A New Way of Teaching the Special Theory of Relativity

American Journal of Physics, 2009

This paper explores the evolution of Einstein's understanding of mass and energy. Early on, Einstein embraced the idea of a speed-dependent mass but changed his mind in 1906 and thereafter carefully avoided that notion entirely. He shunned, and explicitly rejected, what later came to be known as "relativistic mass." Nonetheless many textbooks and articles credit him with the relation E = mc 2 , where E is the total energy, m is the relativistic mass, and c is the vacuum speed of light. Einstein never derived this relation, at least not with that understanding of the meaning of its terms. He consistently related the "rest energy" of a system to its invariant inertial mass.

2021

It is well-known that Einstein’s first attempt to explain E = mc2 which was published in Annalen der Physik in 1905, has been criticized as problematic. In particular, it has been shown by Ives and reiterated by Jammer that it suffers from the error of circular reasoning. Attempts have been made in the scientific literature to discount the circular reasoning objection of Ives, Jammer, Arzelies and others. Fritz Rohrlich in 1990 gave a remarkably simple and concise derivation of E = mc2 along lines similar to Einstein’s but based on both momentum and energy conservation, in contrast to Einstein’s which uses only energy considerations. Rohrlich’s approach using momentum conservation is an alternative to Einstein’s, which is free from objection in logical error, and we make it quite clear on the importance of the implicit assumption of momentum conservation in any attempt to refute the circular reasoning error in Einstein’s paper. It is our contention that this point is overlooked or a...

American Journal of Physics

An extensive review of Einstein's theory of special relativity and his writings from today's scientific and philosophical perspectives found that at the turn of the 20th century, the scientific and philosophical views were not sufficiently developed to understand the problems that physicists faced and that Einstein tried to solve with his theory. Regardless how brilliant a scientist he was, in his pursuit, Einstein was guided by incorrect philosophical views; views prevalent at that time. These views misled him into an incorrect method and unrealistic theory with circular definitions, inconsistencies in the explanations and principles that contradict those developed from the empirical evidence. In particular, this study found that neither Einstein nor Poincaré expressed sufficiently the " inertial frames of reference " (coordinate systems) in their respective relativity principles. They expressed them in terms of the uniform movement of translation instead of absence of external forces. Because of that they both overlooked that fields generated in one frame of reference cause forces at a distance in the other frames of reference turning them into noninertial ones. Thus, their respective principles of relativity cannot be valid for field-based processes when field is generated outside of the frame of reference. Einstein's use of his relativity principle for conditions when it cannot be valid, in combination with an incorrect idealistic ontological view of the term " Law of Nature " and insufficient rationalistic understanding of the term " time, " misled him into an incorrect method of developing his theory and to incorrect inferences of the other principles and concepts of this theory. Thus, the foundations of Einstein's theory of special relativity, his two postulates (principle of relativity and the invariance of velocity of light) as well as the relativity of simultaneity cannot be any longer justified. With that, Einstein's attempt to unify light and electro-magnetism with mechanics, his concept of light, space, time and the whole theory of relativity with its other consequences cannot correctly represent the realities of the physical world. Apart from the philosophical, conceptual and logical problems of this theory, the invariance of velocity of light is in serious need for the experimental verification or refutation. Although the technology of Einstein's time was insufficient to carry out such test, it is technologically feasible to do so today. Therefore, it is recommended, and it should be of the utmost importance, for physicists to carry out such a test today. V C 2014 Physics Essays Publication. [http://dx. Résumé: Un examen approfondi de la théorie de la relativité restreinte d'Einstein et de ses e ´crits, réalisé au travers des connaissances scientifiques et philosophiques actuelles, montre qu'a ` l'orée du 20 ième siècle, les visions scientifiques et philosophiques n'e ´taient pas suffisamment développées pour comprendre les problèmes auxquels les physiciens faisaient face alors quand Einstein essayait de les résoudre avec sa théorie. Quand bien même il fut un brillant scientifique, Einstein e ´tait guidé par une approche philosophique incorrecte, approche qui e ´tait courante a ` l'e ´poque. L'environnement philosophique d'alors l'a amené a ` développer une méthode incorrecte et une théorie irréaliste basée sur des assertions, des explications inconsistantes et des principes qui contredisent ceux développés a ` partir de l'e ´vidence empirique. Cette e ´tude montre, en particulier que ni Albert Einstein ni Henri Poincaré n'ont suffisamment approfondi les " référentiels inertiels " dans leurs respectifs principes de la relativité. Ils les ont définis par le mouvement de translation uniforme au lieu de les définir par l'absence de forces extérieures. Pour cette raison, ils ont tous les deux négligé le fait que des champs générés dans un cadre de référence provoquent des forces a ` distance dans les autres cadres de référence les transformant en noninertiels. Ainsi leurs respectifs principes de la relativité ne peuvent e ˆtre valides pour des processus basés sur le champ quand le champ est généré en dehors du cadre de référence. L'utilisation par Einstein de ses principes de la relativité dans des conditions qui ne peuvent e ˆtre validées, en combinaison avec une vision ontologique incorrecte et idéaliste du terme " Loi de la Nature " et une compréhension rationnelle a) [email protected] 0836-1398/2014/27(3)/411/37/$25.00 V C 2014 Physics Essays Publication 411 PHYSICS ESSAYS 27, 3 (2014) insuffisante du terme " Temps " , l'amenèrent a ` développer sa théorie au moyen d'une méthode incorrecte et tirer des conclusions erronées sur les autres principes et concepts de sa théorie. Ainsi, les bases de la théorie d'Einstein sur la relativité restreinte, ses deux postulats (principe de la relativité et l'invariabilité de la vitesse de la lumière) ainsi que la relativité de la simultanéité ne peuvent plus e ˆtre justifiés. Avec cela, la tentative d'Einstein d'unifier lumière et e ´lectromagnétisme avec la mécanique, son concept sur la lumière, l'espace, le temps et toute la théorie sur la relativité y compris ses autres conséquences ne peuvent pas représenter les réalités du monde physique. Mis a ` part les problèmes philosophique, conceptuel et logique de sa théorie, l'invariabilité de la vitesse de la lumière a un sérieux besoin d'une vérification ou réfutation expérimentale. Mais si la technologie au temps d'Einstein e ´tait insuffisante pour mener a ` bien un tel test, c'est techniquement faisable de nos jours. C'est pourquoi, il est conseillé aux physiciens, et c'est de la plus haute importance, de procéder a ` ce test aujourd'hui.

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 1998

Einstein's 1935 derivation of mass-energy equivalence is philosophically impor tant because it contains both a criticism of purported demonstrations that proceed by analogy and strong motivations for the definitions of the 'new' dynamical quantities (viz relativistic momentum, relativistic kinetic energy and relativistic energy). In this paper, I argue that Einstein's criticism and insights are still relevant today by showing how his derivation goes beyond Friedman's demonstration of this result in his Foundations of Spacetime ¹heories. Along the way, I isolate three distinct physical claims associated with Einstein's famous equation that are some times not clearly distinguished in philosophical discussions of spacetime theory.

If the mass-energy equivalence is introduced into the Newtonian dynamics, the altered formulae for inertia (inertial mass), force and acceleration, momentum and energy are obtained. All the mentioned quantities are in the function of the relative velocity of two bodies and they are essentially classical Newton's formulae for low velocities (the velocities significantly lower than the speed of light), while for high velocities (the velocities comparable with the speed of light) they are significantly different from classical Newton's formulae. The results of this paper show that STR (Special Theory of Relativity) is not correct. In addition, this paper has studied the mass and energy of photons and it has been shown that they also depend on the speed of two bodies (the body emitting photons and the body receiving photons) and on the relationship of the masses of these two bodies. Thus, photons with the same frequencies can have different speed, wavelength and energy depending on the Doppler Effect (which is in the function of speed of two bodies and the relationship of their masses). Copyright©2016, Mihailo M. Jeremić. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. INTRODUCTION The classical Newtonian dynamics uses the notion of mass which expresses the quantity of substance which is unique and independent of the body's speed [Newton, 1999]. Thus, for Newton, inertial mass m i which resists the change of motion is constant and equal to the quantity of substance m 0. This results from the premise that the inertial mass and the energy of the body are independent quantities and that the body which is relatively motionless (in relation to the reference body) has no energy. However, the studies of Lorentz [1904], Poincaré [1900] and others have shown that there is dependence between the total mass and total energy of the body, i.e. that the total mass has the energy equivalent and that the total energy has the mass equivalent, and that the body which is relatively motionless (in relation to the reference body) has energy. It is the " hidden " energy, the rest energy E 0 , equivalent to the body mass (the quantity of the substance), which would be released if the total body mass m 0 was turned into the electromagnetic radiation in the direction of the body's motion, into the photons with the speed c 0. When a body moves at the velocity of v, it also gains the kinetic energy E k , so the total energy of the body in motion E is the sum of the rest energy E 0 and kinetic energy E k. In accordance with the above mentioned, inertial mass, force, acceleration, momentum and energy are in the function of the body mass m 0 , the relative velocity of the body v and the speed of the emitted photons c 0. Since the photon reaching the reference body from another body which is in relative motion in relation to the reference body has different frequency from the emitted frequency (the Doppler shift) and different energy, and since the mass of the emitted photon (as the quantity of the substance) is unchangeable, and due to the fact that the photon's energy is in the function of its frequency and its speed, it means that the received photon has the speed different from the emitted photon, and it is in the function of changing the frequency (the Doppler shift), i.e. in the function of the relative velocity of the two bodies (emitter and receiver) and the relationship between their masses. ARTICLE INFO ABSTRACT If the mass-energy equivalence is introduced into the Newtonian dynamics, the altered formulae for inertia (inertial mass), force and acceleration, momentum and energy are obtained. All the mentioned quantities are in the function of the relative velocity of two bodies and they are essentially classical Newton's formulae for low velocities (the velocities significantly lower than the speed of light), while for high velocities (the velocities comparable with the speed of light) they are significantly different from classical Newton's formulae. The results of this paper show that STR (Special Theory of Relativity) is not correct. In addition, this paper has studied the mass and energy of photons and it has been shown that they also depend on the speed of two bodies (the body emitting photons and the body receiving photons) and on the relationship of the masses of these two bodies. Thus, photons with the same frequencies can have different speed, wavelength and energy depending on the Doppler Effect (which is in the function of speed of two bodies and the relationship of their masses). Copyright©2016, Mihailo M. Jeremić. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. INTRODUCTION The classical Newtonian dynamics uses the notion of mass which expresses the quantity of substance which is unique and independent of the body's speed [Newton, 1999]. Thus, for Newton, inertial mass m i which resists the change of motion is constant and equal to the quantity of substance m 0. This results from the premise that the inertial mass and the energy of the body are independent quantities and that the body which is relatively motionless (in relation to the reference body) has no energy. However, the studies of Lorentz [1904], Poincaré [1900] and others have shown that there is dependence between the total mass and total energy of the body, i.e. that the total mass has the energy equivalent and that the total energy has the mass equivalent, and that the body which is relatively motionless (in relation to the reference body) has energy. It is the " hidden " energy, the rest energy E 0 , equivalent to the body mass (the quantity of the substance), which would be released if the total body mass m 0 was turned into the electromagnetic radiation in the direction of the body's motion, into the photons with the speed c 0. When a body moves at the velocity of v, it also gains the kinetic energy E k , so the total energy of the body in motion E is the sum of the rest energy E 0 and kinetic energy E k. In accordance with the above mentioned, inertial mass, force, acceleration, momentum and energy are in the function of the body mass m 0 , the relative velocity of the body v and the speed of the emitted photons c 0. Since the photon reaching the reference body from another body which is in relative motion in relation to the reference body has different frequency from the emitted frequency (the Doppler shift) and different energy, and since the mass of the emitted photon (as the quantity of the substance) is unchangeable, and due to the fact that the photon's energy is in the function of its frequency and its speed, it means that the received photon has the speed different from the emitted photon, and it is in the function of changing the frequency (the Doppler shift), i.e. in the function of the relative velocity of the two bodies (emitter and receiver) and the relationship between their masses. ARTICLE INFO ABSTRACT If the mass-energy equivalence is introduced into the Newtonian dynamics, the altered formulae for inertia (inertial mass), force and acceleration, momentum and energy are obtained. All the mentioned quantities are in the function of the relative velocity of two bodies and they are essentially classical Newton's formulae for low velocities (the velocities significantly lower than the speed of light), while for high velocities (the velocities comparable with the speed of light) they are significantly different from classical Newton's formulae. The results of this paper show that STR (Special Theory of Relativity) is not correct. In addition, this paper has studied the mass and energy of photons and it has been shown that they also depend on the speed of two bodies (the body emitting photons and the body receiving photons) and on the relationship of the masses of these two bodies. Thus, photons with the same frequencies can have different speed, wavelength and energy depending on the Doppler Effect (which is in the function of speed of two bodies and the relationship of their masses). Copyright©2016, Mihailo M. Jeremić. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

TIJER, 2024

I have classified motions into four types: Perfect Motion (PM), Normal motion (NM), Freefall Motion (FM) and Stubborn Motion (SM), and made three different formulas for those types of Motions: MV for Perfect Motion, n(MV) for Normal Motion and MV 2 for Freefall Motion and Stubborn Motion. E=MC 2 is the quantity of work required to accelerate a body of mass M to the speed C in Stubborn Motion, and not the Mass-Energy Equivalence Formula as Einstein claimed.

Caspian Journal of Applied Sciences Research, Vol. 1, No. 13, pp. 1-15, 2012

The essence of mass and its relation to the relativistic energy is considered. It is assumed that the rest energy is equal to the total binding energy of the body and can be found through the energies of fundamental fields associated with the substance of the body. Mass as a measure of inertia is calculated by relativistic energy and relativistic momentum. The conclusion is made that after radiation of energy from a system the mass of the system must not decrease, but increase. The opposite case is heating of bodies by external sources, which must be accompanied by an increase in entropy and decrease in the mass of the bodies. On the basis of strong gravitation the mass defect of atomic nuclei is explained. Conclusions of the general theory of relativity and the covariant theory of gravitation with respect to the mass and energy of gravitational field are opposite – in the general theory of relativity, relativistic energy and mass of a body are reduced by the mass-energy of its own gravitational field, and in the covariant theory of gravitation the mass-energy of the gravitational field increases the relativistic energy and body mass.