Postulates of Special Relativity Need to be Supplemented for Wigner Thomas Rotation to Exist

Tam Hunt, UC Santa Barbara, tam.hunt@psych.ucsb.eduThe Lorentz transformations form the mathematical core of the 1905 theory of Special Relativity as well as the earlier version of relativity created by Lorentz himself, originally in 1895 but developed further in the ensuing years. These two theories interpret the physical significance of the transformations quite differently, but in ways that are generally not considered to be empirically distinguishable. It is widely believed today that Einstein’s Special Relativity presents the superior interpretation. A number of lines of evidence, however, from cosmology, quantum theory and nuclear physics present substantial evidence against the Special Relativity interpretation of the Lorentz transformations, challenging this traditional view. I review this evidence and suggest that we are now at a point where the sum of the evidence weighs against the Special Relativity interpretation of the transformations and in favor of a Lorentzian or neo-Lorentzian approach instead.1. IntroductionI’m sitting in a public square in Athens, Greece, biding my time as I write these words. The battery on my phone ran out as I was trying to navigate to my lodgings on my first night in this historic city, forcing me to stop and charge my phone for a little while. I’m waiting for the passage of time.The nature of time has been debated vigorously since at least the age of Heraclitus and Parmenides in ancient Greece. “All things flow,” said Heraclitus. “Nothing flows,” said Parmenides as a counter-intuitive rejoinder, suggesting that all appearances of change are an illusion. How could Parmenides make the case that nothing flows, nothing changes? It would seem, from easy inspection of the world around us that indeed all things do flow, all things are always changing. So what was Parmenides talking about?Parmenides’ arguments illustrate well the rationalist approach that Plato was later to more famously advocate, against the empiricist or “sensationist” approach that Heraclitus and Aristotle too would champion as a contrary approach. Parmenides and Plato saw reason as the path toward truth and they were not afraid to allow reason to contradict what seemed to be obvious sensory-based features of the world. Apparent empirical/sensory facts can deceive and, for these men, Parmenides, Plato and their followers, reason alone was the arbiter of truth. Wisdom entailed using reason to see through the world’s illusions to the deeper reality.Heraclitus and Aristotle, to the contrary, stressed the need to be empirical in our science and philosophy (science and philosophy were the same endeavor in the era of classical Greece). Reason was of course a major tool in the philosopher’s toolbox for these men too, but it seems that reason unmoored from evidence should not be used to trump the obvious facts of the world. The Aristotelian approach is to find a pragmatic balance between empirical facts and reason in attempting to discern the true contours of reality.Einstein was firmly in the camp of Parmenides and Plato (Popper, et al. 1998). He famously considered the passage of time, the distinction between past, present and future, to be a “stubbornly persistent illusion.” This view of time, as an illusory construct hiding a deeper timeless world, was based on his theories of relativity. Einstein and his co-thinkers held this view, of time as illusory, despite the obvious passage of time in the world around us, no matter where we look. The widely-held view today is that Einstein finally won the long war, decisively, between Heraclitus and Parmenides. Despite appearances, nothing flows and the passage of time is just that: only appearance.I suggest in this paper, however, that this conclusion is premature. Einstein’s thinking is indeed an example of rationalism trumping empiricism and it is time for us to take a more empirical approach to these foundational questions of physics and philosophy. Today’s physics lauds empiricism rhetorically, but in practice a rationalist approach often holds sway, particularly with respect to the nature of time.2. An overview of Special Relativity and Lorentzian RelativityIn discussing the nature of time with respect to modern physics, I will focus on the Special Theory of Relativity (SR) and avoid discussion of the general theory. Einstein’s 1905 theory of relativity adopted the Lorentz transformations directly, unchanged from Lorentz’s own version of these equations (Einstein 1905, Lorentz 1895 and 1904, in Lorentz 1937). Einstein’s key difference from Lorentz’s version of relativity (first put forth in 1895, but developed further in later work) was to reinterpret Lorentz’s equations, based on a radically different assumption about the nature of physical reality. Lorentz interpreted the relativistic effects of length contraction and time dilation—which follow straightforwardly from the Lorentz transformations—as resulting from interaction with an ether that constituted simply the properties of space (Lorentz’s ether was not some additional substance that pervades space, as was the case in some earlier ideas of the ether). Einstein, to the contrary, interpreted these effects as resulting from the dynamics of spacetime, a union of space and time into a single notion, and dismissed the ether as “superfluous.”Because Lorentz’s and Einstein’s versions of relativity both use the Lorentz transformations, they will yield in many cases the same empirical predictions. The prevailing view today, then, is that while these two theories are empirically indistinguishable there are other considerations, relating to parsimony primarily, that render special relativity the preferred approach. I discuss below, however, why we now have good empirical reasons to distinguish between these two interpretations—in favor of the Lorentzian approach.Length contraction and time dilation occur as a result of the assumed absolute speed of light because either space or time, or both, must distort if we consider the speed of light to be invariant. This is because speed is measured simply by dividing distance traveled by the time elapsed; and if the speed of light remains the same in all circumstances then space and/or time must distort in order to maintain this invariance. As an object travels closer and closer to the speed of light, its length must decrease (length contraction) and/or the time elapsed must increase (time dilation) – but only from the perspective of an observer in a different inertial frame. In the original inertial frame there is no length contraction or time dilation.“Moving clocks run slow” is a good shorthand for relativistic time dilation, but again only from the perspective of a different inertial frame. Time moves at the same rate for an observer in the moving frame of reference, no matter what one’s speed in relation to other frames. Relativistic effects only occur when considering the relationship between two different frames of reference, not in the same frame.

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.

Before explaining how the God’s-eye view resolves the impasse of theoretical physics and foundations of physics created by the ant’s-eye view, the book presents a detailed argument for the block universe. Accordingly, the main thread of chapter 2 shows how the relativity of simultaneity resolves the paradoxes associated with time dilation and length contraction that result from special relativity. A short argument is then presented showing how the relativity of simultaneity implies a block universe, that is, the co-reality or co-existence of the past, present, and future. Philosophy of Physics for Chapter 2 provides a detailed argument for block universe, taking into account all counterarguments and assumptions of the abridged argument in the main thread. Foundational Physics for Chapter 2 shows how the second postulate of special relativity leads to time dilation and length contraction, and it contains the Lorentz transformations for the spacetime events used in the main thread.

A rank-two tensor is built out of the 4-velocities of two inertial observers, which corresponds precisely to the most general Lorentz matrix connecting the two Cartesian frames of the observers. The Lorentz tensor is then factorized as the product of two ’’complementary’’ space-time reflections. It is shown that the first tensorial factor performs the very essential tasks (i.e., FitzGerald contraction and time dilation) of the corresponding Lorentz transformation, while the second factor is just an internal reflection performed in one and the same intertial frame. Thus, in its essential features, a Lorentz transformation between two different inertial frames obtains upon performing just one space-time reflection. It is also shown that the (same) Lorentz tensor of the two inertial observers can be factorized into ’’complementary’’ reflections either by two hyperplanes with spacelike normals, or else by tow hyperplanes with timelike normals, which geometric meaning is rather simple. An application of the presented formalism to Dirac’s 4-spinor transformation law is also briefly discussed.

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.

Our mind seems to be formatted to imagine a “motionless” material particle (or more accurately a region of spacetime at rest relative to that material particle) fixed in space as an absolute reference and to consider the existence of space and time as independent universal entities, as we perceive when we measure them with a ruler and a clock, respectively. Instead, let us first hypothesize that singularities are the absolute reference for the universe, that the speed of light in vacuum ( c = 299 792 458 m/s) is universal and absolute, and that deceleration/acceleration is the “driving force” that defines spacetime. Frames of reference anchored on material particles/objects may be grouped as having zero acceleration (inertial frames), nonzero, constant acceleration (pseudoinertial frames) or nonzero, variable acceleration (noninertial proper frames), so that a noninertial proper frame may be considered as composed of an infinite number of pseudoinertial frames. The universality of c is ensured by its absolute constancy, when both observer and moving beam of photons are in frames of reference differing neither in speed nor in acceleration, as is the case within inertial or pseudoinertial frames, respectively. However, its value (as that of any other speed) is measured as different when the observer is at an inertial or pseudoinertial frame and the beam of photons is moving in another, thus differing in Lorentz factor ( γ ) or acceleration, respectively. Speed, velocity, and acceleration (including the effect of gravity on a material particle/object) are all defined in terms of space and time. However, space and time do not exist as independent universal entities, as they are integral components of one and the same inextricable physical entity, spacetime. Assuming spacetime forms a continuum, it is expected that anything affecting one will affect the other. This has been widely recognized for gravity, but not for speed—something which becomes clearer if we assume that it should in fact be acceleration/deceleration that moves a material particle from one frame of reference into another. Several conditions that are grouped under gravity-dependent and non-gravity-dependent act individually or in combination to submit a matter particle to acceleration. Therefore, when perceived from the Earth (or any other place at v < 299 792 458 m/s), any departure from c caused by deceleration should expand space and contract time. Any further deceleration or subsequent acceleration (for as long as v < c ) will alter spacetime. Hence, in astrophysics, deceleration rather than acceleration should be the main driving or direct physical quantity. It is proposed that any deceleration/acceleration distorts spacetime. A method to combine the effects of several conditions that define the acceleration status of a material particle in spacetime is proposed. The higher v / c and/or gravity-dependent acceleration, the greater time dilation and space contraction will be. At the singularity, time dilation and space contraction will be maxima. The actual “position” of a material particle in spacetime may therefore be defined by the sum of all changes it suffered in deceleration/acceleration (due to changes in gravity-dependent and non-gravity-dependent accelerations) since the singularity. The impossibility of exceeding the speed of light in vacuum is discussed and tentatively demonstrated. In line with the present hypothesis, both time and space are relative, but only partially due to the limits imposed by c , opening the possibility for the concept of spacetime partial relativity. According to our proposal, spacetime is defined by a special form of deceleration, which we have termed relativistic or Lorentz deceleration: it is a deceleration-dependent elastic property of any matter particle moving at v < c . It expands/contracts precisely because of the effect of deceleration/acceleration on matter particles moving at v < c . According to these views, defining a singularity should depend on the perspective. When perceived from the Earth or any other place at v < c , a singularity is a spaceless point of infinite density, associated with the speed of light and where a second lasts forever. However, when “perceived” from within a singularity, space is there and time flows. Based on this work, a singularity may be defined in higher detail as the embryonic state of the universe (or a part of it), associated with two universal absolute constants: the speed of photons ( c = 299 792 458 m/s) and the quantity of spacetime. It also corresponds to a standard spacetime condition, in which time is dilated and space contracted to maximum values. The Big Bang is interpreted not as an explosion or bang, but rather as an infinitesimal deceleration from the singularity, thus triggering the initial exponential space expansion and time contraction and leading to matter formation. Neither space nor time are created or destroyed—They are always there since the singularity but vary widely in contraction/expansion magnitude with each precise spacetime condition, as deceleration-dependent fluctuations take place in spacetime. Gravity, an inherent property of matter, and entropy are key players in the subsequent evolution of the universe. Uncountable successive and cumulative changes in deceleration suffered by material particles determine the precise conditions they occupy at each moment in spacetime, thus allowing the build-up of a gigantic and highly dynamic noninertial frame of reference, i.e., our universe. Individual observers at single points of the universe should all see light photons moving in vacuum at 299 792 458 m/s (or any material particle/object moving at v < 299 792 458 m/s) and perceive space and time identically, each within their own spacetime condition. Differences arise only when one observer “looks” at other observers in distinct spacetime conditions. An attempt is made to interpret spacetime and light when we “look” at frames of reference distinct from our own, since this is precisely what we “see” when we observe the universe from the Earth. Cosmological models are typically based on several assumptions. The hypothesis formulated in the present article is no different, with a singularity as its major reference. We conceptualize on a cosmological model that challenges some currently accepted views of the universe.

Akin to the wave–particle duality in the microscopic world, relativity between observers coexists with the absoluteness of the coordinate system in an inertial system. This duality can be checked by rulers and clocks used in stationary and constantvelocity systems. The light and atomic clocks used in these systems establish relativity between observers, whereas rigid rulers (which can be used only in stationary systems) establish the absoluteness of the coordinate system. This relativity– absoluteness coexistence is known as relative absoluteness. In the relative absolute theory, the Lorentz transformation and its inverse are based on three axioms: the unchanging structure of rigid rods, the law of the periods of atomic clocks, and the constancy of light speed. The relativity of physical laws cannot be an independent axiom because it is established due to the law of invariance of the speed of light. Examples of interobserver relativity include the direction and inverse cosine of light, velocity addition, and the results of the Michelson–Morley experiment. Examples of absoluteness in coordinate systems include the twin paradox, normal direction of a reflecting mirror, and results of electrostatic force experiments. As light moves by proximity, its direction and time change gradually according to changes in the gravitational field, but it is received as if it came from an origin that is momentarily stationary with respect to the observer in an inertial frame. The stationary and constant-velocity systems observe the same acceleration and inertial force acting on the charge, but different electromagnetic and mechanical accelerations and different acceleration and inertial masses. Because the speed of a charge accelerated by an electromagnetic force in a stationary system experiences an increasing inertial force, it cannot exceed the speed of light.

Light Speed in vacuum, instead of being a constant, it changes with those observers moving at different speeds and directions with respect to light origins. Time, on the other hand, instead of moving slower with the traveler, it always keeps the same rate. These facts disagree with Einstein’s Special Relativity. Light speed in vacuum is a constant only if it is observed from light origins and those positions in stationary with light origins in Absolute Space System. This is because the emission of a Yangton and Yington circulation pair (Wu’s Particle or Still Photon) from the surface of a matter (String Structure or Higgs Boson) to form a free photon traveling in vacuum is a Non-Inertia Transformation and it only requires a small fixed amount of Force of Separation. Since light speed is not a constant to those observers moving at different speeds and directions with respect to light origins, Velocity Time Dilation derived from Einstein’s Special Relativity is not true and could never exist. Absolute Space System, Vision of Light and Non-Inertia Transformation are introduced to explain the relationships between Space, Time and Relativities. Doppler Effect, Blue Shift and Red shift are due to the Non-Inertia Transformation of light emission. Length contraction is caused by the difference of Visions of Light instead of Velocity Time Dilation. In an Inertia System, because of the same Visions of Light, the same light speeds in vacuum can be observed by all observers. Furthermore, Michelson - Morley Experiment proves that for two split light beams traveling in vacuum, the same light speeds can also be observed. Time is the measurement of the cycles of a fundamental process from start to end of an event. Both time and light speed at large gravitational field have relatively slower rates, which may be caused by the longer period and lower frequency of Yangton and Yington circulation due to the influence of large gravitational field. This agrees well with Gravitational Time Dilation in Einstein’s General Relativity.

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.

Criticism of the Sadeh experimental evidence for the second postulate of special 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.

In this paper the Lorentz Transformation is shown to be merely a set of restricted equations stemmed from the Galileo transformation applied to a particular conversion reflecting the theorized principle of the speed of light invariance implemented in the direction of the relative motion between the inertial reference frames. Consequently, the Lorentz transformation is shown to be restricted to time and longitudinal space coordinate values different from zero. The deduction of the time dilation and length contraction becomes unfeasible under such restrictions. It follows that the Lorentz transformation possesses no other effects than mathematically expressing the speed of light postulate in the relative motion direction; that is, the coordinate of the tip point of a light ray traveling in the direction of the relative motion, given by x=ct in the “stationary” frame, is transformed to x'=ct' with respect to the “traveling” frame, with c being the light speed in empty space. Furthermore, the application of the Lorentz transformation to events having restricted coordinates is shown to result in mathematical contradictions.

The Lorentz transformation (LT) makes three predictions which are not consistent with one another: Lorentz-FitzGerald length contraction (FLC), time dilation (TD) and light-speed equality for observers in relative motion to one another. The LT also stands in violation of the Law of Causality because it fails to recognize that inertial clocks can never change their rate spontaneously. Einstein’s light-speed postulate (LSP) is shown to be unviable by considering a case in which a light source passes by a stationary observer at the same time that it emits a light pulse in the same direction. It is found that, in contradiction to the LSP, that the classical velocity (Galilean) transformation (GVT) is applicable when two observers in relative motion deduce the speed of a light wave. The Newton-Voigt transformation (NVT) is consistent with the Law of Causality because it assumes space and time do not mix. The NVT is nonetheless consistent with the relativistic velocity transformation (RVT) and also with Einstein’s mass-energy equivalence relation E=mc2. The ratio Q of clock rates for two inertial rest frames S and S’ is required input for the NVT. Experimental data obey the Universal Time-dilation Law (UTDL) which states that the measured time Δt obtained by a inertial clock for a given event is inversely proportional to γ(v)= (1-v2c-2)-0.5v, where v is the speed of the clock relative to a specific rest frame referred to as the objective rest frame ORS. The value of Q when the clock of the observer in at rest in S while that of another observer is at rest in the object’s rest frame S’ is obtained from the UTDL as the ratio γ(v’)/γ(v). The Uniform Scaling method considers Q to be a conversion factor between the units of time in the two rest frames. It is found that the conversion factors for all other physical properties are integral multiples of Q. Kinetic scaling of the properties insures that the laws of physics are the same in each inertial frame, as required .........

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.

The Lorentz transformations between the space-time coordinates of a point in two inertial frames with arbitrary relative velocity, are reformulated as Galilei transformations with length and time contractions, by introducing the ether rest frame (in which light signals propagate isotropically with the vacuum speed of light). The generalized Galilei transformations for the (longitudinal) space coordinates (x1,2) and the time variables (t1,2) of a point in two inertial frames ∑1,2 are not only of analogous structure, but have remarkable symmetry properties, too. The appearing length and time contractions are absolute effects in the sense of Lorentz-Fitzgerald, i.e., a rod has its largest length and a clock its fastest rate when at rest in the ether frame ∑0. Thus, an analytical reformulation and a physical interpretation of the Lorentz transformations within Galilean relativity physics is achieved.