This chapter focuses on the fact that by definition, empty spacetime cannot be observed. Therefore, there is room here not only for different mathematical models of the information void (the spacetime region devoid of any detection apparatus) but also for different interpretations as to what space and time actually mean there. The chapter discusses Mach’s relationalism and Einstein’s view of the aether. It discusses Planck’s quantization hypothesis, photons, and the possibility of modelling the information void with something other than Minkowski spacetime. The chapter finishes with a discussion of Hartland Snyder’s quantized spacetime algebra, a modification of standard relativistic quantum theory that may yet provide a better model for the void than classical Minkowski spacetime. The chapter shows that in Snyder’s model, space is quantized but time is not.
This chapter focuses on the fact that by definition, empty spacetime cannot be observed. Therefore, there is room here not only for different mathematical models of the information void (the spacetime region devoid of any detection apparatus) but also for different interpretations as to what space and time actually mean there. The chapter discusses Mach’s relationalism and Einstein’s view of the aether. It discusses Planck’s quantization hypothesis, photons, and the possibility of modelling the information void with something other than Minkowski spacetime. The chapter finishes with a discussion of Hartland Snyder’s quantized spacetime algebra, a modification of standard relativistic quantum theory that may yet provide a better model for the void than classical Minkowski spacetime. The chapter shows that in Snyder’s model, space is quantized but time is not.
In this chapter we are going to discuss some aspects touching upon the discretization of time in the context of Einstein's theories of special relativity (SR) and general relativity (GR). Snyder's quantized spacetime At first sight SR seems the wrong theory for temporal discretization. In Newtonian mechanics, time is absolute, which means that simultaneity is absolute: it is the same for all inertial observers. Therefore, if absolute time is discretized for one inertial observer, it is discretized in exactly the same way for all other inertial observers. In that respect, Newtonian discrete time mechanics does not require a preferred inertial frame. Simultaneity is not absolute in SR, however, which suggests that discretizing time will break Lorentz covariance: the use of a preferred inertial frame in which to temporally discretize seems inevitable. This conclusion is based on classical thinking. The example of quantized angular momentum demonstrates that it is possible to reconcile having a continuous parameter space with a discrete spectrum of observable values. Suppose that an observer is conducting a Stern–Gerlach (SG) experiment, firing a beam of electrons through an apparatus containing a strong inhomogeneous magnetic field (Gerlach and Stern, 1922a). In such an experiment, the observer will first fix the orientation of the apparatus relative to the source. Then it will be found that an electron passing through the apparatus will be detected finally in only one of two possible angular momentum states.
@As a way of honoring Professor Wheeler on his sixtieth birthday, I propose to take this opportunity to elaborate upon certain somewhat speculative ideas which I have tried to hint at on occasion, concerning the possible nature of a quantized space-time. The reader will not need to be too discerning to recognize some substantial dierences between the ideas I am proposing here and those which Professor Wheeler has on many occasions so eloquently and forcefully put forward. Nonetheless, there is little doubt in my own mind as to the very great inspirational inuence that Professor Wheeler’s own views have had in the development of several of the thoughts which I am expressing here. To begin with, let me make clear that I do not necessarily mean by \quantized space-time something which could be obtained by applying standard (or even non-standard) techniques of quantization to Einstein’s general theory of relativity. What I wish to say has its roots in something which is really more primitive than either quantum theory or relativity as such. This is the question of the fundamental role played by the mathematical concept of continuum in virtually the whole of accepted present-day physical theory. Not only does the continuum occupy a basic position in our mathematical models of space and time (with the concomitant implication of a continuous nature for many related physical concepts such as velocity, energy, momentum, temperature, etc.), but so also does present-day quantum theory rest crucially on a continuum concept, namely on the two-dimensional complex continuum of probability amplitudes, this being the continuum which also occurs in the superposition law. Let me say at the outset that I am not happy with this state of aairs in physical theory. The mathematical continuum has always seemed to me to contain many features which are really very foreign to physics. This point = @ @
Although the standard viewpoint in theoretical physics is that the unification of quantum theory and general relativity requires the quantization of gravity and spacetime, there is not consensus about whether spacetime must fundamentally have any quantum features. Here we show a theorem stating that spacetime degrees of freedom and a quantum system violate a Bell inequality in a background Minkowski spacetime if a few properties of general relativity and quantum theory have a broad range of validity, and if the quantum state reduction upon measurement is a real physical process that is completed superluminally when acting on distant quantum particles in a quantum entangled state. We argue that this implies that spacetime cannot be sensibly called classical if the assumptions in our theorem hold. In contrast to the Eppley-Hannah argument for the necessity of quantizing the gravitational field, we discuss the validity of our assumptions, our thought experiment does not require to manipulate or detect gravitational waves, and our theorem does not rely on the conservation of momentum or on the uncertainty principle.
In analogy with Bohm's elucidation of special relativity, in this paper we criticize the Copenhagen interpretation and seek the way to re-interpret quantum theory in the light of new evidence of quantum optics. In doing this, we are led to regard the real photon as only expressing an elemental relationship established between a quantized light field and a detector in the actual detection processes. With such a kind of relational approach to quantum physics, new concepts then are needed to describe physical phenomena, and the mathematical structure of quantum theory of radiation is viewed as a conceptual map, in the same way as the Minkowski diagram in Einstein's special relativity, which already has the perspective of the observer implicit in it.
In modern quantum information theory one deals with an idealized situation when the spacetime dependence of quantum phenomena is neglected. However the transmission and processing of (quantum) information is a physical process in spacetime. Therefore such basic notions in quantum information theory as qubit, channel, composite systems and entangled states should be formulated in space and time. In this paper some basic notions of quantum information theory are considered from the point of view of quantum field theory and general relativity. It is pointed out an important fact that in quantum field theory there is a statistical dependence between two regions in spacetime even if they are spacelike separated. A classical probabilistic representation for a family of correlation functions in quantum field theory is obtained. A noncommutative generalization of von Neumann`s spectral theorem is discussed. We suggest a new physical principle describing a relation between the mathematical formalism of Hilbert space and quantum physical phenomena which goes beyond the superselection rules. Entangled states and the change of state associated with the measurement process in space and time are discussed including the black hole and the cosmological spacetime. It is shown that any reasonable state in relativistic quantum field theory becomes disentangled at large spacelike distances if one makes local observations. As a result a violation of Bell`s inequalities can be observed without inconsistency with principles of relativistic quantum theory only if the distance between detectors is rather small. We suggest a further experimental study of entangled states in spacetime by studying the dependence of the correlation functions on the distance between detectors.
Introduction In this chapter the modelling of spacetime is discussed, with the aim of maintaining a clear distinction between the local properties of a model and those attributes which are global. This separation of attributes (into local and global type) logically motivates the construction of the non-Hausdorff branched model for spacetime. Of course, much of the physical motivation for this construction is derived from the stochastic nature of quantum mechanics. The Many-World Interpretation is seen to be (at least, topologically) a consistent and complete interpretation of quantum mechanics. In any serious inquiry into the nature of spacetime (on either the quantum or cosmological level), mathematical models will be constructed which are in substantial agreement with the collective empiricism of experimental physics. If such a mathematical model is to be more than just a prescription for prediction, then it is necessary to give careful consideration to the appropriate level of mathematical generality of the model. Common sense, as well as the history of science, appear to indicate the need to maintain as general (i.e., unrestricted) a model as possible, constrained only by empirical data on one side, and the limits of our mathematical sophistication and imagination on the other. In the spirit of generalization, I will construct a model of the time parameter , which extends the usual concept of a time-line , and can be used to model spacetime locally, with the usual product structure of Minkowski spacetime. Our imagination will be constrained only by the mathematical discipline of topology and a clear view of all underlying assumptions.