom of the tower would measure their velocity to be greater than C. This is due to their clocks running at different rates. If both emitters are set to produce photons with the same time intervals between them, the top emitter will produce more photons per second than the emitter at the bottom.
While both Relativity Theory and Absolute Motion Theory predict that atomic clocks tick faster at high altitudes than they do at sea level, this effect is far too small in Absolute Motion Theory to account for the Pound-Rebka results. The only explanation of this effect that is compatible with the Equivalence Principle is that this clock slowing at sea level is a relativistic time dilation caused by the earths escape velocity at the clocks location. We can calculate that a one kilogram clock falling from a position of rest in deep space will collide with the earths surface at escape velocity (esV= 2gR = 11,178.86275 m/s). If g = 9.807 m/s2 at the bottom of the tower, at an earth radius of (R = 6,371,315 m), then g = 9.806307344 m/s2 at earth radius (R = 6,371,337.5 m) at the top of the tower where the escape velocity is 11,178.84301 m/s. This velocity causes the clock to slow (t = 1-V2/C2) at the earths surface so that each second the clock registers will take 1.0000000007 second to pass compared to its beginning position of rest in deep space. This slowing does not occur until the clock comes to rest at the earths surface and acquires its upward escape velocity during impact.
Photons produced by the clocks light source would be red-shifted from =1 in deep space to =1.0000000007 at the earths surface. However, the difference in the clocks rate between the top and bottom of the tower is very small. The difference in the earths escape velocity between the top of the tower is .01974 m/s (11,178.86275 - 11,178.84301 = .01974). The clock slowing and resulting red shift caused by this velocity difference is only about 2.17 x 10-21. This is over 1,000,000 times smaller than the 2.5 x 10-15 red shift measured by Pound-Rebka and is thus too small to even be detected by present-day instruments. A relativistic time dilation of 2.5 x 10-15 would require a velocity of 21m/s which is the velocity that a body would attain falling from rest at the top of the tower to the bottom over a period of about 2.142 seconds.
The claim is also made by some relativity buffs that it is gravitational energy that causes the clocks to slow and the wavelengths of photons to be shifted but this idea also fails to adequately explain the measured shifts. We know that it takes 220.64 joules of kinetic energy to lift a one kilogram clock to the top of the tower 22.5 meters tall (E = Mgh). We must conclude from the clocks accompanying rate increase that this is negative energy which actually decelerates the clock to a location with a lower intrinsic absolute velocity. To determine the amount of clock slowing and relativistic Doppler shift caused by this 220.64 J loss in energy we must first translate it into a velocity. Again, this energy can be attributed to the difference in the earths escape velocity between the top and the bottom of the tower (.01974 m/s). The energy needed to decelerate a one kg mass from 11,178.86275 m/s to 11,178.84301 m/s is (E = mv2/2) 62,483,486.192 J - 62,483,265.548 J. = 220.64 J. Energy can thus not be translated into clock slowing because all one kilogram bodies falling past the tower to the ground would acquire 220.64 J of energy between the top of the tower and the bottom but each would acquire a different velocity increase depending of their velocity as they passed the top of the tower. As we have seen, this velocity increase can vary anywhere from 21m/s for a body beginning at rest to only .000000736m/s for a body moving a C.
In the drawing of tower #4, the Pound-Rebka experiment is evaluated strictly in terms of the values obtained by the measuring instruments and is not then reinterpreted to fit the ad hoc and purely metaphysical assumption of the Equivalence Principle. Accelerometers placed at the top and bottom of the tower will measure an upward acceleration of 9.807m/s2 at the bottom and 9.806307 m/s2 at the top. The photons in this depiction all move at exactly C within the same inertial reference frame common to all other photons. The accelerometers clearly show that in the time (7.5052x10-8s) that it takes for the photons to travel between source and observer, both observers have accelerated upward to a velocity of .000000736m/s. This relative velocity between source and observer causes the descending photons to be measured with shorter wavelengths and the ascending photons to be measured with longer wavelengths by the amount of 2.455x10-15. This value rounds off to the 2.5x10-15 shifts measured by Pound and Rebka.
This is by far the simplest and most logical explanation of the Pound-Rebka measurements. Although, this explanation is perfectly compatible with the Equivalence Principle, it in no way implies the necessity for any such metaphysical assumption.
It must be noted that there is a fifth explanation of this experiment that the most entrenched of the Relativity enthusiasts usually fall back on when confronted with the above paradoxes. This is the idea that the gravitational interaction occurs within a four dimensional space-time continuum that cannot be illustrated by such drawings and can only be understood in terms of very complex non-Euclidean geometry. The claim is made that gravity causes this space-time to curve in a non-intuitive way that cannot be visualized. As the photons move through this curved space, they acquire its curvature and are thus measured to be red- and blue-shifted. While there are no experimental measurements that could serve as evidence for the space-time continuum, a prior belief in the Equivalence Principle allows one to suspend belief in physical measurement and say that acceleration exists where it cant be measured (falling bodies) and it is measured where it doesnt exist (earths surface).
Accelerometer readings are the most basic and reliable of all physical measurements. Just ask a carpenter when was the last time his level didnt work. It is faulty physics to begin a theory with the premise that accelerometer readings must mean the opposite of what they say, when they dispute the purely emotional belief that the earth doesnt move.
The Equivalence Principle is bogus not because inertia and gravity are unequal but because they are exactly the same thing. Before the paradoxical equivalence explanations of Pound-Rebka can even be considered, the gravitational expansion solution must first be shown experimentally or mathematically to be false.
The same non-Euclidean geometry used to support the curved space-time interpretation of gravity can be used equally as well to support gravitational expansion. In the first system, mass remains passive while space-time actively changes its dimensions, and in the second, mass actively changes its dimensions within an inert and infinite void. While the mind creates very different images for each process the mathematical description of both is exactly the same.
If experimental evidence could ever be found to invalidate the principle of gravitational expansion, it the would also serve as a falsification of the Equivalence Principle, because the principle of gravitational expansion, in effect, demands that the Equivalence Princile be both absolute and unnecessary.
Because the Equivalence Principle is basically negative in nature, all experimental verification of it has been with null results. If no physical experiment can be performed to show a difference between gravity and inertia what kind of logic would permit the adoption of a metaphysical principle that demands such a difference.
Any simple measurement will show that all of the kinetic energy attributed to a falling body is actually contained within the rising surface of the earth and is not transferred to the falling body until impact. Any relevant experiment will verify this, including Pound-Rebka. The changes in photon wavelength measured by Pound-Rebka can only be interpreted as a Doppler shift resulting from the upward change in motion of the earths surface caused by the constant expansion of matter.
Doppler shifts produced by relative motion are among the most well-established phenomena in experimental physics and have been accurately verified in all experiments involving relative motion. To attribute the red and blue shifts measured by Pound and Rebka to a gravitational field is to deny the validity of Doppler shifts, in favor of the Equivalence Principle which has never been positively verified by any experiment. The Equivalence Principle is always added as a metaphysical precondition to the experiment in order to invalidate any measurements that are not pleasing to the human intuition.