Relativity in an Absolute Frame of Reference
postulates, diagrams and analysis
Cite the book, Relativity Trail
Luebeck, R. Relativity Trail. Mpls: L B Writ Publishing, (2008)
Cite this web page
See also: Relativity in Absolute Terms
It is a concise overview document.
Einstein's treatment of relativity employs a hopelessly circular definition of inertial frame, making the resolution of the twin paradox impossible within Einstein's treatment, despite any claims made by commentators (other than Einstein) which you might have encountered.
In Spacetime & Electromagnetism, Lucas and Hodgson, using the spacetime paradigm, wrestle with the twin paradox for fifteen pages, and claim no resolution.
In a footnote on page 73, they write: "Is it fair to give the Earthbound twin the vertical world line? Does not that beg the question in his favour? Why not draw another diagram with his world line set at an angle to the vertical, and his lines of simultaneity correspondingly inclined (but at a contrary angle) to the horizontal?" [J.R. Lucas & P.E. Hodgson, Spacetime & Electromagnetism, p 7084.]
That alternative diagramming of the situation is identical to the consideration that one might just as well consider that it is the Earth, along with the entire cosmos, that changes inertial frames. That, in fact, is something we hear often from commentators on the twin paradox. Of course, that simply makes the twin paradox unresolvable, as either party can then lay equal claim to being the party that ages the least. This is demonstration that one must consider the entirety of the cosmos, the imparter of inertial properties, to be the judge of the matter regarding actual motion.
It has been known for 111 years that relativity developed in absolute terms is consistent with Einstein's purely relative treatment, yet the public remains largely misinformed.
John A. Wheeler, in his book "Spacetime Physics", states that there is no physical experiment which can distinguish Einstein's purely relative approach from an absolute approach. [Wheeler, J., Taylor, E. (1992). Spacetime Physics, second edition. W. H. Freeman: New York, p. 88.]
Although the absolute approach to Einstein's relativity is 111 years old, it remained essentially undeveloped in any sound manner until Relativity Trail appeared in 2008.
In Relativity Trail:
1. A natural and instinctive basis is provided for two
postulates which parallel Einstein's postulates.
2. Clock functioning is defined in conjunction with
the first postulate.
3. The process of measuring across inertial frames is diagrammed.
This includes the diagramming of the measuring of the clock rate,
length and speed of the object in the other inertial frame.
4. Einstein's clock synchronization is diagrammed in absolute terms.
None of those four things was done in Einstein's, Poincare's, Lorentz's, or anyone else's treatment.
Poincare and Lorentz, the most famous of the "absolutists", had merely argued from a "bottom line" mathematical premise. They had both postulated "actual clock slowing" without any basis, and they had both postulated "actual length contraction" without any basis. They did not define clock functioning, and they didn't diagram anything.
Nor did Einstein define clock functioning. Einstein also provided no basis for his postulates other than to say they were necessary in order to conform to the results of recently conducted experiments. Einstein merely assigned measures to the parties of each inertial frame so as to satisfy his postulates of measure. Einstein could provide no diagramming of the measuring process, due to his purely relative approach.
For a comprehensive and concise overview of the situation, click:
Relativity in Absolute Terms
For a free pdf file of the book Relativity Trail, see:
Luebeck, R. (2008, Sept 1). Relativity Trail. relativitytrail.com
Relativity Trail is a complete mathematical treatment of Einstein's special theory in absolute terms. In addition to being consistent with Einstein's treatment  it subsumes Einstein's treatment. It reveals precisely what is transpiring behind the scenes of Einstein's treatment. It incorporates an (experimentally indiscernible) frame of reference at rest with the sum total of the cosmos. The machian principle of the universe as the imparter of inertial properties is appealed to  the very principle Einstein embraced in an on and off again manner.
Relativity Trail has 192 pages, with 65 diagrams, covering every aspect of Special Relativity.
The details  some basic diagrams and analyses:
Actual length contraction works in combination
with actual timekeeping contraction to preserve the
symmetry of measures across inertial frames.
This can all be charted out against an absolute frame of
reference, which is simply a system at rest with respect to the sum total of the cosmos, or
equivalently, the view from a higher dimension, where light
rays and all other phenomena are charted in absolute terms.
From that vantage point, clock speeds and lengths of rigid
bodies are seen in absolute terms and the time differential
between reunited clocks is easily explained by virtue of actual differences in clock
rates.
In this treatment of special relativity, incorporating an
absolute frame of reference, clock functioning is seen
to be dependent on the speed of light. Similarly, the
postulated need for stability (synchronization) at the atomic
scale (which parallels the Principle of Relativity) in
combination with the constant speed of light and the notion
that no transmission of information can exceed the speed of
light, dictates length contraction for objects in motion
relative to the absolute frame of reference.
(In fact, all processes  chemical, biological, measuring
apparatus functioning, human perception involving the eye and
brain, the communication of force  everything, is constrained
by the speed of light. There is clock functioning at every
level, dependent on light speed and the inherent delay at even
the atomic level.)
Postulate 1:
The speed of light is constant and is the
maximum speed for any phenomena, including
the transmission of positioning information.
Basis:
Experiments towards the end of the nineteenth
century pointed towards a transformational
relationship between matter and energy
(radioactivity experiments).
Einstein's interpretation of Max Planck's
solutions for discreet energy levels
introduced the notion of light existing as
a massless photon. Being massless, the photon
would necessarily possess constant and maximum
speed.
Postulate 2:
Stability (synchronization) is required
at the base of our structures (specifically
atomic functioning).
Basis:
This simply parallels the Galilean Principle
of Relativity.
All of Einstein's results stem from these two postulates. These two
postulates may look similar to Einstein's postulates, but are not his
postulates.

Here a few snippets from Relativity Trail, explaining clock rate contraction, length contraction, and the process of measuring across inertial frames.
Photons, being massless, necessarily move at the maximum possible speed and necessarily at a constant speed. They dictate clock functioning at every level:
8 R E L A T I V I T Y T R A I L
We wish to make the point that communication within an atom can occur only at light speed, and that atomic processes are thus restrained by that absolute speed of light.
Regardless of the complexity of the regulating motions of these massless particles – the atom's true time keepers – they can be considered in terms of their vector components and reduced to a study in two dimensions.
In diagram 4, we compel clock B to move relative to our stationary reference frame (and relative to clock A). Clock B is moving at half the speed of light, according to the universal reference frame. We see the actual path of each clock's light beam against the universal reference frame.
We see that the photon of clock B cannot, while moving forward, complete a cycle in one second universal time, for to do so would require the photon to exceed the speed of light.
But completing one cycle is what generates one second of time, from the perspective of the clock. So clock B ages more slowly than clock A. What has happened is that we have traded some time for distance. After all, did we really think there was such a thing as a free lunch?
.... jump to length contraction:
30 R E L A T I V I T Y T R A I L
So length, at the bottom of things, is about positioning. Electrons think they are positioned the same distance from the nucleus when in a parallel orientation with respect to a line of translatory motion as they are when in a perpendicular orientation.
We're saying that the need for stability trumps the need for maintaining equal distance, to the meaningless satisfaction of the onlooking universal reference frame.
Regardless of what precise communication processes actually govern electron positioning, the arithmetic will reduce to fundamentally the same argument we've just made; just as all timekeeping processes reduce to the fundamental equivalent of a photon clock.
These considerations apply even in the context of the quantum description of atoms, with a shifting of the standing waves of probability of electron distribution.
If one thinks of electrons as simply popping in and out of existence, rather than shifting about, then the relocation events would still be considered to be restrained by light speed.
Also more abstract, would be the use of wave forms. In that case, it is the spacing of peaks and valleys whose adjustments are constrained by light speed.
As mentioned earlier in this book, this length contraction, absolute in nature, leads members of all reference frames in uniform motion relative to each other to measure each other's length (and clock rates) as equally contracted.
44 R E L A T I V I T Y T R A I L
MUTUALLY MEASURED LENGTH CONTRACTION ACROSS INERTIAL FRAMES
One cannot take measure of the length of a rod in motion relative to oneself without first assessing the relative speed of the rod to be measured. This relative speed will of necessity be considered an absolute speed by the party taking the measurement, as he can make no considerations about his own state of motion.
A person who considers himself to be at rest must, of course, consider his length and time to be not contracted. These considerations are used in the process of taking stock of the "moving" rod.
We'll consider two spaceships, A and B, each with a rest length of 1 light second, as established by their laying out of rods. On board ship A are two clocks, CT1 and CT2.
The diagram on the opposite page shows ship A in motion relative to the universe U. Ship B is at rest with respect to U. A is moving at .6 c, thus contracted to .8 ls (light second) from its rest length of 1 ls.
CT2 sends a light ray towards CT1 as CT2 lines up with point Y of ship B. CT1 is triggered by the reception of this ray, and ship A must necessarily allow that 1 second was required to effect the triggering. CT1 then ticks off .67 second during the interval in which CT1 proceeds to point Y of ship B.
Thus A calculates B's velocity as follows:
distance = velocity * time
1 = v * 1.67 which implies v = .6
(Remember, A considers its own length to be 1 ls.)
To calculate B's length, A uses the fact that CT2 has ticked off 1.33 during the interval in which CT2 travels from Y to X. (Ut during this interval is 1.67 seconds.) d = vt yields .6(1.33) = .8 ls.

U = universal frame Ut = universal time
EQUIVALENCE OF INERTIAL FRAMES 45
We can see from this same diagram that A will measure the rate of a clock which B has placed at point Y to have a rate of 0.8 times its own:
As clock Y passes from CT2 to CT1, where clock readings are exchanged, it registers a change of 1.33 seconds, the same as Ut. This is the interval during which A determines its own time passage to be 1.67 seconds.
So A regards B's clock to be slowed.
46 R E L A T I V I T Y T R A I L
In diagram 17, we showed that even though A is in motion relative to U, A still measures B's length as contracted, and to the same extent as its own contracted length as seen by U.
In diagram 18 on the opposite page, we again have A in motion relative to U, with B at rest relative to U.
Now let's have B take stock of A.
As point X of ship A lines up with CT3, CT3 sends a light ray towards CT4. CT4 is triggered by the reception of this ray, and B considers 1 second to have passed. CT4 then ticks off .67 seconds during the interval in which point X travels from CT3 to CT4.
Thus B calculates A's velocity as follows:
distance = velocity * time
1 = v * 1.67 which implies v = .6
To calculate A's length, B uses the fact that CT3 has ticked off 1.33 during the interval in which CT3 travels from X to Y. d = vt yields .6(1.33) = .8 ls.
In these calculations, we have been making use of the fact that the party doing clock triggering always regards his measuring rods (the very rods he uses to position his two clocks) to be noncontracted.
The reader can verify for himself or herself that these relationships hold even when both ships are assigned a nonzero speed.
EQUIVALENCE OF INERTIAL FRAMES 47
We can see from this same diagram that B will measure the rate of a clock which A has placed at point X to have a rate of 0.8 times its own:
As clock X passes from CT3 to CT4, where clock readings are exchanged, it registers a change of 1.33 seconds, in keeping with its time contraction of .8 Ut. This is the interval during which B determines its own time passage to be 1.67 seconds.
So B regards A's clock to be slowed.
This establishes the mutuality of measured clock rate slowing.

Download the free pdf file of the book Relativity Trail to see the diagrams and math for other phenomena, such as round trips (twin paradox), mutually measured mass increase, the formal derivation of length contraction, and much more.
Other documents which are recommended
reading before reading the book:
Relativity in Absolute Terms. My most comprehensive online document. A concise overview of why special relativity must be diagrammed in absolute terms.
Twin Paradox Animation on youtube. Contains textual description not found in the document below.
Twin Paradox Animation. Alternative text, and animation of the twin paradox. (Embedded youtube animation.)
Twin Paradox Analysis. Diagrams and equations demonstrating the symmetry of measures and time differential regarding case 1 and case 2.
Free pdf file of the book:
Relativity Trail, free pdf format, with 192 pages, 65 diagrams
and 75 illustrations, will provide you with complete
detailed algebraic derivations of all the
kinematical effects of special relativity.
Everything is charted out in absolute terms against
a system at rest with respect to the totality of the universe for perfect clarity
as well as soundness of theoretical basis. It is
the totality of the universe that imparts the
inertial properties of clock rates and lengths
which generate the effects of relativity. This
is explained in detail in Relativity Trail.
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