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Special Relativity explained in absolute terms -

eliminates the twin paradox, shows Einstein's clock sychronization
diagrammed in absolute terms, and ends all confusion regarding
relative frames of reference.  Completely compatible with, and in
fact subsumes, Einstein's relativity.  Not Lorentzian relativity.
Reveals what is transpiring behind the scenes of Einstein's


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.
Light rays and traveling twins are charted in absolute terms, 
free of the misleading space-time diagram.

Twin Paradox Animation.
Expanded text, and animation of the twin paradox.  (Same youtube animation.)

Twin Paradox Explained.
A similar discussion of the failure of spacetime diagrams.  

Twin Paradox Animation.
Alternative text, and animation of the twin paradox.  (Same youtube animation.) 

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.

Excerpts from the book Relativity Trail with included images.

Einstein explained in excerpts from Relativity Trail.

Diagrams and derivations from the book Relativity Trail.


Chaos etc - equations and graphical output.
Eight equations generating exotic behavior,
along with the program code and graphical output.

RogCAD - 3D CAD software for Windows and DOS

featuring keyboard entry of points, lines, planes, cubic
elements and curved elements.  Your design elements are
guaranteed to fit together seamlessly.  Text file data
allows for easy and robust editing of design elements.
There is automatic surface modeling with light source
direction, and an advanced customizable color palette.

RogCAD Girder and Panel Building Set
3D CAD virtual building set, modeled after the 
1957 - 1962 Kenner Girder and Panel building set.



end links

A few excerpts from Relativity Trail

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.

introduction ii
In Relativity Trail, our basis for assuming an absolute frame of reference is the fact of the time differential which exists between reunited clocks. Any cosmological picture we paint is simply for the purpose of gaining insight into the general evolution of such an underlying structure.

We find the simplest conception of the beginning of the universe to be perfectly adequate for that discussion. In this simple conception, the point of origin of the universe lies within our three spatial dimensions, as opposed to the modern conception that such point of origin lies outside our three spatial dimensions, this being the concept of inflation.

We'll be illustrating both cases and will show that they each allow for the same fundamental understanding of an evolving structure of space with a reference point (or points) of departure. Such reference frame gives meaning to the notion of actual clock rates just as it does to motion itself.

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.

introduction iii
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 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.

introduction iv
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.

introduction vii
The Principle of Relativity concerns only inertial frames. An inertial frame is any rigid coordinate system which is not in a state of acceleration or following any curved path. Thus, an inertial frame is an environment which is considered to be at rest or in a state of uniform rectilinear motion with respect to another fixed coordinate system which itself is at rest or in uniform rectilinear motion. The most common example cited is a railroad coach car, enclosed so as to block out the effects of air resistance for the purpose of conducting experiments.

To avoid the circular reasoning present in our preceding definition of an inertial frame, note that an object can be considered to be in an inertial frame if, while it be far removed from any gravitational influence, is also not registering any force which could be construed as gravity; i.e., feels no affects of acceleration. (You might recall that the effects of inertial change and gravity are equivalent. Also note that we are already appealing to the matter of the universe at large and its relation to initial and final states of inertial motion.)

We will use the terms "inertial frame" and "reference frame" synonymously.

Galileo's Principle of Relativity states that the laws governing mechanics hold equally as well in one inertial frame as in any other. Stated another way, there is no mechanical experiment which can determine that one's inertial frame is in motion relative to any other. Experiments involving billiard balls and dripping water inside a moving railroad coach car are employed as demonstration of the principle. [note 1]

1. In this situation, the x-y plane of the coach car is an inertial frame, while gravity acts along the z axis.

page 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.

page 8
We wish to make the point that communication within an atom can occur only at light speed, and that atomic processes are thus restrained by that absolute speed of light.

Regardless of the complexity of the regulating motions of these massless particles – the atom's true time keepers – they can be considered in terms of their vector components and reduced to a study in two dimensions.

We would now like to use just such a simple two dimensional clock to make our argument. This will allow us to derive the formula for time contraction in a straightforward manner.

Our clock will consist of a single photon bouncing forth and back between two mirrors.

As you can see from diagram 3, we have two photon clocks. The clocks themselves are not in motion in this diagram. Their only working parts are the photon each of them contains. These photons are busy bouncing forth and back off the mirrors, ticking off units of time, which we will call clock seconds. We say the light beam will travel from one mirror to the other and back again in one second. That is, a round trip cycle generates one second on the clock.

In diagram 4, we compel clock B to move relative to our stationary reference frame (and relative to clock A). Clock B is moving at half the speed of light, according to the universal reference frame. We see the actual path of each clock's light beam against the universal reference frame.

Again we see that the photon of clock B cannot, while moving forward, complete a cycle in one second universal time, for to do so would require the photon to exceed the speed of light.

But completing one cycle is what generates one second of time, from the perspective of the clock. So clock B ages more slowly than clock A. What has happened is that we have traded some time for distance. After all, did we really think there was such a thing as a free lunch?

To bring about this conversion of time into distance, we had to expend some energy, perhaps rocket fuel. This is not surprising. All the conversions with which we are familiar in ordinary life involve expenditures of energy just to facilitate the conversion.


Even though the word dilatation (or dilation) is the term most commonly used for time-keeping fluctuation, it's a poor choice of word for our treatment of relativity. Dilatation is defined as a stretching, and is used in conjunction with the inverse of the equation we derived above, referring to the dilatation of a clock cycle, which in turn implies the slowing of a clock rate.