The Twin Paradox

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
High Speed ◽  
Point Of View ◽  
Introductory Physics ◽  
Twin Paradox ◽  
Classic Problem ◽  
Galilean Relativity ◽  
Inertial Frames ◽  
Cognitive Overload ◽  
Spacetime Diagram ◽  
Thinking Tools

To prepare for the high‐speed world where Galilean relativity breaks down, we now practice the skill of thinking in different frames. Practicing this in our familiar lowspeed world will help us avoid cognitive overload when we enter the more counterintuitive high‐speed world. We examine two problems that illustrate the process of thinking in different frames. Te frst is a brain‐teaser that suddenly becomes easier in a particular frame; the second is a classic problem from introductory physics that we can solve in a new way using symmetry and frame-based thinking tools alone. Along the way, we will learn how to use the spacetime diagram, a major tool that will appear throughout this book. Te chapter concludes with another look at accelerated vs. inertial frames, from the spacetime diagram point of view.

Reasoning with Frames and Spacetime Diagrams

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
High Speed ◽  
Point Of View ◽  
Introductory Physics ◽  
Classic Problem ◽  
Galilean Relativity ◽  
Inertial Frames ◽  
Cognitive Overload ◽  
Spacetime Diagram ◽  
Thinking Tools ◽  
The Way

To prepare for the high‐speed world where Galilean relativity breaks down, we now practice the skill of thinking in different frames. Practicing this in our familiar lowspeed world will help us avoid cognitive overload when we enter the more counterintuitive high‐speed world. We examine two problems that illustrate the process of thinking in different frames. Te frst is a brain‐teaser that suddenly becomes easier in a particular frame; the second is a classic problem from introductory physics that we can solve in a new way using symmetry and frame‐based thinking tools alone. Along the way, we will learn how to use the spacetime diagram, a major tool that will appear throughout this book. Te chapter concludes with another look at accelerated vs. inertial frames, from the spacetime diagram point of view

The Elements of Relativity

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
General Relativity ◽  
Geometric Model ◽  
Experimental Tests ◽  
Big Bang ◽  
Twin Paradox ◽  
Space And Time ◽  
Galilean Relativity ◽  
Time Work ◽  
Thinking Tools ◽  
Working Out

Relativity is a set of remarkable insights into the way space and time work. The basic notion of relativity, first articulated by Galileo, explains why we do not feel Earth moving as it orbits the Sun and was successful for hundreds of years. We present thinking tools that elucidate Galilean relativity and prepare us for the more modern understanding. We then show how Galilean relativity breaks down at speeds near the speed of light, and follow Einstein’s steps in working out the unexpected relationships between space and time that we now call special relativity. These relationships give rise to time dilation, length contraction, and the twin “paradox” which we explain in detail. Throughout, we emphasize how these effects are tightly interwoven logically and graphically. Our graphical understanding leads to viewing space and time as a unified entity called spacetime whose geometry differs from that of space alone, giving rise to these remarkable effects. The same geometry gives rise to the energy?momentum relation that yields the famous equation E = mc2, which we explore in detail. We then show that this geometric model can explain gravity better than traditional models of the “force” of gravity. This gives rise to general relativity, which unites relativity and gravity in a coherent whole that spawns new insights into the dynamic nature of spacetime. We examine experimental tests and startling predictions of general relativity, from everyday applications (GPS) to exotic phenomena such as gravitomagnetism, gravitational waves, Big Bang cosmology, and especially black holes.

scholarly journals Lorentz Boosts and Wigner Rotations: Self-Adjoint Complexified Quaternions

Physics ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 352-366
Author(s):  
Thomas Berry ◽  
Matt Visser
Keyword(s):  
Point Of View ◽  
Sufficient Condition ◽  
Use Of Self ◽  
Necessary And Sufficient Condition ◽  
Wigner Rotation ◽  
Inertial Frames ◽  
Explicit Formulae ◽  
Specific Implementation ◽  
Necessary And Sufficient ◽  
Lorentz Boosts

In this paper, Lorentz boosts and Wigner rotations are considered from a (complexified) quaternionic point of view. It is demonstrated that, for a suitably defined self-adjoint complex quaternionic 4-velocity, pure Lorentz boosts can be phrased in terms of the quaternion square root of the relative 4-velocity connecting the two inertial frames. Straightforward computations then lead to quite explicit and relatively simple algebraic formulae for the composition of 4-velocities and the Wigner angle. The Wigner rotation is subsequently related to the generic non-associativity of the composition of three 4-velocities, and a necessary and sufficient condition is developed for the associativity to hold. Finally, the authors relate the composition of 4-velocities to a specific implementation of the Baker–Campbell–Hausdorff theorem. As compared to ordinary 4×4 Lorentz transformations, the use of self-adjoint complexified quaternions leads, from a computational view, to storage savings and more rapid computations, and from a pedagogical view to to relatively simple and explicit formulae.

Comparison of the reluctance laminated and solid rotor synchronous machine operating at high temperatures

2019 ◽  
Vol 38 (4) ◽  
pp. 1111-1119 ◽  
Author(s):  
Marcin Lefik ◽  
Krzysztof Komeza ◽  
Ewa Napieralska-Juszczak ◽  
Daniel Roger ◽  
Piotr Andrzej Napieralski
Keyword(s):  
High Speed ◽  
Design Methodology ◽  
Three Dimensional ◽  
Synchronous Machine ◽  
Point Of View ◽  
Heat Sources ◽  
Model Calculations ◽  
Content Type ◽  
Thermal Phenomenon ◽  
Practical Implications

Purpose The purpose of this paper is to present a comparison between reluctance synchronous machine-enabling work at high internal temperature (HT° machine) with laminated and solid rotor. Design/methodology/approach To obtain heat sources for the thermal model, calculations of the electromagnetic field were made using the Opera 3D program including effect of rotation and the resulting eddy current losses. To analyse the thermal phenomenon, the 3D coupled thermal-fluid (CFD) model is used. Findings The presented results show clearly that laminated construction is much better from a point of view of efficiency and temperature. However, solid construction can be interesting for high speed machines due to their mechanical robustness. Research limitations/implications The main problem, despite the use of parallel calculations, is the long calculation time. Practical implications The obtained simulation and experimental results show the possibility of building a machine operating at a much higher ambient temperature than it was previously produced for example in the vicinity of the aircraft turbines. Originality/value The paper presents the application of fully three-dimensional coupled electromagnetic and thermal analysis of new machine constructions designed for elevated temperature.

scholarly journals New Dzungaria Gates for wmlt-corridor: historical necessity

2019 ◽  
Vol 5 (3) ◽  
pp. 36-44
Author(s):  
Viktor A. Bogachev ◽  
Yuri A. Terentyev ◽  
Viktor V. Koledov ◽  
Taras V. Bogachev
Keyword(s):  
Mathematical Models ◽  
Variational Methods ◽  
High Speed ◽  
Optimization Problem ◽  
Point Of View ◽  
The North ◽  
Computer Math ◽  
Pass Through ◽  
Historical Necessity ◽  
North Western

Background: Research is ongoing relating to the analysis of a set of issues that arise in connection with the creation of the operating on the basis of vacuum magnetic technologies a transcontinental high-speed land transport corridor, connecting the eastern regions of China with Russia. As part of the variation calculus task, the geopolitical, economic, social, logistic, geographic, geomorphological, seismological, topographic components of the project are considered, in which it is assumed that the high speed overland route will pass through the north-western part of the historical region of Dzungaria. Aim: Find the most optimal from the point of view of the above components the location of the most important section of high speed overland route passing through Central Asia. Methods: Variational methods for solving an optimization problem with the use of a computer math system. Results: After creating a fairly informative and versatile picture of the region in question, the foundations of the corresponding mathematical models are built. Conclusion: The New Dzungarian Gates is a key element in choosing the location of a high-speed overland route based on VMLT.

3D Electromagnetic Modeling of Through Silicon Vias and Interposers in Electronic Packaging

2012 ◽  
Vol 2012 (1) ◽  
pp. 001057-001067
Author(s):  
Darryl Kostka ◽  
Antonio Ciccomancini Scogna
Keyword(s):  
High Speed ◽  
Signal Transmission ◽  
Form Factors ◽  
Point Of View ◽  
Electromagnetic Modeling ◽  
Electromagnetic Simulations ◽  
Full Wave ◽  
3D Ics ◽  
Silicon Vias ◽  
Delivery Networks

3D ICs promise “more than Moore” integration by packing a lot of functionality into small form factors. Interposers along with TSVs play an important role in 3D integration from an electrical, thermal and mechanical point of view. The goal of this paper is to electrically model TSVs and 3D interposers by means of three 3D full wave electromagnetic simulations. A comparative analysis of various configurations of signal delivery networks in 3D interposers for high speed signal transmission is presented.

Lorentz Transformation as a Galilei Transformation with Physical Length and Time Contractions

1988 ◽  
Vol 43 (10) ◽  
pp. 859-864
Author(s):  
H. E. Wilhelm
Keyword(s):  
Rest Frame ◽  
Lorentz Transformations ◽  
Speed Of Light ◽  
Analogous Structure ◽  
Galilean Relativity ◽  
Symmetry Properties ◽  
Inertial Frames ◽  
Ether Frame ◽  
Light Signals ◽  
Time Variables

Abstract The Lorentz transformations between the space-time coordinates of a point in two inertial frames with arbitrary relative velocity, are reformulated as Galilei transformations with length and time contractions, by introducing the ether rest frame (in which light signals propagate isotropically with the vacuum speed of light). The generalized Galilei transformations for the (longitudinal) space coordinates (x1,2) and the time variables (t1,2) of a point in two inertial frames ∑1,2 are not only of analogous structure, but have remarkable symmetry properties, too. The appearing length and time contractions are absolute effects in the sense of Lorentz-Fitzgerald, i.e., a rod has its largest length and a clock its fastest rate when at rest in the ether frame ∑0. Thus, an analytical reformulation and a physical interpretation of the Lorentz transformations within Galilean relativity physics is achieved.

scholarly journals A Stop-Probability Approach for O-D Service Frequency on High-Speed Railway Lines

2019 ◽  
Vol 11 (24) ◽  
pp. 6996
Author(s):  
Shuo Zhao ◽  
Xiwei Mi ◽  
Zhenyi Li
Keyword(s):  
High Speed ◽  
Travel Demand ◽  
Mathematical Formulation ◽  
Real Life ◽  
Point Of View ◽  
High Speed Railway ◽  
Passenger Travel ◽  
Optimal Service ◽  
Service Frequency ◽  
Railway Operation

Train stop planning provides appropriate service for travel demand and stations and plays a significant role in railway operation. This paper formulates stop planning from the point of view of direct travel between origin-destination (O-D) stations and proposes an analytical method to theoretically derive optimal service frequencies for O-D demand on different levels. Considering different O-D demand characteristics and train service types, we introduce the concept of stop probability to present the mathematical formulation for stop planning with the objective of minimizing per capita travel time, which is solved by an iterative algorithm combined with local search. The resulting optimal stop probabilities can be used to calculate the required service frequency for each train type serving different demand categories. Numerical examples, based on three real-life high-speed railway lines, demonstrate the validity of the proposed method. The proposed approach provides a more flexible and practical way for stop planning that explicitly takes into account the importance of different stations and passenger travel characteristics.

A practical guide to IT OT convergence – getting value from your business analytics

2019 ◽  
Vol 59 (2) ◽  
pp. 526
Author(s):  
Russell Byfield
Keyword(s):  
High Speed ◽  
Data Gathering ◽  
Point Of View ◽  
Regulatory Control ◽  
Business Analytics ◽  
Business Operation ◽  
Service Companies ◽  
Industrial Internet ◽  
Hybrid Solution ◽  
Different Sources

A lot of time, effort and money has been and is being spent by operating companies and service companies in collecting data from many different sources, agglomerating that data, carrying out analytics on that data with the intention of turning that data into actionable insights that positively impact safety, environment, operations and profitability. This has been done with varying levels of success by approaching the problem from either an information technology (IT) or an operational technology (OT) point of view. What we are finding is that the best outcomes are achieved by having IT and OT domain experience with operational industry expertise within the same team. This has proven to be the case in other industries. There is also a need to understand edge and cloud actionable insights delivery in order to determine the optimal balance of edge and cloud delivery in a hybrid solution model. There is a continuum of analytics from high speed analytics at the edge, for such things as assisting regulatory control and real-time safety system diagnostics, to data lake analysis in the cloud, for planning, supply chain and business prioritisation and optimisation. Some analytics are best done at the edge; some are better done in the cloud. It’s a ‘horses for courses’ approach. The nature of the desired outcome, the required actionable insight and the nature of the data gathering are critical in determining the most effective approach. This paper discusses several examples of how this integrated IT OT approach took a desired outcome and turned it into an analytics platform that delivered significant value to the business. This paper cites examples of edge and cloud analytics that are enabled by integrating clever and sufficient industrial internet of things (IIoT) connectivity, which lead to actionable insights. These, in turn, ensured the correct action was effectively applied to the correct part(s) of the business operation, resulting in effective achievement of the desired outcome.

Sharing Tracks With High Speed Trains in Urban Area: Risk due to Drivers and Pedestrian Perception

2020 ◽  
Author(s):  
Oren Masory
Keyword(s):  
Urban Area ◽  
High Speed ◽  
Human Perception ◽  
Point Of View ◽  
Time To Contact ◽  
High Speed Trains ◽  
Rail Traffic

Abstract Sharing operations of high-speed passenger and heavy slow freight trains on the same rail tracks presents additional risks to vehicle and pedestrians who cross the tracks. This is due to increase in rail traffic at crossing; drivers and pedestrians overestimate the amount of time they have to cross the intersection in front of a higher speed train; and due to the fact that circuited crossings are not adaptable and might lead to confusion and bad decisions. From human perception point of view these accidents happen in particular when the high speed trains were just introduced since the drivers as well as the pedestrians are used to interact with slower trains. Looming is a major factor that contributes to the perception error experiences by a driver or pedestrian. On one hand a faster train is being detected at farther distance than a slower one but its time to contact (the time it will reach the crossing) is shorter. Thus, a pedestrian might think that he has enough time to cross the railroad but actually he does not. Horn sound has the same effect on human perception. This paper discusses issues related to human perception which contribute to accidents in these cases.

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