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
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
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
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 )
(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).
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
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
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.