Einstein's Relativity in absolute terms
Luebeck, R. Relativity Trail. Mpls: L B Writ Publishing, (2008)
Cite the book, Relativity Trail
See also: Relativity in Absolute Terms
A comprehensive and concise overview
From the preface to Relativity Trail:
The standard accounts of special relativity have left readers feeling more dissatisfied than have the accounts of perhaps any other subject matter, as evidenced by the thoughtful protests we regularly encounter among the readership. This author's own dissatisfaction goes back almost forty years. With all of life's distractions, he allowed that dissatisfaction to remain largely unacted upon until this past year. In the very back of his mind however, this book has been brewing for a long time.
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 = mc2.
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.
From the introduction to Relativity Trail:
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.
We'll demonstrate directly, that there is no incompatibility between Einstein's postulates of SR and the existence of a physically defined universal reference frame 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.
The structure of the universe is evolving. It imparts inertial properties and produces the effects of special relativity. But no meaning can be attached to any movement of its point (to use the term broadly) of departure (origin). That "point" is therefore considered fixed, and is the universal frame of reference. The terms "stationary", "at rest", "absolute" and "God's eye view" are suitable synonyms.
It must not be confused with the term, "preferred" (or "privileged") reference frame, which would imply that such a frame is experimentally detectable.
If you have read other books about special relativity, you have undoubtedly come across statements similar or identical to the following, concerning the relative merits of two or more inertial frames: “There is no truth of the matter.”
On the Relativity Trail, we can phrase it only as follows: “There is no possibility of a person within any inertial frame of determining the truth of the matter regarding his or anyone else's inertial frame using any type of mechanical or electrodynamical experiment.”
This concept goes to the heart of Einstein's second postulate of special relativity, and identically, to the issue of being able to provide clear diagrams and descriptions of measurement taking. A crystal clear understanding of the underpinnings of special relativity depends on giving this aforementioned statement correct form, as we've done in the preceding paragraph.
Einstein's first postulate is a restating of the Galilean Principle of Relativity, except to include all electromagnetic phenomena. Thus, his first postulate contends that there is no possible experiment one can conduct to determine that one is in motion relative to a stationary aether.
In his initial wording, his second postulate states that “light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.”
With the word "definite", Einstein seems to imply that light has an absolute (actual) speed in reality. But he doesn't explicitly state that there is a physically defined universal reference frame against which light has this definite velocity. This might not seem to be a problem at first, but when he restates this postulate several paragraphs later, he uses a new wording which changes the meaning considerably. These alternate forms of his second postulate have caused a fair bit of anxiety among students of special relativity.
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.
From page 6 of Relativity Trail:
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 – we'll show plainly that only totality can impart the specific properties of clock functioning and length contraction to an object. These will be referred to as inertial properties. 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.
From page 12 of Relativity Trail:
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 time-keeping 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.
From pages 20-21 of Relativity Trail:
The experimenters were trying to detect the aether wind, based on light having a wave nature. They didn't detect any aether wind, and to explain the results, were forced to assume that an object underwent length contraction in the direction of its motion through the aether. Specifically, they had to assume that the test apparatus shrunk when aligned parallel with its motion through the aether. It was as if the pressure of the aether wind shrunk the object.
Now this assumption came about as a result of assuming a wave nature for light. Yet, since physicists had assumed that the speed of light is constant, they would have needed to assume length contraction even if they considered that light had only a (special) particle nature and that there was no aether. And the amount of contraction they needed to assume is the same in either case.
This strikes us as a curious thing. The following is also curious:
Physicists had three other pertinent concepts available to them at the time of the MM experiment that went unutilized. Einstein had already shown there existed a quantum nature of light, indication of it being a particle. Mass associated with light was considered nil or zero. Studies of radioactive material pointed towards a transformational relationship between matter and energy.
Yet no one made the conceptual leap that therefore light might be a special particle of zero mass and therefore pure energy, which should in turn mean that it possesses the greatest possible speed in the universe, that speed of course being constant, so long as it remained a photon.
Even Einstein did not make this connection. Oddly enough, that connection was made by our sleepy western gent earlier in this book, whom, we point out, had the benefit of doing his contemplating seventy years later.
And that is where Relativity Trail begins. It is the pivotal point.
But to repeat, if a physicist of the era had made such connections, he should still expect asymmetry in the MM results, just as he would if he held to a wave theory of light through the aether. Thus he would still be surprised at the results, which showed only symmetry.
Our sleepy western gent took notice of this as well. Even though a massless photon had provided our gent with his certainty of time-keeping fluctuation, it did not immediately explain away the symmetry of the MM experiment.
Something we seldom see mentioned about this whole business of trying to detect ones motion through the aether, is that physicists were trying to detect something which really was as untenable a concept as Newton's absolute space. Like Newton's absolute space, the aether was regarded as something which had a one way relationship with the objects it contained, for it was considered to be not only an absolute of the moment, but for all time, fixed.
Furthermore, the hypothesized pressure of the aether used to explain length contraction would necessitate continuous energy expediture regarding light transimission, just as with our swimmer in the water. Even sound waves peter out due to the resistance of the medium they disturb.
We'll be utilizing the particle nature of light in our treatment of relativity, and like Einstein, disregard the existence of an aether. (If you're familiar with the dual nature of subatomic particles and are wondering why an aether is not needed for the wave nature of light, you might find a satisfactory answer in the description of wave forms as a distribution of the probability of photon location.)
From pages 36-37 of Relativity Trail:
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 not it 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.
Note that length must be contracted to the same degree as time-keeping is contracted in order to achieve symmetrical measures across inertial frames.
Time contraction = length contraction = (1 - v^2)^ 1 / 2
Next, we'll formally derive the length contraction equation in a completely straightforward manner. Not a single step will be baffling or abstruse, as we find in the derivations based solely on relative frames.
From page 42 of Relativity Trail:
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.
From page 59 of Relativity Trail:
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.
While an awareness of special relativity will affect our interpretation of our measures, no level of contemplation regarding relativity can possibly affect the actual measuring paradigm of an entity, since he can make no considerations about the state of his own motion relative to the universe. (Of course, he could arbitrarily assign a particular motion to his frame of reference; but he would then be expected to apply his knowledge of relativity twice more to adjust his calculations, once for his frame and once for the entity he takes measure of. But why bother.)
From page 64 of Relativity Trail:
Having "synchronized" their clocks by way of A sending a light ray to B, A and B now engage themselves in measuring how long it takes for a passing light ray to travel from A to B. As trivial as this is, in light of the fact that A and B have based their assumption of time lag on the speed of light, we still wish to illustrate the symmetrical results obtained when measuring a passing ray of light.
Clock B will read 1.6 when it receives the light ray, but for a reason different from what A and B can assume, since they can't know that they are not at rest.
The results obtained are the same as in the case of an inertial frame at rest with respect to the universal frame.
From pages 74-75 of Relativity Trail:
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).
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?
From page 76 of Relativity Trail:
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. 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.
From pages 82-85 of Relativity Trail:
Einstein begins his analysis with what he calls a definition of synchronism for two spatially separated clocks. A light beam is sent from A to B where it reflects back to A. tA is the initial reading of clock A, tB is the reading of clock B when it receives the light beam, and t'A is the reading of clock A when the light beam returns to it.
He states that if: tB - tA = t'A - tB, then the two clocks are synchronized.
He thus defines a “common” “time” passage “for A and B” (of the same inertial frame) for light traveling in each direction between the two as being equal, regardless of the motion of the AB system.
This correlates with RT's noting that an entity, when making measurements, will always regard the time passage for a light ray between its two clocks to be equal, regardless of the direction of the light ray, being unaware of ones own motion. But whereas we based our derivation on absolutes, then took note of how entities take measure of each other, Einstein is assigning equal time passages without defining time, and using it to launch his derivation.
The equating of tB - tA and t'A - tB will prove to be simply a means to disregard physical absolutes in favor of absolutes of measure. (RT, on the other hand, has shown that physical absolutes generate absolutes of measure.)
He moves on to his next section, where he restates his postulates, using the new version of his second postulate in which "definite" is replaced with "determined".
He then proceeds with the essence of the kinematics part of his paper where he relates two inertial systems to each other, based on his postulates.
He confers the status of "stationary system" upon an inertial frame K, thus granting it the status of "absolute" length measure and "absolute" time. (Einstein does not use the word "absolute".)
Now the concepts of distance, speed and time can each have meaning only in relationship to the other two. Each is defined by the other two. Therefore, in a given inertial frame, all three must be defined together.
The velocity of any entity moving through this system K is therefore also the "absolute" measure of that entity's velocity in whatever manner "absolute" applies to system K's time and distance.
He then introduces a second system k, in a motion uniformly different from K, stipulating that both K and k assess light speed as the same ratio of distance/time.
He also stipulates that k and K must regard each other's coordinate scale identically to satisfy the POR.
No problems arise as a result of Einstein's assignment of "absolutes" to system K even if K were not actually at rest in a truly physical sense.
Although his analysis of 1905 is monumentally complicated, and much of it incomprehensible, there is nothing incorrect about his conclusion regarding a registered deficit of time elapsed on k's clock (kc) compared to K's clock (KC) when kc returns to KC.
kc's return to KC is more than a statement of relative motion between kc and KC. Specifically, kc is the clock that changes inertial frames and facilitates the return if it is to show the least amount of recorded time upon the return.
This is where we need our universal reference frame, with its absolute attributes, if we are to see what's going on:
If KC really is keeping absolute time (i.e., is actually at rest with respect to the universe), then kc is running slower while the two increase their distance from each other. And if KC continues to keep absolute time as the two clocks reapproach, then it is kc that has changed frames and also continues to keep time more slowly.
If KC changes frames by virtue of pursuing and catching kc, then kc runs slower than KC on the out trip, and KC runs slower than kc on the "in" trip.
Even though one clock will be running either faster or slower than the clock from which it is departing due to relative motion, it is the clock whose change of frame brings the two clocks back together again that will show the lesser elapsed time since the two were last together.
The time contraction formula, being non-linear, naturally gives KC, in case 2, the lesser recorded time over the "round trip" by virtue of the higher speed of KC over the comparatively long pursuit stage.
Diagram 38 shows the underlying asymmetry of the situation, pointing us in the direction of what gave K and k their underlying clock and length properties – the universal reference frame.
And in fact, we might well learn that both KC and kc changed frames to facilitate their return to one another. In that case, the time differential between them will be less than if just one changed frames. It can even be zero.
None of this is to say that K or k can determine anything about their motion with respect to the universal frame.
We'll return to this very diagram in chapter six, when we use it to illustrate the relativistic addition of velocities. We will, at the same time, use it as another refutation of the clock contradiction.
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.
From pages 88-89 of Relativity Trail:
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:
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 the appendix for the formal derivation of this.
(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.
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.)
From pages 90-91 of Relativity Trail:
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'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 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 RT.)
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.
From page 93 of Relativity Trail:
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.
From page 95 of Relativity Trail:
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 (time-keeping). 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.
From page 103 of Relativity Trail:
We've seen that relativity has everything to do with round trips, for that is what gets us back to mutual place-moments. Much attention is naturally focused on the "turn-around" of a clock, which we'll now discuss in detail.
Since the popular interpretation of SR is that it has nothing to say about which inertial frame has the slower clock, many writers will claim that a jump in time occurs at the moment of B's turn-around. But we showed, trivially, in diagram 7 that no such jump occurs, as measured or as an actuality. (Also see the appendix.) We'd like to refer these writers to the diagram, which shows a creeping measure, by both parties, of time differential beginning at the turn-around.
1. In Spacetime Physics, by Taylor and Wheeler, p. 130, it is stated that the earth clock “jumps way ahead at turn-around” for the traveler. Such convolution fits right in with their seven page section devoted to wrangling with the clock contradiction. They take this up again on page 170, stating that the returning astronaut “has only herself to blame for her misperception of a "jump" in the Earth clock reading.” She actually has only Taylor and Wheeler to blame for not having the outgoing astronaut simply transfer his clock reading to her. Instead they assign her, at the moment of "turn-around", a reading for the Earth clock that makes up the entire differential. They throw out the outgoing past/future cone and replace it with a new one suited to the inbound astronaut at the moment of turn-around. Such lack of horse sense is necessitated by the denial of an absolute frame of reference.
From page 104 of Relativity Trail:
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.
From pages 110-111 of Relativity Trail:
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.
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).
From page 130 of Relativity Trail:
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.
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. Embedded youtube animation.
Twin Paradox Animation on youtube. Light rays and traveling twins are charted in absolute terms, free of the misleading space-time diagram. Expanded textual content.
Twin Paradox Explained. A discussion of the failure of spacetime diagrams.
Absolute Frame of Reference Absolute frame of reference in the physics community.
Diagrams and derivations from the book Relativity Trail.
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.