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Relativity in Absolute Terms
A Twins Paradox Animation

diagramming special relativity in the absolute frame of reference.



This diagram will be animated further down the page.

Before moving on to the twin paradox animation,
you should take a minute to familiarize yourself
with some basic information by reading these
few paragraphs:


Consider the following simple situation which all physicists will agree upon:

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 and distance covered in absolute terms. Thus, the party that changes inertial frames will be the party whose clock registers the least time.)

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.

Just as acceleration is not involved in the "paradox", niether is any force. Yet, without fail, examiners appeal to the experience of force associated with a change of inertial frames, as if some force could affect the transfer of a clock reading from one inertial frame to another.

Another fatal mistake made by examiners of the "paradox" (a paradox strictly of their own making) is to apply Einstein's clock synchronization (identically space-time) to the "paradox". It is responsible for the notorious "jump in time".

Without Einstein's clock synchronization, there is no spacetime. Einstein's clock synchronization is a convention. It is optional. All the measuring results of relativity can be deduced independent of Einstein's clock synchronization. Therefore, spacetime is optional. Spacetime is simply a geometrical representation of Einstein's clock synchronization. A person cannot travel along a world line, because there is no world line. A world line is simply a geometrical construct. A person can travel through space while his clock is ticking. That is all a person can do.

A spacetime diagram is not an explanation for what has created the time differential between two reunited clocks. With or without Einstein's clock synchronization, there will be a time differential, and the party who changes frames to facilitate the reunion will be the one who ages the least. Recall that the time dilation equation is not linear.

What has created the time differential? The rate at which one ages is dependent on ones speed relative to the speed of light. The total aging of a person is dependent on the combination of his speed and distance traveled in absolute terms.

A simple discussion of the twins paradox of special relativity must incorporate the transfer of clock information from an "outgoing" astronaut to an "incoming" astronaut; otherwise acceleration would need to be involved, and acceleration is not involved in any kinematical effects of special relativity. The time differential between two reunited clocks is deduced through purely uniform linear motion considerations, as seen in Einstein's original paper on the subject, as well as in all subsequent derivations of the Lorentz transformations.

The twins paradox (and special relativity) can be analyzed in the context of the absolute frame of reference, wherein the sum total of the universe constitutes an experimentally indiscernable rest state. Though experimentally indiscernable, such frame of reference shows, in an actual sense, what is generating the observational effects of special relativity.

Photons, being massless, move at constant speed relative to the universe, and dictate time-keeping of every nature. (At the subatomic level, we also speak of virtual photon events, wherein communication occurs at light speed without any energy exchange.)

(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.)

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. The time contraction formula is not linear. Thus, the party that changes inertial frames will be the party whose clock registers the least time over the course of a "round trip".

Note that time-keeping, distance and speed are interminably bound in one equation. Thus, to acknowledge various states of actual motion relative to the universe (as opposed to merely observed differences) is to acknowledge various states of actual clock rates (as opposed to merely observed differences) and various states of actual lengths of rigid bodies (as opposed to merely observed differences).

======================================================


The animations below illustrate two basic possibilities for completing a round trip between two parties. They show the symmetry in time differentials, and corollary to that, the impossibility of anyone determining their true motion status relative to the universe.

For maximum clarity, the trips themselves involve just a light second or two in distance, and all parties make use of photon clocks which are a whopping 1/2 light second in width. The photon clocks tell the story of time contraction.

In the twins paradox animation below, an astronaut and a space station occupant start their clocks as the astronaut passes by. A second, incoming, astronaut starts his clock as he passes by the first astronaut. The incoming astronaut and the space station occupant stop their clocks as the incoming astronaut passes by the space station.



In the twin paradox animation below, an astronaut and a space station occupant start their clocks as the astronaut passes by. A second, also outbound, astronaut starts his clock as he passes by the space station. This second astronaut chases down the first astronaut. As the first astronaut is caught, both astronauts stop their clocks.




The time contraction formula is easily obtained from the above diagrams.
For instance, in the first diagram (animation), the clock at rest with the
universe ticks off one cycle while the traveling clock ticks off .8 of a cycle.
A simple application of the Phythagorean Theorem yields:

         t' =  t * sqr rt of ( 1 - V^2 )

where t' is the time recorded by the traveler,
t is universal time (full clock rate, since at rest with the universe),
and v is the speed of the traveler.

Keep in mind that the traveler, moving at .6 light second 
per second of universal time, went a distance, in absolute 
terms, of .6 light second.

A photon went the same distance in the station's clock as 
it did in the traveler's clock, namely, 1 light second.


Thus,    .8 = 1 * sqr rt of ( 1 - .6^2)

            = 1 * sqr rt of ( 1 - .36)

            = 1 * sqr rt of ( .64 )

            = .8

(There is no need to use c (light speed) in the equation, since
we are using units of light seconds.  Light travels one light
second in one second.)

See the book Relativity Trail for more details, including
an analysis of how all parties involved assess each other's 
clock speed and lengths in mutually symmetrical fashion,
as well as detailed derivations of length contraction,
the Lorentz transformations and e = mc^2.

==================================================

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.

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.

From the vantage point of a higher dimension, clock speeds and lengths of rigid bodies are seen in absolute terms and the time differential is easily explained by virtue of actual differences in clock rates.

In this treatment of special relativity, incorporating the absolute (universal) 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).




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.


=========================================================

Accepting the fact that there is an interconnectedness between all particles in the universe, just as we see in general relativity, is the key to understanding that clock rates and lengths of rigid bodies vary in an absolute (or universal) sense. The complexity of the universe insures that all physical phenomena (including relativistic effects) have a smoothness, a high degree of predictability, a virtual absoluteness of character.

Again - there is no twins paradox, and there is no jump in time, either real or as measured by any traveler. A clear presentation of relativity, utilizing the absolute (and constant) speed of light through an absolute frame of reference, both precludes any such paradox and subsumes Einstein's treatment. Detailed diagrams and arithmetical anaylsis in absolute terms of all kinematic effects of special relativity can be found in the book Relativity Trail.



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.

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.


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