Constancy of Speed of Light in Inertial Frames

The Frontiers Collection, 2009

It is shown that the complete description of the propagation of light in a gravitational field and in non-inertial reference frames in general requires an average coordinate and an average proper velocity of light. The need for an average coordinate velocity of light in non-inertial frames is demonstrated by considering the propagation of two vertical light rays in the Einstein elevator (in addition to the horizontal ray originally discussed by Einstein). As an average proper velocity of light is implicitly used in the Shapiro time delay (as shown in the Appendix) it is explicitly derived and it is shown that for a round trip of a light signal between two points in a gravitational field the Shapiro time delay not only depends on which point it is measured at, but in the case of a parallel gravitational field it is not always a delay effect. The propagation of light in rotating frames (the Sagnac effect) is also discussed and an expression for the coordinate velocity of light is derived. The use of this coordinate velocity naturally explains why an observer on a rotating disk finds that two light signals emitted from a point on the rim of the disk and propagating in opposite directions along the rim do not arrive simultaneously at the same point.

A reanalysis of the effect of a moving frame of reference on the Maxwell's equations of light is done, showing that the null result of the Michelson-Morley's experiment of 1887 on the possibility of detecting the variation of the velocity of light with respect to a moving observer, i.e., therefore with no need of new ad hoc hypotheses to explain it in the classical framework. In fact, it will be shown that behind those equations is hidden the fascinating phenomenon of the absolute motion. (This is an old paper which I did not succeed in publishing 20 years ago and since then has been dismissed, but I hope somebody else can have some fun in reading it.) 1 Such an Aristotelian formula was condemned even in the Greek Antiquity as representing a naïve thought and this adoption by the Catholic Roman Church led to the anti-scientific minded Middle Age .

Henok Tadesse

A new model and theoretical framework of absolute motion and the speed of light is proposed in this paper. 1. For absolutely co-moving light source S and observer O, with uniform rectilinear motion, the effect of absolute motion is to create an apparent change in the position of the source relative to the observer. The apparent source, just as the real source, is at rest relative to the observer and the speed of light is constant relative to the apparent source. Therefore, the procedure of analysis of a light speed experiment in this case is to replace the real source by an apparent source and analyze the experiment by assuming that the speed of light is constant relative to the apparent source. Once the real source is replaced with an apparent source to account for absolute velocity, we assume emission theory in which the group velocity of light is constant relative to the (apparent) source and depends on mirror velocity. The position of the apparent source is determined by assuming the ether to calculate the time delay of light emitted by the source and detected directly by the observer and interpreting the change in time delay as being due to an apparent change in the source position relative to the observer, rather than as being a result of varying speed of light which would be the case if the ether existed. In this paper it is revealed that the ether doesn't exist but absolute motion does exist. 2. For all other cases/experiments in which the light source S, an observer A and mirrors have independent, arbitrary absolute and relative velocities, for uniform rectilinear motion and for accelerated motion, including rotation, the experiment is analyzed according to the following principle: an observer A who is at a given point relative to the light source, at a given instant of time, observes what a co-moving observer at that point is observing at that instant of time. A co-moving observer O is defined in this paper as an observer who is at a given point in the reference frame of the source at the instant of light emission and continues to move with the same velocity (magnitude and direction) as the velocity of the source at the instant of light emission. For example, to determine the time instant when light emitted by a source is observed by an arbitrary observer (A) with known initial position and motion (velocity and acceleration) at the instant of light emission, we find a point relative to the source where a co-moving observer O at that point observes light at the time instant that observer A is passing through that point. 3. The phase velocity of light is constant, independent of source, observer and mirror velocity. The group velocity of light is independent of source absolute velocity, but depends on observer absolute velocity and on mirror velocity. 4. A new law of Exponential Doppler effect of light is proposed as: λ' = λ eV/c and f ' = f e - V/c , where V is the source observer relative velocity. 5. Light has dual natures: local and non-local, constant (phase) velocity and variable ( group) velocity, behaving according to both ether (wave) theory and emission (particle) theory. Static electric and magnetic fields also have dual nature: finite and infinite speed of transmission 6. Inertia is electromagnetic radiation reaction. The speed of light is the universal limit on absolute velocities of all physical objects in the universe. The mass (inertia) increase of electrons with velocity is due to non-linear law of electromagnetic radiation power and radiation reaction. As the absolute velocity of a body approaches the speed of light, any further acceleration will result in or require increasingly infinite amounts of radiation power and radiation reaction. 7. Gravity is a difference between electrostatic attraction and repulsion forces. 8. Absolute velocity of an object is the resultant of its mass weighed velocities relative to all massive objects in the universe. The universal principle that applies to all light speed experiments is : an observer at a given point relative to the source, at a given instant of time , observes the same light phenomenon being observed by a co-moving observer at that point, at that instant of time. A co-moving observer is an observer that continues to move at the same velocity the source had at the instant of light emission. However, a more convenient procedure for experiments involving rectilinear motions is : 1. Replace the real source by an apparent source 2. Determine the velocity of the apparent source relative to the observer 3. Analyze the experiment by assuming that the speed of light is constant relative to the apparent source; i.e. once the real source is replaced by an apparent source , we apply (modified) emission theory in which the group velocity is constant relative to the apparent source and depends on mirror velocity, but the phase velocity is always constant. Physically ( intuitively ) the group velocity ( magnitude and direction) of light varies relative to the real source, due to absolute motion of the source. AST is a modified emission theory, a fusion between emission theory and ether theory. In the Sagnac experiment, the source appears farther away than its physical distance when looking in the backward direction and closer than its actual/ physical distance in the forward direction, relative to the detector. Physically this means that the velocity of light is c + Vabs in the backward direction and c - Vabs in the forward direction, relative to the source , hence a fringe shift at the detector. In the case of the Michelson-Morley experiment, an apparent change in the position of the light source relative the detector does not create a fringe shift, for the same reason that an actual ( physical ) change of the source position doesn't create any significant fringe shift. The group velocity of light relative to the source moving with absolute velocity Vabs is c - Vabs in the forward direction and c + Vabs in the backward direction. Therefore, the velocity of light relative to a stationary observer will be: (c - Vabs ) + Vabs = c and (c + Vabs ) - Vabs = c . The (group) velocity of light changes relative to the source in such a way that it will not be affected by source velocity.

The invariance of the speed of light in all inertial frames is shown to be an inevitable consequence of the relativity principle of special relativity contrary to the view held by Hsu and Hsu in taiji relativity where the speed of light is no longer a universal constant.The present approach is not only new but also much simpler than the existing approaches.

viXra, 2015

To this date, there is no known existing theory of the speed of light that can explain the many contradictory experimental evidences within the same theoretical framework. For example, no existing theory of light, including ether theory, emission theory and Special Relativity (SRT) , can explain even three of the conventional experiments: the Michelson-Morley experiment, the Sagnac effect and moving source experiments, within the same theoretical framework. A new theoretical framework has been developed by this author that can resolve the apparent contradictions in the light speed experiments. The new theoretical framework consists of two theories: Apparent Source Theory ( AST ) and Exponential Doppler Effect of light ( EDE). According to AST, the effect of absolute motion for inertially co-moving light source and observer is to create an apparent change in position (distance and direction) of the source relative to (as seen by) the observer/detector. In the case of the Michelson-Mo...

Henok Tadesse

This author has already proposed a new theory, Apparent Source Theory (AST), that can explain the Michelson-Morley experiment, the Sagnac effect, the Silvertooth experiment, the Roland De Witte experiment, the Venus planet radar range data anomaly (analyzed and reported by Bryan G Wallace) and other experiments. According to AST, there will be an apparent change in position of a light source as seen by the observer, for absolutely co-moving source and observer. The 'null' result of the Michelson-Morley experiment (MMX) is explained as follows. The effect of absolute motion is just to create an apparent change in position of the light source relative to the detector. There will be no (significant) fringe shift in the MMX for the same reason that there will be no (significant) fringe shift if the source position was actually, physically shifted slightly. The fringe shift in Sagnac effect is explained as follows. The source will be apparently shifted away relative to the detector when looking in the backward direction and shifted towards the detector when looking in the forward direction, hence creating a path difference. Einstein's thought experiment ('chasing a beam of light') is re-interpreted and used as one of the foundational arguments in this paper. The new interpretation is that it is the phase velocity of light that is always constant irrespective of source, observer and mirror velocity. The group velocity behaves in a more conventional way: it is independent of source (absolute) velocity but depends on observer and mirror velocity. For an observer moving near the speed of light away from a light source, the phases will still move past the observer at the speed of light while the group will be at rest relative to the observer. The new theoretical framework consists of two theories: 1. Apparent Source theory 2. Exponential Doppler Effect of light theory. The results of many light speed experiments can be derived from these two theories. Apparent Source Theory determines the phase and group delay of light, whereas Exponential Doppler Effect theory determines the frequency/wavelength of light.

Concepts from the special theory of relativity are widely held, including time dilation theory, perceived to have experimental confirmation, and believed to have no disproof from well controlled prospective experiments. Demonstrated here is that although relativity for light is special, in being an entity always traveling at fixed speed in the propagation direction from its source coordinate, the notion that time "dilates" for objects in motion was an unfortunate extrapolation: (1) An element is derived, missing from the original analysis, which demonstrates that for bodies in motion, the time required to be illuminated differs compared with that in the absence of motion, but absolute time itself does not "dilate." The times required for a moving rod and for a stationary rod are identically calculated by both an observer in motion and one stationary. (2) Experiments with laser light sources, observed while the earth revolves and orbits and produces variable lateral source velocity, demonstrated that light pulses shift laterally along with the source and target while propagating at speed c to intercept the target. Pulses have a lateral velocity imparted by the orbiting earth, a necessary finding to understand special relativity. Examples are provided that clarify thought experiments commonly presented in Physics texts, and (3) intrinsic properties of light photons, such as self propagation, intrinsic speed, and relative velocity, are discussed. Les concepts issus de la théorie de la relativité restreinte, et notamment la théorie de la dilatation du temps, sont largement acceptés et sont considérés comme ayant été confirmés expérimentalement sans possibilité d'être invalidés par des expériences contrôlées. Nous démontrons ici que malgré le caractère spécial de la relativité pour la lumière, s'agissant d'une entité qui voyage toujours à une vitesse constante dans la direction de propagation à partir de sa coordonnée source, la notion que le temps se 'dilate' pour des objets en mouvement était une extrapolation malheureuse: 1) On déduit un élément, manquant dans l'analyse initiale, qui démontre que pour les corps en mouvement, la durée d'illumination nécessaire change par rapport à l'absence de mouvement mais que le temps absolu lui-même ne se 'dilate' pas. Les durées nécessaires pour une tige en mouvement et une tige stationnaire sont calculées avec un observateur en mouvement et un observateur stationnaire. 2) Des expériences avec des sources de lumière laser, observées pendant que la Terre tourne sur elle-même et autour du soleil en créant ainsi une source de vitesse latérale variable, ont démontré que les impulsions lumineuses étaient latéralement décalées comme la source et la cible tout en voyageant à la vitesse c pour intercepter la cible. Les impulsions ont une vitesse latérale communiquée par la révolution de la Terre, un résultat nécessaire pour comprendre la relativité restreinte. Des exemples sont fournis afin de clarifier des expériences de pensée couramment présentées dans des ouvrages de physique. 3) Enfin, les propriétés intrinsèques des photons, telles que l'auto-propagation, la vitesse intrinsèque et la vitesse relative, sont discutées.

Henok Tadesse

Albert Einstein was right when he proposed the constancy of the speed of light regardless of motion of the source and motion of the observer. The constancy of the speed of light follows directly from the non-existence of the ether. However, Einstein"s principle of relativity of space and time, which was derived from the light postulate and the principle of relativity, was wrong because: 1. it led to many paradoxes, and 2. absolute motion has been detected in other experiments. Special relativity was therefore a wrong interpretation of the light postulate. This paper provides a new insight that reveals the deep mystery underlying the many mutually contradicting light speed experiments. The new theory, known as Apparent Source Theory, states that the speed of light is constant and absolute motion exists at the same time. The speed of light is fundamentally constant relative to the observer but appears to be variable when measured. At the heart of Apparent Source Theory is the (one-way and two-way) constancy of the speed of light regardless of motion of the source, motion of the observer, motion of the mirror, for uniform velocity or acceleration.

"The Special Theory of Relativity postulates that the velocity of light would always be invariant at 186,000 miles per second at all inertial frames. The paper examines this aspect of the Theory."

Henok Tadesse

In this paper, a new theoretical framework for absolute motion and the speed of light is presented. The new theoretical framework consists of two parts: 1. Constancy of phase velocity of light 2. Apparent Source Theory. The theory of constancy of phase velocity of light is a consequence of non-existence of the ether. Thus the phase velocity of light in vacuum is always constant c, irrespective of absolute or relative motion of the light source, the observer and the mirror, for uniform or accelerated motions. The constancy of phase velocity of light leads to a new Exponential Doppler Effect of light: f ' = f e V/c and λ' = λe-V/c , which fulfills the constant phase velocity condition : f ' λ ' = f e V/c λe-V/c = f λ = c. The Exponential Doppler Effect theory can also explain the Ives-Stilwell experiment. The Michelson-Morley disproved the ether hypothesis but failed to detect absolute motion, which was decisively detected by the Silvertooth experiment, in combination with the NASA CMBR anisotropy experiment. Absolute motion is not motion relative to the ether. According to Apparent Source Theory, the effect of absolute motion is to create an apparent change in the point of light emissionrelative to an inertial observer, in the reference frame of an absolutely moving inertial observer. In the case of the Michelson-Morley experiment, an apparent change in point of light emission relative to the observer/detector will create only a small fringe shift for the same reason that an actual/physical change in the source position (actual change in point of light emission) will result only in a small fringe shift. This is the small fringe shift observed in the original Michelson-Morley experiment and in the Miller experiments. A profound prediction of Apparent Source Theory regarding the phenomenon of stellar aberration is that the apparent change in star position in not in the same direction as the observer's velocity, but in the opposite direction ! Thus, an observer in absolute motion needs to tilt his telescope backwards, not forward, to see star light.A formulation of Apparent Source Theory for a non-inertial observer is also presented. For a non-inertial observer/detector, the light speed experiment is analyzed based on thefollowing principle.An imaginary inertial observer is assumed who will be at the same point and moving with the same velocity as the instantaneous velocity of the real accelerating observer at the instant of light detection. In other words, the real accelerating observer and the imaginary inertial observer will detect the light at the same point in space, simultaneously, while moving with the same instantaneous velocity.This general formulation ofApparent Source Theory is applied to analyze the Sagnac effect. The Sagnac effect is shown to be an acceleration effect, not an absolute motion effect. Apparent Source Theory is also applied to static electric, magnetic and gravitational sources. A qualitative analysis of Mercury perihelion advance is presented.It is proposed that magnetic field is a form of electric field as described by Weber's formula for electrostatic force between two charges.Weber's formula, which is a modification of Coulomb's formula, is adopted and combined with Apparent Source Theory, which may explain all electromagnetic phenomenon.Analogous Weber's formula for gravitation, which is a modification of Newton's law of gravitation, might solve some of the outstanding problems in physics, such as dark matter, dark energy and Pioneer anomaly. 2