Reconsidering the interpretation of the Lorentz transformations

It is known that neutrinos propagate faster than light. For that reason the Einstein’s special theory of relativity cannot be applied to these phenomena. On the other hand the Matscie’s special theory of relativity based on the Matscie’s transformation is valid for any velocity including the velocities greater than the velocity of light in free space. The relativistic phenomena consisting of the length contraction and the time dilation can be verified successfully by the Matscie’s special theory of relativity. In this case, the velocity of light in free space acts as the critical velocity. Only about 81.6% of the rest mass of a body can be converted into energy. At very low velocities, the kinetic energy of a moving body is practically the same as that in the classical mechanics. And also at velocities of much higher than the critical velocity, it almost reduces to the classical expression. For moderate velocities, the Matscie’s special theory of relativity reduces to the Einstein’s special theory of relativity. For velocities close to (below or above) the velocity of light in free space, the kinetic energy of a moving body differs from that predicted by the classical mechanics.

In the year 1905, Albert Einstein presented his theory of Special Relativity and revolutionized our understanding about matter and energy by telling that they were the same. He derived the famous E = mc 2 formula from his realization that space and time have the same status. This realization, in turn, was complimented by his assumption that the speed at which light travels in vacuum is constant in any reference frame. Now what is this reference frame? It is not difficult to visualize the concept of reference frame. Imagine that you are traveling in a train and you throw a ball to a co-passenger in the same direction the train was running. The average speed of the ball should be the distance between you and your co-passenger divided by the time taken by the ball to reach your co-passenger. However, if someone outside the train watches it, one would find that the distance traveled by the ball is the sum of the distance traveled by the train during the time you throw the ball and your co-passenger receives it and the distance traveled by the ball from you to your co-passenger. Consequently, the outside observer would find a higher speed of the ball. The most important thing to notice here is that the time taken by the ball to move from one point to the other will appear to be the same to you and to the outside observer although the distance traveled by the ball would differ. You and your co-passenger measure the speed of the ball inside the train which is one reference frame attached with the train. The outside observer measures the speed of the ball in another reference frame attached to the Earth. One reference frame is moving at a constant speed with respect to another reference frame. If another train passes you with a different speed as compared to the speed of your train and a passenger inside that train measures the speed of the ball, he or she will derive a different speed of the ball. So, the speed of the ball is “relative” to the reference frame wherein it is measured. Einstein considered that light would not follow this rule; the speed of light would remain the same in all reference frames. In order to describe any cosmic event, one has to consider both space and time together. Einstein’s Special Theory of Relativity becomes significant only when the speed of an object is comparable to the speed of light. But nothing can exceed the speed of light. Now, if the speed of the ball or the train varies; i.e., if the ball or the train accelerates or retards, Special Theory of Relativity does not apply. For an accelerating reference frame, General Theory of Relativity has to be invoked. The contraction in length and the dilation of time is special relativistic effects whereas the acceleration due to gravitation is a general relativistic effect. Therefore, Special Relativity is a particular case of General Relativity. According to General Theory of Relativity, one can cancel the effect of gravitation locally by moving in an accelerating reference frame such as a free falling lift or aircraft. But it cannot be canceled globally. We know that the universe is expanding. All the galaxies are receding from each other. Since the rate of expansion of the universe changes, the dynamic of the universe is described by General Theory of Relativity.

إن النظرية النسبية العامة والخاصة تسببتا في حالة من التناقضات في علم الفيزياء. فبالرغم من أن النظرية النسبية تقدم قيماً صحيحة رياضياً، إلا أن بها قصور في العديد من الجوانب بما في ذلك التفسير النسبي لميل الجاذبية "تمدد الوقت" وانحناء أشعة الضوء على أسطح الكتل الكبيرة. وعند دراسة النظرية النسبية الخاصة نجد أنها مشتقة من تحويلات لورنتز، والتي جاءت نتيجة فشل تجربة مايكلسون مورلي. ويمكن القول بأن ما تعبر عنه تحويلات لورنتز، هو ليس المسافة الفعلية بين المشاهد والحدث. فجاءت النظرية النسبية الخاصة بمعادلات نتائجها غير دقيقة في وصف الطول والزمن والكتلة وجمع السرعات. لأن قوانين النظرية النسبية هي تطبيق تحويلات لورنتز على تلك المعادلات. لذا استوجب البحث عن تحويلات جديدة تصف المسافة الفعلية بين كل من المراقب الساكن، والمراقب المتحرك، والحدث. وأن الإلكترون هو جسيم يتحرك بواسطة موجة، وليس هو بذاته الذي يتصرف كموجة، يُمكّننا ذلك من فهم سبب سلوك الإلكترون الموجي في تجربة الشق المزدوج. اعتمدت الدراسة على التدقيق في الأسباب الضرورية اللازمة لوجود النسبية الخاصة وأصل اشتقاقها. فكانت تجربة (مايكلسون ومورلي) التي لـم يستطع العلماء تفسير نتائجها الغير متوقعة، وهي التي أدت إلى اشتقاق تحويلات (لورنتز) بهذه الصيغة الغير موفقة، والتي منها جاءت النظرية النسبية. وقد ابتكر الباحث أداة لتوضيح حركة الضوء، حيث تصف الأداة تجربة عملية لحركة الأجسام عندما تكون السرعة قريبة من سرعة الضوء. توصلت الدراسة إلى أن هناك تأثير واضح للوسط الناقل على الموجة في اتجاهها وسرعتها، والذي يمكننا من تفسير تجربة (مايكلسون ومورلي). وفي ضوء ذلك تم إيجاد تحويلات جديدة تصف المسافة والطول والزمن والسرعة بشكل صحيح. لذلك، تم وضع قوانين جديدة لتصحيح القوانين التي جاءت بها نظريات النسبية العامة والخاصة.

Siva’s theories explained the necessity of new theory for description of the Universe, space ,time ,space-time and matter. It explained the formation of ‘space time continuum’ in terms of ‘Films of the universe’ and an effect of consciousness associated to living things. Thus it is required to bring consciousness in to physical laws and transformations. The relation between physical world and consciousness has been analyzed clearly and explained that consciousness, if we interpret in physics, must be an inertial frame of reference which can be transformed in to inertial frames defined by ‘Special Theory of Relativity’. It is possible only by changing the signal velocity from ‘c’ to ‘c√2’ . Thus the ‘Special Theory of Relativity’ has been modified and named as ‘Super theory of Relativity’. The relativistic factor for it is also calculated as [1+(v2/c2)]1/2 where v = vo [{1- (vo2/c2)}]-1/2 here vo is its absolute velocity .The necessity to adopt a new signal velocity which is greater than that of light has been discussed and the ‘Principle of Relativity’ and ‘Principle of simultaneity’ which are basics for transformation has been applied to interpret it in terms of relativity. It has been concluded that velocity of light is a part of signal velocity and photon will have rest mass. It says that the observable velocity is a result of absolute velocity multiplied by relativistic factor for ‘Super Theory of Relativity’. Thus infinite signal transformation is introduced for transformation between Inertial frames of reference. Infinite signal velocity will explain the ‘Quantum entanglement’ in terms of transformation of physical laws from one frame to another as explained in ‘Special & General Theories of Relativity’.

The special theory of relativity (STR) is based on two apparently contradictory postulates: The equality of all physical laws in all inertial reference systems and the invariance of the speed of light ( <mml:math display="inline"> <mml:mi>c</mml:mi> </mml:math> ). This results in counterintuitive conclusions, including time dilation, object length contraction (i.e., Lorentz contraction), and mass increase at relativistic speeds as well as the unification of mass and energy. Although the STR has been empirically confirmed, the ultimate cause of special relativity as well as the reason for the invariance of c and its actual value (2.99 × 108 m/s) remain unknown. We have recently postulated that a hypothetical displacement of the three-dimensional (3D) space where we live throughout a fourth spatial dimension, which would be the basis for time, is a requirement for the gravitational effects contemplated by the general theory of relativity. This tetra-dimensional model of the universe explains that the actual value of <mml:math display="inline"> <mml:mi>c</mml:mi> </mml:math> equals the speed at which our 3D space displaces along the fourth dimension. It also explains time dilation, Lorentz contraction, Lorentz transformation, and mass increase at relativistic speeds, as well as the unification of mass and energy, as epiphenomena derived from the projection of the fourth dimension to our 3D space. We conclude that our universe model can intuitively explain special relativity as well as the reason for the invariance of <mml:math display="inline"> <mml:mi>c</mml:mi> </mml:math> and its actual value.

The Lorentz transformations and special relativity are unable to provide a realistic physical explanation of the behavior of matter and light. We will show that all these phenomena can be explained using Newton's physics and mass-energy conservation, without space contraction or time dilation. We have seen previously that the principle of mass-energy conservation requires that clocks run at a slower rate in a moving frame, and physical bodies become longer because of the increase of the Bohr radius. These results allow us to answer the question: With respect to what does light travel? For example, when we move away at velocity v from a source emitting light at velocity c, the relative motion of the radiation is observed from the Doppler shift. How can we explain logically that these photons appear to reach us at velocity c and not (c-v)? The conventional explanation relies on special relativity, but it implies an esoteric space-time distortion, which is not compatible with logic. This paper gives a physical explanation how the velocity of light is really (c-v) with respect to the observer, even if the observer's tools always measure a velocity represented by the number c. We explain how this problem is crucial in the Global Positioning System (GPS) and in clock synchronization. The Lorentz' transformations become quite useless. This apparent constant velocity of light with respect to a moving frame is the most fascinating illusion in science.

called the special theory of relativity, no doubt one of the boldest and most interesting theories ever designed.' Generations of physicists, mathematicians and philosophers were inspired by it. Bitter battles were fought over its principles and deductions which clashed with many an honourable idea backed up by honourable philosophical and scientific traditions. Yet all the knocks and bites from left and right seem to have left Einstein's theory unshaken. Today the battle-grounds of yesterday look rather deserted. The critic is likely to be silenced in the face of the theory's spectacular success. In the following I shall try to throw some new light on one or two old problems which Einstein's theory gives rise to. Section z is concerned with the obstacles we are faced with when we try to combine Einstein's special theory of relativity with a causal account of relativistic phenomena. The argument does not show, of course, that Einstein's theory is false, but it points to a possible incompleteness and to certain limitations inherent in the special theory of relativity. In section 3 a substratum theory of relativity is outlined which seems to be as simple and coherent as Einstein's special theory of relativity; the Lorentz transformations are deduced from two basic principles without making use of the principle of relativity. Finally, in section 4, the two theories are compared and some general conclusions are drawn. But let us first have a short look at the ideas underlying Einstein's theory. To begin with, the special theory of relativity is a transformation theory. This is its most fundamental aspect. Suppose we know the space and time co-ordinates of an event particle e (event with negligible spatiotemporal extension) in an inertial frame of reference F; then the theory

Since my undergraduate days, I have been puzzled by the fact that we have Newton’s laws of motion but only Einstein’s theory of special relativity. We have finished celebrating the 100th anniversary of the publication of the theory of special relativity, and it seems to me that after a century of validation, it’s time to rename it as more than just a theory. I propose that we, as physicists, define a set of Einstein’s laws, just as we have Newton’s laws, Coulomb’s law, or Faraday’s law. I begin the discussion by offering the following three laws: ▸ The laws of physics are identical in all non-accelerating (that is, inertial) frames.▸ The vacuum speed of light, c, is the same for all inertial frames.▸ The total energy E of a body of mass m and momentum p is given by E=m2c4+p2c2. In particular, the energy of a body measured in its own rest frame is given by E = mc 2, and the energy of a massless body is E = pc. Collectively, these laws should, in my opinion, be called Einstein’s laws of special relativity. Others may prefer slightly different wording, or more lawyerly definitions; with that I have no quibble. Time dilation, length contraction, and the relativity of simultaneity could be considered corollaries of these laws.Some may ask what is the consequence of renaming a “theory” to a “law”; obviously Nature does not care. To my way of thinking a theory is speculation based on incomplete knowledge, and a law is valid in all cases where the appropriate circumstances apply. I believe that the special theory of relativity falls into the latter category equally with Newton’s laws, Coulomb’s law, or Faraday’s law. If nothing else, this change would help us impress upon students and nonscientists (a) the importance of special relativity to our understanding of nature and (b) the multitude of advances in science made possible as a consequence of its formulation.© 2007 American Institute of Physics.

The twin paradox is often misunderstood, both in textbook and science popularizations. This article is intended to help clarify misconceptions involving the famous thought experiment. Of special importance is how we define the inertial frame in special theory of relativity. Another common factor that is overlooked involves the difference between time dilation, which is a consequence of the Lorentz transformations and the concept of look back time, which is independent of that. The concept of the invariant space-time interval and Minkowski diagrams are used in making these issues clearer.

We present a comprehensive discussion of the formulation of the kinematics of special relativity, i.e., the Lorentz transformation. We begin with a concise new proof that the principle of relativity implies that the transformation of event coordinates between inertial reference frames is linear. We then give a clear derivation of the pre-Lorentz transformation, which follows from the principle of relativity. We then show that the pre-Lorentz transformation and the inertial invariance of the speed of light together result in the Lorentz transformation. This, of course, is essentially the traditional formulation. We next present two additional formulations, one using Lorentz–Fitzgerald contraction and one using time dilation, instead of inertial invariance. This is reasonable since Lorentz–Fitzgerald contraction and time dilation are about as well established as and are arguably less abstract than inertial invariance, and thus may profitably be used instead of inertial invariance to complete the formulation. We then present a complete proof that the pre-Lorentz transformation and the requirement of closure upon composition together imply that the transformation is either a Galilean transformation or a generalized Lorentz transformation. This is noteworthy in that it gets ever so close to the Lorentz transformation without invoking light. In the course of this, we obtain a generalized velocity addition rule, which reduces to the velocity addition rule of special relativity. We next show that the generalized Lorentz transformation, together with inertial invariance, Lorentz–Fitzgerald contraction, and time dilation, used one at a time, yields three more formulations. We then show that the unspecified, nonzero, constant speed in the generalized Lorentz transformation can be determined without any reference to light, thereby obtaining a seventh formulation. Light plays no explicit role in the four formulations employing Lorentz–Fitzgerald contraction and time dilation and plays no role whatsoever in the seventh formulation. Thus, and this is a fact which should be strongly emphasized, the formulation of special relativity in no way depends upon the nature of electromagnetic radiation. We conclude by briefly discussing these seven formulations of the kinematics of special relativity and some associated implications.

Steve Adams' Relativity is a comprehensive and highly readable introduction to a subject of broad interest and enduring popularity. It is pitched at just the right level for serious sixth-formers or for undergraduates striving to understand the physics that underpins more mathematical treatments of relativity, and will also be of interest to their teachers. The book richly deserves a place in school and college libraries, but the present edition is marred by so many minor misprints that I would be reluctant to make it required reading for novice students, despite its many attractive features. Relativity has an admirably straightforward structure: an introductory chapter outlining classical physics is followed by two substantial chapters on special relativity and a single chapter on general relativity and cosmology. The first of the two special relativity chapters is pivotal since it establishes the `physics-led' rather than `mathematics-led' approach of the book. It achieves this by basing many of its arguments on the behaviour of `light clocks' that measure time by counting the successive reflections of a light pulse as it bounces back and forth between two parallel mirrors separated by a fixed distance. Judicious use of these idealized clocks enables the author to expose all the well known phenomena of special relativity without having to call on the Lorentz transformations at all. The Lorentz transformations are included, but they don't make their first appearance until page 111, and even then their main function is to prepare the way for Chapter 3, which takes the reader deeper into the structure of (Minkowski) space-time and revisits, in a more mathematical way, many of the topics introduced physically in Chapter 2. This double approach to issues such as time dilation and length contraction has been well thought-out and well executed, and seems certain to aid effective learning on the part of students, even those who are reading the book on their own, without the guidance of a teacher or lecturer. The survey of general relativity and cosmology that occupies the book's fourth chapter is much less detailed than that of special relativity, but equally engaging. The treatment of Einstein's geometric theory of gravity is again primarily physical, though the use of elementary calculus is more evident than in the earlier chapters. Only a small proportion of the chapter is devoted to cosmology as such, but the basics are well explained and the chapter is neatly rounded off by 20 pages on black holes and gravitational waves. Students can sometimes lose their way in lengthy chapters, so a book of 280 pages with only three major chapters may seem a somewhat daunting prospect to some. However, each of those chapters starts with a very helpful block diagram showing the relationship between key ideas, and there are plenty of subheadings to help guide and orient the reader. These signposting devices, together with the summaries and problem sets that end each chapter, make Relativity a useful and effective guide to the endlessly fascinating world of space-time. Unfortunately, as indicated earlier, this potentially very valuable text is marred by a number of small but irritating errors. The most prevalent of these concerns the gamma factor that appears in the Lorentz transformations and in many of the results that follow from them. In several different places (pages 118/9, 121, 159) gamma makes an unannounced transformation to g, presumably as a result of some kind of font problem in the production process. Similar problems beset Figure 3.25 and one or two of the other figures. Another kind of gremlin seems to have been at work in some of the summaries; what should have been neatly stacked equations and uniformly indented paragraphs have somehow become misaligned or disarrayed. Other problems, more clearly of the author's own making, result from the decision to use the symbol p4 to indicate an energy-momentum four-vector, and from the rather old fashioned practice of using ict, rather than ct, as the zeroth component of the position four-vector. All of these problems are quite minor, but they are of just the sort that might confuse algebraically timorous students who half expect that relativity will be incomprehensible. Despite its production problems, Relativity is a well planned and well written book which I am pleased to own. I will recommend it to those who will not be confused by its misprints, and I hope that a corrected edition will eventually be published so that the book can achieve the full readership it deserves.

In the perspective to guiding undergraduate students on advanced topics in theoretical physics, this article approaches a brief study about some aspects of the Lorentz transformations. The two fundamental postulates of Einstein's Theory of Special Relativity (or special relativity) are explained. The detailed process of constructing the Lorentz transformations and in particular the transformations performed considering the rectilinear and uniform motion of a frame of reference in relation to the other along the x-axis direction are presented. Some consequences resulting from Lorentz transformations such as Length contraction, Time dilation and the Relativity of simultaneity are highlighted.

Chapter 3 adopts a more traditional approach to special relativity. Rather than using the k-calculus, it gives the standard derivation of the Lorentz transformations, working in non-relativistic units in which the speed of light is denoted by c, and restricting attention to two inertial observers S and S′ in standard configuration. As before, it shows that the Lorentz transformations follow from the two postulates, namely, the principle of special relativity and the constancy of the velocity of light. It then shows how these leave the distance between two ‘events’ in space-time invariant. This chapter also examines the key physical attributes of special relativity, namely length contraction and time dilation as well as the relativistic Doppler effect. The chapter also discusses uniform acceleration and the twin paradox.

The study of the emission, propagation, and reflection of balls leads to the mechanical ballistic law that applies to balls with and without mass. A natural extension of the ballistic law is to encompass massless entities such as light. According to the ballistic law, a ball or a light wavefront emitted by a source inherits the velocity of its source in the absolute frame. The ballistic law governs the kinematics of balls and light in inertial frames from the background of the absolute frame. The mathematical expression of the ballistic law gives the propagation velocity of a ball and light wavefront as the vector sum of the ball's or the light wavefront's velocity emitted by a source and the source's velocity. The ballistic law explains why the speed of light is a universal constant <mml:math display="inline"> <mml:mi>c</mml:mi> </mml:math> in any inertial frame in which a source and a mirror are at rest, the laws of physics have the same form in any inertial frame, and no experiment in such a frame can prove its motion. By understanding the kinematics of light, we can understand the multiple issues rooted in Lorentz's transformation and Einstein's special relativity. For example, the theory of special relativity misapplies the symmetry observed in some phenomena to two inertial frames. Thus, it duplicates a physics phenomenon from one inertial frame, considered stationary, to another. The Lorentz transformation confirms the speed of light <mml:math display="inline"> <mml:mi>c</mml:mi> </mml:math> in the moving and opposite direction of the inertial frame. Simultaneously, it varies in any other direction, converging to infinity. Lorentz's transformation has no length contractions or dilations as special relativity pretends. This study confirms the constancy of time passage in the universe and the variability of the propagation speed of light wavefronts in the absolute frame.

is a difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravita -tional fields [1], [2]. It means that astro-nauts return from space having aged less than those who remained on Earth; to the traveling party, those staying at home are living faster, while to those who stood still, their counterparts in motion lived at a slower rate. The theory predicts such behavior, and experiments have dem-onstrated it beyond doubt. The phenom-enon is due to differences in velocity and in gravity (and it is called time dilation because the moving clock ticks slower). The effect would be greater if the astro-nauts were traveling nearer to the speed of light (approximately 300,000 km/s). Both factors—gravity and relative veloc-ity—are the culprits and actually opposed one another.Albert Eintein’s theory briefly states [3], [4]:1) In special relativity (hypothetically, far from all gravitational masses), clocks that are moving with respect to an inertial system of observation run slower. This effect is described by the Lorentz transformation.2) In general relativity, clocks within a gravitational field (as in closer prox-imity to a planet) are also found to run slower.The first paper by Einstein, published in 1905, introduced the special relativity theory (SRT), and the second one, pub-lished in 1916, dealt with the much more difficult general relativity theory (GRT).The Lorentz transformation (named for Hendrik Antoon Lorentz, 1853–1928) explains how the speed of light is indepen-dent of the reference frame. Lorentz shared the 1902 Nobel Prize in Physics with Pieter Zeeman (1865–1943) for the discovery and theoretical explanation of the Zeeman effect (the splitting of a spectral line into several components in the presence of a static magnetic field). The transformation describes how measurements of space and time by two observers are related, reflect-ing the fact that observers moving at dif-ferent velocities may measure different distances and elapsed times. It was derived well before special relativity.The first postulate of the TR, or prin -ciple of relativity, states that the laws of physics are the same in all inertial frames of reference. The speed of light