Special Relativity Research Articles

What should we understand by the four-momentum of physical system?

It is shown that, in general, in curved spacetime, none of the known definitions of four-momentum correspond to the definition, in which all the system’s particles and fields, including fields outside matter, make an explicit contribution to the four-momentum. This drawback can be eliminated under the assumption that the primary representation of four-momentum is the sum of two nonlocal four-vectors of the integral type with covariant indices. The first of these four-vectors is the generalized four-momentum, found with the help of Lagrangian density. The time component of the generalized four-momentum, in theory of vector fields, is proportional to the particles’ energy in scalar field potentials, and the space component is related to vector field potentials. The second four-vector is the four-momentum of fields themselves, and its time component is related to the energy given by tensor invariants. As a result, the system’s four-momentum is defined as a four-vector with a covariant index. The standard approach makes it possible to find the four-momentum in covariant form only for a free point particle. In contrast, the obtained formulas for calculating the four-momentum components are applied to a stationary and moving relativistic uniform system, consisting of many particles. In this case, the main fields of the system under consideration are taken into account, including the electromagnetic and gravitational fields, the acceleration field and the pressure field. All these fields are considered vector fields, which makes it possible to unambiguously determine the equations of motion of the fields themselves and the equations of motion of matter in these fields. The formalism used includes the principle of least action, charged and neutral four-currents, corresponding four-potentials and field tensors, which ensures unification and the possibility of combining fields into a single interaction. Within the framework of the special theory of relativity, it is shown that due to motion, the four-momentum of the system increases in proportion to the Lorentz factor of the system’s center of momentum, while in the matter of the system the sum of the energies of all fields is equal to zero. The calculation of the integral vector’s components in the relativistic uniform system shows that the so-called integral vector is not equal to four-momentum and is not a four-vector at all, although it is conserved in a closed system. Thus, in the theory of relativistic vector fields, the four-momentum cannot be found with the help of an integral vector and components of the system’s stress-energy tensor, in contrast to how it is assumed in the general theory of relativity.

Ideal gas thermodynamics with an invariant energy scale

A viable approach towards Quantum Gravity is the Doubly Special Relativity (DSR) framework in which an observer-independent finite energy upper bound (or a finite smallest length scale) appears quite naturally. In this work, we have studied the thermodynamic properties of an ideal gas in a specific DSR framework, known as the Magueijo-Smolin (MS) Model. We use the fact that DSR can be considered as nonlinear representation of Lorentz Group. Subsequently, various thermodynamic parameters of ideal gas have been derived in this modified framework to compare the corresponding deviations from the usual scenario due to the presence of the invariant energy (length) scale.

On the Supposed Mass of Entropy and That of Information.

In the theory of special relativity, energy can be found in two forms: kinetic energy and rest mass. The potential energy of a body is actually stored in the form of rest mass, the interaction energy too, but temperature is not. Information acquired about a dynamical system can be potentially used to extract useful work from it. Hence, the "mass-energy-information equivalence principle" that has been recently proposed. In this paper, it is first recalled that for a thermodynamic system made of non-interacting entities at constant temperature, the internal energy is also constant. So, the energy involved in a variation in entropy (TΔS) differs from a change in the potential energy stored or released and cannot be associated to a corresponding variation in mass of the system, even if it is expressed in terms of the quantity of information. This debate gives us the opportunity to deepen the notion of entropy seen as a quantity of information, to highlight the difference between logical irreversibility (a state-dependent property) and thermodynamical irreversibility (a path-dependent property), and to return to the nature of the link between energy and information that is dynamical.

EXPLANATION OF NULL RESULTS OF MICHELSON AND MORLEY EXPERIMENT BY CLASSICAL MECHANICS PART II

Interferometry is the branch of optics in which experiments are conducted on wave nature of light. The light waves are superimposed to generate interference fringes and measurements are made. In these experiments where diffraction and interference are observed, the wavefront of light plays a very important role. While interpreting the results of these experiments the role of wavefront is completely ignored resulting into wrong predictions. In such an experiment conducted by Michelson and Morley to measure the velocity of earth in space the role of wavefront was ignored. It has been established by the results of Fizeau experiment and other similar experiments that speed of light is constant and it is not effected by the motion of source of light and motion of medium in which it propagates. Which later on become the second postulate of special theory of relativity. In the present article null results of Michelson and Morley experiment is discussed in a very different way keeping in view constancy of speed of light, wavefront of light and Huygen's principle according to classical mechanics.

СЛОЖНОСТЬ ФОРМУЛ И МЕТОДОВ РЕШЕНИЯ ЗАДАЧ ПО МКТ, ТЕРМОДИНАМИКЕ, ОПТИКЕ, ФИЗИКЕ МИКРОМИРА И ЧТО

The article is devoted to the problem of determining the complexity of formulas and methods used to solve school problems in molecular physics and thermodynamics, optics, microcosm physics and the special theory of relativity. As a result of the content analysis of school textbooks, all formulas related to the listed sections were written out and 17 topics are identified, each of which corresponds to its own method of solving problems. In order to determine semantic complexity, formulas are presented in the form of statements that are stored in a text file Formuli.txt. To a file Slovar.txt the list of concepts denoting physical quantities is placed, indicating their complexities. Using a special computer program that analyzes the file Formuli.txt the semantic complexities of the formulas, their volume and the information folding coefficient are determined. The complexities of the methods are calculated, the distributions of formulas in the space of "semantic complexity - volume" signs are analyzed. Based on the number of formulas in each method and the number of methods in each section, the complexity of choosing a suitable formula for independent solving a single-formula task is estimated. It is shown how to take into account the uncertainty of the choice of formulas when solving two- and three-formula tasks to find their complexities.

Small-Scale Cosmology Independent of the Standard Model

‘Small-scale cosmology’ is a theory designed to incorporate the linear redshift versus distance relation, which is inferred from observations, into the theoretical framework independent of the global Robertson–Walker–Friedman (RWF)-type models. The motivation behind this is that the RWF cosmological models, based on the assumptions of homogeneity and a constant matter density, as well as the concept of expanding space inherent to them are not applicable on the scales of observations from which the linear Hubble law is inferred. Therefore, explaining the Hubble law as the small redshift limit of the RWF model or as an effect of expanding space is inconsistent. Thus, the Hubble linear relation between the redshift of an extragalactic object and its distance should be considered an independent law of nature valid in the range of the distances where the RWF cosmology is not valid. In general, the theory, based on that concept, can be developed in different ways. In the present paper, ‘small-scale cosmology’ is formulated as a theory operating in the (redshift–object coordinates) space, which allows developing a conceptual and computational basis of the theory along the lines of that of special relativity. In such a theory, the condition of invariance of the Hubble law with respect to a change in the observer acceleration plays a central role. In pursuing this approach, the effectiveness of group theoretical methods is exploited. Applying the Lie group method yields transformations of the variables (the redshift and space coordinates of a cosmological object) between the reference frames of the accelerated observers. In this paper, the transformations are applied to studying the effects of the solar system observer acceleration on the observed shape, distribution and rotation curves of galaxy clusters.

Proposal for a realtime Einstein-synchronization-defined satellite virtual clock

Abstract The realization of high performance satellite onboard clock is vital for various PNT applications. For further improvement of the synchronization-based satellite time and frequency references, this paper proposes a geosynchronous (GEO) satellite virtual clock concept based on ground–satellite synchronization and presents a beacon transponder structure for its implementation (scheduled for launch in 2025), which does not require atomic clocks to be mounted on the satellite. Its high performance relies only on minor modifications to the existing transponder structure of GEO satellites. We carefully modeled the carrier phase link and analyzed the factors causing link asymmetry within the special relativity. Considering that the performance of such synchronization-based satellite clocks is primarily limited by the link’s random phase noise, which cannot be adequately modeled, we designed a closed-loop experiment based on commercial GEO satellites for pre-evaluation. This experiment was aimed at extracting the zero-means random part of the ground-satellite Ku-band carrier phase via a feedback loop. Ultimately, we obtained a 1σ value of 0.633 ps (two-way link), following the Gaussian distribution. From this result, we conclude that the proposed real-time Einstein-synchronization-defined satellite virtual clock can achieve picosecond-level replication of onboard time and frequency.

Understanding and Differentating General and Special Relativity

This article stresses the importance of comprehending projectile motion for its extensive applications in both science and real-world contexts. This understanding not only enhances our grasp of physics and mathematics but also demonstrates how straightforward motions can embody complex scientific concepts.

From Spherical Cows to Schrödinger’s Cat: what students want to learn in physics

This paper reflects on feedback received from 161 Ontario grade 12 physics students between 2017–2018 and 2020–2023, on the content and delivery in different modes (face-to-face, online, hybrid) of the 2008 Ontario Grade 12 Physics—University Preparation course (SPH4U). Across modes, students considered Revolutions in Modern Physics significantly more interesting and less stressful than any of the other four units. Students also identified Dynamics as significantly less interesting than all of the units, and found it significantly more stressful than all units other than Fields. Students were most interested in topics not previously studied (e.g. Special Theory of Relativity) that they felt promoted new ways of thinking. Adjusting to grade 12 expectations combined with more challenging course concepts were the primary contributors of stress. Included is a discussion of physics education reform, and the role of physics education in science, technology, engineering and mathematics.

Rethinking on Foundation of Special Theory of Relativity by Showing Irrational Use of Lorentz Transformation

Rethinking on Foundation of Special Theory of Relativity by Showing Irrational Use of Lorentz Transformation

Mountain pass periodic solutions for the Lorentz force equation via the Poincaré action functional

In this paper, we study the Lorentz force equation with the rest mass [Formula: see text] and periodic boundary conditions on a fixed interval [Formula: see text] [Formula: see text] where [Formula: see text] are the electric and magnetic fields. From the Poincaré paper concerning the special relativity it is well known that this is the Euler–Lagrange equation of the action functional given by [Formula: see text] defined for all [Formula: see text]-periodic Lipschitz functions [Formula: see text] such that [Formula: see text] In this paper, under some assumptions on the potentials [Formula: see text] and [Formula: see text] around zero and infinity, we prove that [Formula: see text] has nonzero critical points which are [Formula: see text]-periodic solutions of the Lorentz force equation. To prove our main results we use new “mountain pass” methods for the Poincaré action functional [Formula: see text]

An analysis of students’ misconceptions on Special Relativity

Special Relativity is one of the key theories describing our reality but its accommodation among students at different level is still a critical issue. Even after instruction, students’ answers continue to be biased by Classical Mechanics. We present the analysis of high-school students’ answers to open questions concerning topics on Classical Mechanics and Special Relativity showing the persistence of pre-relativistic reasoning. This study is part of an experimentation on the teaching of Special Relativity with the use of a mechanical instrument that allows students to explore by hand the effects of a change of reference frame.

Special relativity at Czech schools: a half-century comparison

In this contribution, we present the results of one bachelor and one master theses both devoted to the teaching of special relativity at an upper-secondary or intro-university level in the Czech Republic. We compare the test results of the grammar-school students in the school years 1976/1977 and 2021/2022, which are close to average and very similar in both cases, so the level of understanding has not changed in the meantime. We also present a set of interactive spacetime diagrams used in the preparation of future physics teachers within our relativity course.

An online teaching learning sequence with home experiments and simulations on relativity of motion and the equivalence principle in classical mechanics

We designed a teaching-learning sequence on relative motion in classical mechanics, based on the fundamental design principle of highlighting those conceptual elements which could be valuable in the future learning of special and general relativity In order to highlight selected key concepts and motivate students in their exploration, we used a series of experiments based on video analysis and interactive simulations, which can be modified on the fly by the students. In this study, we introduce a pilot investigation focused on testing the instructional sequence, and we provide initial outcomes regarding students’ understanding. The sequence of activities was tested with a group of 24 undergraduate students in an online laboratory course during the COVID-19 pandemic.

Symmetry, Music and Water

There is a deep link existing between symmetry and nature that may be best apprehended by using group theory. In physics, giving a symmetry group is entirely equivalent to fix natural laws (Noether’s theorem). Within such a framework, it follows that all fundamental mechanical laws may be given by defining a group of symmetry operations belonging to the Gal (3,1) symmetry group having ten generators (3 + 3 + 3 + 1 = 10). The move to special relativity amounts simply to substitute another group ISO (3,1) to Gal (3,1) and having the same number of generators. In both cases, one immediately perceives that we live in universe with 3 dimensions of space and 1 dimension of time. A further progress could be made by looking for the symmetry group that leaves Maxwell’s equations invariant. The answer to this fundamental question is the group ISO (4,2) ⊗U (2) ⊗U (2) characterized by 23 generators: 15 = 10 + 5 for the conformal group ISO(4,2), 4 for U(2) and hence 8 = 4 + 4 for the compact part U(2) ⊗U(2) that could be related to the existence of quantum physics besides relativity. As ISO (3,1) is a sub-group of ISO (4,2), the two numbers 4 and 2 suggests that, taking into account the existence of light besides matter, we live in an universe having 4 spacelike dimensions and 2 time-like dimensions. Here, it is proposed that, as music is characterized by a scale-invariant symmetry operation (transposition by octaves) and that as time may be perceived differently in shamanic trance for instance, the two “new” dimensions of our universe may be related to music and consciousness. Related to the fifth dimension of music, the notion of diapason linking physical frequencies to a musical note is revisited. It is thus proposed to adopt a new A4 = 429.62 Hz value based on universal physical constants of our universe and on the mass of the water molecule H₂O, "The most abundant heteronuclear molecule in the entire universe". Demonstration is done that this new diapason is superior to other diapasons based on frequencies of 440 Hz or even 432 Hz.

Introducing General Relativity in High Schools: a proposal for a Teaching-Learning Module

A teaching-learning module, aimed at introducing basic concepts of general relativity at the high school level, is proposed. Emphasis is on conceptual rather than technical aspects, and only familiarity with simple calculus is required on the mathematical side. The starting point is a critical overview of the principles of Newtonian mechanics, in particular the role of fictitious forces, as well as of the limits of special relativity. Part of the module is devoted to the discussion and the reproduction of key thought or real experiments, for example experiments involving non-inertial frames, or the Einstein elevator.

Polarized signatures of orbiting hot spots: Special relativity impact and probe of spacetime curvature

Context. The Galactic Center supermassive black hole is well known to exhibit transient peaks of flux density on a daily basis across the spectrum. Recent infrared and millimeter observations have strengthened the case for the association between these flares and circular orbital motion in the vicinity of the event horizon. The strongly polarized synchrotron radiation associated with these events leads to specific observables called QU loops, that is, looping motion in the Stokes QU plane of linear polarization. These patterns have been observed by the Submillimeter Array, VLTI/GRAVITY, and ALMA. Aims. We want to deepen the understanding of the QU loops associated with orbiting hot spots. To this end, we computed such loops in Minkowski and Schwarzschild spacetimes in order to determine which aspects of the observed patterns are due to special- or general-relativistic phenomena. Methods. We considered a parcel of energized plasma in circular motion in Minkowski spacetime and in Keplerian orbit in the Schwarzschild spacetime. We computed, using the GYOTO ray-tracing code, the polarized radiative transfer associated with this orbiting hot spot and derived the evolution of the flux density, astrometry, and Stokes Q and U parameters. Results. We show that QU loops in Minkowski spacetime at low or moderate inclination i ≲ 45° (where i = 0° is a face-on view) share all the qualitative features of Schwarzschild QU loops. There exist QU loops for all setups considered (including for the face-on view and vertical magnetic field), there may be one or two QU loops per orbital period for a vertical magnetic field configuration, and there are always two QU loops in case of a toroidal magnetic field. The simplicity of Minkowski spacetime is a key asset for allowing us to provide analytical formulas that explain the details of this behavior. Moreover, we analyzed the flux variation of the hot spot and show that it is dictated either by the angular dependence of the radiative transfer coefficients or by relativistic beaming. In the former case, this can lead to extreme flux ratios, even at a moderate inclination. Finally, we highlight the increasing mirror asymmetry of the Schwarzschild QU track with increasing inclination and show that this behavior is a specific Schwarzschild feature caused by light bending. Conclusions. Although special-relativistic effects have not been extensively discussed in this context, they are a crucial part in generating the observed QU loops. However, general-relativistic light bending leads to a specific observable feature encoded in the asymmetry of the observed loops, and this feature might allow the spacetime curvature to be quantified.

The Convincing Cosmic Energy Gravitational Genesis of the Strongest Geomagnatic Anomalies of the Magnetic Field of the Earth

The author presents convincing evidence of the cosmic (planetary and solar) energy gravitational origin (related to the maximal and minimal combined planetary and solar integral energy gravitational influences on the internal rigid core of the Earth) of the maximal temporal intensifications of the global magnetic processes of the Earth. In fairly good agreement with the calculated date 2007.416666666 AD (of the local minimal planetary and solar integral energy gravitational influence on the internal rigid core), it was observed the very rapid changes of the geomagnetic field near the date March 2007 AD (corresponding approximately to 19-20 April 2007 AD). This fairly good agreement gives the additional convincing argument that the date March 2007 AD can be considered as the possible beginning of the geomagnetic reversal during the evaluated range (2007÷2216) AD. The strong magnetic anomaly occurred on 6 January 2020 AD in perfect agreement with the calculated date 2020.016666667 AD (corresponding to 6 January 2020 AD) related to the local maximal planetary and solar integral energy gravitational influence on the internal rigid core. In fairly good agreement with the calculated date 2023.26666666 AD (corresponding approximately to 7 April 2023 AD) of the local maximal planetary and solar integral energy gravitational influence on the internal rigid core, it was observed the strongest (during the last 6 years) magnetic anomaly on 23 March 2023 AD. These convincing agreements demonstrate the physical validity of the established global prediction thermohydrogravidynamic principles, which can be considered as the proven physical basis for the development of the general unified geophysical theory (describing the possible geomagnetic reversal during the evaluated range (2007 ÷ 2216) AD) combining the Special Theory of Relativity, the relativistic electrodynamics and the relativistic theory of the non-stationary gravitation, which can be developed based on the established physical analogy between the established relation for the energy flux (of the gravitational energy) and the Lorentz’s calibration condition (for the vector potential related with the scalar potential of the non-stationary electromagnetic field).

Analysis of Moving Bodies with a Direct Finite Difference Time Domain Method

This paper proposes an original and thorough analysis of the behavior of electromagnetic waves in the presence of moving bodies by using the finite difference time domain (FDTD) method. Movements are implemented by changing positions of the objects at each time step, through the classical FDTD time loop. This technique is suitable for non-relativistic speeds, thus for most encountered problems in antennas and propagation domain. The numerical aspects that need to be considered are studied. Then, different bodies in motion are examined: plane wave source with matching resistors, observation point, inclined partially reflecting surface (PRS), line source, and metallic cylinder illuminated by a plane wave. The results are compared with those of special relativity which are considered as the references. Some aspects of special relativity are present in the direct FDTD approach, such as the independence of the velocity of electromagnetic wave propagation with the speed of the source and Lorentz local time (with a different physical interpretation). It is shown that the amplitude of the electric field for a moving plane wave source does not increase with the speed of motion, if the impedance of the source is small. Moreover, for a moving scattering metallic wire, one can observe a phenomenon similar to shock waves.

The Theory of Absoluteness —The Relations among Matter, Space, Time and Motion

In this paper, the absolute static reference frame of the universe is established, the Galileo's relativity principle and the essence of light are analyzed, and the zero result of Michelson-Morey experiment is re-recognized. The conclusion is that the light in two directions reaches the eyepiece at the same time, and when the interferometer is rotated at any angle, the light in two directions still reaches the eyepiece at the same time, and the interference fringes will not move, so the zero result of the experiment is inevitable. This paper analyzes Lorenz's explanation of the zero result of the Michelson-Morey experiment, and points out that there are many contradictions and mistakes in it. Michelson confused the reference frame in his analysis and calculation, and the result was necessarily wrong. The Michelson-Morey experiment wants to measure the speed of the earth relative to the "ether" on the earth. According to the Galileo's relativity principle, it is impossible to measure it. This experiment is meaningless. Because Michelson's wrong calculation result is not consistent with the zero result of the experiment, Lorenz had to set up "length shortening", "clock slowing down" and a Lorenz transformation factor to piece together the zero result of the experiment.It is precisely because these assumptions are incorrect that all the relations and related theories that use Lorentz transformation factors are incorrect, and the special theory of relativity is completely wrong. Only the Galileo's relativity principle can correctly explain the zero result of Michelson-Morey experiment, and the Galileo’s transformation is the correct theory to describes motion. This paper also re-understands the relations among matter, space, time, motion, inertia, field, field wave, force and energy, analyzes the essence of nuclear energy, and establishes a new model of the universe. It makes physics return to the correct track of classical theory and deepens and develops classical theory.