HannonRJ

Have any of you done a rigorous analysis of any of Einstein's three (?) derivations of his SR tansformation equations?

Does an equation that describes a physical situation apply to a situation in which one of its parameters does not exist?

To KLAYNOS. Thanks for the links! The 1899 article appears (at first glance) to be the predecessor of the 1904 article. The earliest contributor to "relativity" I have found, so far, is Woldemar Voigt. He published something similar to the Lorenta transformation in 1887.

HannonRJ: Einstein's "relativistic mass equation" was derived vi his SR transformation equations. If you want to reasd one version of that derivation, it is in section 5.13 of ELECTROMAGNETIC FIELDS AND WAVESm by Lorrain and Corson, WH Freeman and Co., NY

The actual derivation of Einstein's transformation is in section I-3 of OEMB. The previous sections are preparatory. The following sections are applications of thos transformations. There are no "reference frames" or "systems of coordinates" in Einstein's second postulate STRINGRAY78, Are you questioning my education? Are you familiar with Section I-3 of OEMB? If you are, you would not make such a statement. If you aren't you will not be able to follow this discussion To ajb. I have been intensively studying SR for about 18 years. If the original premises were invalid, all that follows from them cannot be valid. Einstein was a relative newcomer to the subject, but he is credited as its originator. Whatever later physicists may have contributed, we still represent SR as the equations now known as "the Lorentz transformation". In my studies, I learned that later contributors to SR were more concerned with rationalizing what Einstein said, or interpreting what he said. Too often Einstein is misquoted or misinterpreted. Only Minkowski attempted something different, but that is not my current subject. My objective in starting this thread was to obtain the views of others regarding the mathematical and logical validity of Einstein's 1905 derivation of his transformations of coordinates and times. There are aspects of that derivation that are open to interpretation, and some which seem to me to be invalid. To KLAYNOS: Thanks, but I am looking for an article by H.A. Lorentz himself in which he performs the complete derivation of what is now known as "the Lorentz transformation". It is not in Lorentz's 1904 article that you cited. I will attempt to find a copy of the 1899 article. Derivations by others are numerous, but there must be a reason why the equations bear Lorentz's name.

My interpretation of Einstein's Second Postulate is that light behaves as if its emitting body has no state of motion at the instant it emits light. Since an instant has no duration, a moving body has no motion at any instant.

I see that I made a mistake. Strike "i.e. to the first approximation". I have read the first three sections of OEMB at least a huindred times over the last 18 years. Einstein's model is kinematic, and it has only a verbal description which is open to interpretation. I have learned this fact through many discussions of those sections of OEMB with many other people who have also read them. That will become apparent as discussion of section I-3 unfolds. The mathematics is purportedly an algebraic-correct description of Einstein kinematic model. "Modern perspectives" are irrelevant to what Einstein said in 1905. In his 1915 derivation, he doesn't mention his Second Postulate, per se. In his 1912 derivation, he abandoned the Second Postulate. Since you raise "the Lorentz Group", by which I assume you mean "the Lorentz transformation", have you ever seen an article by H.A. Lorentz in which he details his derivation of the transformation equations that now bear his name? If you know of such an article, please tell me how I can obtain a copy. A few years ago, I tried to find one, enlisting the aid of the US Library of Congress. They could'nt find it. No, it is not in his 1904 article in which he propounds his "contraction". By chance, I did find what was purported to be Lorentz's own derivation of those equations in a book by Sir Edumund Whittaker, who did not cite a source. I did a step-by step analysis of that derivation, that was published as THE MYSTERIES OF THE LORENTZ TRANSFORMATION in Galiliean Electrodynamics, Vol 15, No. 3 (2004).

HannonRJ ASKS: What has this to do with my questions?

Einstein first derived his transformations of coordinates and times in section I-3 of ON THE ELECTRODYNAMICS OF MOVING BODIES. The physical predicates of that derivation were his two Postulates, which Einstein believed were "only apparently irreconcilable". The implicit purpose of all that follows was to remove that irreconcilability. Einstein's First Postulate: "...to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good*i.e. to the first approximation." Einstein's Second Postulate: "...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." Bearing in mind that in his subsequent analysis, Einstein treats his "ray of light" as a point that moves along his coincident xi and x axes, is there actually a conflict between his two postulates? What is the physical meaning of Einstein's Second Posulate? It is unfortunate that Einstein did not provide a diagram of his kinematic model, but relied on a verbal description that is open to interpretation

Please define "OP" I am prepared to enter into a detailed discussion of Einstein's algebra in section I-3 of ON THE ELECTRODYNAMICS OF MOVING BODIES. IMO, that is where the faults of Einstein's Special Relativity reside.

HANNONRJ REPLIES: To raise questions or to disagree is "straw-manning"? There is no "authority" as to the nature of the universe. There is only opinion. Current physics in that regard is nothing but the generally accepted opinion of members of the physics establishment. ----------------------------------- Why has the anti-relativity forum been closed? It had barely started, and for no apparent reason was "locked".

HANNONRJ: Please define "at rest". HANNONRJ: In my opinion, SPACE is void, and is analogous to the "stage" on which TIME and ENERGY interact to produce the dynamic universe in which we exist. Our universe had no beginning and will have no end, but its contents have changed and will continue to change. ------------------------------------ insane_alien said:"your physics is lacking in many areas with that. i suggest you read some university level books on the subject to get a better understanding of what you are dealing with." HANNONRJ: So "university level books" constitute what we are to believe? Who has decided this?

How do I attach a .doc file? Thanks! I am still unfamiliar with this forum. For your information, this article has been reviewed by qualified physicists. They found nothing wrong. I recently offered it to SCIENCE magazine for publication. They found nothing wrong, but declined its publication because they considered it would not be of interest to any but specialists, rather than to their general readership. Surely you are aware that Einstein's equation (cited early in my article) was published years before Einstein by a German high-school teacher. I can't recall his name.

On Minkoski's SPACE AND TIME: In 1908, in an address to the 80th Assembly of German Natural Scientists and Physicians, Hermann Minkowski presented his view (subsequently published as “Space and Time” [1]) that “Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve and independent reality.” The he went on to say, “First of all I should like to show how it might be possible, setting out from the accepted mechanics of the present day, along a purely mathematical line of thought, to arrive at changed ideas of space and time. The equations of Newton’s mechanics exhibit a two-fold invariance. Their form remains unaltered, firstly, if we subject the underlying system of spatial co-ordinates to any arbitrary change of position; secondly, if we change its state of motion, namely, by imparting to it any uniform translatory motion; furthermore the zero point of time is given no part to play. We are accustomed to look upon the axioms of geometry as finished with, when we feel ripe for the axioms of mechanics, and for that reason the two invariances are probably rarely mentioned in the same breath. Each of them by itself signifies, for the differential equations of mechanics, a certain group of transformations. The first group is looked upon as a fundamental characteristic of space. The second group is preferably treated with disdain, so that we with untroubled minds overcome the difficulty of never being able to decide, from physical phenomena, where space, which is supposed to be stationary, may not be after all in a state of uniform translation. Thus the two groups, side by side, lead their lives entirely apart. Their utterly heterogeneous character may have discouraged any attempt to compound them. But it is precisely when they are compounded that the complete group, as a whole, gives us to think.” [1] Comment: 1. What follows in “Space and Time” results from a “purely mathematical line of thought”, but is now widely accepted as representing physical reality. Minkowski continued, “We will try to visualize the state of things by the graphic method. Let x,y,z be rectangular co-ordinates for space and let t denote time. The objects of our perception invariably include places and times in combination. Nobody has ever noticed a place except at a time, or a time except at a place. But I still respect the dogma that both time and space have independent significance. A point in space at a point in time, that is, a system of values x,y,z,t I will call a world-point. The multiplicity of all thinkable x,y,z,t systems of values we will christen the world. With this most valiant piece of chalk I might project upon the blackboard four world axes. Since merely one chalky axis, as it is, consists of molecules all a-thrill, and moreover is taking part in the earth’s travels in the universe, it already affords us ample scope for abstraction; the somewhat greater abstraction associated with the number four is for the mathematician no infliction. Not to leave a yawning void anywhere, we will imagine that everywhere and everywhen there is something perceptible. To avoid saying ‘matter’ or ‘electricity’ I will use for this something the word ‘substance’. We fix our attention on the substantial point which is at the world-point x,y,z,t, and imagine that we are able to recognize this substantial point at any other time. Let the variations dx, dy, dz of the space co-ordinates of this substantial point correspond to a time element dt Then we obtain, as an image, so to speak, of the everlasting career of the substantial point, a curve in the world, a world-line, the points of which can be referred unequivocally to the parameter t from -∞ to +∞. The whole universe is seen to resolve into a number of similar world-lines, and I would fain anticipate myself by saying that in my opinion physical laws might find their most perfect expression as reciprocal relations between these world-lines. Comment: 2. Minkowski’s “world axes” are abstractions, per se: imagined scales of reference “projected” not just upon his blackboard, but upon empty space. His fourth ”axis”, presumably orthogonal to the three of space, exists only as an abstraction. Minkowski continued, “The concepts of space and time cause the x,y,z manifold t=0 and its two sides t>0 and t<0 to fall asunder. If, for simplicity, we retain the same zero point of space and time, the first-mentioned group signifies in mechanics that we may subject the axes of x,y,z at t=0 to any rotation we choose about the origin, corresponding to the homogeneous linear transformations of the expression x^2 + y^2 + z^2. (1) But the second group means that we may—also without changing the expression of the laws of mechanics—replace x,y,z,t by x-at, y-bt, z-gt, t with any constant values of a, b, g. Hence we may give the time axis whatever direction we choose toward the upper half of the world, t>0. Now what has the requirement of orthogonality in space to do with this perfect freedom of the time axis in an upward direction. To establish the connexion, let us take a positive parameter c, and consider the graphical representation of c^2t^2 - x^2 - y^2 - z^2 = 1 (2) It consists of two surfaces separated by t=0, on the analogy of a hyperboloid of two sheets. We consider the sheet in the region t>0, and now take those homogeneous linear transformations of x,y,z,t into four new variables x’,y’,z’,t’ for which the expression for this sheet in the new variables is of the same form. It is evident that the rotations of space about the origin pertain to these transformations. Thus we gain full comprehension of the rest of the transformations simply by taking into consideration one among them, such that y and z remain unchanged. We draw (Fig. 1) the section of this sheet by the plane of the axes of x—the upper branch of the hyperbola c^2t^2-x^2=1, with its asymptotes. Comments: 3. The preceding discussion leads us to assume that x,y,z,t, are the system of values (co-ordinates) of a specific world-point plotted relative to the world-axes. If so, x,y,z, (and their squares) are spatial distances measured relative to (x=y=z=t=0) in the x, y, z, directions, respectively. In order for (2) to describe a physical situation, ct must also be a spatial distance, requiring c to be a velocity or speed. In multiplying t by c, Minkowski changed an interval of time into a spatial distance. Hereafter, t appears only as ct. In effect, Minkowski’s “t-axis” is the “ct-axis”, except only in Minkowski’s diagrams. Does this mean time can no longer be distinguished from space? No, it means only that “motion” requires both time and space. Minkowski subsequently tells us that c is “the velocity of propagation of light in empty space”. c is not an ordinary velocity; it is isotropic. So the ct-axis is not limited to any one direction, but extends in all spatial directions from its origin at all times. 4. Why are ct, x, y, and z, respectively, squared? Minkowski didn’t say. We can but assume that he is setting the stage for what follows. 5. Why are x^2, y^2, and z^2 all subtracted from c^2t^2? Why does c^2t^2 - x^2 - y^2 - z^2 equal 1? Minkowski didn’t say. 6. What is in motion at speed c? Since t is the time “co-ordinate” of the world-point located at spatial co-ordinates x, y, z, we must assume that it is that specific world-point that is in motion at speed c. 7. What is the direction of ct? c is “the velocity of propagation of light in empty space”. c is not an ordinary velocity; it is isotropic, that is, it is of equal magnitude in all spatial directions from the point and instant of light’s emission, at all times. This means that at any time t>0, there are rays of length ct extending in the x, y, and z directions (among all others). Thus c^2t^2 really means [(x/t)t]^2 + [(y/t)t]^2+ [(z/t)t]^2 = +x^2 + y^2 + z^2, where x,y,z are the co-ordinates of the world-point at time t. If so, (2) actually says: +x^2 + y^2 + z^2 - x^2 - y^2 - z^2 = 1, or 0 = 1, which is obviously meaningless. Since all that follows in “Space and Time” depends on (2), it appears that Minkowski’s “Space and Time” cannot represent reality. Reference: [1] Hermann Minkowski: “Space and Time”, (21 September 1908). English translation in “The Principle of Relativity”, Dover Publications, Inc. New York, NY, 1952. _________________________________________________________ REGARDING HANNONRJ's article in the Precession of Mercury's orbit: HANNONRJ It is possible that Mercury also is a captured body. INSANE: possible but HIGHLY unlikely. HANNONRJ REPLIES: In your opinion. What is your premise for that opinion? Some Astronomers believe Pluto is a captured body. Others believe that many of the various moons in the solar system are captured bodies. So why not Mercury? HANNONRJ: As it orbits the sun, Mercury loses kinetic energy because it must supply the energy necessary to move the sun’s mass around an ellipse of the same proportions as its own orbit, but much smaller. INSANE:Wow, this is just plain wrong. Mercury will not lose energy because of this. otherwise nothing would stay in orbit for very long. the sun moves because of the conservation of angular momentum. there is no energy transfered. HANNONRJ REPLIES: Wrong. The Angular momentum of the Sun-Mercury system is preserved. Apparently you don't comprehend that in order for the major axis of Mercury's orbit to appear to be precessing. Mercury must be continually losing velocity along its orbit. Each orbit requires a longer time for completion. Loss of velocity means a loss of kinetic energy, which is possible only if that loss is a transfer to the sun, where it is dissipated as heat. HANNONRJ: The net transfer of kinetic energy to the sun will cease when Mercury’s orbit becomes circular (when all other perturbations are excluded). INSANE: hold on a sec, last sentence you said that it expends energy keeping the sun moving round in an elipse, a circle IS an ellipse, and the sun would be moving in one. Why is ther e supposedly no energy transfer here yet there is earlier? HANNONRJ REPLIES: A circle is not an ellipse. If a truly circular orbit exists, the asymmetry required for energy transfer does not exist. Even Eart's orbit is not perfectly cicular. HANNONRJ: As it loses kinetic energy to the sun, Mercury’s speed along its orbit slows, and it moves further from the sun INSANE: you seem to have an unexplained energy input around here. please explain this in detail. HANNONRJ REPLIES: No unexplained energy. Read my article more carefully HANNONRJ: During the half-revolution when Mercury moves toward aphelion it loses kinetic energy Km>s=MsVs2/2=2.08225x1026 N-m to the sun. Thus the net KE of Mercury at aphelion is KEmp-Km>s=3.1910504x1032 N-m INSANE: I think this is where your problem lies, you are applying equations for a circular orbit to an elliptical orbit. HANNONRJ REPLIES: Not so. See my calculations of KE at aphelion and perihelion. To ajb: The only geometry in Einstein's 1905 SR is that of his coincident xi and x axes sliding along one another at constant speed v, while a "ray of light" moves forth and back along a distance of arbitrary value common to those axes. Please tell me about "today's" SR geometry. It seems to me that I keep on seeing the same century-old equations, now called "The Lorentz Transformation". That in itself is odd. A few years ago I tried to find an article by H.A. Lorentz in which he derived the transformation that now bears his name. I enlisted the help of the US Library of Congress, but even they could find no such article. By chance, I found what was purported to be Lorentz's own derivation, although the author (Sir Edmund Whittaker) did not cite a source. I did a step-by-step analysis of that derivation which was published in Galilean Electrodynamics a few years ago. When did serious alternatives to current physics become "pseudoscience"? Real science is the search for the truth about nature, and always encompasses consideration of rational alternatives. To insane_alien; I thought you were going to post my entire article. Instead you have posted only your criticisms of isolated sentences.

The aether was immaterial. It was the electromagnetic medium that was considered necessary for the propagation of EM "waves", analogous to the necessity for a fluid as the medium for acoustic waves. While there were a few "variations" among physicists as to the exact nature of the aether, it was generally agreed that light (EM radiation) moved at c IN the aether, but if the source of that radiation was in motion relative to the aether, that radiation acquired the velocity of its source. The aether itself was assumed to be at absolute rest, but after the MM experiment it was proposed that the aether was "dragged" along with massive bodies as they moved. It is not generally recognized today that the Fitzgerald-Lorentz "contraction", which was developed to "explain the result of the MM experiment", was predicated on the aether as defined by Lorentz. Oddly, the "null" result of the MM experiment really was in accord with the aether theory, but M+M made mistakes in calculating their prediction of its result. If light acquires the velocity of its source, the prediction agrees with the results.