Does time flow? It will be shown in this chapter that if the spacetime structure of the world has a certain branched dynamic form, then time flows. In addition to the flow and direction of time, two issues in quantum mechanics, those of non-locality and the definition of ‘measurement’, are shown to be illuminated by the hypothesis that the world has the spatio-temporal form described. I call the form the branched model , and the interpretation of quantum mechanics to which it gives rise I call the branched interpretation . Objective time flow The branched model is a four-dimensional spacetime model in the shape of a tree, each branch of which is a complete Minkowski manifold in which are located objects and events. The trunk represents the past, the first branch point is the present, and the branches constitute the set of all physically possible futures. The scheme is shown in figure 1. Of the many possible futures which split off at the first branch point, one and only one is selected to become part of the past. The unselected branches vanish, so that the first branch point moves up the tree in a stochastic manner and the tree ‘grows’ by losing branches. This progressive branch attrition is what in the model constitutes the flow of time. Suppose for example that 1000 lottery tickets have been sold to 1000 different purchasers. Then at the time of the draw, assuming the procedure is completely fair, there will be at least 1000 different kinds of branch at the first branch point: branches on which A wins, branches on which B wins, etc.
Does time flow? It will be shown in this chapter that if the spacetime structure of the world has a certain branched dynamic form, then time flows. In addition to the flow and direction of time, two issues in quantum mechanics, those of non-locality and the definition of ‘measurement’, are shown to be illuminated by the hypothesis that the world has the spatio-temporal form described. I call the form the branched model , and the interpretation of quantum mechanics to which it gives rise I call the branched interpretation . Objective time flow The branched model is a four-dimensional spacetime model in the shape of a tree, each branch of which is a complete Minkowski manifold in which are located objects and events. The trunk represents the past, the first branch point is the present, and the branches constitute the set of all physically possible futures. The scheme is shown in figure 1. Of the many possible futures which split off at the first branch point, one and only one is selected to become part of the past. The unselected branches vanish, so that the first branch point moves up the tree in a stochastic manner and the tree ‘grows’ by losing branches. This progressive branch attrition is what in the model constitutes the flow of time. Suppose for example that 1000 lottery tickets have been sold to 1000 different purchasers. Then at the time of the draw, assuming the procedure is completely fair, there will be at least 1000 different kinds of branch at the first branch point: branches on which A wins, branches on which B wins, etc.
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.
Abstract This book develops a rigorous theory of indeterminism as a local and modal concept. Its crucial insight is that our world contains events or processes with alternative, really possible outcomes. The theory aims at clarifying what this assumption involves, and it does it in two ways. First, it provides a mathematically rigorous framework for local and modal indeterminism. Second, we support that theory by spelling out the philosophically relevant consequences of this formulation and by showing its fruitful applications in metaphysics. To this end, we offer a formal analysis of modal correlations and of causation, which is applicable in indeterministic and non-local contexts as well. We also propose a rigorous theory of objective single-case probabilities, intended to represent degrees of possibility. In a third step, we link our theory to current physics, investigating how local and modal indeterminism relates to issues in the foundations of physics, in particular, quantum non-locality and spatio-temporal relativity. The book also ventures into the philosophy of time, showing how the theory’s resources can be used to explicate the dynamic concept of the past, present, and future based on local indeterminism.
In relativistic mechanics the time-like vector characterize the motion in spacetime with speed faster than the speed of light in vacuum c in which the line element ds2=c2dt2-dx2-dx2-dz2 is less than zero (where is infinitesimal change in time, and are infinitesimal change in space), thus the time in relativistic mechanics can instantaneously flow [1], however in quantum mechanics although the time is treated as unobservable parameter (without any Hermitian observable operator have engine-value equivalent to time) any two physical quantity described by two non-commuting observable operatorsand fulfill , the knowledge of one immediately produce the knowledge of the other [2], thus in quantum mechanics if two particles interacted in finite temporal epoch and then separated in space the gaining of knowledge by the local measurement of physical quantity runs on one them (for example the measurement of spin direction of one particle using Stern-Gerlach experiment) immediately produce the knowledge of the complementary physical quantity of the other particle (for example the opposite spin direction of the other particle), this simply called quantum entanglement the concept that so much advanced after publication of the Jon Bell’s 1964 celebrated paper [3] in which he illustrated that we can add parameters to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, and then he conclude “there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously so that such a theory could not be Lorentz invariant”. The question now what these signals that can propagate instantaneously? The answer in this paper will be the time signals field which is defined for each constituent matter particle M and at each space point P as the measure of the total length of all occupation and leaving epochs of P by M which is representing a sequence function compactly supported only at the space point occupied by it and indexed by the number of occupation epochs of P by M, thus the flow of this time signal field from the far future to near future through the present to the near past to the far past inferable by the flow of matter particles constituting the system(such as sun, moon earth and clocks hands). Thus the present will represent in this paper a local absolute feature of time signals field defined at each space point as the set of all occupation epochs of it by matter particle, however the past and future will represent relativistic non-local features of the time signal field defined at each space point as a set of all leaving epochs between each two sequential occupation epochs, so the future after one occupation epoch is representing a past of the next one. Thus according to current representation of time, the two Mc-Taggard’s A and B series of time [4] will exist together as temporal set and then the time is real, the A-series in current theory is a set of all occupation and leaving epochs of space point by the matter particle that is consisting of the present, past and future epochs, and the B-series is the set of all leaving epochs of space points between each two sequential occupation epochs which are taking position before or after the discrete occupation epochs between them and then before or after each other.
Abstract This study extends the complex-time framework introduced in Part I, where time was formulated as an intrinsic complex coordinate . Within this framework, the imaginary unit is reconsidered not as an algebraic symbol but as an operator of indeterminacy, representing the undetermined future phase of physical existence.The real component corresponds to the determined past. Temporal evolution is thus interpreted as a continuous projection through which potential states become actualized. Building upon this model, we propose a unified interpretation of measurement, entropy, entanglement, and nonlocality. Measurement may be viewed as a temporal projection fixing latent existence from the imaginary phase into the real domain; entropy growth corresponds to the cumulative conversion of undetermined futures into fixed pasts, giving rise to the arrow of time. Quantum indeterminacy is reinterpreted as the openness of the future, while entanglement appears as a form of temporal coherence connecting events through a shared phase structure. When correlations become fully realized, the internal -phase vanishes and the relation attains , implying a null-temporal state beyond spacetime separation. At the macroscopic level, matter with rest mass can be regarded as a dense network of such microscopic fixations. Each quantum interaction functions as a micro-instance of temporal fixation, producing the statistical rhythm perceived as continuous time. This interpretation suggests that reality may evolve through a self-referential process in which the universe continuously projects its potential phase into realized history—a dynamic structure of physical reality emerging from complex-time geometry. Running Title: Complex-Time Structure and Physical Reality Keywords: Complex Time; Temporal Projection; Quantum Measurement; Quantum Entanglement; Decoherence; Entropy; Information Dissipation; Physical Reality
An operational approach to quantum mechanics has been developed in the past decades in our group in Brussels. A similar approach is taken in this work, making use of the extra operational depth offered by this approach, to show that the construction of spacetime is specific to each observer. What is usually referred to as the block universe then emerges by noting that parts of the past and future are also contained in the present, but without the limitations that a four-dimensional block universe usually implies, of a reality in which change would be impossible. In our operational approach, reality remains dynamic, with free choice playing a central role in its conceptualization. We also show that, when operationally analyzed, the theory implies that objects move not only in space, but also and especially in time, and more generally in spacetime, with their rest mass being a measure of their kinetic time energy. We therefore claim that Einstein’s relativity revolution has not been fully realized, since most physicists are not ready to accept these consequences of the theory although the formula’s showing them, when operationally analyzed, are in every relativity textbook. In particular, when relativistic motion is revisited as a genuine four-dimensional motion, it becomes possible to reinterpret the parameter c associated with the coordinate speed of light, which becomes the magnitude of the four-velocity of all material entities. We observe that this four-dimensional motion in Minkowski space can also be better understood if placed in the broader perspective of quantum mechanics, provided that non-locality is interpreted as non-spatiality, thus indicating the existence of an underlying non-spatial reality, the nature of which could be conceptual, consistent with the conceptuality interpretation of quantum mechanics. This hypothesis is reinforced by noting that when observers, or experiencers, as they will be referred to in this article, are described by acknowledging their cognitive nature of entities moving in a semantic space, Minkowski metric emerges in a natural way.
At present, there are two possible, and equally plausible, explanations for the physics of quantum measurement. The first explanation, known as the many-worlds interpretation, does not require any modification of quantum mechanics, and asserts that at the time of measurement the Universe splits into many branches, one branch for every possible alternative. The various branches do not interfere with each other because of decoherence, thus providing a picture broadly consistent with the observed Universe. The second explanation, which requires quantum mechanics to be modified from its presently known form, is that at the time of measurement the wave-function collapses into one of the possible alternatives. The two explanations are mutually exclusive, and up until now, no theoretical reasoning has been put forward to choose one explanation over the other. In this article, we provide an argument which implies that the collapse interpretation is favored over the many-worlds interpretation. Our starting point is the assertion (which we justify) that there ought to exist a reformulation of quantum mechanics which does not refer to a classical spacetime manifold. The need for such a reformulation implies that quantum theory becomes non-linear on the Planck mass/energy scale. Standard linear quantum mechanics is an approximation to this non-linear theory, valid at energy scales much smaller than the Planck scale. Using ideas based on noncommutative | >=