## Excerpts from Relativity Trail
The standard accounts of special relativity have left readers feeling more
dissatisfied than have the accounts of perhaps any other subject matter,
as evidenced by the thoughtful protests we regularly encounter among
the readership. This author's own dissatisfaction goes back almost forty
years. With all of life's distractions, he allowed that dissatisfaction to
remain largely unacted upon until this past year. In the very back of his
mind however, this book has been brewing for a long time.
Since a primary purpose of this book is to establish precisely how clocks,
all clocks – mechanical, electrodynamical or biological – keep time in
accordance with various states of motion, we'll begin by addressing an
issue which has to do with the establishing of clock fluctuation.
You may have read that Einstein's special theory of relativity was long
ago shown to be consistent with a modified form of aether theory, in
which clock slowing was postulated in order to allow for mutually
measured effects. In aether theory (and in Einstein's), clock functioning
itself was not defined. Also, in aether theory, length contraction was
attributed to a mysterious interaction with the aether.
We will show, when we examine Einstein's kinematical section, that his
treatment in fact can be diagrammed against the absolute reference frame
of the universe in the same manner as we will do with our treatment. Our
treatment is not only consistent with Einstein's, it actually subsumes
Einstein's treatment.
With what system of coordinates do we associate the "universe as a
whole"? In the simplest model of the universe, the universe is finite,
occupies a purely Euclidean space, and its point of origin lies within its
three spatial dimensions.
Note: If the point of origin, i.e., center of gravity, actually lies within the three spatial dimensions of the universe, it would still not be experimentally discernible. In fact, from an observational standpoint, any point in the universe could pass for such a point, though the universe be Euclidean. We'll discuss these matters in chapter 8, and at that time also, consider the inflation model, both in the Euclidean and non-Euclidean case. Meanwhile, this simplest of models is all we really need to "provide background" for our treatment of relative motion.
Thus, we've already come to a vital and consistent theme in our
presentation. We make the observation that whenever we depict the
motion of an object on paper, we do so by using a line of some length.
This is of course also true of our depiction of the motion of a light ray.
We further observe that we, the readers, see this depiction on paper as if
we are in a higher dimension, noting the various lengths resulting from
various speeds of objects. In fact, all lengths (thus speeds) are
established using the length (speed) of light as the base.
It goes like this: The standard interpretation of special relativity is
dismissive of any universal reference frame serving as a baseline from
which to analyze uniform motion. Some popular writers on the subject
have said, “There is no truth of the matter” concerning reference frames.
And so, when two gents part company and then meet up again, how do
we know which party has really traveled (or traveled more than the other)?
Either gent might seem to be "at rest" or "traveling" if there is no
association by which to analyze motion relative to the overall structure
of the universe, and the standard interpretation affords no such analytical
association of a party's motion relative to the universe.
To inquire of what is causing the length of a rigid body to contract is to
inquire of what is causing that rigid body to have any particular inertial
property, such as mass.
L E N G T H C O N T R A C T I O N 27
Identically, the absolute nature of light dictates an inertial property
stemming from the orientational relationship of uniform motion.
It's easy to see the naturalness of MM when you consider it on the atomic
scale. The Principle of Relativity (POR) and the synchronicity of the
atom are more than closely related, they're the same thing.
Without a structure producing actual different clock rates and lengths,
not only can the measure of time and length not rise above abstractions,
it cannot even acquire the form of identical mutuality, as we'll see in the
pages ahead.
The preceding point might seem to be a subtle one. But it needn't be.
Don't let the word "perception" mislead you. It's a simple matter of
assuming that one's ruler has not shrunk.
We'll look at Einstein's original 1905 paper, his presentation in his 1916
book, Relativity, and his derivation of 1916.
EINSTEIN DIAGRAMMED IN ABSOLUTE TERMS 74
To appreciate the fundamental difference between RT's use of a
universal reference system and Einstein's use of a system to which he
merely accords the status of being "stationary", we need to consider how
inertial system is defined.
EINSTEIN DIAGRAMMED IN ABSOLUTE TERMS 75
And of course, the same difficulty arises even when the notion of force
is not considered. Without the effect of force, we can appeal only to
kinematic measures of acceleration between two reference frames.
EINSTEIN DIAGRAMMED IN ABSOLUTE TERMS 76
We'll examine how Einstein includes in his derivation, a tacit assumption
of a universal frame of reference, while defining clock synchronization
in such a manner as to have no need for it – at least not for the purpose
of defining simultaneity, and not for the purpose of addressing a host of
electrodynamical phenomena. Thus happens a popular interpretation of
SR which recognizes no universal frame imparting inertial properties
such as clock rate and length.
Regardless of what we might wish Einstein had kept in mind concerning
the nature of the "stationary system" of his second postulate, his ensuing
development accords the status of "baseline length" and "baseline clock
rates" to a system K, with length and clock rates of a second system k in
motion relative to K to be related to K's lengths and clock rates by
mandating that both systems measure light speed as the same ratio of
length/time in all directions, in keeping with the POR.
As inferred from pages 62-67, in RT, we make the following observation
about two clocks of the same inertial frame, spatially separated by the
laying out of rods:
Clock B is in the positive direction of the AB motion from clock A, the
AB system has an absolute velocity of .6, and A and B have a rest spatial
separation of 1 ls (.8 contracted) as seen against the universal reference
frame:
-------------------------------------------------------- 1. See the appendix for the formal derivation of v = .6. EINSTEIN'S CLOCK SYNCHRONIZATION IN ABSOLUTE TERMS 89
In his 1916 book, Relativity, Einstein introduces the concept as follows:
Of course, in the context of a universal frame of reference in which light
moves at a constant speed, they must conclude no such thing. In fact,
they would conclude, after comparing notes with the people on the
embankment, that the train had motion relative to the embankment. And
this is not the same as saying they could determine whose motion was
zero or even closer to zero. So the POR is safe.
EINSTEIN DIAGRAMMED IN ABSOLUTE TERMS 90
Imagine clock A and clock B synchronized according to Einstein's
formula. If lightning struck at clock B and was observed by someone
stationed at the spatially separated clock A, the observer at clock A
would report a reading 1 second greater than clock B for the lightning
strike. Thus the concept of absolute time passage permeates the inertial
frame of the AB system in a manner consistent with direct observation.
EINSTEIN DIAGRAMMED IN ABOSULTE TERMS 91
Einstein's approach then, becomes utilitarian in nature, elevating the act
of direct observation to a pseudo-reality.
So what does one expect a higher dimensional being would see if he
were to view our universe? Non-contracted lengths of all inertial
frames? Uniform clock rates? If this is what he saw, there would not be
the relationships of motion as we know them in Einstein's treatment;
there would be no symmetrically measured length contraction or clock
slowing. The reader can easily check this for himself or herself with
simple diagrams such as the ones we've been using to illustrate how
entities take measure of each other's properties.
EINSTEIN DIAGRAMMED IN ABSOLUTE TERMS 93
Upon adopting the point of view that the structure of the universe can be
seen as a totality, that a photon is massless, and that mass and energy are
interchangeable, one immediately adopts the speed of light as an
absolute against that totality, followed immediately by a realization of
what clock functioning is, and why it is subject to slowing.
EINSTEIN DIAGRAMMED IN ABSOLUTE TERMS 94
On page 27 of Relativity, Einstein states to his imaginary dissenter that
without a definition of time, we are arguing in a circle if we try to
examine a supposition that the velocity of light from A to B equals the
velocity of light from B to A. Rather, he stipulates that the time passage
be equal in both directions, without making any supposition about the
actual nature of light. He does this “of his own free will” to define
simultaneity regarding events occurring at A and B. He has no
definition of velocity by which to define time passage, but obviously
something has to give – since time, distance and velocity must all be
bound together in one equation.
EINSTEIN DIAGRAMMED IN ABSOLUTE TERMS 95
But we can reconcile Einstein's approach with our own:
EINSTEIN DIAGRAMMED IN ABSOLUTE TERMS 96
Much as we did in RT, with our perpendicular and parallel ray photon
clock, Einstein considers the round trip of the light beam for the purposes
of learning what the time and length contractions must be. It is the round
trip consideration that addresses the synchronicity aspect of the POR.
EINSTEIN DIAGRAMMED IN ABSOLUTE TERMS 97
Even though Einstein concerns himself with only the imposition of
relative results for clocks and length assessment in his two frames of
reference, it's not surprising that he achieves the Lorentz transformation
with its included time and length contractions, seeing as to how his
introduction of mu and lambda correspond with an absolute frame of reference.
In RT, we utilize the absolute nature of both space and time, not in the
sense of "agreed upon measures" by different reference frames, but in the
sense of the God's eye view. In Einstein's treatment, only the measured
speed of light is an "absolute", in the sense that all reference frames will
be in agreement as to its measure. But in Einstein's treatment, that
constant of measure works in conjunction with his clock
synchronization, which causes the measured speed of light to be an
absolute by way of considering only the relative aspects of space and
time.
SPACETIME 101
Spacetime is a geometrical interpretation of relativity which simplifies
physical theories that involve relativistic speeds. Just as in Einstein's
treatment, it does not explicitly incorporate an absolute frame of
reference. In fact, it arises from, and is limited by, Einstein's clock
synchronization. It cannot be employed to account for the time
differential between reunited clocks.
The change of inertial frame creates no time differential, actual or
measured. It merely dictates, depending on the new inertial frame
adopted, what the clock rate will be for the clock that changes frames.
Banesh Hoffmann, a collaborator with Einstein late in Einstein's life,
writes in Einstein, Creator and Rebel p. 76-78:
SECURING LOOSE ENDS 110
Physicists take the mutual effects of relativity as confirmation that
uniform motion is purely relative, and that there is therefore no meaning
to be attached to absolute uniform motion, and therefore of course, to
actual differences in clock rates, etc. But the time differential present in
the Twins Paradox, showing up at the same place-moment, does not fit
with that interpretation.
SECURING LOOSE ENDS 111
All clock paradox studies presented by examiners who are committed to
not acknowledging the underlying absolute frame of reference, against
which light speed and the properties of objects can be understood in
absolute terms, are doomed to fail.
SECURING LOOSE ENDS 112
Although the twins paradox is strictly an effect of special relativity,
where no inertial force is involved, 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."
The concept of such a vantage point is nothing new to mathematicians
or physicists; so it is surprising to find such silence regarding that
vantage point, which so easily demystifies the relations of uniform
motion.
SECURING LOOSE ENDS 131
J.R. Lucan and P.E. Hodgson argue that Einstein offered a new
“Gestalt ... a new view of what really was the case, and not merely a
convenient convention for talking about relations between the motions
of ordinary material bodies ... thus we should see length itself altered,
instead of thinking of objects suffering a Lorentz contraction.” [see note 1]
SECURING LOOSE ENDS 132
In keeping with our goal, Relativity Trail relegated abstractions to the
lowest level, allowing the machinery of relativity to appear in clear,
concrete form, devoid of mystery.
SECURING LOOSE ENDS 133
In RT, one can conceive of a couple natural physical postulates, not
postulates of measure; then check to see what measures of time and
length are arrived at by the entities in our studies when they make their
assessments, such assessments being completely diagrammed. Lo and
behold, we learn that they arrive at measures that agree with the Lorentz
transformations.
Some more diagrams from the book Relativity Trail, from the chapter on E = mc^2: The preceding excerpts are not a substitute for the book Relativity Trail (Luebeck, Roger. L B Writ Publishing, 2008). The book is available in free pdf format: download book In the book: Clock functioning is defined. The basis for postulates which establish constant light speed and the POR in absolute terms, rather than as merely measured effects, are presented. Complete derivations for clock slowing, length contraction, consistent light speed measure, symmetrical measures of clock rates and length contraction across inertial frames, and the Lorentz transformations are presented. The twins paradox (twin paradox) is debunked. And much more.
Relativity Trail.
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