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Relativity in Absolute Terms
Relativity and the Twins Paradox with Diagram and Animation.
A Space-time Diagram (Spacetime Diagram) does not address the cause of the time differential.
Consider the following simple situation upon which all physicists
will agree:
An outbound astronaut can start his clock as he passes by Earth.
That outbound astronaut's clock might record 100 hours during his
outbound journey. An inbound astronaut can start his clock at the
moment he passes by the outbound astronaut. The inbound astronaut's
clock might record 100 hours during his inbound journey. The Earth
clock might show a reading of 250 hours at the moment the inbound
astronaut passes by Earth. Thus, the Earth clock will register 250
hours while the combined recorded time for the outbound and inbound
astronauts' clocks is only 200 hours. One can thus hold two renunited
clocks in ones hand and see a disparity of 50 hours.
(If, instead, a second astronaut had started his clock as he passed
Earth, and were traveling fast enough to overtake the first astronaut,
then the combined recorded time of the Earth clock and the second
astronaut's clock would be less than the recorded time of the first
astronaut's clock. The time contraction formula is not linear. The
time registered on a clock is dependent on the combination of speed relative to light speed
and distance covered in relation to the universe. Thus, the party
that changes inertial frames will be the party whose clock registers
the least time.)
The preceding scenarios comprise the Twins Paradox. Refer to the
diagram below. There is a link to an animation of this diagram,
with included photon clocks, at the bottom of this page.
You might find the following surprising: Most relativists state in no uncertain terms
that during no interval of the preceding scenarios does anyones clock
run any slower than anyone elses. Often, they attribute the disparity
in the clock readings to a "sudden tilt of a line of simultaneity".
That "sudden tilt" (or "jump in time") is dictated by Einstein's clock synchronization, a clock synchronization which is not required to deduce any of the measured effects of relativity.
Einstein's clock synchronization does nothing but create a pseudo reality of simultaneity for parties in various inertial frames. Should any party change inertial frames, his pseudo reality must be instantly exchanged for a different pseudo reality to satisfy Einstein's clock synchronization.
Refreshingly, Einstein never commented on where the missing time went regarding his conclusion that two clocks, once synchronized in keeping with his formula, would show a time differential upon being reunited at the end of a uniform linear motion journey. He merely called this unexpected result "peculiar", and let that comment stand the rest of his life.
Einstein's formula (tB - tA = t'A - tB) for clock synchronization nullifies the universal frame of reference (absolute frame of reference), wherein clock rates, length, and the speed of light itself, have meaning in absolute terms (actual vs. measured). His formula has the "jump in time" built in for any situation involving a change of inertial frame.
Einstein's clock synchronization is defined such that light serves as the messenger of moments. By that I mean that Einstein tells us to call simultaneous whatever appears simultaneous, with observers in different inertial frames thus free to form opposing conclusions of what is simultaneous.
They form these opposing conclusions due to the fact that light, the messenger of moments, has a finite speed, causing a delay in ones perception of any distant event, regardless of the distance involved.
But this can all be charted out against an absolute frame of reference, which is simply the sum total of the cosmos, or equivalently, the view from a higher dimension, where light rays and all other phenomena are charted out in absolute terms.
From that vantage point, clock speeds and lengths of rigid bodies are seen in absolute terms and the time differential of the Twins Paradox is easily explained by virtue of actual differences in clock rates. The reality of the time differential builds incrementally. And when light or radio signals are sent forth and back between the parties involved for the purpose of keeping tabs on each other's clock times, so too does the observed asymmetry in time-keeping build incrementally.
Just as clock information is exchanged across inertial frames to effect the observation of mutually measured clock rate slowing, so too does the transfer of clock reading from an outbound traveler to an inbound traveler effect an observed incremental build up of clock rate asymmetry.
All the results of relativity can be deduced independent from Einstein's clock synchronization, with the bonus of having explanations for the results.
Regardless of the fact that the structure of space is ever evolving,
the twins paradox (twin paradox or clock paradox) can be understood
only in the context of an absolute frame of reference, in which the
speed of light is constant in an absolute sense, while clock rates
and lengths of rigid bodies vary in an absolute sense. "Absolute
sense" here refers to the "God's eye view" or the view from a
higher dimension, not to an unchanging structure. In this context,
no twins paradox arises because clock rates do actually vary. Such
treatment of special relativity is completely consistent with, and in
fact subsumes, Einstein's special relativity, with its effective
(observational) equivalence of inertial frames, including the consistent
measured speed of light in all inertial frames. Einstein's treatment
of special relativity can easily be diagrammed against a
stationary frame of reference.
In this treatment of special relativity, incorporating the universal
(absolute) frame of reference, clock functioning is seen to be dependent
on the speed of light. Similarly, the postulated need for stability at
the base of our structures (which parallels the Principle of Relativity)
in combination with the constant speed of light and the notion that
no information can exceed the speed of light, dictates length contraction
for objects in motion relative to the universal frame of reference
(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.
(One quick comment about General Relativity (GR) is in order:
Just as in Special Relativity (SR), GR, as formulated, addresses strictly
measures (identically observations). The key feature the two theories
share is that the speed of light is treated as a constant only as measured.
Just as there is an advantage in treating the speed of light as simply
a measured constant in SR, so too is there such an advantage in GR.
For an actual understanding of what generates the measured effects
of SR, we begin with the absolute nature of light, meaning we acknowledge
that it has a constant speed in reality. In the process, we obtain
all Einstein's results of measured effects.)
Again:
While a spacetime diagram (space-time diagram) will predict a time differential
between two reunited clocks, it cannot explain where the missing time has gone,
space-time itself being based on Einstein's clock synchronization. Nothing in
Einstein's treatment addresses actual clock rates (or actual length or
actual light speed). Einstein's treatment is limited to measures obtained
by an observer within a given inertial frame.
Einstein, and everyone since him, has focused on the symmetrically
mutual measures obtained across inertial frames, for which Einstein's
clock synchronization scheme works fine (although it is not needed).
His clock synchronization sheds no light on where the missing time has
gone regarding two reunited clocks (actually regarding any two clocks
where one has undergone a change of frame, reunited or not).
That two reunited clocks show a disparity in their recorded time is
proof that the two clocks experienced actual differing clock rates
while in differing states of uniform linear motion. If the disparity
one can see at the same place moment is a reality, then so too is the
notion of actual differing clock rates a reality. Those two realities
are inseparable. They are one and the same reality.
I have other documents online which expand on this topic: Twinparadox.pdf includes a table of an analysis of the incrementally building time differential of the Twins Paradox. Relativitytrail_abstract.pdf discusses the absolute version of Einstein's postulates. Twins Paradox Resolution discusses the basics of motion in absolute terms. A Twin Paradox animation. Light rays and traveling twins are diagrammed in absolute terms against the (experimentally undetectable) rest state of the universe. Twins Paradox Explained Relativity Trail, with 210 pages, 65 diagrams and 75 illustrations, will provide you with complete detailed arithmetical derivations of all the kinematical effects of special relativity. Everything is charted out in absolute terms against the rest state 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. Copyrighted material. © relativitytrail.com