Special Relativity Research Articles

Superluminal matter waves

The Dirac equation has resided among the greatest successes of modern physics since its emergence as the first quantum mechanical theory fully compatible with special relativity. This compatibility ensures that the expectation value of the velocity is less than the vacuum speed of light. Here, we show that the Dirac equation admits free-particle solutions where the peak amplitude of the wave function can travel at any velocity, including those exceeding the vacuum speed of light, despite having a subluminal velocity expectation value. The solutions are constructed by superposing basis functions with correlations in momentum space. These arbitrary velocity wave functions feature a near-constant profile and may impact quantum mechanical processes that are sensitive to the local value of the probability density as opposed to expectation values. Published by the American Physical Society 2024

Limits and Potentials of Special Relativity

This paper presents the application of special relativity to different thought experiments. Some issues will be noted and a modification of special relativity will be presented. That modification can be tested and one interpretation of the preliminary result supports the modification. After presenting the history of special relativity, the non-simultaneity of special relativity is questioned in our macro world. In addition, some issues between light-clocks and the application of Lorentz transformation are presented. All this indicates that there is something not right with special relativity. A new proposal is presented based on an adaptation of special relativity; this new proposal solves the anomalies and could be a solution to the twin paradox. It has a prediction: a difference with special relativity which has been tested with a new experiment and the preliminary results support the new proposal. Previously, a lack of special relativistic effects has been observed in the universe [Davis et al., 2004]; that second observation is also explained with the new proposal.

A relativistic approach to teaching electrodynamics: Deriving Maxwell's equations from first principles

This paper presents a novel methodology for teaching classical electrodynamics based on special relativity theory. Traditional approaches often rely heavily on empirical laws, potentially obscuring the fundamental unity of electromagnetic phenomena. We demonstrate how the core principles of electrodynamics, including Maxwell's equations, can be derived from just two fundamental postulates: the principle of relativity and Coulomb's law. By consistently applying relativistic reasoning, we show how key concepts such as the Lorentz force, Biot-Savart law, and electromagnetic induction emerge naturally. This approach provides a logically coherent framework for understanding electrodynamics, emphasizes its inherently relativistic nature, and resolves apparent paradoxes that arise in non-relativistic treatments. We discuss the pedagogical advantages of this method, including its potential to foster deeper conceptual understanding and develop students' theoretical reasoning skills. The paper also addresses practical aspects of implementing this approach in higher education physics curricula and its implications for physics education research.

Classical-quantum hybrid canonical dynamics and its difficulties with special and general relativity

Classical-quantum hybrid canonical dynamics and its difficulties with special and general relativity

Dispersive vacuum as a decoherence amplifier of an Unruh–DeWitt detector

Abstract Recently, interest has been growing in studies on discrete or "pixelated'' space-time that, through modifications in the dispersion relation, can treat the vacuum as a dispersive medium. Discrete spacetime considers that spacetime has a cellular structure on the order of the Planck length, and if this is true we should certainly have observable effects. In this paper, we investigated the effects caused by the dispersive vacuum on the decoherence process of an Unruh-DeWitt detector, our setup consists of a uniformly accelerated detector, initially in a qubit state, which interacts with a massless scalar field during a time interval finite. We use dispersion relations drawn from doubly special relativity and Hořava-Lifshitz gravity, with these modifications the vacuum becomes dispersive and has a corresponding refractive index. We calculate the probability transition rates, the probability of finding the detector in the ground state, and the quantum coherence variation. Our results indicate that the decoherence process occurs more quickly in cases with changes in the dispersion relation in the regime of high accelerations and interaction time. Additionally, the decoherence increases as the vacuum becomes more dispersive due to the increase in the order of modification in the dispersion relation, and this happens because the dispersive vacuum amplifies the effects of quantum fluctuations that are captured by the detector when interacting with the field.

Inconsistences persisting in the conceptual structure of thermal physics and the nature of fundamental constants

AbstractConceptual structure of contemporary thermal physics is by no means simple, understandable and free of contradictions or ambiguities. As many students claim, it is a rather complicated doctrine which is far from to be easy comprehensible (Meltzer in Am J Phys 72:1432–1446, 2004). Therefore, in this polemic contribution, originally the summer school lecture, we will address some lesser-known points, which are likely responsible for such a situation. We start with Black’s path breaking discovery of two aspects of heat, namely the “matter of heat” and the “intensity of heat,” which were later identified with the quantities known as entropy (S) and temperature (T). It can be shown that the product of these two quantities can enter the energy balance equation, which is apt to interconnect various parts of physics. The genesis of these key concepts was, however, not straightforward. An original hypothetical model of heat, a subtle imponderable fluid, caloric (ς), was abandoned after the non-critical acceptance of the “milestone of thermodynamics,” Mayer–Joule’s postulate claiming the equivalence of heat and work. Heat then became a pure energy without any material carrier, but with seriously limited transformation abilities. In addition, the situation is also complicated by the very fact that the definition of Kelvin absolute thermodynamic temperature scale (T) is fully based on the caloric theory. Partial reconciliation brought about only introduction of Clausius’ entropy. This, however, was afterward recognized to be practically identical with the Carnot’s caloric. Furthermore, by analogy identification of phenomenological variables S and T with statistical parameters appearing in the kinetic theory has not withstand extension to the domain of special relativity. Thus, the full equivalence between thermodynamics and statistical physics is not feasible. Another realm of problems is generated by the recent tendency in metrology to define units by means of defining constants with fixed numerical values instead of materialized étalons. In case of thermal physics, one can be skeptic about such an approach, because the universal constancy of entropy and its unit, Boltzmann constant k = 1.380649 × .10−23 J K-1, are only unjustified assumptions, which can be a potential source of future difficulties.

On the Mass of (Gravitational) Potential Energy

In classical mechanics, when a body freely moves or is externally forced to move in a conservative force field, such as a planet moving away from a star or a weight lifted from the floor, its kinetic energy or the work done on it is converted and stored as potential energy. The concept of potential energy was developed to uphold the fundamental principle of conservation of energy. According to the widely accepted interpretation of mass-energy equivalence, every form of energy has mass. This leads to the natural questions: does potential energy have mass? And if so, where is that mass located? We will start by briefly reviewing the issue through an examination of some key literature on the topic. The current consensus is that potential energy gets stored in the field energy of the interacting system. As a result of mass-energy equivalence, the equivalent mass is distributed throughout the entire space in some manner. However, this presents some difficulties. Here, like some other scholars in the past, we show that it contradicts the principles of special relativity and argue that potential energy does increase the mass of the bodies composing the system. We present an accessible thought experiment that heuristically corroborates that view specifically for the gravitational potential energy. We finally speculate on how that mass increase is distributed among the interacting bodies.

Analysing the breakdown of Astronomical Theories

This paper investigates the limitations of Newton's law of gravity, general relativity, special relativity, dark matter, dark energy, and the big bang theory in describing the universe's origins, development, and properties. It aims to illuminate the boundaries of these theories, furthering our understanding of where these theories apply and how their alternative solutions address their problems. By evaluating these theories, this research aims to provide an assessment of our current understanding of the universe and identify the primary obstacles and future directions in cosmological research.

Exact solutions of the (3+1)-dimensional DKP oscillator in Doubly Special Relativity

Exact solutions of the (3+1)-dimensional DKP oscillator in Doubly Special Relativity

Enhanced Special Relativity Search Algorithm Based Lorentz Force for Structural Optimization

Enhanced Special Relativity Search Algorithm Based Lorentz Force for Structural Optimization

Overlooked effects of wavefront reception with or without speed limit, from aberration to time measurement

A general approach to wavefront reception applicable to any type of wave allows to point out some overlooked aspects and ignored consequences of established theories. The Doppler and aberration effects of electromagnetic waves, the cosmological redshift and the measurement of durations are all perceptual phenomena, and as such require the use of reception rather than Lorentz-transformed coordinates, since perceived durations relate proper to proper durations whereas the famous time dilation of special relativity relates proper to improper durations. Taking this subtlety into account rehabilitates the controversial Poincaré ellipsoid whose polar equation is just the relativistic Doppler effect. The application of this approach to the Galilean case whose transformed and received wavefronts are homothetic, reveals new aberration relations and the existence of a transverse Doppler effect very similar, in proportion to the respective wave velocities, to the relativistic one, thus forbidding in practice the test of his theory proposed by Einstein. The reasons for the long persistence of a classical angular Doppler formula divorced from wavefront reception are discussed, one of them ironically being the theory of special relativity.

Doubly special relativity as a nonlocal quantum field theory

In this work, we explore the quantum theories of the free massive scalar, the massive fermionic, and the electromagnetic fields in a doubly special relativity scenario. This construction is based on a geometrical interpretation of the kinematics of this kind of theory. In order to describe the modified actions, we find that a higher (indeed infinite) derivative field theory is needed, from which the deformed kinematics can be read. From our construction, we are able to restrict the possible models of doubly special relativity to those that preserve linear Lorentz invariance. We quantize the theories and also obtain a deformed version of the Maxwell equations. We analyze the electromagnetic vector potential for both an electric pointlike source and magnetic dipole. We observe that the electric and magnetic fields do not diverge at the origin for some models described with an anti–de Sitter momentum space, but they do for a de Sitter space in both problems. Published by the American Physical Society 2024

Relativity and the Magnitude of Velocities

In modern physics, relativity is primarily understood through the framework of Einstein’s theory. According to the special theory of relativity (STR), Galilean relativity serves as a very accurate approximation at low velocities, where ‘relativistic effects’ can be neglected. However, at high velocities, these effects become significant and are accurately described by STR. This paper challenges this understanding, arguing that the opposite is true. In Galilean relativity, the relativity of time is substantial and cannot be ignored. Thus, relative time is more negligible in STR than in Galilean relativity. By comparing Galilean relativity and STR through physical, mathematical, and specific examples, two conclusions are drawn: first, the current categorization of relativity theories based on velocity magnitude is artificial and inaccurate; second, the relativity of time can be ignored in special relativity, while it remains significant and cannot be overlooked in Galilean relativity.

The cosmological constant and energy quantization in hydrogen atom in light of a doubly special relativity with a minimum speed

We show the existence of an invariant minimum speed in space–time as a new fundamental constant of nature by forming the basis of a doubly special relativity so-called Symmetrical Special Relativity (SSR). Such an observer-independent minimum speed emerges from the Dirac’s Large Number Hypothesis (LNH), which leads us to build SSR-theory. This allows us to understand that the hydrogen atom represents the most stable bound state in the universe as being a fundamental structure in space–time with two speed limits, i.e., the speed of light c and a minimum speed V. So the symmetry in space–time given by an invariant minimum speed, which has origin in the electrical and gravitational bound states in hydrogen atom is able to provide a deeper understanding of the proton-electron mass ratio. We investigate how the minimum speed plays a fundamental role in the quantization of energy in hydrogen atom. The minimum speed V is related to a preferred background frame (ultra-referential SV) represented by the surface of a dark cone forbidden to the world line of any particle. It is related to the vacuum energy that leads to the cosmological constant. An investigation of SSR is done and a hypothetical experiment of Bose–Einstein condensation is proposed to detect the minimum speed as a possible Lorentz violation at very low energies.

Gravitational redshift revisited: Inertia, geometry, and charge

Gravitational redshift effects undoubtedly exist; moreover, the experimental setups which confirm the existence of these effects—the most famous of which being the Pound–Rebka experiment—are extremely well-known. Nonetheless—and perhaps surprisingly—there remains a great deal of confusion in the literature regarding what these experiments really establish. Our goal in the present article is to clarify these issues, in three concrete ways. First, although (i) Brown and Read (2016) are correct to point out that, given their sensitivity, the outcomes of experimental setups such as the original Pound–Rebka configuration can be accounted for using solely the machinery of accelerating frames in special relativity (barring some subtleties due to the Rindler spacetime necessary to model the effects rigorously), nevertheless (ii) an explanation of the results of more sensitive gravitational redshift outcomes does in fact require more. Second, although typically this ‘more’ is understood as the invocation of spacetime curvature within the framework of general relativity, in light of the so-called ‘geometric trinity’ of gravitational theories, in fact curvature is not necessary to explain even these results. Thus (a) one can often explain the results of these experiments using only the resources of special relativity, and (b) even when one cannot, one need not invoke spacetime curvature. And third: while one might think that the absence of gravitational redshift effects would imply that spacetime is flat (indeed, Minkowskian), this can be called into question given the possibility of the cancelling of gravitational redshift effects by charge in the context of the Reissner–Nordström metric. This argument is shown to be valid and both attractive forces as well as redshift effects can be effectively shielded (and even be repulsive or blueshifted, respectively) in the charged setting. Thus, it is not the case that the absence of gravitational effects implies a Minkowskian spacetime setting.

Welt: The concept that changed physics

Abstract This paper explores a pivotal moment in history when the integration of space and time took place within a unified theoretical framework. The spacetime unification was embodied by the notion of Welt, the German term for world, originating during the period spanning 1907 to 1909 in between the publications on special and general relativity. Emphasis will be placed on elucidating the significance of a connected spacetime and providing a contextual backdrop to key historical advancements. While the conventional narrative often attributes the development of these concepts to a select group of renowned physicists, such as Albert Einstein and David Hilbert, it is essential to recognise the substantial involvement of numerous scientists and mathematicians. Their collective contributions, although sometimes overlooked, laid the foundation for the groundbreaking papers on relativity penned by Albert Einstein. In shedding light on this collaborative effort, the paper aims to underscore the intricate set of ideas that paved the way for Einstein’s seminal work. Furthermore, this paper also hints at the contemporary relevance of spacetime in ongoing research, highlighting its enduring importance in the scientific landscape.

The theory of thermodynamic relativity.

We introduce the theory of thermodynamic relativity, a unified theoretical framework for describing both entropies and velocities, and their respective physical disciplines of thermodynamics and kinematics, which share a surprisingly identical description with relativity. This is the first study to generalize relativity in a thermodynamic context, leading naturally to anisotropic and nonlinear adaptations of relativity; thermodynamic relativity constitutes a new path of generalization, as compared to the "traditional" passage from special to general theory based on curved spacetime. We show that entropy and velocity are characterized by three identical postulates, which provide the basis of a broader framework of relativity: (1) no privileged reference frame with zero value; (2) existence of an invariant and fixed value for all reference frames; and (3) existence of stationarity. The postulates lead to a unique way of addition for entropies and for velocities, called kappa-addition. We develop a systematic method of constructing a generalized framework of the theory of relativity, based on the kappa-addition formulation, which is fully consistent with both thermodynamics and kinematics. We call this novel and unified theoretical framework for simultaneously describing entropy and velocity "thermodynamic relativity". From the generality of the kappa-addition formulation, we focus on the cases corresponding to linear adaptations of special relativity. Then, we show how the developed thermodynamic relativity leads to the addition of entropies in nonextensive thermodynamics and the addition of velocities in Einstein's isotropic special relativity, as in two extreme cases, while intermediate cases correspond to a possible anisotropic adaptation of relativity. Using thermodynamic relativity for velocities, we start from the kappa-addition of velocities and construct the basic formulations of the linear anisotropic special relativity; e.g., the asymmetric Lorentz transformation, the nondiagonal metric, and the energy-momentum-velocity relationships. Then, we discuss the physical consequences of the possible anisotropy in known relativistic effects, such as, (i) matter-antimatter asymmetry, (ii) time dilation, and (iii) Doppler effect, and show how these might be used to detect and quantify a potential anisotropy.

Accounting for the expansion of the universe using an energy/momentum model to construct the space-time metric

Background The success of the theories of special and general relativity in describing localised phenomena, such as objects undergoing high speed motion or located in gravitational fields, needs no further elaboration. However, when applied to the evolution of the universe several problems arise which can require an additional model, e.g., inflation during the early expansion, and adjustments to parameters to account for phenomena such as the late-time acceleration of the universe. Methods Focusing on the difference between the ways in which space and time are measured, this paper shows that there are two paths which allow the equations of special relativity to be produced from the same basic postulates. Results Both the standard theory and the energy/momentum, or dynamic model, utilise the Minkowski metric, but with different coordinate systems. The dynamic model transforms Cartesian coordinates into an Euclidean form by multiplying the coordinates by functions of γ (=(1–ν 2)c 2)-1⁄2). When utilising these coordinates, the relativistic equations are unchanged for local phenomena such as the Lorentz coordinate transformation and the energy/momentum equation for high-velocity objects. Conclusions However, the derived coordinates alter the perceived overall structure of the universe in a manner that, for the simplest model under this system, allows the reproduction of observed cosmological features, such as the intrinsic flatness of the universe and the apparent late-time acceleration of its expansion, without the need of additional models or changes in parameter values.

A novel approach for buckling optimization of stiffened piezolaminated composite plates

This study presents a novel approach for optimizing the critical buckling load of the stiffened piezolaminated composite plates using a self-adaptive special relativity search (SASRS) algorithm. The fiber orientations in the layers are considered as design variables. The stability equations are first derived based on the classical laminated plate theory (CLPT) with von Karman nonlinearity. The optimization problem is implemented in MATLAB. The optimization results are obtained to indicate the effecs of various boundary conditions, applied voltages, grid shapes, angles of diagonal ribs, and plate aspect ratios on the optimal design. Numerical investigations are carried out for 10-ply symmetrical stiffened piezolaminated plates. The robustness and efficiency of the proposed SASRS algorithm in maximizing the critical buckling load of the stiffened piezolaminated plates are demonstrated by comparing the optimized results from the standard special relativity search (SRS) algorithm. It is found that the proposed optimization method has better performance than the SRS algorithm.

Laws of conservation of mass and momentum for an ideal fluid in the inertial framework of special relativity

In the realm of Newtonian fluids, fundamental conservation laws such as those governing mass, momentum, and energy are rigorously upheld within absolute reference frames. However, within the framework of special relativity and the concept of space -time, the notions of separate conservation of mass and momentum no longer hold. Instead, the theory relies on Lorentz transformations and relative reference systems, typically denoted as S and S', moving uniformly relative to each other, each with its own temporal framework. Within the context of special relativity, particularly in the study of particles, significant findings pertain to the energy-momentum vector. These findings underscore the necessity, when studying fluids within inertial frames, to apply conservation principles to the energy-momentum tensor.