In this paper I consider the concept of time in a general way as daily human time and then within physics with relation to mathematics. I consider the arrow of time and then focus the attention on quantum mechanics, with its particular peculiarities, examining important concepts like temporal asymmetry, complexity, decoherence, irreversibility, information theory, chaos theory. In conclusion I consider the notion of time connected to a new theory in progress, called “Primordial Dynamic Space” theory.
In this paper I consider the concept of time in a general way as daily human time and then within physics with relation to mathematics. I consider the arrow of time and then focus the attention on quantum mechanics, with its particular peculiarities, examining important concepts like temporal asymmetry, complexity, decoherence, irreversibility, information theory, chaos theory. In conclusion I consider the notion of time connected to a new theory in progress, called “Primordial Dynamic Space” theory.
In this paper I consider the concept of time in a general way as daily human time and then within physics with relation to mathematics. I consider the arrow of time and then focus the attention on quantum mechanics, with its particular peculiarities, examining important concepts like temporal asymmetry, complexity, decoherence, irreversibility, information theory, chaos theory. In conclusion I consider the notion of time connected to a new theory in progress, called “Primordial Dynamic Space” theory.
In this paper I consider the concept of time in a general way as daily human time andthen within physics with relation to mathematics. I focus the attention on quantum mechanics, with its particular peculiarities, examining peculiar important questions like the temporal asymmetry, the Prigogine’s position and the time-reversal operator of Wigner. I conclude considering the theme of the temporal asymmetry in relation to decoherence and irreversibility. Interesting imputs related to education science will be done.
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 nature of time has long been debated in human history and nowadays is considered of central importance for understanding quantum gravity. We focus on and advocate the relational concept of time, which was put forward in the 17th century in opposition to Newton's absolute time, and only in 1990 explored in a quantum mechanical framework by Carlo Rovelli. After a historical introduction the mathematical models of time are carefully analyzed in chapter 1, followed by a discussion of the role of time played in fundamental theories. Using as an example nonrelativistic mechanics, the process of parametrization is explained, leading to a separation of a 'canonical time coordinate' from an arbitrary evolution parameter. The discussion of the role of time in special and general relativity as well as in quantum mechanics shows that more fundamental theories use less structure of time. This is followed by an exposition of the history of the relational concept of time, which negates the existence of an absolute duration and therefore often is called "timeless". Next it is shown how fundamental theories can be formulated and re-interpreted using this concept. We put emphasis on the hitherto neglected connection between relationalism and non-extensibility, while absolute time is shown to be unproblematic in classical mechanics just because of the possibility to extend the system without changing its nature. We conclude chapter 1 with a new axiomatic basis for the construction of time observables based on a simultaneity relation between 'observations', which are treated as a primitive concept and intuitively correspond to measurement events, but without knowing 'when' these events occur. There is no fundamental time observable; any observable qualifies as a time observable, if it allows to separate all instants. Chapter 2 gives a brief account of three main problems connected with time: a) The problem of the arrow of time. This has to be disentangled from the problem of irreversibility: a solution of the latter essentially excludes cyclic motions and is required for a solution of the former, which consists in showing that a fundamental direction between any two non-identical instants is physically meaningful. We give a formal definition of the arrow of time. This classical analysis is followed by a review of the problem of the arrow of time in quantum theory, where the situation becomes more complicated because of indeterminism. The discussion shows that there is no experimental evidence for a fundamental arrow of time, so that no contradiction with the relational concept of time arises. b) The problem of time measurement, which is of particular importance for the relational approach, in which time has no reality except if measured by a clock. In quantum theory useful time operators seem to be possible only within the more general formalism of positive operator valued measures (POVM). Clocks based on an oscillation mechanism do however require phase measurements; quantum phase operators can be defined as certain POVMs. Phase difference operators do also exist in the traditional Hilbert space formalism, if another quantization is used, as is done with relational quantization. c) The problem of quantum gravity is sketched only briefly. Chapter 3 introduces and discusses a model of Rovelli consisting of two oscillators with no external time. In this model one oscillator is considered as a clock and defines a relational time for the other one. In the first section we introduce this model and generalize it to a free massless scalar field in one dimension. We establish the relation between a single field mode and the infrared behaviour of the field through constants of motion. In the second section after a short review of canonical quantization we review Rovelli's quantization and generalize it to the free field. We could not prove the existence of the quantization map, but calculations using computer algebra indicate that the quantization does exist. For an enlarged algebra we are able to prove the nonexistence of a quantization map similar to a proof by Groenewold and van Hove. In chapter 4 we observe that a clock time always requires infinitely many degrees of freedom, and we make the hypothesis that a time observable is given by the infrared behaviour of quantum fields, leading to a classical notion of time when using algebraic quantum mechanics. This does however not solve the main problem of quantum relationalism: Which conditions determine a particular evolution?
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.
I explain in what sense the structure of space and time is probably vague or indefinite, a notion I define. This leads to the mathematical representation of location in space and time by a vague interval. From this, a principle of complementary inaccuracy between spatial location and velocity is derived, and its relation to the Uncertainty Principle discussed. In addition, even if the laws of nature are deterministic, the behaviour of systems will be random to some degree. These and other considerations draw classical physics closer to Quantum Mechanics. An arrow of entropy is also derived, given an arrow of time. Lastly, chaos is given an additional, objective meaning.