The notions of time in the theories of Newton and Einstein are reviewed so that certain of their assumptions are clarified. These assumptions will be seen as the causes of the incompatibility between the two different ways of understanding time, and seen to be philosophical hypotheses, rather than purely scientific ones. The conflict between quantum mechanics and (general) relativity is shown to be a consequence of retaining the Newtonian conception of time in the context of quantum mechanics. As a remedy for this conflict, an alternative definition of time -- earlier presented in Kitada 1994a and 1994b -- is reviewed with less mathematics and more emphasis on its philosophical aspects. Based on this revised understanding of time it is shown that quantum mechanics and general relativity are reconciled while preserving the current mathematical formulations of both theories.
The notions of time in the theories of Newton and Einstein are reviewed so that certain of their assumptions are clarified. These assumptions will be seen as the causes of the incompatibility between the two different ways of understanding time, and seen to be philosophical hypotheses, rather than purely scientific ones. The conflict between quantum mechanics and (general) relativity is shown to be a consequence of retaining the Newtonian conception of time in the context of quantum mechanics. As a remedy for this conflict, an alternative definition of time -- earlier presented in Kitada 1994a and 1994b -- is reviewed with less mathematics and more emphasis on its philosophical aspects. Based on this revised understanding of time it is shown that quantum mechanics and general relativity are reconciled while preserving the current mathematical formulations of both theories.
The notions of time in the theories of Newton and Einstein are reviewed so that the difficulty which impedes the unification of quantum mechanics (QM) and general relativity (GR) is clarified. It is seen that GR by itself contains an intrinsic difficulty relating to the definition of local clocks, as well as that GR still requires a kind of absolute that can serve as an objective reference standard. We present a new understanding of time, which gives a consistent definition of a local time associated with each local system in a quantum mechanical way, so that it serves the requirements of both GR as well as QM. As a consequence, QM and GR are reconciled while preserving the current mathematical formulations of both theories.
This thesis is a study of the notion of time in modern physics, consisting of two parts. Part I takes seriously the doctrine that modern physics should be treated as the primary guide to the nature of time. To this end, it offers an analysis of the various conceptions of time that emerge in the context of various physical theories and, furthermore, an analysis of the relation between these conceptions of time and the more orthodox philosophical views on the nature of time. In Part II I explore the interpretation of nonrelativistic quantum mechanics in light of the suggestion that an overly Newtonian conception of time might be contributing to some of the difficulties that we face in interpreting the quantum mechanical formalism. In particular, I argue in favour of introducing backwards-in-time causal influences as part of an alternative conception of time that is consistent with the picture of reality that arises in the context of the quantum formalism. Moreover, I demonstrate that this conception of time can already be found in a particular formulation of classical mechanics. One might see that one of the central themes of Part II originates from a failure to heed properly the doctrine of Part I: study into the nature of time should be guided by modern physics and thus we should be careful not to insert a preconceived Newtonian conception of time unwittingly into our interpretation of the quantum mechanical formalism. Thus, whereas Part I is intended as a demonstration of methodology with respect to the study of time, Part II in a sense explores a confusion that can be seen as arising in the absence of this methodology.
Modern Physics rests on two pillars: General Relativity (GR) and Quantum Mechanics (QM). The former describes gravitation as the continuous geometry of spacetime, based on differential fields. The latter, in turn, operates in a discretized regime, where energy levels, frequencies, and experimental results arise in quantized packets. The tension between both arises because GR assumes absolute continuity of time and space, while QM presents intrinsically discrete phenomena. Historically, the search for a unified theory started from the assumption that one of the two formulations must be modified — either GR should be discretized, or QM should emerge from an underlying continuous theory. In this work, we argue that the conflict is not fundamental: it stems from the traditional interpretation of time in Special Relativity (SR). When analyzed correctly, the proper time of distinct observers does not evolve synchronously, and this produces beating and discretization effects that explain, without additional postulates, many behaviors labeled as "quantum."
Time in quantum theory By 1920, the spectacular confirmation of general relativity, during the solar eclipse of 1919, had made Einstein a household name. Not only did relativity theory (both special and general) upset the long-received Newtonian ideas of space and time, it also stimulated a widespread ‘operationalist’ attitude to physical theories. Physical quantities came to be seen as inextricably interwoven with our means of measuring them, in the sense that any limits on our means of measurement were taken to imply limits on the definability, or ‘meaningfulness’, of the physical quantities themselves. In particular, Einstein's relativity paper of 1905 – with its operational analysis of simultaneity – came to be widely regarded as a model for the new operationalist approach to physics. Not surprisingly, then, as the puzzles continued to emerge from atomic experiments, in the 1920s a number of workers suggested that the concepts of space and time would require still further revision in the atomic domain. Thus, Campbell (1921, 1926) suggested that the puzzles in atomic physics could be removed if the concept of time was given a purely statistical significance: ‘time, like temperature, is a purely statistical conception, having no meaning except as applied to statistical aggregates’ (quoted in Beller 1999, p. 97).
The chief object of my paper is to clarify the notion of relativity to the means of observation as the basis for description of physical phenomena. This concept is so important that it deserves the name "the principle of relativity to the means of observation." This principle is particularly important to a correct understanding of quantum mechanics. The notion of relativity to the means of observation is, in a certain sense, a generalization of the notion of relativity to the system of reckoning. The two notions play analogous roles in the corresponding theories. But while relativity theory, which rests upon the notion of relativity to the system of reckoning, takes into consideration only the motion of the means of observation as a whole, in quantum mechanics it is also necessary to take note of deeper properties of the means of observation.
The understanding of time in physics has undergone profound changes from classical mechanics to relativity and quantum mechanics. In Newtonian mechanics, time is regarded as an absolute and uniform passage, independent of external phenomena, and is a fundamental parameter of the equations of motion. Relativity emphasises the relativity of time and its close connection with the motion of matter, proposes an operational definition of the simultaneity of distant events, and develops Minkowski’s view of spacetime and Riemannian curved spacetime. In quantum mechanics, time is often regarded as a parameter external to the microscopic system rather than an observable quantity. Although some scholars have attempted to introduce time operators, they have not yet gained widespread recognition. Overall, the understanding of time in physics continues to deepen with the development of theory. Still, the unity of classical and quantum mechanics in time remains an unsolved problem.