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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]

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]

General relativity predicts that clocks run more slowly near massive objects. The effect is small--a clock at sea level lags behind one 1000m above sea level by only 9.4 ns/day. Here, we demonstrate that a measurement of this effect can be done by undergraduate students. Our paper describes an experiment conducted by undergraduate researchers at Colorado College and the United States Air Force Academy to measure gravitational time dilation. The measurement was done by comparing the signals generated by a GPS frequency standard (sea-level time) to a Cs-beam frequency standard at seven different altitudes above sea level. We found that our measurements are consistent with the predictions of general relativity. [ABSTRACT FROM AUTHOR]

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. [DOI: 10.1119/1.2135319]

An experiment to study the effect of relativistic time dilation on secondary muon fluxes observed at different altitudes is described in this article. Muons, produced as secondary particles from the interaction of primary cosmic rays with the upper atmosphere, form a natural and abundant source of subatomic 'clocks' moving at very high speeds. The measured muon flux on a mountain relative to that measured at sea level can be compared to predictions from calculations that take into account the relativistic time dilation in the muon frame. Situations under which such an experiment can be successfully performed are explored with a day-long field trip to a nearby mountain. This experiment has been developed at Smith College as a module in the Five College cooperative undergraduate advanced laboratory course (other participating institutions are Amherst College, Mount Holyoke College, and the University of Massachusetts).

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]

Explores the possibility of giving a causal interpretation of time dilation for some simple electromagnetic clocks in a stationary and in a moving reference frame. Calculations exploring the concept of time dilation; Cause of the slowing down of the clocks; Time dilation as a dynamic cause-and-effect phenomenon.

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]

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]

The article focuses on relativistic addition of parallel velocities. It states that there are several publications, on different derivations of the formula for the relativistic addition of parallel velocities that do not require the use of Lorentz transformation. It stresses that these derivations has gained favorable response, especially for a first course in special relativity, for the fact that time dilation and Lorentz transformation are complicated to use. The article cites a derivation of the relativistic velocity addition formula which is based on Lorentz contraction and time dilation. It claims that this derivation is simpler because time dilation are scaled down into two, "rod enters the detector" and "rod leaves the detector."

We give a variation of the twin paradox of special relativity in which the relationship of acceleration of the rocket twin and time dilation is clarified.

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]

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]

"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]

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]

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.

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]

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.

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]

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]