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:

download book


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 systems intact.


                     .
                     .
                  [break]
                     .
                     .



            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 absolute nature.

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 relativity.


                     .
                     .
                  [break]
                     .
                     .



            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 Einstein's treatment.

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 relativity.

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 concrete footing.

The reader will be happy to learn that certain old absolutes are secure. In fact, without them, there can be no relativity.


                     .
                     .
                  [break]
                     .
                     .



            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.


                     .
                     .
                  [break]
                     .
                     .



         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 the paper.

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.


                     .
                     .
                  [break]
                     .
                     .



        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.)


                     .
                     .
                  [break]
                     .
                     .



      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 the universe. 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, meaning atoms.

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 inseparable.

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.


                     .
                     .
                  [break]
                     .
                     .



      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.


                     .
                     .
                  [break]
                     .
                     .



      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


 



 



                     .
                     .
                  [break]
                     .
                     .



       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 pages ahead.

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.


                     .
                     .
                  [break]
                     .
                     .



       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 light speed.)

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.


                     .
                     .
                  [break]
                     .
                     .



     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 manner.

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 arbitrary.

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.


                     .
                     .
                  [break]
                     .
                     .



     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 contrived, derivation.

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.


                     .
                     .
                  [break]
                     .
                     .



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 frame:

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 flash B.”

   

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 - 125.)

     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.

                     .
                     .
                  [break]
                     .
                     .


     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 clocks.

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.

                     .
                     .
                  [break]
                     .
                     .


                  SPACETIME         100

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.

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         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 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.

                     .
                     .
                  [break]
                     .
                     .


           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 clocks.

      

                     .
                     .
                  [break]
                     .
                     .


           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 common sense.”

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.

                     .
                     .
                  [break]
                     .
                     .


              SUMMATION         130

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.

To review:

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 assigned measures.

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 effects.

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 all.

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 natural.

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 concepts.

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 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.



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.



© relativitytrail.com