In the previous chapters, we have made an imaginary travel in a ship which we might call “time” for analyzing how this concept is present in the physical theories which describe our world and the diverse interactions which make possible its existence as we perceive it under our notion of reality. We have traveled from the submicroscopic scale—requiring a quantum description— up to the cosmological dimensions where gravity acquires a crucial role distorting the space-time of the special relativity theory. In this chapter, we discuss some of the most recent publications related to physical theories about time, starting with the cellular automation interpretation of quantum mechanics (QM) formulated by Gerard’t Hooft, where information loss is considered as the cause of the time-reversal asymmetry. Then we continue with the thermal time hypothesis of Carlo Rovelli, who asserts that it is possible to formulate classical mechanics in a way in which the time variable is treated on equal footing as other physical variables, and not considered as a special and independent variable. Afterward, we analyze theories which propose quantization of time, and then continue with the discussion of proposed time operators for non-relativistic and relativistic QM. At the end of that section, we discuss theories related with time in quantum gravity and then we briefly explore in the physics of time travel.
In the previous chapters, we have made an imaginary travel in a ship which we might call “time” for analyzing how this concept is present in the physical theories which describe our world and the diverse interactions which make possible its existence as we perceive it under our notion of reality. We have traveled from the submicroscopic scale—requiring a quantum description— up to the cosmological dimensions where gravity acquires a crucial role distorting the space-time of the special relativity theory. In this chapter, we discuss some of the most recent publications related to physical theories about time, starting with the cellular automation interpretation of quantum mechanics (QM) formulated by Gerard’t Hooft, where information loss is considered as the cause of the time-reversal asymmetry. Then we continue with the thermal time hypothesis of Carlo Rovelli, who asserts that it is possible to formulate classical mechanics in a way in which the time variable is treated on equal footing as other physical variables, and not considered as a special and independent variable. Afterward, we analyze theories which propose quantization of time, and then continue with the discussion of proposed time operators for non-relativistic and relativistic QM. At the end of that section, we discuss theories related with time in quantum gravity and then we briefly explore in the physics of time travel.
Time is used in non-relativistic quantum theory as a classical concept. On the one hand, time is the parameter entering Schrödinger's equation and measured by an external laboratory clock. But it could be considered that time also plays the role of an observable when a given event occurs (e.g., when a particle crosses through a potential barrier), and one would expect that like every observable, it should be represented in the theory by an operator whose properties are predictors of the outcome of time measurements made on physical systems. Several time operators have been proposed in different publications, but still, there is not a widely accepted consensus. That subject, among others concerned with time in quantum mechanics, is analyzed in the present chapter, where we focus on the analysis of time-reversal symmetry in non-relativistic quantum systems. The search for symmetries in Physics helps to study the structure of theories. Briefly speaking, a symmetry is a transformation that does not change the structure of the theory. We start with the analysis of Schrödinger’s Equation verifying that for obtaining a time-symmetric description of the dynamics of a particle, the operation of time-reversal must include conjugation represented by the action of an antiunitary operator acting over a wave function. In particular, we analyze quantum systems whose evolution is determined by a set of external parameters varying cyclically, discussing how even though these parameters return to their initial values, the state of the system acquires a geometric phase, which depends on the path followed by the external parameters in the parameter space and which in general can be associated with the lack of the time-reversal symmetry of the system.
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.
Time – what it is and its nature – has from the beginning held mysteries for layman, philosopher, and physicist alike. Periodic phenomena from motions of heavenly bodies and pendulums to quantal atomic clocks provide the means to measure time intervals, and Newton’s absolute time is a background flow against which classical and non-relativistic quantum physics is played out. While internally consistent, these two fields of physics are incompatible with the requirement of treating space and time on an equal footing. Quantum field theories provide the answer, as both treated as parameters, physics residing instead in the states and operators. But even in classical physics and quantum mechanics, time-independent descriptions provide an alternative to an explicitly time-dependent one. These, including a general method of approach called invariant imbedding, are discussed as alternative representations of an underlying reality that is the concern of physics.
We think of time as one of four dimensions appearing in the equations of motion of Newtonian and quantum physics, but participating independently of space. In these pages we explore the way the time variable affects how space is perceived. We show first that non-commutation may be interpreted as the difference between electron and photon cycling during radiation processes. For every electron cycle of a quantum oscillator there are two photon cycles. Secondly, the difference between relativistic and non-relativistic quantum mechanics is shown to be related to time evolution. Only relativistic models evolve continuously. The reasoning of Einstein is implicit to an understanding of both physical models. Previously obtained derivations of relativistic quantum mechanics are reaffirmed by following the ideas of Dirac.
Following a line of research that I have developed for several years, I argue that the best strategy for understanding quantum gravity is to build a picture of the physical world where the notion of time plays no role. I summarize here this point of view, explaining why I think that in a fundamental description of nature we must forget time, and how this can be done in the classical and in the quantum theory. The idea is to develop a formalism that treats dependent and independent variables on the same footing. In short, I propose to interpret mechanics as a theory of relations between variables, rather than the theory of the evolution of variables in time.
In general, a physical theory is based on some fundamental principles concerning space, time, matter, and the laws prescribing how matter is distributed in space and how it evolves in time, and even how spacetime itself changes in response to the changes of matter. The spectrum of the known theories is very diverse, since they are based on different assumptions. Some theories assume that space and time are totally independent, some that they are warped in a continuum named "spacetime", and some even that there are more dimensions than the usual 3+1. Most theories consider that space and time are continuous, but many recent theories consider them to be discrete. Most dynamical laws of fundamental Physics are deterministic, but apparently Quantum Mechanics shows that they may have an indeterministic component. Despite these distinctions between various theories, our intuition and experience tells us that they have a lot in common. In this paper I will try to capture the common features in a single mathematical structure. This is not a Theory of Everything, but only a mathematical structure which is common to most physical theories known so far. We will see that these theories can be obtained as particular cases of this structure, which I will call "world". In particular, the worlds described by the Classical Mechanics, the Theory of Relativity and the Quantum Mechanics are examples of worlds according to this definition, but also some theories attempting to unify gravity and QM, like String Theory. The purpose of this distillation is to provide a mathematical common background to both physical and metaphysical discussions about the various theories of the World.