Twin Paradox Explained
in Special Relativity
with a link to an animation
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 and more comprehensive document.
Einstein never commented on where the missing time went regarding
his conclusion that two clocks, once synchronized, would show a
time differential upon being reunited at the end of a uniform
linear motion journey.
This scenario became known as the twin paradox, with the clocks being
replaced by twin brothers, one of whom journeys away and then returns
to find his stayathome brother has aged more than himself.
An exhaustive search through relativity books, articles and now the
Internet, typically turns up the standard "jump in time" explanation,
whereby a returning astronaut suddenly inherits, at her turnaround
point, "a new meaning of simultaneity" in keeping with Einstein's
clock synchronization, causing hundreds of years to disappear in a
twinkling.
While a spacetime diagram will predict a time
differential between two reunited clocks, it cannot explain where the
missing time has gone, spacetime 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
of a given inertial frame. Identically, spacetime has no physical reality.
It is strictly a convenient mathematical construct, limited in scope by
Einstein's particular clock synchronization method.
Small wonder that the eminent physicist John A. Wheeler, in his book Spacetime Physics,
made three attempts to resolve the twin paradox and failed, by his own admission, considering that he limited himself to Einstein's narrow
interpretation.
Einstein himself never attempted to explain what he called
a "peculiar consequence"  the time differential between
reunited clocks, now known as the twin paradox.
Even Wheeler, who promotes the purely relative approach used by Einstein, acknowledges in his book that there is no physical experiment which can distinguish the purely relative approach from an absolute approach, which Wheeler refers to as "ether theory B".
[Wheeler, J., Taylor, E. (1992). Spacetime Physics, second edition. W. H. Freeman: New York, p. 88.]
Einstein focused on the symmetrical 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. They are one and
the same reality.
Regardless of the fact that the structure of the universe is ever
evolving, the twin 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 a system at rest with the sum total of the cosmos. In this context,
no twin 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. And note that such frame of reference, a frame
at rest with the sum total of the cosmos, cannot be
experimentally discerned.
Although the universe is expanding, special relativity easily holds true at any conceivable scale of distance at which we might test the theory.
A discussion of the twin 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.
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
and distance covered in absolute terms. Thus, the party
that changes inertial frames will be the party whose clock registers
the least time.)
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 commentators on relativity state in no uncertain terms that during
no interval of the preceding scenarios does anyone's
clock run any slower than anyone elses. Commentators will
often appeal to the experience of force associated with
a change of inertial frames, as if some force could
affect the starting of a clock. Just as acceleration is
not involved in the "paradox", neither is any force.
More frequently, commentators attribute the disparity in
the clock readings to a "sudden tilt of a line of
simultaneity". These commentators don't realize it, but
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.
As we noted, John A. Wheeler, in his book Spacetime Physics, made three
attempts to resolve the twin paradox and failed three
times. He never stood a chance, as he limited himself to
Einstein's narrow interpretation  that of simply assuming
symmetrical measures across inertial frames.
Without Einstein's clock synchronization, there is no
spacetime and there are no lines of simultaneity or world
lines. Einstein's clock synchronization is a convention.
It is optional, and limited in scope. 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, and has no physical reality.
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.
Rather, it can only repeat Einstein's prediction, devoid
of explanation, just as Einstein never had an explanation.
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.
When an actual change of clock rate is denied, a "jump in time"
is automatically incorporated. But that "jump in time" simply stems
from Einstein's clock synchronization, a clock synchronization which
is not required to deduce the mutual and symmetrical effects
of relativity. 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 about what is simultaneous.
They form these opposing conclusions due to the fact that light
has a finite speed, causing a delay in ones perception of any
distant event, regardless of the distance involved. That leads
directly to the conclusion, by a party that
changes inertial frames, of a "jump in time for the other party", whereby they use a lattice of clocks synchronized
according to Einstein's formula (tB  tA = t'A  tB), with the
"jump in time" built in for any situation involving a change of
inertial frame.
Using a rational measuring paradigm, whereby the two
parties check each other's clock status with the regular
sending of radio signals, a noted asymmetry in time keeping
differences between A and B builds incrementally, with the asymmetry
being first noted at the moment of B's turnaround. [William Geraint Vaughan Rosser (1991). Introductory Special Relativity, Taylor & Francis Inc. USA, pp. 6768.]
What has created the time differential?
The time registered on a person's clock is dependent on
the combination of their speed relative to light speed
and distance covered in absolute terms. The
party that changes inertial frames will be the party
whose clock registers the least time over the course
of a "round trip".
The actual distances in absolute terms and actual speeds
relative to light speed will vary depending on which party
changes frames, but the parties involved cannot possibly detect
that. That is in keeping with the postulates and deductions of
special relativity.
The time contraction formula [t' = t * sqr rt of (1  v^2)] is
not linear. That is why the party who changes frames to bring
the two parties back together will register the least amount
of time on his clock with the symmetry of the situation
preserved. This is seen with clarity when everything is charted
out in absolute terms.
Timekeeping, distance and speed are bound in one equation.
Therefore, actual differences in clock rates implies actual
length contraction dependent on actual speed relative to
light speed. 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 out in absolute terms.
From that vantage point, 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 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 universal (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.
A few details from Relativity Trail:
Symmetry of Measuring. Diagrams and equations
demonstrating the symmetry of clock rate and length
measures across inertial frames.
Twin Paradox Analysis. Diagrams and equations
demonstrating the symmetry of measures and time
differential regarding case 1 and case 2.
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.)
Symmetry of Measuring. Diagrams and equations demonstrating the symmetry of clock rate and length measures across inertial frames.
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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