The laws of classical mechanics and quantum theory do not distinguish between the past and the future. But a lot of phenomena tell us that the "arrow of time" points only in one direction. For example, in biology we discover evolutionary processes leading to diversification and increasing complexity; it is a typical feature of such evolutionary processes that "forward" in time is possible but "backward" in time is impossible. At what level can phenomena like these be described? There is another problem in connection with time: within usual quantum theory, space-coordinates and time are not symmetrical to each other, which is in contrast to the basic results of special theory of relativity. In usual quantum theory coordinates are operators and play the role of statistical quantities; time however does not behave statistically and remains a simple parameter when we go from classical to quantum mechanics. For this reason there is no uncertainty relation for the time and energy within usual quantum theory which would agree in its physical content with that for the coordinates and momenta. The purpose of this paper is to show, on the basis of new aspects, that both one-sidedness of time and its uncertainty are charateristics at the fundamental level of quantum theory. We have extended usual quantum theory on the basis of space-time arguments. In this connection a time-operator appeared and there is in general temporal asymmetry at the microscopic level. The picture might be important in the description of phenomena with an "arrow of time", i.e., processes which belong to the physics of becoming. Furthermore, we have derived an uncertainty relation for the energy and time which agrees in its physical content with the uncertainty relation for the momentum and the coordinate; this relation is different from that of usual quantum theory. Within the frame of this physical picture all the concepts (diversity, natural selection, mutation), which are presently used in connection with the evolution of biological systems, are already established at the quantum mechanical level and, therefore, our theoretical picture might also be the foundation for the explanation of the phenomena at the biological (macro-molecular) level.
The laws of classical mechanics and quantum theory do not distinguish between the past and the future. But a lot of phenomena tell us that the "arrow of time" points only in one direction. For example, in biology we discover evolutionary processes leading to diversification and increasing complexity; it is a typical feature of such evolutionary processes that "forward" in time is possible but "backward" in time is impossible. At what level can phenomena like these be described? There is another problem in connection with time: within usual quantum theory, space-coordinates and time are not symmetrical to each other, which is in contrast to the basic results of special theory of relativity. In usual quantum theory coordinates are operators and play the role of statistical quantities; time however does not behave statistically and remains a simple parameter when we go from classical to quantum mechanics. For this reason there is no uncertainty relation for the time and energy within usual quantum theory which would agree in its physical content with that for the coordinates and momenta. The purpose of this paper is to show, on the basis of new aspects, that both one-sidedness of time and its uncertainty are charateristics at the fundamental level of quantum theory. We have extended usual quantum theory on the basis of space-time arguments. In this connection a time-operator appeared and there is in general temporal asymmetry at the microscopic level. The picture might be important in the description of phenomena with an "arrow of time", i.e., processes which belong to the physics of becoming. Furthermore, we have derived an uncertainty relation for the energy and time which agrees in its physical content with the uncertainty relation for the momentum and the coordinate; this relation is different from that of usual quantum theory. Within the frame of this physical picture all the concepts (diversity, natural selection, mutation), which are presently used in connection with the evolution of biological systems, are already established at the quantum mechanical level and, therefore, our theoretical picture might also be the foundation for the explanation of the phenomena at the biological (macro-molecular) level.
It is brought forward that viable theories of the physical world that have no variable at all that can play the role of time, do not exist; some notion of time is one of the very first ingredients a candidate theory should possess. Almost by definition, time has an arrow. In contrast, time reversibility, or even the possibility to run the equations of motion backwards in time, is not at all a primary requirement. This means that the direction of the arrow of time may well be uniquely defined in the theory, even locally. It is explained that a rigorous definition of time, as well as a formulation of the causality and locality concepts, can only be given when one has a model for the physical phenomena described. The only viable causality condition is one that is symmetric under time reversal. We explain these statements in terms of the author’s favoured deterministic cellular automaton interpretation of quantum mechanics, also to be referred to as 'vector space analysis', and expand on these ideas. It is also summarised how our more rigorous causality condition affects Bell’s theorems. What distinguishes quantum systems from classical ones is our fundamental inability to control the microscopic details of the initial state when phenomena are studied in the light of some theoretical model.
The problem of time’s arrow is (roughly) to understand why macroscopic physical processes typically evolve in a specific direction (the one we call “the future”) even though the underlying laws of physics describing the individual microscopic systems are time-reversal invariant. The standard answer to this problem is given by Boltzmann’s explanation of the II law of thermodynamics: a classical system starting in a non-equilibrium state spontaneously (i.e. with a high level of probability) tends towards equilibrium, thus implementing an irreversible process. However, this explanation has two drawbacks: 1. it needs a further assumption on the entropy of the initial state of the universe (past hypothesis); 2. microscopic systems (e.g. molecules in a box) should be represented as quantum states and not classical states. In this talk, I want to propose a different hypothesis to explain the origin of time’s arrow, based on quantum mechanics, specifically on decoherence theory. Differently from isolated systems, open quantum systems described by decoherence theory showirreversible behavior, as they evolve towards decoherence and von Neumann entropy increase. Is this behavior a sign of genuine irreversibility? And, if so, can this be linked to thermodynamic irreversibility?
Abstract Our conception of time changed from the lofty absolute coordinate of the classical paradigm to merely a connection between local reference frames, thanks to the Special Theory of Relativity, a connection that depends on knowing the relative velocity between frames, and that entails knowing local velocities. We measure local velocities using a clock that cannot give us precise time because knowing time depends solely on knowing the process that we use to generate time. In the case of both macroscopic and microscopic clocks, an intrinsic uncertainty blocks us from knowing both the dynamic and static states of the variables involved. By focusing on the conceptual process that we use to describe physical systems, we can approach a common epistemology of both microscopic and macroscopic dynamical systems. We find that both systems of description require that we inser t time implicitly into the formalism to account for the conservation of identity through our own psychological experience of time. Although we cannot define exactly the nature of the conserved identity, we can describe its evolution with pairs of conjugate variables, one tracking the static state and one the dynamic state. Uncertainty extends from our conceiving system into our descriptive theories. An epistemology that emphasizes the balance between the conjugate variables as they serve to describe the evolution of the identity provides a common ground on which to discuss both the Heisenberg uncertainty principle of quantum mechanics and the bounded randomness of a deterministic macroscopic system. We have seen time go from a global to a local phenomenon, and perhaps now we must allow time to become an epiphenomenon even at the local level, one that we ourselves insert to account for the continuity of our own conscious experience.
Some aspects of the interpretation of microscopic physics in terms of quantum theory are discussed. It is first emphasized that quantum theory is formulated in a Cartesian coordinate system; in other coordinates the result obtained with the help of the Hamiltonian formalism and commutation relations between ''canonically conjugated'' coordinate and momentum operators leads to a wrong version of quantum mechanics. In this connection the Feynman integral formalism is also discussed. In this formalism the measure is not well defined, and there is no idea how to distinguish between the true version of quantum mechanics and an incorrect one. In this respect, the Feynman approach consists of a mnemonic rule to generate perturbation series from an undefined zero-order term. The origin of time in the quantum framework is then analyzed in detail and illustrated by the example of atomic collisions. It is shown that the time-dependent Schr ¨ odinger equation for the closed three-body (two nuclei + electron) system has no physical meaning because in the high-impact energy limit it transforms into an equation with two independent time-like variables; time naturally appears in the stationary Schr ¨ odinger equation as a result of extraction of a classical subsystem (two nuclei) from a closed three-body system. Finally, following the well-known Einstein-Rosen-Podolsky experiment and Bell's inequality, we reiterate that the wave function must be interpreted as an actual field of information, in a form as elementary as the usual material particles and electromagnetic fields. In fact, experimental measurements transfer this quantum information field into the classical world, which is directly discernable. In my conclusion, the relation between physical reality and its mathematical formulation is discussed. 2012 Physics Essays Publication. (DOI: 10.4006/0836-1398-25.1.27) R ´
One of the most profound and difficult problems of physics in the last century is the construction of a simple theory which unites the ideas of quantum mechanics and relativity. The concepts which are used in quantum mechanics related to the measurements of positions, momenta, energy and time, are the same concepts in terms of which the special relativistic postulates are formulated. Hence, it is at least possible to formulate the requirement of special relativistic invariance for quantum theories and to ascertain whether these requirements are satisfied. The fact that the answer is nearer to no than to yes, that quantum mechanics has not yet been fully adjusted to the postulates of the special theory, is perhaps irritating. In the general theory of relativity, the situation is different: the space-time coordinates are only auxiliary quantities to which arbitrary values for every event could be given. Hence, the measurement of position, that is, of the space coordin ates, is certainly not a significant measurement if the postulates of the general theory are adopted: any arbitrary value can be given to the coordinates. The same holds for momenta. The purpose of this brief paper is to make in principle some personal and particular remarks on the fundamental concepts of time and mass. Some comments about the consequences on the relativistic dynamics of quantum systems are also formulated.
In present-day physics the fundamental dynamical laws are taken as a time-translation-invariant and time-reversal-invariant one-parameter groups of automorphisms of the underlying mathematical structure. In this context-independent and empirically inaccessible description there is no past, present or future, hence no distinction between cause and effect. To get the familiar description in terms of causes and effects, the time-reversal symmetry of the fundamental dynamics has to be broken. Thereby one gets two representations, one satisfying the generally accepted rules of retarded causality (no effect can precede its cause). The other one describes the strange rules of advanced causality. For entangled (but not necessarily interacting) quantum systems the arrow of time must have the same direction for all subsystems. But for classical systems, or for classical subsystems of quantum systems, this argument does not hold. As a cosequence, classical systems allow the conceptual possibility of advanced causality in addition to retarded causality. Every mathematically formulated dynamics of statistically reproducible events can be extended to a description in terms of a one-parameter group of automorphisms of an enlarged mathematical structure which describes a fictitious hidden determinism. Consequently, randomness in the sense of mathematical probability theory is only a weak generalization of determinism. The popular ideas that in quantum theory there are gaps in the causal chain which allow the accommodation of the freedom of human action are fantasies which have no basis in present-day quantum mechanics. Quantum events are governed by strict statistical laws. Freedom of action is a constitutive necessity of all experimental science which requires a violation of the statistical predictions of physics. We conclude that the presently adopted first principles of theoretical physics can neither explain the autonomy of the psyche nor account for the freedom of action necessary for experimental science.