Showing papers on "Special relativity (alternative formulations) published in 2018"

Two Miracles of General Relativity

Abstract: We approach the physics of minimal coupling in general relativity, demonstrating that in certain circumstances this leads to (apparent) violations of the strong equivalence principle, which states (roughly) that, in general relativity, the dynamical laws of special relativity can be recovered at a point. We then assess the consequences of this result for the dynamical perspective on relativity, finding that potential difficulties presented by such apparent violations of the strong equivalence principle can be overcome. Next, we draw upon our discussion of the dynamical perspective in order to make explicit two ‘miracles’ in the foundations of relativity theory. We close by arguing that the above results afford us insights into the nature of special relativity, and its relation to general relativity.

Figures of light in the early history of relativity (1905-1914)

Abstract: Albert Einstein's bold assertion of the form-invariance of the equation of a spherical light wave with respect to inertial frames of reference (1905) became, in the space of six years, the preferred foundation of his theory of relativity Early on, however, Einstein's universal light-sphere invariance was challenged on epistemological grounds by Henri Poincare, who promoted an alternative demonstration of the foundations of relativity theory based on the notion of a light-ellipsoid Drawing in part on archival sources, this paper shows how an informal, international group of physicists, mathematicians, and engineers, including Einstein, Poincare, Hermann Minkowski, Ebenezer Cunningham, Harry Bateman, Otto Berg, Max Laue, A A Robb, and Ludwig Silberstein, employed figures of light during the formative years of relativity theory in their discovery of the salient features of the relativistic worldview

Observers and their notion of spacetime beyond special relativity.

Abstract: It is plausible that quantum gravity effects may lead us to a description of Nature beyond the framework of special relativity. In this case, either the relativity principle is broken or it is maintained. These two scenarios (a violation or a deformation of special relativity) are very different, both conceptually and phenomenologically. We discuss some of their implications on the description of events for different observers and the notion of spacetime.

Voigt transformations in retrospect: missed opportunities?

Abstract: The teaching of modern physics often uses the history of physics as a didactic tool. However, as in this process the history of physics is not something studied but used, there is a danger that the history itself will be distorted in, as Butterfield calls it, a “Whiggish” way, when the present becomes the measure of the past. It is not surprising that reading today a paper written more than a hundred years ago, we can extract much more of it than was actually thought or dreamed by the author himself. We demonstrate this Whiggish approach on the example of Woldemar Voigt’s 1887 paper. From the modern perspective, it may appear that this paper opens a way to both the special relativity and to its anisotropic Finslerian generalization which came into the focus only recently, in relation with the Cohen and Glashow’s very special relativity proposal. With a little imagination, one can connect Voigt’s paper to the notorious Einstein-Poincare priority dispute, which we believe is a Whiggish late time artifact. We use the related historical circumstances to give a broader view on special relativity, than it is usually anticipated.

Observers and Their Notion of Spacetime beyond Special Relativity

Abstract: It is plausible that quantum gravity effects may lead us to a description of Nature beyond the framework of special relativity. In this case, either the relativity principle is broken or it is maintained. These two scenarios (a violation or a deformation of special relativity) are very different, both conceptually and phenomenologically. We discuss some of their implications on the description of events for different observers and the notion of spacetime.

Unitary quantum theories are incompatible with special relativity

Abstract: It is shown that the combination of a unitary quantum theory and special relativity may lead to a contradiction when considering the statistics of certain measurement results in different Lorentz frames in a Gedankenexperiment. This result seems to imply that either unitary quantum theories are wrong or if a unitary quantum theory is right then there must exist a preferred Lorentz frame.

A new model of special relativity and the relationship between the time warps of general and special relativity

Abstract: Einstein's two theories of relativity were introduced over 100 years ago. High school science students are seldom exposed to these revolutionary ideas as they are often perceived to be too difficult conceptually and mathematically. This paper brings together the two theories of relativity in a way that is logical and consistent and enables the teaching of relativity as a single subject. This paper introduces new models and analogies which are suitable for the teaching of Einstein's relativity at a high school level, exposing students to our best understanding of time, space, matter and energy.

Kinetic Energy and Conservation of Momentum

Abstract: In the history of physics, kinetic energy has been represented by two expressions. One from Issac Newton, the other from Special Relativity. Both expressions are expected to describe a physical system that demands conservation of momentum. By examining the expression of momentum in a projectile motion, the kinetic energy from Issac Newton is found to obey conservation of momentum while the kinetic energy from Special Relativity is found to violate conservation of momentum.

Very special conformal field theories and their holographic duals

Abstract: Cohen and Glashow introduced the notion of very special relativity as viable space-time symmetry of elementary particle physics. As a natural generalization of their idea, we study the subgroup of the conformal group, dubbed very special conformal symmetry, which is an extension of the very special relativity. We classify all of them and construct field theory examples as well as holographic realization of the very special conformal field theories.

On the Incompatibility of Special Relativity and Quantum Mechanics

Abstract: Some of the strategies which have been put forward in order to deal with the inconsistency between quantum mechanics and special relativity are examined. The EPR correlations are discussed as a simple example of quantum mechanical macroscopic effects with spacelike separation from their causes. It is shown that they can be used to convey information, whose reliability can be estimated by means of Bayes' theorem. Some of the current reasons advanced to deny that quantum mechanics contradicts special relativity are refuted, and an historical perspective is provided on the issue.

Space and Time as a Consequence of Ghirardi-Rimini-Weber Quantum Jumps

Abstract: Abstract The Ghirardi-Rimini-Weber theory of spontaneous collapse offers a possible resolution of the quantum measurement problem. In this theory, the wave function of a particle spontaneously and repeatedly localises to one or the other random position in space, as a consequence of the hypothesised quantum jumps. In between jumps, the wave function undergoes the usual Schrödinger evolution. In the present paper, we suggest that these jumps take place in Hilbert space, with no reference to physical space and a physical three-dimensional space arises as a consequence of localisation of macroscopic objects in the universe. That is, collapse of the wave-function is responsible for the origin of space. We then suggest that similar jumps take place for a hypothetical time operator in Hilbert space and classical time, as we know it emerges from localisation of this time operator, for macroscopic objects. More generally, the jumps are suggested to take place in an operator space-time in Hilbert space, leading to an emergent classical space-time.

Klein-Weyl's program and the ontology of gauge and quantum systems

Abstract: We distinguish two orientations in Weyl's analysis of the fundamental role played by the notion of symmetry in physics, namely an orientation inspired by Klein's Erlangen program and a phenomenological-transcendental orientation. By privileging the former to the detriment of the latter, we sketch a group(oid)-theoretical program—that we call the Klein-Weyl program —for the interpretation of both gauge theories and quantum mechanics in a single conceptual framework. This program is based on Weyl's notion of a “ structure-endowed entity ” equipped with a “ group of automorphisms ”. First, we analyze what Weyl calls the “ problem of relativity ” in the frameworks provided by special relativity, general relativity, and Yang-Mills theories. We argue that both general relativity and Yang-Mills theories can be understood in terms of a localization of Klein's Erlangen program: while the latter describes the group-theoretical automorphisms of a single structure (such as homogenous geometries), local gauge symmetries and the corresponding gauge fields (Ehresmann connections) can be naturally understood in terms of the groupoid-theoretical isomorphisms in a family of identical structures . Second, we argue that quantum mechanics can be understood in terms of a linearization of Klein's Erlangen program. This stance leads us to an interpretation of the fact that quantum numbers are “ indices characterizing representations of groups ” ((Weyl, 1931a), p.xxi) in terms of a correspondence between the ontological categories of identity and determinateness .

Isochrony in 3D Radial Potentials: From Michel Hénon’s Ideas to Isochrone Relativity: Classification, Interpretation and Applications

Abstract: Revisiting and extending an old idea of Michel Henon, we geometrically and algebraically characterize the whole set of isochrone potentials. Such potentials are fundamental in potential theory. They appear in spherically symmetrical systems formed by a large amount of charges (electrical or gravitational) of the same type considered in mean-field theory. Such potentials are defined by the fact that the radial period of a test charge in such potentials, provided that it exists, depends only on its energy and not on its angular momentum. Our characterization of the isochrone set is based on the action of a real affine subgroup on isochrone potentials related to parabolas in the $${\mathbb{R}^2}$$ plane. Furthermore, any isochrone orbits are mapped onto associated Keplerian elliptic ones by a generalization of the Bohlin transformation. This mapping allows us to understand the isochrony property of a given potential as relative to the reference frame in which its parabola is represented. We detail this isochrone relativity in the special relativity formalism. We eventually exploit the completeness of our characterization and the relativity of isochrony to propose a deeper understanding of general symmetries such as Kepler’s Third Law and Bertrand’s theorem.

Special Relativity Leads to a Trans-Planckian Crisis that is Solved by Haug’s Maximum Velocity for Matter

Abstract: In gravity theory, there is a well-known trans-Planckian problem, which is that general relativity theory leads to a shorter than Planck length and shorter than Planck time in relation to so-called black holes. However, there has been little focus on the fact that special relativity also leads to a trans-Planckian problem, something we will demonstrate here. According to special relativity, an object with mass must move slower than light, but special relativity has no limits on how close to the speed of light something with mass can move. This leads to a scenario where objects can undergo so much length contraction that they will become shorter than the Planck length as measured from another frame, and we can also have shorter time intervals than the Planck time. The trans-Planckian problem is easily solved by a small modification that assumes Haug’s maximum velocity for matter is the ultimate speed limit for something with mass. This speed limit depends on the Planck length, which can be measured without any knowledge of Newton’s gravitational constant or the Planck constant. After a long period of slow progress in theoretical physics, we are now in a Klondike “gold rush” period where many of the essential pieces are falling in place.

Underlining some mathematical and physical aspects about the concept of motion in general relativity

Abstract: The Einstein initial foundations of general relativity have to do with his great intuition and they are not clear as it is for special relativity. As has been widely emphasized, for example, in the book of Ohanian and Ruffini, the very name of the theory indicates a misconception. Despite this, the high school textbooks (at least the Italian ones) and books of scientific divulgation introduce the Einstein gravitational theory still following the initial approach leading, in our opinion, to misinterpretations. A careful student, for example, immediately asks: it is not true that the Earth rotates because I can consider it at rest thanks to general relativity theory. The relativity of motion is trivial in mathematics while it has deep meaning in physics and it is not sufficiently analyzed. Similarly, the arbitrary choice of the origin and the perfect equivalence between all coordinate systems are mathematical properties satisfied by general relativity and students can confuse it with physical equivalence between reference systems that have a deeper meaning and the Einstein theory does not verify it. Gravitational force does not exist and this is the real core of Einsteinian revolution. As happens in Newtonian physics and Special Relativity, also in general relativity the relative motions are the geodesic motions with the difference that spacetime can be curved and geodesics may not be a straight line. Similarly, in general relativity forces cause non-geodesic motion. Geodesic and non-geodesic are tensorial properties and for this reason they are absolute.

Reflection and Outlook on Special Relativity Education from the Perspective of Einstein: Focusing on Research Papers Published in Korea

Abstract: The purpose of this paper is to examine what are the most important ideas of special relativity (SR) education from Einstein’s perspective, to reflect on the previous studies of special relativity education up to the present through Einstein’s ideas, and to give prospects for its future direction. We analyzed Einstein’s book, The Evolution of Physics, focusing on three questions: Why should we teach SR? What kinds of the content knowledge of SR should we teach? How should we teach SR? Based on this analysis, we formulated three criteria for SR education: (1) intrinsic value, (2) integral knowledge, and (3) hermeneutic/communicative approach. In addition, research papers on SR education published in South Korea were analyzed based on these criteria. As a result, we have found that many studies are very different from Einstein’s perspective on SR education. And we discussed that, despite the researchers’ intentions, their studies are likely to lead other research on SR and educational practices toward the opposite of Einstein’s emphasis (i.e., instrumental purpose, fragmentary content knowledge, and partial/functional approach). Finally, we suggest Einsteinian Physics Education as a new way to improve not only SR education but also physics education in general from Einstein’s perspective.

Tense and Relativity

Abstract: Those inclined to positions in the philosophy of time that take tense seriously have typically assumed that not all regions of space-time are equal: one special region of space-time corresponds to what is presently happening. When combined with assumptions from modern physics this has the unsettling consequence that the shape of this favored region distinguishes people in certain places or people traveling at certain velocities. In this paper I shall attempt to avoid this result by developing a tensed picture of reality that is nonetheless consistent with ‘hypersurface egalitarianism’—the view that all hypersurfaces are equal.

On the Non-Feasibility of Special relativity

Abstract: This paper is divided into three main parts which deal with the feasibility of the Special Theory of Relativity (STR).In Part 1two proofs that vary in complexity are given which show that Einstein’s necessary conditions are not sufficient conditions. The first of these proofs uses the same thought experiment employed in his paper, where it is shown that he didn’t look at his own one-way results. Thus, his round-trip transformations are correct and necessary, but not sufficient. The second proof shows the often-used railroad car thought experiment in many textbooks also fails. In Part 2 Einstein’s equation for mass, which is derived from and dependent on STR, is shown to be an untenable theory. Then in Part 3STR is proved be incorrect as based on this author’s paper on electromagnetic theory. Finally, in Part 4 the experimental verification of STR is challenged. A replacement theory for STR, including relativistic mass, is covered in the third paper in this series.

A De Sitter-Hubble Equation, the Force in Special Relativity and Some Concepts on Symmetry

Abstract: Previous works [1] [2] proposed several relevant characteristics of the Hubble field such as the intensity ΓH, potential VH, force FH, Poisson equation, energy EH and a tensor (Tμν)H as well as Ricci and Hubble scalars. In this paper, it is made a proposal for two new ones: the kind of the Hubble field as well as a De Sitter-Hubble equation. Moreover, it is proposed a necessary change in the equation of force in Special Relativity. It is included a paragraph on the search for Symmetry in Physics, Chemistry and Time. Conclusions mention an eventual mirror image both the intensity of the Hubble and gravitational fields as well as the relative impossibility for a Big Crunch.

Twin Peaks: A Possible Signal in the Production of Resonances beyond Special Relativity

Abstract: It is usually expected that quantum gravity corrections will modify somehow the symmetries of special relativity. In this paper, we point out that the possibility of very low-energy (with respect to the Planck energy) modifications to special relativity in the framework of a deformed relativistic theory is not ruled out, and that, depending on the value of that scale, such a possibility could be tested in accelerator physics. In particular, we take a simple example of a relativistic kinematics beyond special relativity from the literature, and obtain a remarkable effect: two correlated peaks (twin peaks) associated with a single resonance. We analyze this phenomenology in detail, use present experimental data to put constraints of the order of TeV on the scale of corrections to special relativity, and note that such an effect might be observable in a future very high-energy proton collider.

Why the Tsirelson Bound? Bub's Question and Fuchs' Desideratum.

Abstract: To answer Wheeler's question "Why the quantum?" via quantum information theory according to Bub, one must explain both why the world is quantum rather than classical and why the world is quantum rather than superquantum, i.e., "Why the Tsirelson bound?" We show that the quantum correlations and quantum states corresponding to the Bell basis states, which uniquely produce the Tsirelson bound for the Clauser-Horne-Shimony-Holt quantity, can be derived from conservation per no preferred reference frame (NPRF). A reference frame in this context is defined by a measurement configuration, just as with the light postulate of special relativity. We therefore argue that the Tsirelson bound is ultimately based on NPRF just as the postulates of special relativity. This constraint-based/principle answer to Bub's question addresses Fuchs' desideratum that we "take the structure of quantum theory and change it from this very overt mathematical speak ... into something like [special relativity]." Thus, the answer to Bub's question per Fuchs' desideratum is, "the Tsirelson bound obtains due to conservation per NPRF."

The Distance Between Two Inertial Observers in Relative Motion in Special Relativity

Abstract: When two inertial observers A and B in relative motion measure the distance between them, will they obtain the same value? Although there is a lack of detailed expositions on this issue, many relativity articles and books seem to suggest that the observers on the earth measure a longer distance than that measured by the observers moving relative to the earth. The present study has examined this issue in detail, using two fundamental conditions of special relativity: 1) the space time interval between two events in the Minkowski space is independent of the inertial reference frame chosen; and 2) there is no privileged reference frame and all inertial reference frames are equal. The results of the present study shows that the value of the distance between A and B measured by observer B in a frame where B is stationary is the same as that obtained by observer A in a frame where A is stationary. The idea that distance measured by observer A is longer than that measured by observer B contradicts special relativity, because it designates de facto more privileged reference frames, which cannot be correct within the framework of special relativity.

The Schrödinger Equation and Negative Energies

Abstract: We present a nonrelativistic wave equation for the electron in (3+1)-dimensions which includes negative-energy eigenstates. We solve this equation for three well-known instances, reobtaining the corresponding Pauli equation (but including negative-energy eigenstates) in each case.

Covariant fields on anti-de Sitter spacetimes

Abstract: The covariant free fields of any spin on anti-de Sitter (AdS) spacetimes are studied, pointing out that these transform under isometries according to covariant representations (CRs) of the AdS isometry group, induced by those of the Lorentz group. Applying the method of ladder operators, it is shown that the CRs with unique spin are equivalent with discrete unitary irreducible representations (UIRs) of positive energy of the universal covering group of the isometry one. The action of the Casimir operators is studied finding how the weights of these representations (reps.) may depend on the mass and spin of the covariant field. The conclusion is that on AdS spacetime, one cannot formulate a universal mass condition as in special relativity.