Showing papers on "Special relativity (alternative formulations) published in 2021"

Global view of axion stars with nearly Planck-scale decay constants

Abstract: We show that axion stars formed from axions with nearly Planck-scale decay constants $f$ are unstable to decay and are unlikely to have phenomenological consequences. More generally, we show how results at smaller $f$ cannot be na\"{\i}vely extrapolated to $f=\mathcal{O}({M}_{P})$ as, contrary to conventional wisdom, gravity and special relativity can both become relevant in the same regime. We clarify the rate of decay by reviewing and extending previous work on oscillons and axion stars, which imply a fast decay rate even for so-called dilute states at large $f$.

A mechanical model for dark matter and dark energy

Abstract: We present a mechanical model that identifies dark energy and dark matter as singular states. The model introduces the notions of “forces in the direction of time”, and that every particle has a particle energy e and a wave energy $$\mathscr {E}$$ and is based upon an idea due to de Broglie for which he had a concrete physical picture of the coexistence of both particle and its associated wave. The model is a properly Lorentz invariant extension of special relativity and is intermediate between special and general relativity. A logical analysis of the energy statement gives rise to four states of matter, which is meaningful because it is interpreted within the proposed extension of special relativity. This interpretation is not available within the existing special relativity since it lacks the notion of force in the direction of time. Dark matter and dark energy arise as backward and forward waves, respectively, such that there is a particular alignment of the spatial physical force f and the force g in the direction of time, namely $$f = \pm \, gc$$ and for which $$e = \mathscr {E}$$ , respectively. In an actual circumstance, we might expect a situation comparable to a “fuzzy region” where the key equalities are constantly switching on and off dependent upon varying local conditions. The latest Planck data for the relative fractions for a three-component universe are exploited to obtain numerical values for the relative fractions for a four-component universe comprising baryonic matter, dark matter, dark energy, and a fourth state termed here anti-matter. The values so obtained are consistent with expected allowable occupancies for four states given that the higher energy states have a ready access to each of the lower energy states.

Getting tense about relativity

Abstract: Special relativity has been understood by many as vindicating a tenseless conception of time, denying the existence of tensed facts and a fortiori objective temporal passage. The reason for this is straightforward: both passage and the obtaining of tensed facts require a universal knife-edge present moment—yet this structure is not easily reconcilable with the relativity of simultaneity. The above being said, the prospects for tense and passage are sometimes claimed to be improved on moving to cosmological solutions of general relativity. In this paper, we evaluate in detail these arguments, finding that there remain several open questions to be addressed if the introduction of tensed facts into the relativistic context is to be compelling. Moreover, we argue that, even setting aside these issues, objective tense stands and falls in relativity for exactly the same reasons that it does in classical philosophical discussions on the matter.

Some insight into Feynman's approach to electromagnetism

Abstract: We retrace an ab initio relativistic derivation of Maxwell's equations that was developed by Feynman in unpublished notes, clarifying the analogies and the differences with analogous treatments present in the literature. Unlike the latter, Feynman's approach stands out because it considers electromagnetic potentials as primary, reflecting his ideas about the quantum foundations of electromagnetism. Some considerations about the foundations of special relativity, which are naturally suggested by this approach, are given in appendix.

The Invisibility of Time Dilation.

Abstract: Recently, the physics education community has taken a keen interest in modernising physics education. However, while topics in modern physics have great potential to engage students, these topics are abstract and hard-to-visualise. Therefore, many students hold mistaken pictures and misconceptions, which can impede learning. In this article, we expose a pervasive misconception about relativistic time dilation by presenting a thought experiment illustrating the difference between visual observation and coordinate measurement. We also point out how existing language can mislead and confuse students. In response, we describe an instructional approach that introduces world-maps, world-pictures and event-diagrams to clarify the applicability of key equations in special relativity for improved understanding. By unpacking ‘the invisibility of time dilation’ from the perspectives of both physics and pedagogy, we aim to help teachers provide clearer instruction.

A solution of the time paradox of physics

Abstract: Abstract Quantum mechanics for describing the behavior of microscopic entities and thermodynamics for describing macroscopic systems exhibit separate time concepts. Whereas many theories of modern physics interpret processes as reversible, in thermodynamics, an expression for irreversibility and the so-called time arrow has been developed: the increase of entropy. The divergence between complete reversibility on the one hand and irreversibility on the other is called the paradox of time. Since more than hundred years many efforts have been devoted to unify the time concepts. So far, the efforts were not successful. In this paper a solution is proposed on the basis of matter-energy equivalence with an energetic distinction between matter and mass. By refraining from interpretations predominant in modern theoretical physics, the first and second laws of thermodynamics can be extended to fundamental laws of nature, which are also valid at quantum level.

The Relativity of Indeterminacy.

Abstract: A long-standing tradition, largely present in both the physical and the philosophical literature, regards the advent of (special) relativity -- with its block-universe picture -- as the failure of any indeterministic program in physics. On the contrary, in this paper, we note that upholding reasonable principles of finiteness of information hints at a picture of the physical world that should be both relativistic and indeterministic. We thus rebut the block-universe picture by assuming that fundamental indeterminacy itself should as well be regarded as a relational property when considered in a relativistic scenario. We discuss the consequence that this view may have when correlated randomness is introduced, both in the classical case and in the quantum one.

Homogeneously modified special relativity applications for UHECR and neutrino oscillations

Abstract: One of the key open questions in fundamental physics concerns the supposed quantum structure of spacetime. New physical effects are expected as residual evidence of a more fundamental theory of nature. In this fundamental theory the underlying physical symmetries could be modified by the quantized structure of geometry. One of the most important symmetries in our description of Physics is Lorentz Invariance (LI). Nowadays LI is at the root of our understanding of nature and underlies its physical description. Even if there is no definitive evidence to sustain departures from this symmetry, there are consistent points indicating that Lorentz Invariance Violation (LIV) can be a consequence of quantum gravity. A critical issue concerns therefore the necessity of testing this fundamental symmetry validity. Ultra High Energy Cosmic Rays (UHECR) and neutrino flavor oscillation are promising physical processes of investigation for LIV, since the high energy involved and the interaction of different particle species.

Generalizing the Physical Time Impact on the Astronauts Living on the International Space Station to the Theory of Relativity

Abstract: Traveling in the time has been an interesting topic almost for everyone in the world. The representatives of the community who are scientists worked on this project a lot. As time passed by, humanity information has developed more and more so by considering the obtained information throughout history, some scientists have succeeded in explaining some hypothesis that changed the mind of society about being not capable to travel in the time. Anyway in this research we will get familiar with the suggested paths that make us capable to travel in the time and find out how it is possible. Also, by analyzing and checking out some figures and available data about astronauts, it investigated that traveling in time is not a dream anymore and the rate of passing time can be changed by using nowadays technology.

Direct Derivation of Liénard–Wiechert Potentials, Maxwell’s Equations and Lorentz Force from Coulomb’s Law

Abstract: In this paper, the solution to long standing problem of deriving Maxwell’s equations and Lorentz force from first principles, i.e., from Coulomb’s law, is presented. This problem was studied by many authors throughout history but it was never satisfactorily solved, and it was never solved for charges in arbitrary motion. In this paper, relativistically correct Lienard–Wiechert potentials for charges in arbitrary motion and Maxwell equations are both derived directly from Coulomb’s law by careful mathematical analysis of the moment just before the charge in motion stops. In the second part of this paper, the electrodynamic energy conservation principle is derived directly from Coulomb’s law by using similar approach. From this energy conservation principle the Lorentz force is derived. To make these derivations possible, the generalized Helmholtz theorem was derived along with two novel vector identities. The special relativity was not used in our derivations, and the results show that electromagnetism as a whole is not the consequence of special relativity, but it is rather the consequence of time retardation.

Special Relativity and Its Newtonian Limit from a Group Theoretical Perspective

Abstract: In this pedagogical article, we explore a powerful language for describing the notion of spacetime and particle dynamics intrinsic to a given fundamental physical theory, focusing on special relativity and its Newtonian limit. The starting point of the formulation is the representations of the relativity symmetries. Moreover, that seriously furnishes—via the notion of symmetry contractions—a natural way in which one can understand how the Newtonian theory arises as an approximation to Einstein’s theory. We begin with the Poincare symmetry underlying special relativity and the nature of Minkowski spacetime as a coset representation space of the algebra and the group. Then, we proceed to the parallel for the phase space of a spin zero particle, in relation to which we present the full scheme for its dynamics under the Hamiltonian formulation, illustrating that as essentially the symmetry feature of the phase space geometry. Lastly, the reduction of all that to the Newtonian theory as an approximation with its space-time, phase space, and dynamics under the appropriate relativity symmetry contraction is presented. While all notions involved are well established, the systematic presentation of that story as one coherent picture fills a gap in the literature on the subject matter.

The Rates of the Passing of Time, Presentism, and the Issue of Co-Existence in Special Relativity

Abstract: By considering situations from the paradox of the twins in relativity, it is shown that time passes at different rates along different world lines, answering some well-known objections. The best explanation for the different rates is that time indeed passes. If time along a world line is something with a rate, and a variable rate, then it is difficult to see it as merely a unique, invariant, monotonic parameter without any further explanation of what it is. Although it could, conceivably, be explained by the flow of something, it is better explained by the passing of a point present, which faces the problem that there is no absolute simultaneity in special relativity so that the present for an object is confined to just that object. This raises problems about presentism, eternalism, simultaneity, and special relativity. These issues are addressed first by giving accounts of presentism and eternalism and then an account of existence and times for objects relative to world lines. Finally, an analogy between a world of relativistic objects and Leibniz’s ontology of monads.

The indeterminate present

Abstract: A non-solipsist form of presentness is usually thought to require the non-relative co-presentness of space-like separated events, where this requirement further implies the non-relative simultaneit...

Flat limit of the de Sitter QFT in the rest frame vacuum

Abstract: The problem of the flat limits of the scalar and spinor fields on the de Sitter expanding universe is considered in the traditional adiabatic vacuum and in the new rest frame vacuum we proposed recently, in which the frequencies are separated in the rest frames as in special relativity. It is shown that only in the rest frame vacuum can the Minkowskian flat limit be reached naturally for any momentum, whereas in the adiabatic vacuum, this limit remains undefined in rest frames in which the momentum vanishes. An important role is played by the phases of the fundamental solutions in the rest frame vacuum, which must be regularized to obtain the desired Minkowskian flat limits. This procedure fixes the phases of the scalar mode functions and Dirac spinors, resulting in their definitive expressions derived here. The physical consequence is that, in the rest frame vacuum, the flat limits of the one-particle operators are simply the corresponding operators of special relativity.

Explanation of Light Deflection, Precession of Mercury’s Perihelion, Gravitational Red Shift and Rotation Curves in Galaxies, by using General Relativity or equivalent Generalized Scalar Gravitational Potential, according to Special Relativity and Newtonian Physics

Abstract: The development of Geometric theories of gravitation and the application of the Dynamics of General Relativity (GR) is the mainstream approach of gravitational field. Besides, the Generalized Special Relativity (GSR) contains the fundamental parameter (ξ I) of Theories of Physics (TPs). Thus, it expresses at the same time Newtonian Physics (NPs) for ξ I→ 0 and Special Relativity (SR) for ξ I=1. Moreover, the weak Equivalence Principle (EP) in the context of GSR, has the interpretation: m G=m, where m G and m are the gravitational mass and the inertial rest mass, respectively. In this paper, we bridge GR with GSR. This is achieved, by using a GSR-Lagrangian, which contains the corresponding GR-proper time. Thus, we obtain a new central scalar GSR-gravitational generalized potential V=V(k,l,r,r_dot,ϕ _dot), where k=k(ξ I), l=l(ξ I), r is the distance from the center of gravity and r_dot, ϕ _dot are the radial and angular velocity, respectively. The replacement k=1 and l=ξ I 2 makes the above GSR-potential equivalent to the original Schwarzschild Metric (SM). Thus, it explains the Precession of Mercury’s Perihelion (PMP), Gravitational Deflection of Light (GDL), Gravitational Red Shift (GRS) etc, by using SR and/or NPs. The procedure described in this paper can be applied to any other GR-spacetime metric, in order to find out the corresponding GSR-gravitational potential. So, we also use the GR-proper time of the 3rd Generalized Schwarzschild Metric (3GSM) and we obtain the central scalar GSR-gravitational potential V=V(a,k,l,r_dot,ϕ _dot), where a=a(r). The combination of the above with MOND interpolating functions, or distributions of Dark Matter (DM) in galaxies, provides the functions corresponding a=a(r). Thus, we obtain a new GSR-Gravitational field, which explains the PMP, GDL, GRS as well as the Rotation Curves in Galaxies, eliminating the corresponding DM.

In the Footsteps of Hilbert: The Andréka-Németi Group’s Logical Foundations of Theories in Physics

Abstract: Hilbert’s axiomatic approach to the sciences was characterized by a dynamic methodology tied to scientific and mathematical fields under investigation. In particular, it is an analytic art for choosing axioms but, at the same time, it has to include dynamically synthetic procedures and meta-theoretical reflections. Axioms have to be useful, or capture something, or help as part of explanations. The Andreka-Nemeti group use several formal axiomatic theories together to re-capture, predict, recover or explain the phenomena of special relativity, general relativity and classical kinematics. Their scientific methodology is close to Hilbert’s conceptions of how science should be done ideally. In this paper, we compare Formica’s reading of Hilbert’s axiomatic method to the method used by the Andreka-Nemeti group.

Photon Dreams: Years Later

Abstract: The perspectives of sending a manned space mission to other stars are explored. The conclusions are disappointing: it will never be possible.

A Field Theory of Entropy

Abstract: Starting from an argument on the impossibility of emergence of temperature within current physics, we propose to take temperature as a fundamental property of matter, having a rest energy of E = 2k_BT according to special relativity and the theorem of equipartition of energy. As a logical consequence, this fundamental property of matter must produce a field of entropy according to the equation, square S = − (κ/2) k^2 θ, where κ = 8πG/c^4, is Einstein's constant, and θ temperature density (per unit volume).

Criticism to the Twin's Paradox

Abstract: The so-called “twin’s paradox” is considered an important issue in special relativity theory because it implies a profound understanding of space time structure. And yet, since its original formulation in 1911 by Paul Langevin, numerous alleged explanations for this disturbing paradox have been produced; as it seems, unsuccessfully. This remains a subject for heated debate. Why? Because in all those explanations one tries to reconcile the irreconcilable, this is, what seems to be a logical conclusion (based on the phenomenon of time dilation) with what is simply unacceptable: how can it be a difference in aging from twins without breaking the fundamental equivalency between frames of coordinates? The purpose of this research is, first, to point out the basic flaws in the premises of the usual “explanations” and then to provide a consistent answer to the problem. It is proven here that there is no twin’s paradox and this despite the reality of time dilation. Proceeding without prejudice, simply following appropriate premises and mathematical equations, one finally discovers an astoundingly, wonderfully coherent resolution to the problem, and this in the frame of special relativity itself. The key to understand and finally resolve this puzzling issue is relativistic asynchrony, particularly past and future permutation. Finally, the implications of this understanding, as can be easily induced, go far beyond special relativity. If there is no different aging in inertial frames, regardless of their relative velocity, should this conclusion also apply to accelerated ones, this is, to general relativity?

Special Relativity in Superposition

Abstract: By deriving the Lorentz transformation from the absolute speed of light, Einstein demonstrated the relativistic variability of space and time, enabling him to explain length contraction and time dilation without recourse to a "luminiferous ether" or preferred frame of reference. He also showed that clocks synchronized at a distance via light signals are not synchronized in a frame of reference differing from that of the clocks. However, by mislabeling the relativity of synchrony the "relativity of simultaneity," Einstein implied that this effect concerns an actual difference in times from one frame to another rather than merely a failure of clock synchronization across frames. As a theory of length contraction and time dilation on the basis of relative motion in the context of the absolute speed of light, special relativity is the definitive interpretation of the Lorentz transformation and the correct explanation of relativistic phenomena. The relativity of simultaneity, as I demonstrate, plays no role in this explanation but instead provides apparent justification for a view of time in which the present moment is frame-dependent. In contrast to its legitimate application, special relativity fails as a theory of time on the basis of the relativity of simultaneity.

Aether, Dark Energy, and String Compactifications

Abstract: The 19th century Aether died with Special Relativity but was resurrected by General Relativity in the form of dark energy; a tensile material with tension equal to its energy density. Such a material is provided by the D-branes of string-theory; these can support the fields of supersymmetric particle-physics, although their energy density is cancelled by orientifold singularities upon compactification. Dark energy can still arise from supersymmetry-breaking anti-D-branes but it is probably time-dependent. Recent results on time-dependent compactifications to an FLRW universe with late-time accelerated expansion are reviewed.

Mass energy and momentum in the special relativity with variable speed of light

Abstract: On the basis of establishing the special theory of relativity with variable speed of light and obtaining the step function relationship between mass and speed, this article further seeks the proper collocations of mass, energy and momentum allowed by the "ontology" of moving masses which are in various stages of motion properties or in different physical environments. Three ontology collocation types are obtained. If we consider the basic fact that the lower the energy, the more stable it is, the real physical world ranges from astrophysics issues such as white dwarfs, red giants, and celestial space speeds, to the various light and heavy elementary particles existence, combination and performance，which qualitative knowledge can all be derived from the "ontology collocation ". Two of these three types of collocations are derived from the mass-velocity step function relationship contented of quantum properties, so all the quantum phenomena of modern physics will not be obliterated. It is hoped that the modern physics knowledge accumulated in the laboratory and the scattered various theories will be explained under the dominance of a classic theory. The article also deduced the conversion relationship between the inertial system S and S’ of the three collocation types of mass, energy and momentum of the moving mass. Derive the upgrade and downgrade law of the complete special relativity system, this also greatly expands the way to understand modern physics from the theory of relativity.

The effect of deformation of special relativity by conformable derivative

Abstract: In the article, the deformation of special relativity within the frame of conformable derivative is formulated. Within this context, the two postulates of the theory were re-stated. And, the addition of velocity laws were derived and used to verify the constancy of the speed of light. The invariance principle of the laws of physics is demonstrated for some typical illustrative examples, namely, the conformable wave equation, the conformable Schrodinger equation, and the conformable Gordon-Klein equation. The current formalism may be applicable when using special relativity in a nonlinear or dispersive medium.

GPS Satellite Clock Corrections without Relativity Theory

Abstract: The GPS satellite clock corrections (along with gravitational redshift) which are necessary for the proper operation of the GPS are fully described without invoking relativity theory as is the practice today.

Demystifying the Lagrangians of Special Relativity

Abstract: Special relativity beyond its basic treatment can be inaccessible, in particular because introductory physics courses typically view special relativity as decontextualized from the rest of physics. We seek to place special relativity back in its physics context, and to make the subject approachable. The Lagrangian formulation of special relativity follows logically by combining the Lagrangian approach to mechanics and the postulates of special relativity. In this paper, we derive and explicate some of the most important results of how the Lagrangian formalism and Lagrangians themselves behave in the context of special relativity. We derive two foundations of special relativity: the invariance of any spacetime interval, and the Lorentz transformation. We then develop the Lagrangian formulation of relativistic particle dynamics, including the transformation law of the electromagnetic potentials, the Lagrangian of a relativistic free particle, and Einstein's mass-energy equivalence law ($E=mc^2$). We include a discussion of relativistic field Lagrangians and their transformation properties, showing that the Lagrangians and the equations of motion for the electric and magnetic fields are indeed invariant under Lorentz transformations.