Excerpts from Relativity Trail
See also: Relativity in Absolute Terms
A comprehensive and concise overview
Excerpts from Relativity Trail
The following 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:
In the book:
Clock functioning is defined.
The basis for postulates which establish constant
light speed and the Principle of Relativity 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.
Excerpts from Relativity Trail
P R E F A C E
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.
Any book about relativity that doesn't clearly state that the slowing of
clocks and contraction of rigid bodies is a reality which goes beyond our
mutual measurements of these things is not only giving the reader half
the story, it is giving the reader a confusing story. Without a recognition
of this reality, such a book's author is also forcing himself into a
mathematically impossible task – that of resolving a clock paradox of
his own making. Such impossibility generally does not keep him from
trying, and later in this book, we'll check and see how he's fared.
In Relativity Trail, you'll get the full story, with a clear description of
relationships of uniform motion. Time-keeping is concretely defined.
Time-keeping, distance, and the constancy of the speed of light take on
absolute as well as relative meaning. The reader will find unique and
clear answers as to the why of absolute clock rate slowing, mutually
measured clock rate slowing, absolute length contraction, mutually
measured length contraction, the time differential between reunited
clocks, consistent light speed measure, mass increase (including
mutuality of measure), and E = mc^2.
The exact process by which parties take measure of each other is fully
described, using only the familiar diagrams and arithmetic of a
customary stationary reference frame, the physical existence of which
we will demonstrate. Only straight line, uniform motion is considered.
No aether or other sort of immutable reference frame is incorporated;
nor is variable light speed. Additionally, gone is the long, difficult and
abstruse derivation of the Lorentz transformations. These equations
make their appearance in a most natural manner in the course of the
reasoning within Relativity Trail.
In the introduction, we'll further explain the purpose of this book. But
don't worry if much of the content of the introduction seems unfamiliar;
we'll introduce everything from the ground up in the main body of the
book, which begins with a story about the author's independent
discovery of time fluctuation, and then proceeds to a concise and clear
development of special relativity, completely consistent with the
relativity of Einstein, with the effective equivalence of all inertial
I N T R O D U C T I O N ii
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.
In Relativity Trail, we will begin at a more fundamental level, adopting a natural, instinctive form of Einstein's postulates. Whereas Einstein formulated his postulates in the context of measures, our postulates will be formulated in an absolute sense, i.e., pertaining to the actual nature behind the measurements. We'll examine the nature of measuring. The first postulate we'll consider will directly imply actual clock slowing, and our next postulate will directly imply actual length contraction.
Contrary to the impression created by the standard accounts of relativity, this absolute approach will produce a pure form of relativity, logically consistent with Einstein's treatment. Our simple approach will reveal precisely what is transpiring behind the scenes of Einstein's treatment.
Special relativity (SR) is invariably presented devoid of context or of any
baseline from which to define motion. A student might imagine that
general relativity (GR) ought to provide such context or baseline. But in
the manner that GR has been developed, the speed of light remains a
constant only as measured, leaving us still wanting for context of an
We'll demonstrate directly, without appealing to GR, that there is no
incompatibility between Einstein's postulates of SR and the existence of
a physically defined universal frame of reference against which clocks,
rods and light beams display their absolute nature. This reference frame
is nothing other than a system at rest with the sum total of the cosmos,
whether or not the universe actually has an overall Euclidean structure.
We'll find that it brings clarity and simplicity to the study of special
I N T R O D U C T I O N v
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
As we proceed, we'll show that by not maintaining a conscious
connection to the universal reference frame throughout his treatment,
Einstein left himself no means for diagramming the process of
measurement taking, no means for describing what is generating the
properties underlying the assumed measures, and no means for
explaining the time differential between reunited clocks.
It is natural to find seduction in the denial of such a reference frame,
since it is not necessary to consider such a reference frame when doing
computations involving special relativity. In fact, that it cannot be
experimentally detected is something we'll show.
It can also be surmised that the theory retains more glamour and mystery
if the universal reference frame is denied a say in the matter. Perhaps
such appeal has helped to perpetuate such neglect, and not necessarily at
a conscious level.
The fact that it cannot be experimentally detected is perhaps a clue as to
why Einstein did not overly worry about disregarding it once he got past
square one. We'll be looking at some of the possible reasons Einstein
proceeded as he did. What we'll find,
is that our own simple derivation easily accepts Einstein's constraint, so
that we still obtain Einstein's transformation equations.
The value in recognizing the universal frame is that it allows us to see
plainly what is generating the phenomena of relativity, beginning with
clock functioning, length contraction, mutually measured length
contraction, mutually measured clock rate slowing, consistent measure
of light speed in all directions, and the time differential between reunited
clocks. The price, of course, is that we lose all of the mystery and,
therefore, much of the glamour.
Here again, in his original paper on special relativity, On the
Electrodynamics of Moving Bodies, submitted to Annalen der Physik in
1905, is Einstein's initial wording of his second postulate:
“Light is always propagated in empty space with a definite velocity c
which is independent of the state of motion of the emitting body.”
Three pages later, he states it this way:
“Any ray of light moves in the "stationary system" of coordinates with
the determined velocity c, whether the ray be emitted by a stationary or
by a moving body.”
Here he replaces "definite" with "determined" and uses quotes around
stationary system. Thus he is already hedging on what he means by this
postulate. To whatever extent he favors this second wording, he
abandons the absolute character of his postulate as initially worded,
indicating he is already preparing himself to abandon the very reference
frame upon which he implicitly relies at the outset, and which could have
brought clarity to his treatment.
Einstein then begins the body of his paper by writing, “Let us take a
system of coordinates in which the equations of Newtonian mechanics
hold good. In order to render our presentation more precise and to
distinguish this system of coordinates verbally from others which will be
introduced hereafter, we call it the "stationary system".”
This "stationary system" serves as the baseline for Einstein's analysis of
a reference system in motion relative to the "stationary system". From
this analysis are born his conclusions which form what is called special
The electrodynamical portion of Einstein's paper has been described by
authors as a brilliant and lucid “tour de force”. We find ourselves
mostly lost in his complex and abstruse kinematical section, upon which
the dynamical section is based. Of course he manages to come to the
necessary correct conclusions regarding the kinematics, thus assuring
the integrity of his dynamical interpretations which follow.
In Relativity Trail, we begin with a postulate which corresponds – but in
an absolute sense – to Einstein's first postulate, and the original
unqualified version of Einstein's second postulate, then immediately
embark on a completely different type of analysis; one which the reader
will have no trouble following, and which places special relativity on
The reader will be happy to learn that certain old absolutes are secure.
In fact, without them, there can be no relativity.
I N T R O D U C T I O N viii
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.
This would mean that the universe has an easily visualized shape, such
as a sphere. A system of coordinates at rest with the universe as a whole
would simply be at rest with the gravitational center point of such a
universe; a notion we'll address at greater length later in this book.
That no meaning can be attached to movement of this center point is
illustrated by the following analogy: Imagine that only you exist,
floating in the void. Now try to imagine changing the location of your
center of gravity. Since you have nothing to push off against, you cannot
change your center of gravity even though you can change your
configuration. Identically, the universe has nothing to push off against.
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.
C L O C K F U N C T I O N I N G 6
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.
The entities in our study appear as dots on the paper. The lines on the
paper represent the motions of these entities as well as the motion of
light. These entities can perceive things only at the speed of light. Thus
we, the gods, are assigning a length to the speed of their perceptions. No
such assignment is made to our (the readers') perceptions. The notions of
speed, length and time, and the relationships between them are born on
We're making use of the universal reference frame. Our piece of paper
we spoke of represents it well enough. We consider it to not be in
motion. From this reference frame, we monitor the activities of the
objects in all other reference frames.
When we speak of "universal time", we are referring to arbitrarily
defined lengths of light ray travel as viewed by us, the observers of the
piece of paper, or equivalently, the universal reference frame. Later,
we'll expand the argument we made in the introduction that no meaning
can be attached to the overall movement of this reference frame.
We will also show that any arbitrary reference frame might, for all we
(the people actually living in the universe) can ever physically determine
using light signals, be that "at rest" reference frame.
But the reader should note – as Ernst Mach first asserted over a hundred years ago, and as still embraced today – only the totality of the universe can impart inertial properties to an object. As presented here, this encompasses clock functioning and length contraction of rigid bodies. Thus, the fundamental difference between the universal reference frame and some arbitrary reference frame is that only totality can impart the properties being assessed by any particular frame, be it the universal frame (our analytic perspective) or some arbitrary frame. We will make this plain and revisit it frequently.
C L O C K F U N C T I O N I N G 12
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.
This controversy has not gone away after over a century of relativity;
nor can it, without acknowledging the universal frame of reference.
The standard interpretation is that we must simply take notice that one
of the parties underwent a change of inertial frames during the course of
the round trip. But that consideration alone does nothing to relieve us of
the need of a structure which has imparted actual clock rate differences,
considering that reunited clocks, moving in a straight line, strictly
without acceleration, display a time differential of an absolute nature. It
is precisely one's inertial change with respect to the universe that dictates
the new actual clock rate, resulting in the actual time differential upon
reuniting with the other party. And that, of course, is something we'll
diagram with clarity in this book.
Meanwhile, refer to diagram 6 to see what happens when, in the course
of a one way trip by a gent, the two gents involved (stay at home and
traveler) try to determine whether there is any difference in the timekeeping
of their clocks. Their best tool, of course, is the sending of light
signals to each other to relay information about the status of their clocks.
Note the symmetry between case 1 and case 2 of diagram 6. They cannot
detect that one is recording time more slowly than the other.
In diagram 7, B "reverses" direction by way of transferring clock
information to clock B' (B prime) coming from the opposite direction at
the same speed relative to the universe.
Interestingly, even though the two gents cannot agree that one or the
other is recording time more slowly as B moves away, they do note a
lesser recorded time by B as soon as B begins his return, as shown in
diagram 7. This noted time difference builds incrementally as signals are
exchanged ever further beyond B's turn-around point. (In adventures of
this sort, much of what A and B conclude could also simply rely upon
the comparing of notes upon reuniting.)
L E N G T H C O N T R A C T I O N 26
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.
Ernst Mach was the first person to see clearly, as early as the 1870's, that
an object's inertial mass is imparted to it by the sum total of the mass of
If one considers, as did Mach, that an object is imparted its inertial mass,
a property associated with acceleration, from its external environment,
then it would be natural to assume that such object would retain such
properties upon achieving its final state of motion.
In addition to the translatory relationship an object has with its external
environment, it has a secondary relationship to that translation, which is
one of rotation or lack thereof. Any rotation, even at the tiniest scale,
involves translation as a predecessor. To set a point on the
circumference of a disc into motion is to impart translation followed
immediately by a change in direction of the translation, meaning rotation.
Without a rigid system, a continuous force is required to maintain such
a continuous change of orientation, something not required for simple
translatory motion. A uniformly rotating rigid system is imparted a
perpetual system of internal centripetal force, whereas a uniformly
translating rigid system is imparted no internal force. That there are two
relationships of motion to the external environment is clear.
An accelerated object feels its orientation with respect to its line of
translation as it feels its mass. The reader feels his or her mass right now,
as well as an orientation associated with that mass, being the line from
body to ground. When the sensation of mass disappears (due to falling
in a vacuum) so also does the sensation of the associated orientation.
The two associations always appear and disappear as one.
An object's inertial mass, which is associated with acceleration, is
imparted to it at the speed of light. Similarly, the absolute nature of light
dictates the inertial property of clock slowing, this being a translational
relationship of uniform motion.
Note: At relativistic speeds, a translating object is imparted additional mass (chp 9)
which creates additional gravitational force, directed inwards. The centripetal force
within a rotating object amounts to a gravitational type field, directed outward. An
object with a relativistic rotational speed is also imparted mass increase in universal
terms; and who knows how these oppositely directed fields play out.
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.
And as we'll discuss, these relationships evolve over the course of the
history of the universe, with all objects contributing to the evolution of
the environment with which they have their current relationship.
It is the combination of the translational relationship to the universe and
the orientational relationship with the line of translation, which will
prove to dictate an object's "moving" length in relation to its "rest" length.
Only one further consideration is required to see why this is so, and that
is the consideration of the need for stability at the base of our structures,
Actually, we consider it as vital to the stability of our structures at all
scales. It is simply much easier to see the need at the base our structures.
The link between the base and the large scale effect is of course
Just as surely as the absolute nature of light speed dictates clock speed,
so to, when combined with the obvious need for atomic stability, does it
dictate length. This is what we meant when we said on page 7 that an
atom needs to keep time in sync with itself. In other words, we consider
the Principle of Relativity as vital to the stability of the atom.
These considerations are sufficient for allowing us to proceed with the
diagramming of an atom, which proves to be fundamentally no different
than the diagramming of a photon clock or the MM apparatus.
But let's delay that for just a moment, and consider at a little deeper level
the nature of the structure which imparts inertial properties. The
discussion will necessarily be of an abstract nature. Our goal in this
book has been to relegate abstractions to the lowest possible level. The
following discussion involves the realm to which we've relegated
abstractions. It's a good place for them, freeing the actual analysis of
relative motion from all abstractions.
L E N G T H C O N T R A C T I O N 36
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.
Synchronicity is the atom's version of its own POR, i.e., the atom must
behave as though it is unaware of its own motion. The atom would fly
apart if the nucleus was thrown off center; the table would get wet if
Galileo's drips missed the neck of the vase.
The stability of the atom is identical to the requirement that the POR
needs to be true, where light is postulated to be the fundamental agent of
"action at a distance"; because if "instantaneous action at a distance"
was actually true, all physical phenomena would still need to
synchronize to preserve any semblance of reliable physical laws. We
can expect no less of the actual agent of "action at a distance" – light.
The need for stability at the bottom of our physical structures
necessitates length contraction in the direction of motion, which creates
length contraction in large rigid bodies, they being built from the bottom
up, i.e., from atoms. (There is no space between atoms which form
molecules. The chain of atoms which form molecules do so by sharing
valences.) See page 102 for a broader take on this.
Similarly, due to the fact that all time-keeping devices (whether
mechanical or biological) are cyclic and are built up from photon
movements, they exhibit time-keeping changes in the exact manner as
does any simple photon clock, such as an atom or a mirrored apparatus.
Thus, the POR holds precisely true for mechanics for the very reason it
holds true for electromagnetics.
L E N G T H C O N T R A C T I O N 38 , 39
L E N G T H C O N T R A C T I O N 40 , 41
EQUIVALENCE OF INERTIAL FRAMES 43
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
In his book "Einstein", Albrecht Folsing writes on page 190: “..the
question, often asked uncomprehendingly, whether the contraction is
"real" or "apparent" misses the point: the only thing that can be measured
is the kinematic shape, and that is shortened for any measuring rod in
motion relative to an observer.”
By "apparent", Folsing obviously means "as measured". Everyone
knows there is contraction as measured, therefore no one is asking
whether it's real or measured. Some are asking if it's real as well as
measured. Our answer is that identically mutual measured contraction
is dependent on the contraction being real, i.e., absolute, in the sense of
how it would be perceived from a higher dimension, as our upcoming
diagrams will show. This should not be surprising, considering that the
difference in recorded time showing on two reunited clocks is an
absolute. In other words, there is an unavoidable reality which goes
beyond that of our simple measurements of clock rates and rods.
Many authors speak of contraction as though it is an actuality beyond the
mere measurement, but when it comes to their derivations, they do not
utilize it. Instead, they follow Einstein's lead and hold only to
"absolutes" of assigned measures.
On the following pages, we'll demonstrate, with diagrams and simple
analysis, the mutual determination of contracted length and slowed clock
rate between two inertial frames as they pass by one another, consistent
light speed measure, and the absence of any clock paradox in our theory.
In short, we'll show there is an effective equivalence of all inertial
systems for the assessment of all mechanical and electromagnetic
phenomena; and a person cannot determine the state of motion of his
inertial frame with respect to the overall frame of the universe.
EQUIVALENCE OF INERTIAL FRAMES 59
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.
There is really nothing to "perceive". We automatically regard our
measuring apparatus as being true to its markings. All laboratory
experiments carried out by scientists are subject to this condition. The
communication between the various parts of any instrument is
constrained by the speed of light. Even the combination of the human
brain and eye is restrained in its perception by the speed of light, should
one consider the theoretical direct observation of events occurring at
relativistic speeds. (Identically, looking ahead to chapter nine, two
colliding objects will crumple in accordance with this same restraint –
the communication of the crumpling force can be communicated only at
To measure any velocity, we must use two clocks of some distance apart.
We can synchronize them only by using light rays, the sending of which
involves the passage of time. Our consideration of what is involved in
synchronizing them will always be part of the equation. In other words,
the fact that we that we "do nothing special" is part of the equation.
EINSTEIN DIAGRAMMED IN ABSOLUTE TERMS 73
We'll look at Einstein's original 1905 paper, his presentation in his 1916
book, Relativity, and his derivation of 1916.
We'll then show that Einstein's treatment can easily be diagrammed
against the backdrop of the universal frame.
We'll show that without the underlying reference frame of totality, which
is what is needed to impart the inertial properties of clock speed and
length contraction, the symmetrical effects of relativity cannot occur. In
other words, Einstein's results of mutuality depend on the natural
differences between inertial frames, as imparted by the universal frame.
We'll conclude that, contrary to any claim the reader might have heard
that relativity overthrew old absolutes, the old absolutes merely needed
to be better understood. For without an absolute structure producing the
differing inertial properties, there can be no relativity, and there can be
no time differential between reunited clocks.
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.
To define inertial system without appealing to a physical universal
system is to limit oneself to only kinematics (considerations of motions
of objects absent of force), and to define inertial system in a circular
In a physical sense, to be in what is called an inertial system is to have
an absence of experience (detection) of any force that could be construed
as acceleration (or equivalently, gravity) based.
The origin of such force must come from a relationship with the totality
of the environment outside of the system in question, thus implying there
is such an environment and that if you changed your state of motion
relative to it, you would experience force. (Any generation of force
inside the system merely creates a new system within the system, with
no change in the overall motion of the system.) And no meaning can be
attached to a net movement of the totality of the external environment,
which is the universe itself.
There is no way around this.
It won't do you any good to imagine that your little system is all alone in
the universe and that there is therefore no external environment, for all
you would accomplish is to define your little system as the universe
itself, to which no meaning of net motion can be attached, and whereby
any motion inside that little system must now be seen as different from
its net external system, i.e., your original little system (the new universe).
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.
One might say "A is in uniform motion relative to B". But then it might
be noticed that B is accelerated relative to C while C is in uniform
motion relative to D. Who is in an inertial frame, and who is not?
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.
While this clock synchronization scheme makes for a beautifully
utilitarian paradigm for relativity, it has left readers frustrated, in that
they are furnished with no diagrams or descriptions of measurement
taking with which they can feel comfortable. They are always left
wondering what the truth of the matter is behind the symmetrical
measurements entities of different inertial frames make of each other.
They are also left with a treatment that cannot explain where the missing
time has gone in the so called Twins Paradox (reunited clocks).
It's easy to imagine that Einstein struggles with an inner conflict
concerning the matter of the universal reference frame, for at the outset
he relies on quotes at every key moment, conceivably in an attempt to
avoid dealing with the conflict. This is in addition to the alternate use of
the words definite and determined in his second postulate in the opening
paragraphs of his paper.
Others might say that Einstein's use of quotes around "stationary frame"
was merely his way of emphasizing that the choice of reference frame is
We doubt it's that simple. It's hard to imagine that Einstein was oblivious
to the issue we've just discussed. Perhaps he chose to not worry about a
universal reference frame which he already regarded as undetectable. In
fact, that very postulate dictates much of his derivation.
Perhaps he thought that there was no sort of physically at rest reference
frame that would allow the complete set of mutual effects needed to
satisfy the POR. At the time Einstein wrote his paper, Lorentz's theory
did not include actual clock slowing; complete mutuality of measuring
across reference frames had not yet been considered in aether theory.
Perhaps Einstein was imagining the possibility of a non-Euclidean and/or
infinite universe in which he imagined there would be no gravitational
center point locking in a universal reference frame. We'll have much to
say about those matters in the closing chapters of this book.
EINSTEIN DIAGRAMMED IN ABSOLUTE TERMS 85
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.
That a clock functioning is dependent on the speed of light, is something
Einstein never took notice of.
Until perpendicular light rays are considered along with the light rays of
a given line (thus a two-dimensional study), nothing of a concrete nature
can be deduced about time-keeping, and then only in the context of the
universal reference frame.
What is contrived in Einstein's (and modern day) Lorentz transformation
derivations is that the consistent measure of light speed and mutual
length assessments are forced onto the inertial frames for the sake of the
satisfaction of the postulates. This of course is just a restating of our
purpose for writing this book. Without an appeal to the underlying
structure, measures are doomed to be simply assigned. And as we’ve
noted, the time differential between reunited clocks is left unexplained.
Still, we respect the utilitarian and challenging approach Einstein used
in his original paper. In 1916, he managed with a simpler, though still
We'll present that derivation now, then look at not only how Einstein's
treatment can be diagrammed against the universal frame, but how the
effects of relative motion (and therefore Einstein's treatment) are in fact
dependent on the universal frame. That frame is actually represented in
Einstein's derivation, even if unconsciously.
EINSTEIN'S CLOCK SYNCHRONIZATION IN ABSOLUTE TERMS 88
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:
The difference between tA - tB and tB - t'A (A did the triggering) equals
the difference between tB - tA and tA - t'B (B did the triggering).
What we'll do now, is to examine Einstein's assignment of tA - tB =
tB - t'A in the context of the universal frame.
Consider the following situation in the context of the universal frame:
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
Einstein's definition of what constitutes a synchronization of those two
clocks dictates that B's reading will be .6 second less than A's reading as
seen against the universal frame, .6 being the velocity of AB. [see note 1 below]
(Keep in mind that Einstein had no awareness of this superimposition
onto the universal frame.)
Using this convention (the assignment of tA - tB = tB - t'A) amounts to
a disregard for an analytical incorporation of an absolute frame of
reference. It is in keeping with Einstein's notion of simultaneity, wherein
he elevates a direct observation of a distant event to a psuedo-reality of
time passage between the event and the moving observer.
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:
He considers lightning strikes at points A and B, with observers M
(stationary) and M' (in motion) accordingly observing simultaneous and
non-simultaneous events, concluding that “Observers who take the
railway train as their reference-body must therefore come to the
conclusion that the lightning flash A took place earlier than the lightning
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.
What Einstein does here, is call synchronous whatever appears
synchronous to an observer, adopting a utilitarian paradigm for his
treatment, where light is the messenger of moments.
He thus leads himself to his definition of clock synchronization, in which
time passage for light travel is predefined as 1 second for an entity of a
given inertial frame who has separated his clocks a distance of his
particular contracted (such as .8) light second. (The most obvious
limitation of this approach is that it cannot explain where the missing
time has gone in round trip situations, as we'll examine on pages 103 -
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.
When graphed against the universal frame, this synchronization process
takes on practical meaning; with Einstein's clocks preset to readings that
will produce symmetry for both directions of light ray timing. Rather
than RT's clock triggering and subsequent allowance for triggering time,
Einstein has us synchronize our clocks such that the time delay for
triggering is replaced by the notion that we should regard the two clocks
as actually showing the same time.
Who sets these clocks? We do, in a (very large) laboratory. When we
set a pair of spatially separated clocks in keeping with tA - tB = tB - t'A,
we do so unaware that this means tB reads .6 second less than tA against
the universal frame, being unaware of our own speed.
If we simply trigger clock B by sending a ray from clock A, we do not
have this .6 difference (rather -1.6 or +.4), and we use the
straightforward reasoning, as explained on pages 44-47 and 65-66, to
calculate the speed of a passing ray of light or any other passing object.
Yet we are certainly free to recalibrate our clocks until we get identical
time differences between the two clocks, rather than 0 seconds in one
direction and 2 seconds in the other, which is always to be expected
without a recalibration to Einstein's declaration.
EINSTEIN DIAGRAMMED IN ABOSULTE TERMS 91
Einstein's approach then, becomes utilitarian in nature, elevating the act
of direct observation to a pseudo-reality.
Einstein concerns himself only with readings at the same place-moment,
due to not allowing himself to look at the situation from a plane of instant
perception, meaning our universal frame of reference, where we see all
readings at all locations.
The reader will find a synchronization process described in modern
texts, but not in the unambiguous context of a universal frame of
reference where light has an absolute speed in reality. Instead, time
remains a purely relative term, and along with it necessarily, light speed
and lengths of rods.
Substituting our convention of light second measuring rods and velocity
of frame = .6c, we have, in the book Spacetime Physics, clock B set in advance
to 1 second, then activated by a light ray which was sent from clock A
when clock A read 0. Clocks A and B had seperation of .8 ls due to the
velocity of their frame. This yields the identical situation as diagrammed
on our page 88, meaning clock A reads 1.6 second when the ray reaches
clock B, yielding a difference of .6 second, which is the velocity.
None of this is acknowledged anywhere in this widely read relativity
"bible". The authors were clearly not aware of it, and naturally were
defeated in their attempts to resolve the clock paradox. (See pages
103-117 of Relativity Trail.)
1. Spacetime Physics, Taylor and Wheeler, p 37 - 38. The same authors describe as
“strange” and “difficult to understand” the issues involving the relativity of simultaneity
(p 62-63 of their book). But such is the hand dealt by purely relative considerations.
EINSTEIN DIAGRAMMED IN ABSOLUTE TERMS 92
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.
What this higher dimensional entity must see, embedded in totality, is an
inertial frame at rest which has the fastest clock rate and spherically
shaped atoms, along with inertial frames of greater speeds, lesser clock
rates and squished atoms. Only this can generate symmetrical
relativistic effects and create the time differential between reunited
Relativity does not overthrow the concept of absolutes. It confirms it.
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.
A little reflection on the need for stability at the base of our structures
(atomic) shows that length contraction has a physical basis,
fundamentally Machian in nature.
Thus one obtains a vantage point from which to not only monitor, but
also explain why everyone obtains the measures they do.
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.
So again, Einstein here adopts a convention for time that is not
dependent on the actual distance traversed by a light beam. In RT, we
take light as the absolute nature, and define everything in relation to it.
Einstein takes only the measured speed of light as an absolute, thus time
and length are treated as though they have no intrinsic nature to go along
with their measured properties.
What is missing here is the fact that without intrinsic properties, there is
nothing to measure. But intrinsic properties are not what interests
Einstein. He simply doesn't need them (except of course to explain the
time differential between reunited clocks, which he cannot do without
acknowleging the absolute frame).
At any rate, this conventional notion of time passage led directly to the
notion of "relativity of simultaneity".
In Einstein's handy notion of simultaneity, an observer is free to
conclude that a pair of lightning strikes were simultaneous or conclude
that they were not simultaneous, whereas in the context of the universal
frame, the only such observers who would reach such a conclusion are
folks who think light travels from the source to our eyes instantly.
EINSTEIN DIAGRAMMED IN ABSOLUTE TERMS 95
But we can reconcile Einstein's approach with our own:
Whereas, in RT, we describe a process of triggering a clock using a light
ray, then allowing for the time passage of the triggering ray, Einstein has
us synchronize our clocks such that the time delay for triggering is
replaced by the notion that we should regard the two clocks as actually
showing the same time. It is as simple as that. Einstein's results can be
diagrammed against the backdrop of the universal frame.
That Einstein was not conscious of this is clear:
In his original paper of 1905, after completing his derivation of the
Lorentz transformations, he finds it a "peculiar consequence" that a clock
once synchronized with its mate of the same inertial frame will show a
lesser time reading upon being moved to the position of its mate.
This would not seem to him the slightest bit peculiar if he had been
charting everything against the universal frame, where clock readings at
all locations can be seen at any instant of universal time.
No wonder also, that Einstein never defined clock functioning (timekeeping).
Absolute light speed in an absolute frame is what gives us the
direct definition of clock functioning.
Einstein concludes that light is the limiting speed (as measured) only
after his derivation is complete, in keeping with the disregard of the
universal frame of reference in his reasoning.
We'll show, in just a bit, a table and diagram of more of Einstein's
treatment superimposed onto the universal reference frame.
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.
In his derivation, Einstein proceeds to relate k's coordinates and times to
K's by regarding each of them as obtaining the same measured speed of
light, in both positive and negative directions.
In the course of his treatment, Einstein concludes that a clock that
changes inertial frames, though once synchronized with its mate, will
show a lesser time reading than the other clock upon reuniting. This
should indicate to him an asymmetry of an absolute nature, since such an
absolute difference can come about only with an absolute difference of
clock rates. Thus he ought to regard and , which are identically our
t1 and t2, as corresponding with the absolute distance intervals of light as
it passes through any particular frame. (See the diagram on page 38.)
Thus he ought to regard one coordinate scale as actually shorter than the
other, for the satisfaction of the POR of an absolute nature.
His derivation has built into it, the asymmetry needed to obtain the
correct result about ultimate time differential between reunited clocks.
Implicit, yet not acknowledged, in that asymmetry, is the absolute speed
of light, or equivalently, the absolute distance interval of light.
Instead, he regards the asymmetry as merely relative. In his derivation,
he assigns measures of length for the parties in both reference frames
that will simply satisfy his postulates of measure.
The initial wording of Einstein's second postulate in the opening
paragraphs of his 1905 paper seems like nothing more than a remnant
from some earlier stage of his reasoning.
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.
It seems odd that Einstein, upon noting the time differential between
reunited clocks, did not rethink his derivation in the context of the
universal frame, for his own enlightenment.
(Just as mu and lambda are an implicit, albeit unconscious, reference to the
absolute distance intervals of light as it passes through a particular frame,
a strict relativist attempting to dispel the clock contradiction will
sometimes tacitly and temporarily refer to distances as though they are
absolutes, only to get themselves stuck again when they hold to
Einstein's paradigm. More typically they try to place the entire burden
of ultimate time differential on the moment of inertial change, a
ludicrous paradigm, which we’ll further address in a couple pages.)
With his clock synchronization method, Einstein adopts a utilitarian
approach to see him through, defining time passage in keeping with
consistent light speed measure, his only acknowledged "absolute".
The entities in his study, for whom no absolute nature of clock
functioning or length is specified, can only be regarded as having
assessed each others properties in some unspecified manner. The
postulates are satisfied, but no diagramming of the measuring process is
possible. The reader is left baffled as to what is transpiring.
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
When space and time are combined into one concept, a new absolute
emerges which parallels that of the measured speed of light.
The concept, introduced by Minkowski, is none other than the spacetime
interval. And again, it is an absolute in the sense that it is a measure
agreed upon by members of all inertial frames. Spacetime is a
consequence of Einstein's clock synchronization.
The spacetime interval relates the contraction formulas of a moving
system to the measures obtained within a stationary system:
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 combination of space and time is also accommodated by the
Reimaniann geometry upon which is built the general theory of
relativity. Can we build a model for GR while continuing to employ the
absolute nature of space and time-keeping? Certainly in principle:
It is the mathematical entity of spacetime that is described as having
curvature in GR. We on the Relativity Trail take the view that it is space
that has curvature, and that time-keeping, being dependent on the path
light must travel in space, fluctuates in accordance with that curvature.
Enabling the math model of spacetime is the fact that time-keeping and
spatial extension are both dependent on the same phenomena, light.
Throughout the course of our treatment, we've shown this plainly for SR.
It can only be true for GR as well. GR generates SR in a local region
when matter is uniformly distributed, or is absent, in that particular region.
SECURING LOOSE ENDS 104
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.
If A and B clock rates were actually equivalent regardless of their
respective inertial frames, then they must also be equivalent to each other
after the change of inertial frame. This would preclude the symmetrical
effects of measuring as we know them in relativity. And it would leave
only the change of inertial frame to create the entire time differential, an
actual time differential indeed noted upon return.
Instead, diagram 7 showed, as will any physical experiment of that
nature, that no such jump in the time differential, real or measured by
either party, occurs at the turn-around. Rather, clocks A and B of
different inertial frames do keep time differently. And Einstein did
implicitly utilize the universal frame when he introduced mu and lambda,
because only totality can bestow clock functioning properties upon
SECURING LOOSE ENDS 109
Banesh Hoffmann, a collaborator with Einstein late in Einstein's life,
writes in Einstein, Creator and Rebel p. 76-78:
“Though (relativity of simultaneity) may be shocking, we have to learn
to live with it. .... its logical consequences are often such as to outrage
No shock or outrage to our common sense is to be found in the context
of the universal frame of reference, and there is nothing we need to
“learn to live with.” We would be shocked only to learn that clock rates
and lengths were not mutually measured as contracted.
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.
Examiners of relativity routinely fail to realize that the very transfer of
information which is involved in mutual assessments across inertial
frames is also all that is involved in the turn-around associated with the
Twins Paradox; for they routinely appeal to an inertial force associated
with even an instantaneous turn-around, which somehow suddenly
creates the entire time differential, as though some force could actually
affect the transfer of information, which involves nothing more than the
simple act of starting a watch.
Experiments dictated Einstein's postulates, but they did not dictate his
clock synchronization. With Einstein's clock synchronization, each
party calls simultaneous whatever appears simultaneous. Einstein's
postulates lead to a time differential, but his clock synchronization
obscures the cause of that differential.
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.
Their so called resolutions of the paradox amount to no more than a
repetition of Einstein's original conclusion that the party who changes
frames will record the lesser time over the course of the round trip. But
that is not a resolution of the paradox they have created.
The paradox in question, created by themselves, is: "If there is no actual
clock slowing, dependent on one's actual uniform linear speed, then why
do reunited clocks, which have moved with strictly uniform linear
motion, show a time differential upon reuniting?"
Their analyses typically fail to incorporate a transfer of clock reading
from an outbound traveler to an inbound traveler. Such transfer is
requisite for any study involving special relativity, otherwise
acceleration is involved. We cannot use acceleration to explain the
differential: No acceleration is incorporated in Einstein's derivation, yet
the time differential arises from his derivation, just as does the mutuality
of measured clock and length distortion across inertial frames. You
cannot derive one without the other. Just as clock information is
exchanged across inertial frames to effect the observation of mutually
measured clock rate slowing, so too does the transfer of clock reading
from an outbound traveler to an inbound traveler effect an observed
incremental increase in clock rate differences.
This is not to say that spacetime analyses incorporate the effects of
acceleration. Rather they incorporate the examiner's own deduction of
what the time differential will be upon the reuniting of clocks. That
deduction is then construed by the examiner as a misperception on the
part of the party changing frames (due to the examiner's ignorance of the
actual measuring paradigm – the regular sending of radio pulses).
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."
Now A. P. French was on the wrong track regarding the twins
paradox, but read on:
In Mach's Principle, an object is affected by a change in motion
relative to the matter of the universe at large. But such an effect
cannot occur unless the object is in a relationship with the matter of
the universe at large regarding its initial state of 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.
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
Einstein's approach is to impose measurements of properties such that
the postulates will be satisfied, while not addressing in any manner what
these properties are. It does not address the structure beneath the
In order to preserve the consistent measure of light speed in any
direction, Einstein simply declares time passage as equal in both
directions in accordance with that constraint.
Two coordinate systems of undefined spatial extension and undefined
time tied together by their uniform assessment of light speed leave us
with no picture of the situation.
The significance of the time differential between two reunited clocks has
been missed by virtually all students of special relativity; and perhaps
this is largely because Einstein himself never re-examined his treatment
after noticing that unexpected and “peculiar” result. Instead the focus
has been on the mutually measured effects between inertial frames,
which has overshadowed the underlying actual asymmetries implied by
the actual time differential; thus the assumption by most readers of the
standard accounts that there is no universal frame generating these
RT recognizes that the speed of light is constant in an absolute sense. In
the process, we see precisely what time and length are in absolute terms,
and define clock functioning. The time differential between reunited
clocks does not strike us as peculiar, rather as the first obvious thing.
RT notes that the absolute time passage for oppositely directed light rays
through a moving AB system is unequal, yet observes that a consistent
measure of light speed is obtained by virtue of the difference between the
assumed and actual length of measuring rods.
The aforementioned difference is consistent with the consideration, or
lack thereof, of a universal reference frame against which light and all
other phenomena display their absolute character.
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]
But such labels and suggestions of what “we should see” as reality do not
offer any weight at all against the evidence we actually do see, which is
the time differential between reunited clocks. Such differential shows
that we can understand the God's eye view of reality.
Beyond offering no valid reason for the actual time differential between
reunited clocks, the most frustrating aspect of reading presentations of
relativity that recognize only relative frames, is the absence of a
description of any measuring process. Such absence is dictated by such
nature of the development.
1. J.R. Lucas & P.E. Hodgson, Spacetime & Electromagnetism, Oxford Univ Press 1990,
p. 259. The quote is re-arranged from the manner in which it appears in the book.
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.
Even the foundations of our postulates seem to us hardly abstractions at
There is nothing abstract about RT's definition of "inertial frame". There
can be nothing more comfortable than the notion of the universe serving
as the ultimate frame of reference.
We certainly don't consider light's property of absolute speed to be an
abstraction, considering it is massless. Nothing could seem more
Our requirement of the contracted dimension of an atom in the direction
of motion for the purpose of maintaining atomic stability does not seem
abstract. In fact it seems perfectly natural, and is Machian.
All the mutual effects of measuring follow concretely from these simple
In his biography of Einstein, Albrecht Folsing writes, “Einstein must
have begun with some idea of what he wanted to deduce. At an opaque
point in his deduction he introduces, without any warning or
explanation, a slight mathematical operation whose purpose becomes
obvious only if the desired result is already known. This underhand
device, by means of which he rather forcibly "computes his way" to the
Lorentz transformations, deprives the deduction of some of its elegance
and stringency. Thus it is scarcely credible that Einstein actually arrived
at his formulas in the way he presents them in his paper. In fact, in later
years he never again used this rather awkward method.”
We regard "forcible computing" to be present in all derivations
incorporating purely relative inertial frames, for the entities involved are
forced into certain regards in order to satisfy the postulates.
1. Folsing: “This concerns the implicitly performed factoring of a(v) = P(v) (1 - v2 / c2),
which can be understood only in light of the result to be derived.”
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
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:
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,
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.
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. Different textual content from the other twin paradox animation page.
Twin Paradox Explained. A discussion of the failure of spacetime diagrams.
Twin Paradox Animation. Embedded youtube animation,
with textual description.
Absolute Frame of Reference. Absolute frame of reference in the physics community.
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.