The subject of time continues to be a subject of extensive research in the development of new theories of physics. This new volume is addressed to students who are starting a graduate program in physics or electrical engineering interested in complementing their studies of relativity theory and quantum physics, applying the knowledge they have acquired about these themes to the analysis of situations where the issue of time measurement is relevant. This is the case, for example, of clock synchronization, transit times of optical signals through dielectric and absorbing media, lifetimes of excited atomic states, among others. These topics, in addition to being of great importance to theoretical physicists, are the basis of many technological developments. For example, global positional systems (GPS) are based on the predictions of relativity theory about time and the effect of gravity over time measurement.
Divided into six chapters, the volume discusses how the concept of time is present in the main fields of physics, such as classical mechanics, electrodynamics, quantum mechanics and theory of relativity. Illustrative examples and case studies are included in each chapter. The volume includes an analysis of themes related to time such as causality and the arrows of time, spooky action at distance and Einstein-Podolsky-Rosen Paradox, quantum mechanics and entangled states, apparent superluminal velocity, and time reversal.
This book, Looking at Time from a Physics Perspective, will contribute to the understanding of concepts learned in courses on classical mechanics, electrodynamics, quantum mechanics and relativity, reviewing the implications of the time variable for the description of the different physical phenomena at the microscopic and macroscopic level.
1. Time in Classical Mechanics
- Introduction
- Time Reversal Invariance in Classical Mechanics
- Time Reversal for a Simple Case: Dynamics of a Projectile
- Reversible Laws of Motion in Classical Mechanics
- Dissipation and Time Reversal Asymmetry
- Time Reversal of a Conservative System
- Time Reversal of the Dynamics of a Relativistic Particle
- Time Reversal of a Mechanical Wave
- Time Translational Invariance and Energy Conservation
- Conclusions of Chapter 1
2. About Time in Electromagnetic Theory
- Introduction
- Time Reversal Invariance of Maxwell Equations in Vacuum
- Time Reversal of Electromagnetic Waves in Vacuum
- Time Reversal of Material Relations
- Effect of Dispersion in Time Reversal Symmetry
- Time Reversal of Processes with Transfer of Energy
- Doppler Effect and Time Reversal
- Causality in Electrodynamics
- An Arrow of Time for Electromagnetic Radiation
- Optical Dirac-Like Equation and Time Reversal Symmetry
- Electromagnetic Nonreciprocity and Time Reversal
- Application of Time Reversal for Locating Lightning Discharges
- Conclusions of Chapter 2
3. Time in Non-Relativistic Quantum Mechanics
- Introduction
- Time Reversal Symmetry
- Breaking of Time-Reversal Symmetry by An External Magnetic Field
- Time Reversal of the Photoelectric Effect
- Time Reversal Operator for Systems with Spin
- Time Reversal and Geometric Phases
- Effect of Dissipation in a Quantum System
- Entanglement and Causality
- What about Time Symmetry in Quantum Optics?
- PT-Symmetric Quantum Mechanics
- Conclusions of Chapter 3
4. Time in Special Relativity Theory
- Introduction
- Fundamental Postulates of Relativity Theory
- Time and Length Measurements
- The Space Time and Lorentz Transformations
- About the Simultaneity of Events
- Space Time and the Light Cone
- Some Reflections about Time, Causality and Our Life
- Causality and Superluminal Signals
- Relativistic Transformation of Velocities
- Time Dilation of the Lifetime of a Particle
- Time and Relativistic Doppler Effect
- Lorentz Transformations of Other Physical Quantities
- A Note about Superluminal Particles
- Conclusions
5. Time in General Relativity Theory
- Introduction
- Equivalence Principle
- Gravity and Light
- Geometry of Space Time
- Plausibility Arguments for Schwarzschild Metric
- Gravity and Time
- Effects of Gravitational Field due to Earth on Time Measurements
- Application of General Relativity Theory to Global Positioning System
- An Overview of Einstein’s Field Equations
- General Relativity and Blackholes
- Time Reversal Symmetry in an Expanding Universe Model
- Time Reversal Symmetry in Cosmology
- Time Traveling through Wormholes: Is It Possible?
- General Relativity and Quantum Entanglement
- Measurement of the Space Time Interval Between Two Events
- General Relativity Theory and Quantum Mechanics
- Conclusions
6. Glance to Some Recent Theories about Time in Physics
- Introduction
- Time in the Cellular Automaton Interpretation of Quantum Mechanics
- The Thermal Time Hypothesis
- Time as a Discrete Dynamical Variable
- Quantum Operator for the Time in Non-Relativistic Quantum Mechanics
- Quantum Operator for Time in Relativistic Quantum Mechanics
- Time in Quantum Gravity
- Exploring in the Physics of Time Travel
- Conclusions and Epilogue
Biography
Patricio Robles has a long professional and academic career as a physics teacher and researcher, as well as an electrical engineer. Despite being retired, he continues developing research in theoretical physics and teaching courses on electrical projects at Pontifical Catholic University of Valparaíso, Chile. He also works as a consulting engineer in electrical studies related to the analysis of faults in electrical systems and protection schemes. He has published his research concerned with topics about electromagnetic fields and quantum physics in international journals and book chapters. His more recent publications are related to bounded pairs of electrons, massless Dirac fermions, and photon propagation through dispersive media. During last five years, he has collaborated with international journals of physics and electrical engineering as a referee, reviewing articles submitted for publication in journals such as the European Journal of Physics and Nanotechnology Journal.
