Explanation of Pound Rebka experiment results
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
In one light second space fraction, the space-time stretches for the gravitational amount of RF from which measuring is performed. In other words, this is the amount for which speed of light “c” changes:
Considering that the Pound Rebka experiment took place at Earth ‘s surface acceleration space fraction, the light speed value at that point increased for corresponding acceleration amount.
Since “g”, and “a” are the amounts for which particular RF is stretched, that actual speed of light won’t be measurable. So the measured “c” remains constant.
To determine the value “ah” for how much the space-time stretches in Jefferson’s Tower height “h” space-time fraction, where the experiment was performed, we use the equivalence:
In other words, the fraction of space which is equivalent to tower's hight, stretches the same as light speed sttretches in acceleration fraction of space where measuring is performed.
So the “ah“ equals
The obtained value is the actual acceleration and light speed difference for observed space-time fraction “h”.
To calculate gravitational shift amount “Δλ”, i.e. the “λa” change for observed space-time fraction “h”, the lambda-dilatation equivalence is presumed:
So we have:
i.e.
which is
or
Assuming the acceleration and light speed difference expressed with formula;
comes forth that dilatational difference i.e. "Δλ" equals to division of corresponding space markers light speeds;
From there, it implies that gravitational and light speed difference “ah” between space-time markers on bottom and top of measured space fraction, equals to product of “Δλ” and speed of light;
The dilatational value for Earth’s surface acceleration space fraction is obtained by formula:
So we derive the equation:
From equations above we derive the equivalence for acceleration (gravitation in “h” space fraction) and dilatation:
If calculating “ah“ value in Earth’s surface acceleration space fraction (which is about 2,29 times less than Jefferson Tower height) it is to notice that its relation to gravitation is the same as gravitation relates to “c” space fraction which equals to dilatation;
In other words, stretchiness of space or velocity of space, which determines the velocity of mass stretches in space so as space stretches in speed of light. The value of their stretchiness is time.
It means, that in dilatational fraction of time, “c” accelerates (travels over) “a” (“g”) amount,
and in same fraction of time “a” (“g”) accelerates (covers the distance) which corresponds to “ah” (“gh”) amount.
It implies that “ah” (“gh”) relates to acceleration (gravitation) so as acceleration (gravitation) relates to speed of light. Since “a” (“g”) is the value which describes the stretch of speed of light (“a” is for acceleration space fraction and “g” is for one light second space fraction), emerges that “ah” (“gh”) is the value which describes the stretch of acceleration (gravitation).
The “da” equivalence is extended with relation to gravitation and radius of celestial body on which measuring is performed.
Follows that gravitation describes the stretch of celestial body radius which consequence is creation of its time.
For each subsequent acceleration space fraction, starting from celestial body surface, “ah” amount decreases correspondingly to decrease of acceleration of particular space fraction, while their relation reminds unchanged. The same applies for “Δλ” which describes the dilatation of measured space region. So in two acceleration space fractions, “Δλ” amounts a bit less than “2Δλ”. In three ”a” space fraction the dilatation equals to “3Δλ” decreased for a small amount, and so on… When measured distance reaches one light second space fraction, “Δλ” equals to celestial body gravitational dilatation “d” (if space-time is measured in meters and seconds). The “Δλn” change is expressed by function;
In an interrupted free fall, in c/a time fraction, acceleration would equal to speed of light and for one second time fraction its stretch factor “ah“ would alter for acceleration amount. If calculating c/a time fraction in dilatational units instead of seconds (c/ad) the given amount would be "Δλ" part of a second.
In scenario in which h equals “a“,“ah“ is expressed as power of acceleration upon speed of light
or dilatational gravitational product
It means that stone on Earth’s surface, which falls at acceleration “a” and covers the distance of 9,807 meters in one second time fraction, in corresponding acceleration dilatational time fraction travels over ”ah” part of a meter.
According to equivalence;
If we multiply “ah“ value with number which describes how many acceleration (gravitational) space segments are contained in one light second (c/a, c/g), the result we got equals to corresponding acceleration amount of observed space-time fraction. It is because that is the value for how much that fraction stretched. The consequence is corresponding light speed change which can be observed as blue or red shift if measured from different gravitational-dilatational RF which are in Pound-Rebka case the bottom and the top of the tower (fig 01).
In same scenario, when height at which measuring is performed equals to acceleration space fraction amount, dilatational difference i.e. "Δλ" between space markers at bottom and top of the tower equals to power of acceleration upon power of speed of light
and to a acceleration dilatation upon speed of light;
If considering “a” as velocity and according to equation for dilatation calculated through orbital velocity
”Δλ” in equation above represents dilatation expressed through that velocity.
From previous equivalence we derive the equation for acceleration;
which is again analogous to orbital velocity formula;
It further implies the ”Δλ” equivalence to a power of dilatation i.e. to power of lambda;
From there, we derive the equivalence for corresponding dilatation;
In scenario where distance between points i.e. “ah” value equals to distance of space marker acceleration value one light second away (circa. 0,00443 m), square of measured ”Δλ” equals to gravitational dilatation of corresponding one light second space fraction. It means that value obtained in Pound Rebka experiment was in fact the dilatational value for gravitation, which acceleration space fraction corresponds to 22.5-meter-high