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Twin Paradox Theory of Relativity in Absolute Terms
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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.
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Probably ninety nine percent of commentators on relativity will simply state,
without qualification, that there is no absolute frame of reference.
What they are referring to, is our inability to determine whether
any particular inertial frame might be at rest with respect to
an absolute frame of reference, such as the universe itself.
Of those ninety nine percent, probably ninety five percent have
no awareness of the difference between an experimentally
discernible absolute frame of reference and an experimentally
indiscernible absolute frame of reference. In fact, the concept
of an indiscernible absolute frame of reference is something of
which they simply have no conceptual awareness.
That's too bad, because that indiscernible frame of reference is
the underlying reality which dictated the experimental results
which drove Einstein's postulates of measure, which in
turn provided those commentators with relativity as we know it.
And I'm not talking about a fixed aether, which I do not believe in;
rather the sum total of the universe itself, the imparter of our
inertial properties, in the Machian sense.
Relativity, developed in absolute terms, is not only completely
compatible with Einstein's relativity, but in fact subsumes it.
There are more solid common sense reasons to believe in the
underlying reality than one can shake a stick at. Conversely,
without such concept of an absolute frame of reference, one
is left with ludicrous "explanations" of both the twin paradox
and the symmetrically mutual assessments across inertial frames
as we know them in relativity.
One should never suggest (as they so often do) that there was
some sort of "jump in time" involved with the change of inertial
frame (meaning at the turn-around point). The simple act of
starting a clock as an inbound astronaut passes an outbound
astronaut cannot possibly create a "jump in time". (Remember,
the outbound astronaut hands off his clock reading to the
inbound astronaut.)
One should do a search on Einstein's clock synchronization,
and its bearing on spacetime diagrams. He or she will find
that the notorious "jump in time" is built into that clock
synchronization, because it gets instantly replaced with a
different synchronization when a new inertial frame is adopted.
Since there is no jump in time on the earth clock (or a jump in aging for
the earth-bound twin), the suddenly returning astronaut's perception
(identically "calculation") of a "jump in time" for the earth clock is in
fact a misperception (identically a "miscalculation") forced by Einstein's
convention for synchronizing clocks.
All the measuring results as we know them in relativity can be derived
independent of Einstein's clock synchronization. In fact, Einstein's
clock synchronization can easily be diagrammed, and thus seen for what
it is, against the absolute frame of reference.
It is because clocks do actually slow down and aging does actually slow
down, that two reunited clocks show an actual disparity in their readings
and two reunited twins do show an actual disparity in their aging.
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.
The actual distances and speeds relative to the universe 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.
Time-keeping, distance and speed are interminably bound in one equation.
Therefore, actual differences in clock rates implies actual length
contraction dependent on actual speed relative to the universe. Actual
length contraction works in combination with actual time-keeping
contraction to preserve the symmetry of measures across inertial frames.
There is clock functioning at every level, dependent on actual light speed,
at even the atomic level. Our observations and measuring paradigms of
every nature are constrained by the speed of light, as is our "synchronizing"
of clocks.
Special relativity can be charted out in actual terms (absolute terms), where
light speed is constant in an actual sense. All the results of special
relativity, including the consistent measured speed of light,
fall naturally into place when charting these actualities against the
rest state of the universe.
Actual time-keeping and length contraction arise naturally from the fact
that all phenomena are dependent on the speed of light, which is itself
invariant in actuality, being massless.
Consider that A.P. French writes on page 150 of Special Relativity:
"Note, though, that we are appealing to the reality of A's acceleration,
and to the observability of the inertial forces associated with it. Would
such effects as the twin paradox exist if the framework of fixed stars and
distant galaxies were not there? Most physicists would say no. Our ultimate
definition of an inertial frame may indeed be that it is a frame having zero
acceleration with respect to the matter of the universe at large."
And I feel very sorry for any physicist who doesn't understand the
significance of the above consideration, which refers to Mach's Principle.
In Mach's Principle, an object is affected by a change in motion relative
to the matter of the universe at large. But such effect cannot occur
unless the object is in a relationship with the matter of the universe at
large regarding its state of unaccelerated motion to begin with.
Remember, an effect due to a change in motion is not simply an "either or"
effect, rather it is an effect of degree based on "degree of change". No effect
of degree stemming from a degree of change can occur unless there is an effect
based both on initial state of motion and final state of motion. Put another way,
a change in motion in the context of the universe is not meaningful without
motion itself in the context of the universe.
Mach
himself regarded the matter of the universe at large to be an actuality,
and the effect on the object to be actual. We can't have it both ways.
If the matter of the universe at large is a reality which has an actual
relationship with an object concerning a change in motion, then so too is
it a reality which has an actual relationship with an object concerning motion
itself. (And again, our observations (measures) are something fundamentally different
from the underlying reality, a reality which generates our observations (measures),
which can occur only at light speed.)
In SR, Einstein was able to make an absolute frame of reference
superfluous by postulating only the constant measured speed of light.
In GR, he made Mach's Principle superfluous by again holding to only a
postulated measured speed of light.
One can relocate oneself relative to ones house can one not, by traveling from
the living room to the kitchen? Can one not relocate oneself relative to the
universe by traveling through it?
A spatial seperation between two objects can actually be achieved,
rather than merely seem to be achieved.
Thus, there actually is relative motion.
My house actually exists, even though it is not perfectly rigid.
I can actually move relative to my house, despite the fact that
all the elements of which my house is comprised are moving about
relative to the overall structure of my house. I can actually
travel from one end of my house to the other end. And in so
doing, I affect the motion, relative to my house, of each individual
element of my house.
The universe does actually exist, rather than merely seems to exist.
Thus, there actually is motion relative to the universe.
After all, how can you agree that there is actually relative motion,
agree that there actually is a universe, but not agree that there is
motion relative to the universe.
All the elements of the universe are moving about relative to the
overall universe.
As obvious as it should be to anyone that a finite euclidean universe,
whether Big Banged or Steady State, has a barycenter at rest with
the overall mass of the universe, one need not concern himself with
associating a rest state of the universe with such barycenter.
The mass motion of all the individual elements of the universe must
necessarily sum to zero. That is, they must cancel each other other out.
Otherwise, one would need to invent a meaningless asymmetry; meaningless
because there is nothing for the universe to be in an asymmetric
relationship with. There is only the universe.
One need not consider the universe to be euclidean, or even finite,
to maintain this simple logic. In a universe of inflation, positively
curved, it is the membrane of space which becomes the effective barycenter
of the universe; and again we really need only consider that the mass
motion of the individual elements sum to zero.
A negatively curved universe is harder to imagine, but seems to
more closely resemble an euclidean universe than a positively curved
universe.
Also, one obviously does not need to be at the barycenter of
the universe to be at rest with the sum total of the universe.
You don't need to be at the center of your house to be at rest with
your house, do you?
Light, being massless, has a constant and maximum speed as it moves through the
universe, and all objects move at some fraction of that speed, the speed by which
all other speeds must be defined. If the speed of light is real in a real
universe, then the speeds of objects are real in a real universe.
Michio Kaku states on page 80 of Einstein's Cosmos that bringing the twins
together "determines which twin was "really" moving."
Martin Gardner insists throughout his book, Relativity Simply Explained,
that "this is not simply a question of being unable to learn the truth of the
matter...there is no actual truth of the matter." Yet, when faced with the
challenge of explaining the "actual" time differential between two reunited
clocks, Gardner paints himself into a corner and admits on page 114: "There is one
all important difference between the relative motion of the astronaut and
the relative motion of the stay-at-home. The stay-at-home does not move
relative to the universe." The universe is the truth of the matter.
Gardner's book first appeared in 1961 and is the best selling book about
relativity of all time. It was examined by physicists extensively for 35
years and then revised and reprinted in 1996. Unchanged was Gardner's
admission that the universe serves as the frame of reference by which
actual motion is defined, leading to an actual difference in recorded
times by the two parties. In fact, he repeats the admission on page 116:
"the stay-at-home and the cosmos do not move relative to one another."
Gardner's book is full of vagaries, ambiguities, contradictions, even
irrational claims, etc, and is a terrible source for information on relativity
for those reasons. (Kaku fairs almost as poorly.) I mention Gardner's book
and his quotes simply to illustrate
that when an examiner sincerely attempts to resolve the twin paradox, he
ends up painting himself into such a corner as did Gardner.
Both Kaku and Gardner were using the simplest of twins paradox scenarios,
in which one party is assumed to be at rest with the cosmos, and the other
party both has motion relative to the universe and changes frames. But that
need not be the case. There can be any number of "in between" situations --
such as both parties having motion relative to the universe, with still only
one party changing frames (same time differential); or both parties changing frames,
leading to a lesser time differential. It is also not necessary for the
twins to reunite to determine which one was "really moving". The noted
asymmetry (noted by both parties) in the time-keeping difference builds
incrementally, beginning at the moment of inertial change for one
party, when radio or light signals are regularly sent forth and back to
check on current clock status.
One should do a search on Einstein's clock synchronization, and its bearing
on spacetime diagrams. He or she will find that the notorious "jump in time"
is built into that clock synchronization, because it gets instantly replaced with a different
synchronization when a new inertial frame is adopted.
There is all the difference of night and day between predicting and
explaining. We can use Einstein's clock synchronization and spacetime
to predict a time differential, but we must look at relativity in the
universal frame of reference to explain not only that time differential,
but also all the mutually symmetrical measures made across inertial frames.
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"First they tell you you're wrong and they can prove it;
then they tell you you're right but it isn't important;
then they tell you it's important but they knew it all along."
Charles Kettering, former head of General Motors
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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.
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 A lively discussion about the
misperceptions common among leading physicists.
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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