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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.

Smartphones and tablets are packed with sensors that allow us to take experimental data, essentially making them mobile physics labs. Apps exist that make it easy to capture and analyze data from these sensors, allowing users to study diverse phenomena such as free fall acceleration, the speed of sound,radioactivity, and many others. Commonly, the use of apps in the physics classroom focuses on existing apps rather than on the creation of apps themselves. This is for a good reason-writing an app usually requires advanced knowledge of programming languages and experience with app design. These skills are generally regarded as beyond the typical physics student. However, there are app development environments, such as MIT App Inventor 2 for Android, which make the process of creating an app and utilizing the sensors much more accessible to students. Putting the ability to create and configure apps within the reach of students can also help integrate computation into the curriculum. In this article, we discuss our creation of an Android app, Time Dilation Calculator, done as part of a senior undergraduate capstone project, which uses App Inventor and a mobile device's global positioning system (GPS) receiver to calculate the time dilation effect of special relativity.

Undergraduate physics majors typically begin their study of modern physics with special relativity. It is here that physics students first encounter the counterintuitive concepts of time dilation and length contraction. Unfortunately, the derivations of these results are often cloaked in several layers of analysis that render them rather mysterious and otherworldly for novice students. Here we show how a very simple thought experiment leads directly to a student-friendly derivation of time dilation and length contraction. The only assumption needed is the constancy of the speed of light.

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]

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]

Describes the extended general physics course taught at Rutgers University. The course presents to students at the high school algebra level the topic of analyzing a particular thought experiment that yields the time dilation formula and subsequently space contraction, velocity addition, and other 20th-century physics concepts. (MVL)

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.

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]

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]

The article discusses the use of application software in teaching physics. It mentions that developing application software requires advanced knowledge of programming languages and experience with software design. It notes the integration of computer science and programming into K-12 curriculum by developing an application using code blocks which allow users to design and package an Android app solely using the graphical interface environment.

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]

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.

Reports on discussions used in the study and teaching of relativity as a part of the course Extended General Physics at Rutgers. Analysis of a light clock thought experiment; Yielding of time dilation formula, space contraction, velocity addition and other formulas.

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.

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 offers information regarding the aspects of Doppler effect. It mentions that a graphical representation is demonstrated to observe the phenomenon. It informs that everything will actually appear in fast motion when two individuals approach each other. It further highlights that time dilation and change of distance are considered for the calculation of time interval.

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.

The article discusses the Lorentz contraction, one of the concepts related to special relativity. It explores the muons lifetime measurement experiments which were depicted in the film "Time Dilation: An Experiment With Mu-Mesons" and provide background for time dilation and Lorentz contraction. It describes Lorentz contraction, based on the experiments, as the phenomenon in which Mount Washington, New Hampshire contracted and the muons were ridden down the sea levels.

Gravity bends light. One can argue this by reasoning that a beam of light should travel in a curved path when viewed from within an accelerating frame of reference, and then invoking Einstein's principle of equivalence, which asserts that the effects observed in an accelerating frame of reference are indistinguishable from the effects observed in a uniform gravitational field. If light bends in an accelerating reference frame, it must also bend in a gravitational field. [ABSTRACT FROM AUTHOR]

The article describes how to calculate two relativistic corrections to a clock aboard a satellite orbiting the earth, such as a Global Positioning System transmitter. The first correction concerns the time dilation of the clock due to its orbital speed. The second correction concerns the fact that a clock at the higher gravitational potential of orbit runs faster than a surface clock.

Light has a fascinating property: it always travels the path that takes the least time between any two points. This is the motivating property behind optical phenomena such as reflection and refraction. The unreasonable economic efficiency of light is captured by a single proposition: the principle of least action (PLA) in optics. Unlike reflection and refraction, which emerge from optimizing a one-dimensional function, the PLA emerges from optimizing an infinite-dimensional functional. The PLA can be difficult for students to comprehend, as the formulation of the Lagrangian is often left unexplained. To this end, this paper presents various simulations to demonstrate the action principle, including a numerical solution to a generalization of the brachistochrone problem to an arbitrary refractive profile. The interactive simulations discussed in the paper are available at Ref. 1. [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."

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.

There is an ongoing challenge with STEM education: making physics, math, and science, in general, interesting, understandable, and retentive for college science and non-science majors, K-12 students, and the public. If not imparting detailed knowledge, at least one would like to introduce important concepts that will be remembered, appreciated, and hopefully would be pursued in more detail by audience members. One solution: as noted by Socrates, "Wisdom begins in wonder." Indeed, magic as a form of wonderment dates back to Socrates and even earlier. One of the first magic books, The Discoverie of Witchcraft by Reginald Scot, was published in 1584, predating publication of many science texts. In this paper the author, based on recent research, advocates using special forms of magic to both amaze and teach, and in particular to illustrate the wonders of modern physics, i.e., Nature's magic, but with connections also to classical physics. [ABSTRACT FROM AUTHOR]

The global positioning system (GPS) must be familiar to every user of a smartphone as a way to locate one's position on Earth to within several meters. The constellation of orbiting atomic clocks equipped with radio transmitters allows receivers on Earth to determine their own position by measuring the travel times of radio signals from multiple satellites. A physics laboratory for an upper-level majors course involving GPS signals might be assumed to focus on relativistic effects (either special or general), but this paper demonstrates that the ultra-precise time signal from a GPS receiver can be used for a variety of data collection purposes. [ABSTRACT FROM AUTHOR]

The concept of redshift is very often used in teaching physics and astronomy, as well as in science public outreach. Redshift is an interesting topic, used to describe many physical processes such as the Doppler effect or the expansion of the universe. Nevertheless, there are unfortunately also misconceptions about redshift. When facing the redshift topic with students and teachers, we have to focus sometimes on dissolving these misconceptions. Therefore, the idea of this paper, in which the most common misconceptions are treated, arose from direct experience and discussions with colleagues in the field. This article explains what redshift is and how it works. Moreover, since redshift has a great potential for teaching and is usable in many physics and astronomy problems, examples and specifically developed exercises are also used in this article. [ABSTRACT FROM AUTHOR]

The pandemic triggered by the SARS-CoV-2 virus has produced worldwide interruptions of face-to-face teaching activity in both schools and universities. In Italy, the quarantine began in the second half of February 2020 and lasted for all the second semester of lectures. The University of Bologna, where all the authors of the present article are based, developed and activated several interfaces necessary to efficiently deliver online teaching courses with the utmost speed. The framework used by the authors is based on a common platform, Microsoft TEAMS, available to all teachers at Bologna University. [ABSTRACT FROM AUTHOR]

In this paper, we describe a study of cosmic ray muon rates and energies at various elevations on Mauna Kea on the island of Hawaii. The study was originally conceived as an extension to the upper-division modern physics laboratory at the University of Hawaii at Hilo and used the TeachSpin Muon Physics apparatus (abbreviated TSMP below) from that lab. The purpose of this paper is to provide a blueprint for similar experiments appropriate to introductory physics laboratory courses and to make students aware of the variety of investigations possible using this type of apparatus. Plans for future work are outlined in the conclusion. [ABSTRACT FROM AUTHOR]

While the majority of students that pursue a physics education learn mostly in a classroom setting, hands-on experiences can take their appreciation of physics to the next level. Summer internships offer just that, hands-on learning experiences and a taste of what a career in physics is really like. Many research-oriented institutions offer summer internship experiences for students at all levels, from high school through graduate school. The experience and connections made during these summer programs can be transformative to a student's career and science identity. [ABSTRACT FROM AUTHOR]

The article focuses on high school physics teaching experience among high school physics teachers.

Introductory physics courses can be a challenge for some college students, especially those that have not taken Advanced Placement (AP) physics courses in high school. Even some classical mechanics concepts, such as energy, power, or the laws of Newton, can be non-intuitive and hard to grasp. When it comes to evaluating the learning outcome of our students, some of the aspects we evaluate are their abilities to solve numerical problems. By solving problems the students show how well they understood the concepts and the problem-solving methods. But students can practice enough and learn how to solve related numerical exercises without a deep understanding of the physical concepts. When asked more conceptual questions, some students struggle and lack confidence. [ABSTRACT FROM AUTHOR]

The article discusses the planetarium show “Einstein's Playground" thats explains the various branches of astronomy and how its is associated to the finite speed of light and relativity.

Electromagnetic induction, represented by either Faraday's law or the Lorentz force law, produces many paradoxes requiring careful examination and application of these laws. The paradoxical example of induction, presented herein, arose in a class and is resolved within the framework of special relativity. [ABSTRACT FROM AUTHOR]

This is the third of four articles on teaching special relativity in the first week of an introductory physics course. With Einstein's second postulate that the speed of light is the same to all observers, we could use the light pulse clock to introduce time dilation. But we had difficulty introducing the Lorentz contraction until we saw the movie "Time Dilation, an Experiment with Mu-Mesons" by David Frisch and James Smith. The movie demonstrates that time dilation and the Lorentz contraction are essentially two sides of the same coin. Here we take the muon's point of view for a more intuitive understanding of the Lorentz contraction, and use the results of the movie to provide an insight into the way we interpret experimental results involving special relativity.

A quiz concerning the constant buoyant force in a helium-filled balloon is presented.

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.

The article discusses aspects of relativistic momentum and relativistic kinetic energy that may assist physics students in the understanding of the dynamics of special relativity at the undergraduate level. Topics discussed include the highlighting of the principal dissimilarities from their classical counterparts as well as the appropriate relativistic analogues relating classical kinetic energy to classical momentum and velocity.

A great deal has long been known about student difficulties connecting real-world experiences with what they are learning in their physics classes, making learning basic ideas of classical physics challenging. Understanding these difficulties has led to the development of many instructional approaches that have been shown to help students make connections to the real world, think constructively, and learn the material successfully. However, what happens when making connections to the real world is more complicated. It is one thing to try to figure out how pushing a block with a constant force leads to constant speed, but it is very different to try to build toward an understanding of time dilation. Do the same instructional approaches work here? Also, is it possible that improved instructional approaches lead to improved student approaches when trying to make sense of difficult and very unfamiliar material? In this paper we describe a unique opportunity to perform a controlled experiment by interviewing identical twin brothers working together to resolve the twin paradox. These were intelligent and articulate science students with similar backgrounds but with diverging undergraduate experiences. One happened to take traditional physics classes and the other happened to take classes designed through Physics Education Research.

The Doppler shift is a frequency change of a repetitive effect, as measured by a receiver, due to the motion of the wave emitter, to the motion of the wave receiver, or both. A demonstration of the effect is provided by the sound of a car's horn that changes from a higher pitch to a lower pitch when a car drives past. Most derivations of the Doppler formula assume sinusoidal waves. We want to call the attention of readers to a derivation that uses a graphical representation based on a graph of position versus time. We will adopt a particle model of machine gun bullets fired at a constant period, thus getting a derivation that just requires the knowledge of kinematics. Furthermore, we will explain how to introduce the time dilation in order to get the formula for the relativistic Doppler shift.

Many derivations of the relativistic addition law of parallel velocities without use of the Lorentz transformations (LT) are known. Some of them are based on thought experiments that require knowledge of the time dilation and the length contraction effects. Other derivations involve the Doppler effect in the optic domain considered from three inertial reference frames in relative motion. A few derivations simply involve only the principle of constancy of the light velocity. Such derivations are interesting for the teaching of special relativity theory since the relativistic addition of velocities leads directly to the LT. The derivation we propose is based on a machine gun-target analogy of the acoustic Doppler effect, considered from the rest frame of the machine gun and from the rest frame of the target.

The article offers the authors discussion on the potential role of experience with relativity as a tool for teaching. They mention the efforts of physicist George Gamow in recognizing travel closer to the speed of light highlighted in his book "Mr Tompkins in Wonderland" despite its impossibility reported by his colleague Albert Einstein. They also note their development of the video game "A Slower Speed of Light" which is based on a first-person relativity visualization engine .

"What would you see if you were riding a beam of light?" This thought experiment, which Einstein reports to have "conducted" at the age of 16, of course has no sensible answer: as Einstein published a decade later, you could never reach the speed of light. But it does make sense to ask what you would see if you were traveling close to the speed of light, and one of the first physicists to embark on this effort was George Gamow in his "Mr. Tompkins in Wonderland." His protagonist is speeding on a bicycle through a city where the speed of light is lower, thus ingeniously taking advantage of the fact that special relativity scales with "v/c": for it to kick in, you either have to move very fast (in rather unfamiliar territory), or light has to be slow (in which case special relativity kicks in at everyday velocities in everyday situations). Gamow provides drawings of what Mr. Tompkins and people at the curb would see in this slow-light city, at least, what they would see if one only took into account two of the effects: length contraction and time dilation.

In popular accounts of the time dilation effect in Einstein's special relativity, one often encounters the statement that moving clocks run slow. For instance, in the acclaimed PBS program "NOVA," Professor Brian Greene says, "[I]f I walk toward that guy... he'll perceive my watch ticking slower." Also in his earlier piece for The New York Times, he writes that "if from your perspective someone is moving, you will see time elapsing slower for him than it does for you. Everything he does ... will appear in slow motion." We need to be care- ful with this kind of description, because sometimes authors neglect to consider the finite time of signal exchange between the two individuals when they observe each other. This article points out that when two individuals approach each other, everything will actually appear in fast motion--a manifestation of the relativistic Doppler effect. (Contains 1 figure.)

A thought experiment that includes a square light clock is similar to the traditional vertical light beam and mirror clock, except it is made up of four mirrors placed at a 45[degree] angle at each corner of a square of length L[subscript 0], shown in Fig. 1. Here we have shown the events as measured in the rest frame of the square light clock. By studying the same cycle of events measured in a frame of reference where the square light clock is in motion with speed of "v", we can derive both time dilation and, independently, length contraction. This will be done by analyzing the changing dimensions and also the one-cycle timing for this square light clock.

In 2007 many AAPT members received a booklet that is the first chapter of a physics textbook available on a CD. This book espouses the new educational philosophy of teaching special relativity as the first item in the topic of mechanics. Traditionally, special relativity is part of one or more modern physics chapters at the end of the text, and very often this material is never utilized due to time constraints. From a logical standpoint, special relativity is important in satellite communications and in cosmology, as well as in modern physics applications such as atomic theory and high-energy physics. The purpose of this paper is to show that the new philosophy can be carried out in a noncalculus physics course, by demonstrating that all of the principal results of special relativity theory can be obtained by simple algebra. To accomplish this, we shall propose alternate derivations for two results that are usually obtained with calculus. Textbooks typically obtain the equations for time dilation and for length contraction from simple considerations based on Einstein's second postulate. We shall start from this point.

The article reviews the web site Learning about science and religion (LASAR), located at http://faradayschools.com/, from the Faraday Institute for Science and Religion.

The article announces that 30 nontechnical lectures of astronomical research by astronomers including Frank Drake, Mike Brown, and Natalie Batalha are available free of charge in audio and video podcasts through internet and iTunes.