Search

This paper develops the approach to special relativity put forward by John S. Bell. The classical dynamics of an electron orbiting a nucleus in uniform motion is solved analytically and compared to numerical simulations for an accelerated nucleus. The relativistic phenomena of length contraction and time dilation are shown to result from the electric and magnetic forces on the electron when its motion is analyzed in a single frame of reference. The relevance of these results for understanding the theory of special relativity is discussed. In this paper, the author explores a suggestion by John Bell for teaching special relativity: to introduce length contraction and time dilation as dynamical phenomena arising from the laws of motion, without reference to the Lorentz transformations. The paper provides historical and philosophical insight into the development of special relativity alongside an analysis of electron orbits in a classical model of an atom. Using only the Lorentz force law, the author illustrates the deformation of orbits of moving and accelerating atoms with approximate, exact, and numerical calculations that reveal time dilation and length contraction. Instructors may find these derivations useful in teaching courses on modern physics, relativity, classical mechanics, electrodynamics, or numerical methods. [ABSTRACT FROM AUTHOR]

The theory of special relativity is one of the most significant achievements in modern physics, with several important predictions such as time dilation, size contraction for a moving object, and mass-energy equivalence. Recent studies have demonstrated size contraction for an antiferromagnetic (AFM) domain wall (DW). Here, we show the excitation of terahertz (THz) magnons from a moving AFM DW under the magnetic anisotropy energy gradient. The energy of magnons comes from the loss of the effective DW mass due to the reduction in anisotropy energy. Also, the excitation of THz magnons is accompanied by a DW width broadening, overcoming the Lorentz contraction effect. Our results pave the way to study relativistic physics in AFM textures and to efficiently generate THz magnons by DC electric means. [ABSTRACT FROM AUTHOR]

We report on the progress toward a dual-species cadmium and strontium atom interferometer for fundamental physics tests. We have developed and characterized a complete baseline laser system for cadmium, which provides the high power and narrow linewidth necessary for laser cooling and trapping and for performing atom interferometry, with upgraded systems for strontium also implemented. An overview of a design for cooling cadmium is presented, and we outline the basic design of a Cd–Sr atomic fountain, discussing atom launching techniques and the possible role of blackbody radiation. The excellent properties of cadmium and strontium, both individually and as a test pair, are discussed along with the enabled fundamental physics program of tests of the weak equivalence principle and the measurement of relativistic time dilation effects in quantum superpositions of clocks. [ABSTRACT FROM AUTHOR]

Time-resolved studies have so far relied on rapidly triggering a photo-induced dynamic in chemical or biological ions or molecules and subsequently probing them with a beam of fast moving photons or electrons that crosses the studied samples in a short period of time. Hence, the time resolution of the signal is mainly set by the pulse duration of the pump and probe pulses. In this paper, we propose a different approach to this problem that has the potential to consistently achieve orders of magnitude higher time resolutions than what is possible with laser technology or electron beam compression methods. Our proposed approach relies on accelerating the sample to a high speed to achieve relativistic time dilation. Probing the time-dilated sample would open up previously inaccessible time resolution domains. [ABSTRACT FROM AUTHOR]

The precision of optical atomic clocks is approaching a regime where they resolve gravitational time dilation on smaller scales than their own extensions. Hence, an accurate description of quantum clocks has to take their spatial extension into account. In this article, as a first step toward a fully relativistic description of extended quantum clocks, we investigate a quantized version of Einstein's light clock fixed at a constant distance from a large massive object like the Earth. The model consists of a quantum light field in a one-dimensional cavity in Schwarzschild spacetime, where the distance between the mirrors is fixed by a rigid rod. By comparing a vertical and a horizontal clock, we propose an operational way to define the clock time when the clock resolves gravitational time dilation on scales smaller than its extension. In particular, we show that the time measured by the vertical light clock is equivalent to the proper time defined at its center. We also derive fundamental bounds on the precision of these clocks for measurements of proper time and the Schwarzschild radius. [ABSTRACT FROM AUTHOR]

It has long been suspected by general relativists that physicists who do not specialize in general relativity (GR) believe that special relativity (SR) is incapable of modeling dynamics within accelerated reference frames. Consequently, many physicists may conclude that certain phenomena, such as time dilation due to acceleration, can only be described with GR. The fact of the matter is, as long as spacetime is flat, SR is fully capable of describing the dynamics of accelerated reference frames. In the classic textbook Gravitation, the authors state that "special relativity was developed precisely to predict the physics of accelerated objects." To quote Sean Carroll in his textbook Spacetime and Geometry, "The notion of acceleration in special relativity has a bad reputation, for no good reason." Finally, in a quote that drives the main point of this article home, the late general relativist Alfred Schild once said, "A good many believe that [the twin] paradox can only be resolved by the general theory of relativity. They find great comfort in this because they don't know any general relativity." [ABSTRACT FROM AUTHOR]

This article discusses the topic of interstellar travel and its challenges. It highlights the common misconception that distances between celestial objects are much larger than the objects themselves. The article also explores the concept of relativity and its potential implications for space travel. It presents a mathematical equation that can be used to calculate ship time for long journeys, taking into account the effects of acceleration and time dilation. The article concludes by acknowledging the various practical and human factors that would need to be considered for extended space travel. [Extracted from the article]

Teaching special relativity to lower-division students is challenging because results such as time dilation, length contraction, and frame dependence of simultaneity are counterintuitive. The literature is extensive, so only a brief list is given here, with articles divided roughly between discussions of general principles and calculations applied to selected physical systems. [ABSTRACT FROM AUTHOR]

We demonstrate that the de Broglie wave of a particle in a gravitational field turns toward the region of lower gravitational potential, causing the particle to fall. This turning is caused by clocks running slower in the smaller potential. We use the analogy of ocean waves that are slower in shallower water and turn toward beaches. This approach implies that the motion is along a geodesic and explains the free fall qualitatively and quantitatively with only elementary algebra. [ABSTRACT FROM AUTHOR]

This article discusses the misconceptions that some students have about length contraction and time dilation in special relativity. To address these misconceptions, the author presents a thought experiment involving photographing a meter stick moving at relativistic speeds. The experiment demonstrates that length contraction is a real physical phenomenon that exists independently of time dilation and clock synchronization. The article emphasizes the importance of recognizing that synchronicity and simultaneity are relative and reference frame dependent. Overall, the thought experiment helps students understand that length contraction is not a mirage but rather the result of different electromagnetic forces acting on stationary and moving objects. [Extracted from the article]

Captain Einstein is a virtual reality (VR) movie that takes you on a boat trip in a world with a slow speed of light. This allows for a direct experience of the theory of special relativity, much in the same spirit as in the Mr. Tompkins adventure by George Gamow (1939). In this paper, we go through the different relativistic effects (e.g., length contraction, time dilation, Doppler shift, light aberration) that show up during the boat trip, and we explain how these effects were implemented in the 360 ° video production process. We also provide exercise questions that can be used-in combination with the VR movie-to gain insight and sharpen the intuition on the basic concepts of special relativity. [ABSTRACT FROM AUTHOR]

We present a comprehensive discussion of the formulation of the kinematics of special relativity, i.e., the Lorentz transformation. We begin with a concise new proof that the principle of relativity implies that the transformation of event coordinates between inertial reference frames is linear. We then give a clear derivation of the pre-Lorentz transformation, which follows from the principle of relativity. We then show that the pre-Lorentz transformation and the inertial invariance of the speed of light together result in the Lorentz transformation. This, of course, is essentially the traditional formulation. We next present two additional formulations, one using Lorentz–Fitzgerald contraction and one using time dilation, instead of inertial invariance. This is reasonable since Lorentz–Fitzgerald contraction and time dilation are about as well established as and are arguably less abstract than inertial invariance, and thus may profitably be used instead of inertial invariance to complete the formulation. We then present a complete proof that the pre-Lorentz transformation and the requirement of closure upon composition together imply that the transformation is either a Galilean transformation or a generalized Lorentz transformation. This is noteworthy in that it gets ever so close to the Lorentz transformation without invoking light. In the course of this, we obtain a generalized velocity addition rule, which reduces to the velocity addition rule of special relativity. We next show that the generalized Lorentz transformation, together with inertial invariance, Lorentz–Fitzgerald contraction, and time dilation, used one at a time, yields three more formulations. We then show that the unspecified, nonzero, constant speed in the generalized Lorentz transformation can be determined without any reference to light, thereby obtaining a seventh formulation. Light plays no explicit role in the four formulations employing Lorentz–Fitzgerald contraction and time dilation and plays no role whatsoever in the seventh formulation. Thus, and this is a fact which should be strongly emphasized, the formulation of special relativity in no way depends upon the nature of electromagnetic radiation. We conclude by briefly discussing these seven formulations of the kinematics of special relativity and some associated implications. [ABSTRACT FROM AUTHOR]

At six temperatures T between 10 and 50 °C and at mole fractions xg of glycerol (0≤xg≤=0.9) the complex (electric) permittivity ε(ν) of glycerol/water mixtures has been measured as a function of frequency ν between 1 MHz and 40 GHz. The spectra of the glycerol/water mixtures can be well represented by a Davidson-Cole [J. Chem. Phys. 18, 1417 (1950)] relaxation function that reveals an unsymmetric relaxation time distribution. The effective dipole orientation correlation factor derived from the static permittivity displays an unspectacular behavior upon mixture composition. The dielectric relaxation time reveals a simple relation to the shear viscosity of the mixtures, but both quantities are not proportional to one another. The relaxation times at high temperatures nicely complement previously determined low temperature data, following a Vogel-Fulcher-Tammann-Hesse [Z. Phys. 22, 645 (1925); J. Am. Chem. Ceram. Soc. 8, 339 (1923); Z. Anorg. Allg. Chem. 156, 245 (1926)] (VFTH) temperature dependence. When the Eyring behavior is assumed a limiting high temperature form of the VFTH relation, enthalpy, and entropy of activation values are found which adopt significantly higher values in the glycerol rich mixtures than in the water rich liquids. The relaxation time distribution parameter at high water content indicates a dynamically heterogeneous structure of the liquids. Likely there exist glycerol rich and water rich microphases. [ABSTRACT FROM AUTHOR]

Investigates the thermal relaxation of the photoluminescence (PL) in InAs/GaAs quantum dot superlattices having two to more than three times the critical thickness for spontaneous island formation. Role of repopulation in the PL quenching; Attribution of the temperature dependence of PL energy to the dilation of lattice and electron-lattice interaction.

According to Einstein's general theory of relativity, a clock runs more slowly if it is close to a large gravitating object. This principle was highlighted in the movie "Interstellar," in which the main character spends several hours on a planet orbiting a massive black hole, and returns to find that his young daughter has become an elderly woman. In the movie, one hour on the planet equates to seven years on Earth. The same effect can be measured on a much smaller scale by changing locations within Earth's gravitational field. Using atomic clocks, we have compared the ticking of time at Colorado College (elevation 1845 m above sea level), at the United States Air Force Academy (elevation 2165 m), and near the summit of Pikes Peak (elevation 4288 m). Our results confirm that clocks do indeed tick more quickly at higher altitudes, in accordance with Einstein's theory. This work was carried out as a collaboration of physics majors and faculty at Colorado College (CC) and the United States Air Force Academy (USAFA). The experimental technique is straightforward and our results can be reproduced by other students and teachers, given access to an atomic clock and reasonably large changes in elevation. Indeed, a similar endeavor has been reported by amateur clock enthusiasts. [ABSTRACT FROM AUTHOR]

The article describes an activity program for secondary education which asks students to provide graphical and quantitative solutions to the problem regarding special relativity on twin paradox acceleration.

A hierarchical Gaussian mixture model is proposed to characterize shallow water acoustic response functions that are time-varying and sparse. The mixture model is based on the assumption that acoustic paths can be partitioned into two sets. The first is a relatively coherent set of arrivals that on average exhibit Doppler spreading about a mean Doppler and the remaining set is of multiple surface scattered paths that exhibit a spectrally flat Doppler. The hierarchy establishes constraints on the parameters of each of these Gaussian models such that coherent components of the response are both sparse and in the ensemble obey the Doppler spread profile. This is accomplished with a Bernoulli model that indicates the ensonification state of each element in the bi-frequency representation of the acoustic response function. Estimators of the time-varying acoustic response for the full duration of a broadband transmission are developed and employed to compensate for the shared time-varying dilation process among the coherent arrivals. The approach ameliorates response coherence degradation and can be employed to enhance coherent multi-path combining and is a useful alternative to time recursive estimation. The model is tested with acoustic communication recordings taken in shallow water at low signal-to-noise ratios. [ABSTRACT FROM AUTHOR]

In this article, the physics of gravitational waves is explored through the use of an electromagnetic analogy which allows the reader more direct access to the waves' physical effects on detectors. Gravitational waves physics using Fermi coordinates: A new teaching perspective I Matteo Luca Ruggiero i B 89 b (6), p. 639 https://doi.org/10.1119/10.0003513 The study of gravitational waves has never been more topical than in the past decade, but the textbook treatment of gravitational waves remains intimidating. Searching a quantum database with Grover's search algorithm I Ben Kain i B 89 b (6), p. 618 https://doi.org/10.1119/10.0004835 This illustration of a useful quantum computing algorithm can be presented to undergraduate students who have not yet completed a quantum mechanics course, and includes code that can be run on IBM's quantum computers. [Extracted from the article]

Einstein's special theory of relativity includes many non-intuitive and apparently paradoxical conclusions about space and time. One of these is time dilation, the fact that a clock moving relative to an observer runs slower than an identical clock at rest in the observer's reference frame. This is clearly exhibited in the extended mean lifetime of elementary particles moving at high speed, compared to their mean lifetime when at rest, and must be taken into account when processing signals from atomic clocks carried by satellites in the global positioning system (GPS). My intent in this note is not to derive this or other relativistic effects; such derivations may be found in many textbooks. Rather, I would like to share two figures I prepared while teaching elementary physics quite a few years ago, to help understand the apparent paradox that two observers, in relative motion, both measure the other's clock to run slower than their own. It is my hope that instructors can reproduce these two figures and find them useful in discussions to illustrate these basic concepts. The sketches are only approximately drawn to scale. [ABSTRACT FROM AUTHOR]

We provide three examples of the use of geometric reasoning with three-dimensional spacetime diagrams, rather than algebraic manipulations using three-dimensional Lorentz transformations, to analyze problems in special relativity. The examples are the "rising manhole" paradox, the "moving spotlight" problem, and Einstein's light-clock derivation of time dilation. [ABSTRACT FROM AUTHOR]

Special relativity offers the possibility of going on a trip to the center of our galaxy or even to the end of our universe within a lifetime. On the basis of the well known twin paradox, we discuss uniformly accelerated motion and emphasize the local perspective of each twin concerning the interchange of light signals between both twins as well as their different views of the stellar sky. For this purpose we developed two Java applets that students can use to explore interactively and understand the topics presented here. [ABSTRACT FROM AUTHOR]

The scalar dissipation rate transport in both the corrugated flamelet and thin reaction zone regimes is studied using three-dimensional direct numerical simulation (DNS) databases for freely propagating statistically planar turbulent premixed flames. Both flames have comparable turbulent Reynolds number but the flame representing the corrugated flamelet combustion regime has a global Damköhler number, Da>1, whereas the second flame representing the thin reaction zone regime has Da<1. It is demonstrated that the turbulent transport of the scalar dissipation rate and its molecular diffusive transport have strong Da dependence. The contributions of dilatation rate, the turbulence-scalar interaction, the reaction-rate–scalar gradient interaction, and the dissipation processes have leading order contributions for both the flames. However, the turbulence-scalar interaction dissipates scalar gradients in the Da>1 flame, while it produces the scalar gradients in the Da<1 flame. Simple algebraic models for the contributions of the various processes noted above to the scalar dissipation rate evolution are proposed and their a priori assessment is carried out with respect to DNS data. These models explicitly have Da and the Karlovitz number Ka dependence, and thus, they can be viewed and used as unified models for both the corrugated flamelet and thin reaction zone regimes. Physical realizability of the modeled scalar dissipation rate transport equation is studied and the model constants obtained by using the DNS data sets are shown to satisfy the realizability condition. [ABSTRACT FROM AUTHOR]

"Real Time Relativity" is a computer program that lets users move at relativistic speeds through a simulated world populated with planets, clocks, and buildings. The counterintuitive and spectacular optical effects of relativity are prominent, while systematic exploration of the simulation allows the user to discover relativistic effects such as length contraction and the relativity of simultaneity. We report on the physics and technology underpinning the simulation, and our experience using it for teaching special relativity to first year students. [ABSTRACT FROM AUTHOR]

In special relativity, a pair of clocks synchronized in their own reference frame are not synchronized in another. How do two clocks, initially synchronized and at rest in the laboratory frame, fall out of sync as their speed relative to the lab gradually increases? The answer lies in general-relativistic time dilation. The path to the answer sheds light on the thread-between-spaceships paradox (also called the Bell spaceship paradox), on the twin paradox, and on the character of length contraction. [ABSTRACT FROM AUTHOR]

A visual representation of Minkowski spacetime appropriate for a student with a background in geometry and algebra is presented. Minkowski spacetime can be modeled with a Euclidean four-space to yield accurate visualizations as predicted by special relativity. The contributions of relativistic aberration as compared to classical prerelativistic aberration to the geometry are discussed in the context of its visual representation. [ABSTRACT FROM AUTHOR]

The first year of university physics typically starts with a semester of mechanics and the non-immediacy of acceleration. In any case, the introduction of the field concept represents the first big step for the students away from immediacy; in a Freudian sense, it is the toilet training of the physics student. This claim does excite the minority of students who are destined (doomed?) to pursue physics careers, but for the immune herd, the only question is whether it will be on the test. [Extracted from the article]

We describe a compact apparatus for measuring the charge-averaged lifetime of atmospheric muons in plastic scintillator using low-cost, low-power electronics. We present measurements of the stopping rate of atmospheric muons as a function of altitude to demonstrate relativistic time dilation. The apparatus is designed for the advanced undergraduate physics laboratory and is suitable for field measurements. [ABSTRACT FROM AUTHOR]

We show how students can be led to an understanding of the connection between special relativity and general relativity by considering the time dilation effect of clocks placed on the surface of the Earth. This paper is written as a Socratic dialog between a lecturer and a student. [ABSTRACT FROM AUTHOR]

Explores the confirmed hypothesis that neutrinos have mass and that they transform from one type to another. Information on the Solar Neutrino Problem; Kinds of neutrinos; Equation for time dilation.

The article discusses about simplifying time dilation and length contraction to students through a thought experiment. Topics include the Lorentz transformations; experiments conducted using a light clock, the period of oscillation of the photons, and explaining the students about special relativity.

Discusses the twin paradox and superluminal travel on a cylindrical space-time with particular attention to the role of coordinate patching and their physical interpretation. Information on a variation of the twin paradox on a cylinder; Detailed information on coordinate patches; Conclusion reached.

The article presents a science experiment using square light clock to analyze special relativity. The clock is placed at rest and then the light beam is shown starting at position P1, then reflecting from a mirror at P2. The clock is considered moving uniformly with speed v. It is demonstrated that both the length contraction and time dilation can be derived independent from each other.

The article focuses on the derivation of relativistic velocity addition law based on a machine gun-target analogy of the acoustic Doppler effect. The process is considered from the rest frame of the machine gun and from the rest frame of the target. It provides a detailed derivation of the relativistic addition law of parallel velocities without prior knowledge of Lorentz transformations. It notes that the derivation involves special relativity via the time dilation effect formula.

Presents a variation and extension of the twin paradox discussed by S.P. Boughn in the `American Journal of Physics' periodical. Relativity parable with pedagogical power; Occurrence of assymetry in aging as meaningless; Origin of age differences assigned to any specific part of a worldline.