In this paper I shall consider the concept of time used in the quantum theory from the perspective of Bohr’s ideas as presented in what he called the quantum postulate and some of its consequences. In particular, Bohr’s views on the role of the experimental arrangement that defines the context in which we can consider the state of the quantum system to be defined – and the related interpretation of the quantum wave function –, enables a view on the time concept being used in the theory that makes compatible the discontinuous changes in individual physical systems with a continuous description in time of the behavior of an ensemble of systems. A crucial aspect will be to show that Bohr’s ideas are coherent with the use of an external classical time.
In this paper I shall consider the concept of time used in the quantum theory from the perspective of Bohr’s ideas as presented in what he called the quantum postulate and some of its consequences. In particular, Bohr’s views on the role of the experimental arrangement that defines the context in which we can consider the state of the quantum system to be defined – and the related interpretation of the quantum wave function –, enables a view on the time concept being used in the theory that makes compatible the discontinuous changes in individual physical systems with a continuous description in time of the behavior of an ensemble of systems. A crucial aspect will be to show that Bohr’s ideas are coherent with the use of an external classical time.
A brief account of the world view of classical physics is given first. We then recapitulate as to why the Copenhagen interpretation of the quantum mechanics had to renounce most of the attractive features of the clasical world view such as a causal description, locality, scientific realism and introduce a fundamental distinction between system and apparatus. The crucial role is played in this by the Bohr's insistence on the wavefunction providing the most complete description possible for an even individual system. The alternative of introducing extra dynamical variables, called hidden variables, in addition to the wavefunction of the system so as to be able to retain at least some of the desirable features of classical physics, is then explored. The first such successful attempt was that of Bohm in 1952 who showed that a realistic interpretation of the quantum mechanics can be given which maintains a causal description as well as does not treat systems and measuring appeartus differently. We begin with the construction of the Bohm's theory. He introduces particle positions as the hidden variables. The particle positions play a special role in Bohm theory. The particle trajectories are guided by the wavefunction. The Bohm theory is deterministic. The probability enters through a special assumption, ``quantum equilibrium'' hypothesis, for the initial conditions on the ensemble of particle trajectories. The ``wave or particle'' dilemma is resolved by a ``wave and particle'' resolution. The measurements in Bohm theory can be described without mysticism. Bohm's theory is however nonlocal.
Although time is one of our most intuitive physical concepts, its understanding at the fundamental level is still an open question in physics. For instance, time in quantum mechanics and general relativity are two distinct and incompatible entities. While relativity deals with events (points in spacetime), with time being observer dependent and dynamical, quantum mechanics describes physical systems by treating time as an independent parameter. To resolve this conflict, in this work, we extend the classical concept of an event to the quantum domain by defining an event as a transfer of information between physical systems. Then, by describing the universe from the perspective of a certain observer, we introduce quantum states of events with space-time-symmetric wave functions that predict the joint probability distribution of a measurement (observation) at $(t,\stackrel{P\vec}{x})$. Under these circumstances, without assuming collapse, we propose that a well-defined instant of time, like any other observable, arises from a single event, thus being an observer-dependent property. In this manner, we obtain a stationary quantum state written as a sum of a sequence of normalized states of events with increasing memories. As a consequence, a counterfactual asymmetry along this sequence of events gives rise to the flow of time as being successive ``snapshots'' from the observer's perspective. In this proposal, which contrasts strikingly to the view in which time is an illusion, it is the many distinguishable states in which the observer stores information that makes the existence of time possible.
Complementarity and Deconstruction: Plotnitsky's Analysis and Beyond Makoto Katsumori Akita University The philosophical thought of the modern physicist Niels Bohr (1885–1962), which revolves around the concept of complementarity, has long been a major subject of historical and philosophical inquiry. Many prior studies of Bohr's complementarity, however, seem to be limited by the fact that they largely proceed within the conceptual frames of the "mainstream" philosophy of science. This being the case, his radical questioning of traditional scientific and philosophical notions—such as the unambiguity of concepts and words—has not been adequately addressed, insofar as these notions are uncritically presupposed by the commentators themselves. In other words, Bohr's thought has often been interpreted under certain tacit premises of scientific rationality that are precisely of the kind targeted by his epistemological critique. In recent years, however, there have emerged new approaches to Bohr's idea of complementarity that place it in different, less conventional, philosophical contexts. Among the most notable of these is Arkady Plotnitsky's endeavor to connect Bohr's complementarity with Jacques Derrida's project of deconstruction. In the present article, based on my recent doctoral dissertation,1 I take up this contribution by Plotnitsky as a suitable point of reference from which to [End Page 435] explore anew Bohr's thought with its radical philosophical implications. After outlining Bohr's complementarity argument and Plotnitsky's reading thereof (in the first and second sections, respectively), I will examine a series of problems that seem to face, or to be left unsolved by, Plotnitsky's account (in the third section). This critical appraisal will finally lead me to sketch a new interpretive approach of my own (in the fourth section), which both extends and delimits the intersections between complementarity and deconstruction. As regards the historical development of Bohr's complementarity, I will largely restrict myself to the period between 1927 and 1950, in which the most crucial of his innovative ideas seem to have been presented. I. Bohr's Idea of Complementarity In his 1927 lecture delivered in Como, Italy, entitled "The Quantum Postulate and the Recent Development of Atomic Theory," Niels Bohr introduced the concept and framework of complementarity as a pivotal idea in his interpretation of quantum theory. From then on, he continually developed the idea of complementarity with regard not only to quantum theory but to other fields of knowledge as well. In what follows, I will first outline his complementarity argument in its "early" period, stretching from 1927 to the mid-thirties,—or, more precisely, until just before his 1935 debate with EPR.2 Bohr starts by noting that "our usual description of physical phenomena is based entirely on the idea that the phenomena concerned may be observed without disturbing them appreciably."3 This notion of physical phenomena as undisturbed by observation underlies all of classical physics and is still maintained in the theory of relativity. However, Bohr continues, a new situation has arisen with the development of quantum theory, specifically with "the so-called quantum postulate, which attributes to any atomic process an essential discontinuity, or rather individuality, completely foreign to the classical theories"; this "individuality" implies that "any observation of atomic phenomena will involve an interaction with the [End Page 436] agency of observation not to be neglected" (PWNB, 1: 53–54.). In more specific terms, any observation aimed at space-time coordination brings about an exchange of momentum and energy with the measuring rods and clocks. It is crucial here that this interaction between the object and the instrument of observation is not simply unavoidable, but "uncontrollable," which represents a "feature of irrationality" brought into the description of nature (PWNB, 1: 68, 91). For insofar as the measuring instruments are to fulfill their purpose, the interaction itself cannot be taken into account, and thus the magnitude of the disturbance always remains unknown. It follows, in Bohr's view, that "an independent reality in the ordinary physical sense can neither be ascribed to the phenomena nor to the agencies of observation...
In quantum mechanics, time is introduced as a non-measurable quantity, as there is no possibility to build a hermitian operator canonically conjugated to the Hamiltonian. We cannot have, therefore, the time operator, which means that the temporal structure of the evolution of quantum systems is ill-defined. We present an extension to the model, in which the time evolution is based on the projection postulate rather than the unitary operator. This approach is in agreement with all other aspects of quantum mechanics and allows to discuss time as an observable. Using this framework we present a description of the temporal double-slit experiment in which a~single particle interferes with itself from a different instant of time. Such behaviour has already been observed experimentally but lacked a consistent theoretical explanation.
This article reconsiders E. Schrödinger's cat paradox experiment from a new perspective, grounded in the interpretation of quantum mechanics that belongs to the class of interpretations designated as "reality without realism" (RWR) interpretations. These interpretations assume that the reality ultimately responsible for quantum phenomena is beyond conception, an assumption designated as the Heisenberg postulate. Accordingly, in these interpretations, quantum physics is understood in terms of the relationships between what is thinkable and what is unthinkable, with, physical, classical, and quantum, corresponding to thinkable and unthinkable, respectively. The role of classical physics becomes unavoidable in quantum physics, the circumstance designated as the Bohr postulate, which restores to classical physics its position as part of fundamental physics, a position commonly reserved for quantum physics and relativity. This view of quantum physics and relativity is maintained by this article as well but is argued to be sufficient for understanding fundamental physics. Establishing this role of classical physics is a distinctive contribution of the article, which allows it to reconsider Schrödinger's cat experiment, but has a broader significance for understanding fundamental physics. RWR interpretations have not been previously applied to the cat experiment, including by N. Bohr, whose interpretation, in its ultimate form (he changed it a few times), was an RWR interpretation. The interpretation adopted in this article follows Bohr's interpretation, based on the Heisenberg and Bohr postulates, but it adds the Dirac postulate, stating that the concept of a quantum object only applies at the time of observation and not independently.