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:
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.)
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 the reading of the clock time of the other party") is dictated by
Einstein's clock synchronization, a clock synchronization
which is not required to deduce any of the
measured effects of relativity.
The renowned physicist John A. Wheeler, in his book Spacetime Physics, made three
attempts to resolve the twin paradox and failed, by his own admission. He never stood a chance, as he limited himself to
Einstein's narrow interpretation - that of simply assuming
symmetrical measures across inertial frames, which incorporates a hopelessly circular definition of inertial frame.
Regarding that circular definition of inertial frame:
In Spacetime & Electromagnetism, Lucas and Hodgson, using the space-time 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 Earth-bound 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 70-84.]
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.
Einstein himself never attempted to explain what he called
a "peculiar consequence" - the time differential between
reunited clocks, now known as the twin paradox.
Without Einstein's clock synchronization, there is no
space-time 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, space-time
is optional. Space-time 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.
Even John Wheeler, who promotes the purely relative approach used by Einstein, acknowledges in his book Spacetime Physics 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.]
In contrast with the space-time argument: When the two parties check the status of each other's clock with the regular sending of radio pulses, they note an incrementally increasing time differential, first noted at the turn-around point. That real-world experiment reveals the real incremental increase of time differential.
[William Geraint Vaughan Rosser (1991). Introductory Special
Relativity, Taylor & Francis Inc. USA, pp. 67-68.]
[Luebeck, R. (2008). Relativity Trail, L B Writ
Publishing. Mpls, pp. 12-14]
[Luebeck, R. (2008, Sept 1). Relativity Trail.
http://relativitytrail.com/relativitytrail.pdf pp. 12-14]
In short:
Space-time is a construct, dependent on an optional clock synchronization method, and generates a false jump in time reading.
Space itself is not a construct, nor is time-keeping. And a real-world experiment reveals a real-world incremental increase in the time differential.
Why should we expect anything different? The 'stay-at-home' twin does not age several years in a twinkling just because some distant inbound astronaut starts his watch as he passes an outbound astronaut.
It is precisely ones motion with respect to the universe that dictates the actual clock rate, resulting in the actual time differential upon reuniting with the other party.
You should re-read the four previous paragraphs, carefully.
Einstein's clock synchronization method creates a pseudo reality for two inertial frames, whereby the parties of different inertial frames are free to reach opposing conclusions about what distant events are simultaneous. In reality, no one should conclude anything about what is simultaneous, as we know that our perceptions of distant events are constrained by the speed of light.
Einstein's clock synchronization (tB - tA = t'A - tB) has the "jump in time" built in for any situation involving a change of inertial frame.
Thus, a space-time diagram is not an explanation for what has
created the time differential between 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.
What has created the time differential?
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 person's clock is dependent on
the combination of their speed relative to light speed
and distance covered in absolute terms. 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". This is seen with clarity when everything is charted out in absolute terms.
The twin paradox (and all of special relativity) can
be analyzed in the context of the absolute frame of
reference, wherein the sum total of the universe
constitutes an experimentally indiscernible rest
state. Though experimentally indiscernible, such
frame of reference shows, in an actual sense, what
is generating the observational effects of special
relativity.
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.
Note that time-keeping, distance and speed are 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).
Although the universe is expanding, special relativity easily holds true at any conceivable scale of distance at which we might test the theory.
==========================================
The animations below illustrate two basic
possibilities for completing a round trip between
two parties. They produce identical time
differentials, demonstrating the
impossibility of anyone determining their true
motion status relative to the universe.
i.e. - none of the parties involved can assume anything about
their actual state of motion; thus they cannot know whether
they are participating in scenario 1 or scenario 2. The
blue circle in the diagram represents nothing but a point
in space where a clock start/stop event occurs.
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.
The horizontal white lines represent the travelers.
They each carry a photon clock. There are three clock
start/stop events - A, B, and C. The fact that time
differential is identical in both scenarios
(twin paradox animation 1 and twin paradox animation 2)
confirms that one cannot experimentally detect ones true
motion status with respect to the universe.
In the animations below, the space station is
considered to be at rest with the cosmos. One can
also make the analyses when assuming the station
is in motion relative to the cosmos. The diagrams,
and therefore the animations, become more complicated,
but the results are identical.
Scenario 1:
In the twin 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.
If the video has ended, and you want to replay it,
click on the replay button at the lower left corner
of the video box.
Scenario 2:
In the twins 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 Pythagorean Theorem yields the following formula:
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,
0.8 = 1 * sqr rt of ( 1 - 0.6^2)
= 1 * sqr rt of ( 1 - 0.36)
= 1 * sqr rt of ( 0.64 )
= 0.8
(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
symmetrical fashion, as well as detailed derivations
of length contraction, the Lorentz transformations
and e = mc^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.
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.
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.