For quantum systems, whose energy ratios En/E0 are integers, and |E0| is the smallest energy, the time dependent wavefunctions and expectation values of time independent operators have time periodicitiy with a time period T equal to T = h/|E0|, where h is the Planck constant. This periodicity is imposed on the wavefunctions due to undersampling in energy, but following a similarity with aliasing in signal analysis, it may allow to probe future and past events under the condition that our world (...) is in reality a true four-dimensional, “static” space–time. We suggest an experiment to test that possibility. A positive result will indicate that we live in a four-dimensional space–time. A negative result (not getting signals from the future) will indicate that four-dimensional space–time is not physical one and that we live in a three-dimensional space with a time. (shrink)

We propose a new picture of nature in which there are only two fundamental universal constantsè ē (≡e/c) andh(≡ħ/c). Our theory is developed within the framework of a new four-dimensional symmetry which is constructed on the basis of the Poincaré-Einstein principle of relativity for the laws of physics and the Newtonian concept of time. We obtain a new space-light transformation law, a velocity-addition law, and so on. In this symmetry scheme, the speed of light is constant and is (...) completely relative. The new theory is logically self-consistent, and it moreover is in agreement with all previously established experimental facts, such as the “lifetime dilatation” of unstable particles, the Michelson-Morley experiment, etc. There is a difference relative to the usual theory, though, in that our theory predicts a new law for the Dopplerfrequency shift, which can be tested experimentally by measuring the second-order frequency shift. (shrink)

Relativity theory is often said to support something called ‘the four-dimensional view of reality’. But there are at least three different views that sometimes go by this name. One is ‘spacetime unitism’, according to which there is a spacetime manifold, and if there are such things as points of space or instants of time, these are just spacetime regions of different sorts: thus space and time are not separate manifolds. A second is the B-theory of time, according to (...) which the past, present, and future are all equally real and there is nothing metaphysically special about the present. A third is perdurantism, according to which persisting material objects are made up of different temporal parts located at different times. We sketch routes from relativity to unitism and to the B-theory. We then discuss some routes to perdurantism, via the B-theory and via unitism. (shrink)

The purpose of this paper is twofold: a) to explore the compatibility of Minkowski’s space-time representation of the Special theory of relativity with a dynamic conception of space-time; b) to locate its roots in invariant features - like entropic relations - of the propagation of signals in space-time. From its very beginning Minkowski’s four-dimensional space-time was associated with a static view of reality, e.g. a block universe. Einstein added his influential voice to this conception when he wrote: ‘From (...) a “happening” in three-dimensional space, physics becomes (…) an “existence” in the four-dimensional “world”.’ (Einstein, Relativity 1920, 122) Yet it is by no means clear that Minkowski himself was a believer in the block universe. In his 1908 Cologne lecture on ‘Space and Time’ he speaks of a four-dimensional physics but concedes that a ‘necessary’ time order can be established at every world point. Although the conception of the block universe has gained much currency, an alternative view has been in circulation since the 1910s according to which the trajectories of particles constitute histories in space-time. (Robb 1914, Cunningham 1915, Carathéodorys 1924, Schlick 1917, Reichenbach 1924). (shrink)

A space-time theory is studied in a framework of four-dimensional symmetry, In this theory there is a privileged frame (ether frame), and the simultaneity of distant clocks is absolute. The results of such a theory are not only equivalent to special relativity, but also valid to describe the superluminous phenomena.

The mathematical and physical aspects of the conformal symmetry of space-time and of physical laws are analyzed. In particular, the group classification of conformally flat space-times, the conformal compactifications of space-time, and the problem of imbedding of the flat space-time in global four-dimensional curved spaces with non-trivial topological and geometrical structure are discussed in detail. The wave equations on the compactified space-times are analyzed also, and the set of their elementary solutions constructed. Finally, the implications of global compactified (...) space-times for cosmology are discussed. It is argued that the recent discovery of periodic structure of matter distribution on large distances strongly suggests that the global cosmological space-time should be close. Next we analyze the inflation scalar field in the inflationary model of universe evolution considered on the spatially compact Robertson-Walker space-time. It is shown that the energy distribution in this model is periodic and the periods and density decrease with increasing distance, in striking agreement with experimental data. Our model of the universe also provides a definite predictions for the energy distribution, polar and azimuthal, considered as a function of angles θ and φ. These predictions should be tested with the new astronomical data. (shrink)

Although considerations based on contemporary space-time theories, such as special and general relativity, seem highly relevant to the debate about persistence, their significance has not been duly appreciated. My goal in this paper is twofold: (1) to reformulate the rival positions in the debate (i.e., endurantism [three-dimensionalism] and perdurantism [four-dimensionalism, the doctrine of temporal parts]) in the framework of special relativistic space-time; and (2) to argue that, when so reformulated, perdurantism exhibits explanatory advantages over endurantism. The argument builds on (...) the fact that four-dimensional entities extended in space as well as time are relativistically invariant in a way three-dimensional entities are not. (shrink)

In this paper, we continue the study of the Killing symmetries of an N-dimensional generalized Minkowski space, i.e., a space endowed with a metric tensor, whose coefficients do depend on a set of non-metrical coordinates. We discuss here the finite structure of the space–time rotations in such spaces, by confining ourselves to the four-dimensional case. In particular, the results obtained are specialized to the case of a “deformed” Minkowski space M_4, for which we derive the explicit (...) general form of the finite rotations and boosts in different parametric bases. (shrink)

This provocative book attempts to resolve traditional problems of identity over time. It seeks to answer such questions as 'How is it that an object can survive change?' and 'How much change can an object undergo without being destroyed'? To answer these questions Professor Heller presents a theory about the nature of physical objects and about the relationship between our language and the physical world. According to his theory, the only actually existing physical entities are what the author calls 'hunks', (...) four-dimensional objects extending across time and space. This is a major contribution to ontological debate and will be essential reading for all philosophers concerned with metaphysics. (shrink)

_ Source: _Volume 5, Issue 2, pp 290 - 322 Einstein's special theory, as interpreted by Herman Minkowski, suggests that an understanding of space and time requires the replacement of three-dimensional space and one dimensional time with a four-dimensional spacetime continuum, as a natural kind of thing with a characteristic, geometrical, structure. Issues of space and time in general, and of special relativity in particular, are not addressed in Bhaskar's _A Realist Theory of Science_, and their (...) treatment in subsequent realist writings has been patchy and indecisive. Some of Bhaskar's observations in later writings, including his defence of fundamental ontological asymmetries between space and time, and between present, past and future, appear incompatible with a relativistic perspective. Equally problematic, from a critical realist perspective, is the apparent ontological prioritisation of events, and causation as action-by-contact, within the Minkowski interpretation of special relativity. This paper argues that the four-dimensional spacetime continuum of special relativity occupies its own level at the base of the ontological hierarchy of natural kinds, providing lower-order components and laws for higher-order physical, chemical, biological and social structures. While providing no definitive reconciliation of relativistic and realist perspectives, this paper does suggest that A. N. Whitehead's idea of atomic events, or ‘actual occasions’, could pave the way for some possible future reconciliation. (shrink)

Facial information is a powerful channel for human-to-human communication. Characteristically, faces can be defined as biological objects that are four-dimensional (4D) patterns, whereby they have concurrently a spatial structure as well as temporal dynamics. The spatial characteristics of facial objects possess three dimensions (3D), namely breadth, height and importantly, depth. The temporal properties of facial objects are defined by how a 3D facial structure evolves dynamically over time; where time is referred to as the fourth dimension (4D). Our (...) entire perspective of another’s face, whether it be social, affective or cognitive perceptions, is therefore built on a combination of 3D and 4D visual cues. Counterintuitively, over the past few decades of experimental research in psychology, facial stimuli have largely been presented to participants as a spatial pattern that has been flattened into two dimensions (2D), while remaining largely static. The following review aims to advance and update facial researchers, on the recent revolution in computer-generated, realistic 4D facial models produced from real-life human subjects. We delve in-depth to summarize recent studies which have utilized facial stimuli that possess 3D structural cues (geometry and depth) and 4D temporal cues (3D structure + dynamic viewpoint and movement). In sum, we have found that higher-order perceptions such as identity, gender, ethnicity, emotion and personality, are critically influenced by the 4D characteristics embedded within natural human faces. In future, it is recommended that facial stimuli incorporate the 4D space-time perspective with the proposed time-resolved methods. (shrink)

The structures of space and time associated with various four-dimensional symmetries are constructed and examined. It is interesting that some of these four-dimensional symmetries are compatible with the existence of an aether in the Einstein sense. There are two classes of infinitely many four-dimensional symmetries that cannot be ruled out by previous experiments. We discuss some laser experiments that test these two classes of four-dimensional symmetries. An interesting connection between the nonclassical aether (...) and gravity through the equality of inertial and gravitational mass is explored. (shrink)

Within the context of the variational principle, there is the freedom to choose specific evolutional parameters. Different parameters can be associated with physical time, while allowing the physical laws to preserve the property of four-dimensional symmetry. In this sense, the concept of time has flexibility. Besides proper time and relativistic time, another natural choice emerges, which is called the generalized Galilean time. We study the impact of this choice here. This approach provides a deeper understanding of the theory (...) of special relativity, and it also provides a new basis to study other space-time theories. (shrink)

The symplectic quantization scheme proposed for matter scalar fields in the companion paper (Gradenigo and Livi, arXiv:2101.02125, 2021) is generalized here to the case of space–time quantum fluctuations. That is, we present a new formalism to frame the quantum gravity problem. Inspired by the stochastic quantization approach to gravity, symplectic quantization considers an explicit dependence of the metric tensor gμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{\mu \nu }$$\end{document} on an additional time variable, named intrinsic time at (...) variance with the coordinate time of relativity, from which it is different. The physical meaning of intrinsic time, which is truly a parameter and not a coordinate, is to label the sequence of gμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{\mu \nu }$$\end{document} quantum fluctuations at a given point of the four-dimensional space–time continuum. For this reason symplectic quantization necessarily incorporates a new degree of freedom, the derivative g˙μν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{g}}_{\mu \nu }$$\end{document} of the metric field with respect to intrinsic time, corresponding to the conjugated momentum πμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi _{\mu \nu }$$\end{document}. Our proposal is to describe the quantum fluctuations of gravity by means of a symplectic dynamics generated by a generalized action functional A[gμν,πμν]=K[gμν,πμν]-S[gμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}[g_{\mu \nu },\pi _{\mu \nu }] = {\mathcal {K}}[g_{\mu \nu },\pi _{\mu \nu }] - S[g_{\mu \nu }]$$\end{document}, playing formally the role of a Hamilton function, where S[gμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S[g_{\mu \nu }]$$\end{document} is the standard Einstein–Hilbert action while K[gμν,πμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {K}}[g_{\mu \nu },\pi _{\mu \nu }]$$\end{document} is a new term including the kinetic degrees of freedom of the field. Such an action allows us to define an ensemble for the quantum fluctuations of gμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{\mu \nu }$$\end{document} analogous to the microcanonical one in statistical mechanics, with the only difference that in the present case one has conservation of the generalized action A[gμν,πμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}[g_{\mu \nu },\pi _{\mu \nu }]$$\end{document} and not of energy. Since the Einstein–Hilbert action S[gμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S[g_{\mu \nu }]$$\end{document} plays the role of a potential term in the new pseudo-Hamiltonian formalism, it can fluctuate along the symplectic action-preserving dynamics. These fluctuations are the quantum fluctuations of gμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{\mu \nu }$$\end{document}. Finally, we show how the standard path-integral approach to gravity can be obtained as an approximation of the symplectic quantization approach. By doing so we explain how the integration over the conjugated momentum field πμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi _{\mu \nu }$$\end{document} gives rise to a cosmological constant term in the path-integral approach. (shrink)

Mathematically, the fusion of space and time may be explained as follows. In pre-relativity physics, space was envisaged as a three-dimensional Euclidean continuum. Such a continuum is homogeneous and isotropic, and its metrical character can be specified by the definition of the distance between any two points in the continuum: s2 = 2 + 2 + 2. Now, while it is possible to speak of a four-dimensional continuum in pre-relativity physics by adding the time-coordinate to the three (...) space-coordinates, there is no way, corresponding to the definition of s, to define the spatio-temporal "separation" or "interval" between any two points in this new four-dimensional continuum. Thus, while it makes sense from the classical point of view to ask for the distance between two points in space, it does not make sense to ask for the spatio-temporal interval between two events occurring in different places at different times. The spatio-temporal interval between non-simultaneous, spatially separated events is simply not defined in pre-relativity physics. Another way of putting it is that in classical physics space and time are measured in entirely disparate units and no method is provided for making these units comparable with one another. In relativity physics, on the other hand, light--or rather the velocity of light--provides the means for making the results of spatial and temporal measurement comparable quantities: one simply multiplies the time-like intervals by c, the fixed velocity of light, in order to obtain space-like intervals. The interval between any two events is defined as: s2 = 2 + 2 + 2 - c22. Interval, so defined, is an invariant, whereas spatial and temporal "separation" are now relative to the state of motion of the observer. The geometry of the four-dimensional continuum characterized by this formula is called "semi-Euclidean". (shrink)

When the German mathematician Hermann Minkowski first introduced the space-time diagrams that came to be associated with his name, the idea of picturing motion by geometric means, holding time as a fourth dimension of space, was hardly new. But the pictorial device invented by Minkowski was tailor-made for a peculiar variety of space-time: the one imposed by the kinematics of Einstein’s special theory of relativity, with its unified, non-Euclidean underlying geometric structure. By plo tting two or more reference frames in (...) relative motion on the same picture, Minkowski managed to exhibit the geometric basis of such relativistic phenomena as time dilation, length contraction or the dislocation of simultaneity. These disconcerting effects were shown to result from arbitrary projections within four-dimensional space-time. In that respect, Minkowski diagrams are fundamentally different from ordinary space-time graphs. The best way to understand their specificity is to realize how productively ambiguous they are. (shrink)

Abstract.Russell Stannard distinguishes between objective time as measured in theoretical physics and subjective time, or time as experienced by human beings in normal consciousness. Because objective time, or four‐dimensional space‐time for the physicist, does not change but exists all at once, Stannard argues that this is presumably how God views time from eternity which is beyond time. We human beings are limited to experiencing the moments of time successively and thus cannot know the future as already existing in (...) the same way that God does. I argue that Stannard is basically correct in his theological assumptions about God's understanding of time but that his explanation would be more persuasive within the context of a neo‐Whiteheadian metaphysics. The key points in that metaphysics are (1) that creation is contained within the structured field of activity proper to the three divine persons of the Christian doctrine of the Trinity and (2) that the spontaneous decisions of creatures are continually ordered and reordered into an ever‐expanding totality already known in its fullness by the divine persons. (shrink)

Under the eternalist hypothesis that objects or events exist temporally, but independently of being present two different views of persistence are on the market: Persisting objects endure if they are multiply located in time, and persisting objects perdure if they are singly located by having numerically different temporal parts. In the framework of the special theory of relativity, the metaphysics of persistence is confronted with peculiar difficulties. Things persist by being “wholly present” at more than one time; but what are (...) times within a temporally non-separated spacetime? Things persist by having different temporal parts at different times; but what are the temporal parts of a four-dimensional object in Minkowski spacetime? Recently, several authors have argued that SR favours perdurantism over its endurantist rival. In this paper, I intend to show that the purported arguments are only those against endurantism. The first simply fails, but the second, more convincing one, is such that with a similar strategy we should argue against perdurantism as well: Enduring and perduring entities are hence both in conflict with SR which undermines the eternalist hypothesis. (shrink)

Under the eternalist hypothesis that objects or events exist temporally, but independently of being present two different views of persistence are on the market: Persisting objects endure if they are multiply located in time, and persisting objects perdure if they are singly located by having numerically different temporal parts. In the framework of the special theory of relativity, the metaphysics of persistence is confronted with peculiar difficulties. Things persist by being “wholly present” at more than one time; but what are (...) times within a temporally non-separated spacetime? Things persist by having different temporal parts at different times; but what are the temporal parts of a four-dimensional object in Minkowski spacetime? Recently, several authors have argued that SR favours perdurantism over its endurantist rival. In this paper, I intend to show that the purported arguments are only those against endurantism. The first simply fails, but the second, more convincing one, is such that with a similar strategy we should argue against perdurantism as well: Enduring and perduring entities are hence both in conflict with SR which undermines the eternalist hypothesis. (shrink)

This book focuses on the phenomena of inertia and gravitation, one objective being to shed some new light on the basic laws of gravitational interaction and the fundamental nature and structures of spacetime. Chapter 1 is devoted to an extensive, partly new analysis of the law of inertia. The underlying mathematical and geometrical structure of Newtonian spacetime is presented from a four-dimensional point of view, and some historical difficulties and controversies - in particular the concepts of free particles (...) and straight lines - are critically analyzed, while connections to projective geometry are also explored. The relativistic extensions of the law of gravitation and its intriguing consequences are studied in Chapter 2. This is achieved, following the works of Weyl, Ehlers, Pirani and Schild, by adopting a point of view of the combined conformal and projective structure of spacetime. Specifically, Mach's fundamental critique of Newton's concepts of 'absolute space' and 'absolute time' was a decisive motivation for Einstein's development of general relativity, and his equivalence principle provided a new perspective on inertia. In Chapter 3 the very special mathematical structure of Einstein's field equations is analyzed, and some of their remarkable physical predictions are presented. By analyzing different types of dragging phenomena, Chapter 4 reviews to what extent the equivalence principle is realized in general relativity - a question intimately connected to the 'new force' of gravitomagnetism, which was theoretically predicted by Einstein and Thirring but which was only recently experimentally confirmed and is thus of current interest. (shrink)

"The last remnant of physical objectivity of space-time" is disclosed, beyond the Leibniz equivalence, in the case of a continuous family of spatially non-compact models of general relativity. The physical individuation of point-events is furnished by the intrinsic degrees of freedom of the gravitational field, (viz, the "Dirac observables") that represent - as it were - the "ontic" part of the metric field. The physical role of the "epistemic" part (viz. the "gauge" variables) is likewise clarified. At the end, a (...) peculiar four-dimensional "holistic and structuralist" view of space-time emerges which includes elements common to the tradition of both substantivalism and relationism. The observables of our models undergo real "temporal change" and thereby provide a counter-example to the thesis of the "frozen-time" picture of evolution. (shrink)

We apply a method analogous to the eikonal approximation to the Maxwell wave equations in an inhomogeneous anisotropic medium and geodesic motion in a three dimensional Riemannian manifold, using a method which identifies the symplectic structure of the corresponding mechanics, to the five dimensional generalization of Maxwell theory required by the gauge invariance of Stueckelberg's covariant classical and quantum dynamics. In this way, we demonstrate, in the eikonal approximation, the existence of geodesic motion for the flow of mass (...) in a four dimensional pseudo-Riemannian manifold. These results provide a foundation for the geometrical optics of the five dimensional radiation theory and establish a model in which there is mass flow along geodesics. We then discuss the interesting case of relativistic quantum theory in an anisotropic medium as well. In this case the eikonal approximation to the relativistic quantum mechanical current coincides with the geodesic flow governed by the pseudo-Riemannian metric obtained from the eikonal approximation to solutions of the Stueckelberg–Schrödinger equation. The locally symplectic structure which emerges is that of a generally covariant form of Stueckelberg's mechanics on this manifold. (shrink)

This paper deals with a number of technical achievements that are instrumental for a dis-solution of the so-called "Hole Argument" in general relativity. Such achievements include: 1) the analysis of the "Hole" phenomenology in strict connection with the Hamiltonian treatment of the initial value problem. The work is carried through in metric gravity for the class of Christoudoulou-Klainermann space-times, in which the temporal evolution is ruled by the "weak" ADM energy; 2) a re-interpretation of "active" diffeomorphisms as "passive and metric-dependent" (...) dynamical symmetries of Einstein's equations, a re-interpretation which enables to disclose their (up to now unknown) connection to gauge transformations on-shell; understanding such connection also enlightens the real content of the Hole Argument or, better, dis-solves it together with its alleged "indeterminism"; 3) the utilization of the Bergmann-Komar "intrinsic pseudo-coordinates", defined as suitable functionals of the Weyl curvature scalars, as tools for a peculiar gauge-fixing to the super-hamiltonian and super-momentum constraints; 4) the consequent construction of a "physical atlas" of 4-coordinate systems for the 4-dimensional "mathematical" manifold, in terms of the highly non-local degrees of freedom of the gravitational field (its four independent "Dirac observables"). Such construction embodies the "physical individuation" of the points of space-time as "point-events", independently of the presence of matter, and associates a "non-commutative structure" to each gauge fixing or four-dimensional coordinate system; 5) a clarification of the multiple definition given by Peter Bergmann of the concept of "(Bergmann) observable" in general relativity. This clarification leads to the proposal of a "main conjecture" asserting the existence of i) special Dirac's observables which are also Bergmann's observables, ii) gauge variables that are coordinate independent (namely they behave like the tetradic scalar fields of the Newman-Penrose formalism). A by-product of this achievements is the falsification of a recently advanced argument asserting the absence of (any kind of) "change" in the observable quantities of general relativity. 6) a clarification of the physical role of Dirac and gauge variables as their being related to "tidal-like" and "inertial-like" effects, respectively. This clarification is mainly due to the fact that, unlike the standard formulations of the equivalence principle, the Hamiltonian formalism allows to define notion of "force" in general relativity in a natural way; 7) a proposal showing how the physical individuation of point-events could in principle be implemented as an experimental setup and protocol leading to a "standard of space-time" more or less like atomic clocks define standards of time. We conclude that, besides being operationally essential for building measuring apparatuses for the gravitational field, the role of matter in the non-vacuum gravitational case is also that of "participating directly" in the individuation process, being involved in the determination of the Dirac observables. This circumstance leads naturally to a peculiar new kind of "structuralist" view of the general-relativistic concept of space-time, a view that embodies some elements of both the traditional "absolutist" and "relational" conceptions. In the end, space-time point-events maintain a "peculiar sort of objectivity". Some hints following from our approach for the quantum gravity programme are also given. (shrink)

In a recent article, Ned Markosian gives an argument against four-dimensionalism understood as the view that time is one of four identical dimensions that constitute a single four-dimensional manifold. In this paper, I show that Markosian attacks a straw man as his argument targets a theory known to be false on empirical grounds. Four-dimensionalism rightly conceived in no way entails that time is identical to space. I then address two objections raised by Markosian against (...) class='Hi'>four-dimensionalism rightly conceived. (shrink)

An investigation of the views on space and time of the Russian polymath Pavel Florensky. After a brief account of his life, I study Florensky’s conception of time in The Meaning of Idealism, where he first confronts Einstein’s theory of special relativity, comparing it to Plato’s metaphor of the Cave and Goethe’s myth of the Mothers. Later, in his Analysis of spatiality and time, Florensky speaks of a person’s biography as a four-dimensional unity, in which the temporal coordinate (...) is examined in sections. In On the Imaginaries in Geometry, Florensky argues that the speed of light is not, as in Relativity, an absolute speed limit in the universe. When bodies approach and then surpass the speed of light, they are transformed into unextended, eternal Platonic forms. Beyond this point, time runs in reverse, effects precede their causes, and efficient causality is transformed into final or teleological causality, a concept on which Florensky elaborates in his Iconostasis. Florensky thus transformed the findings of Einsteinian relativity in order to make room for Plato’s intelligible Ideas, the Aristotelian distinction between a changing realm of earth and the immutable realm of the heavens, and the notion of teleology or final causation. His notion that man can approximate God’s vision of past, present and future all at once, as if from above, is reminiscent of Boethius’ ideas. (shrink)

We investigate the possibility of inducing the cosmological constant from extra dimensions by embedding our four-dimensional Riemannian space-time into a five-dimensional Weyl integrable space. Following the approach of the space-time-matter theory we show that when we go down from five to four dimensions, the Weyl field may contribute both to the induced energy-tensor as well as to the cosmological constant Λ, or more generally, it may generate a time-dependent cosmological parameter Λ(t). As an application, we construct (...) a simple cosmological model in which Λ(t) has some interesting properties. (shrink)

The development of four-dimensional ultrasound pre-natal scans carries with it an intriguing range of philosophical questions. While ultrasound in pregnancy is a medical test for detecting foetal abnormalities, it has also become a social ritual in Western culture. The scan has become embedded within a discourse of the parent’s ante-relationships with their future child as much as it is a screening function. Within such a scene, the advance of technology – the move, for example, the increasing addition of (...) dimensions to pre-natal imaging, from 2D to 3D and 4D – is inextricably merged with the spatial rhetoric of the foetus. Drawing on both Heidegger’s insights into the relationship between the human and technology, and debates within feminist cultural theory, this paper explores how these spatial and temporal rhetorics of the foetal ultrasound relate to the philosophical motifs around self, knowledge, gender and the technical image. It charts these relationships through an analysis of two classic images of the foetal self, before considering how the fourth dimension of ultrasound – that of real-time image streaming of a foetal scan – enhances, develops and critiques these motifs. (shrink)

The paradoxes of time travel are oddities, not impossibilities. This chapter concerns with the sort of time travel that is recounted in science fiction. It argues that what goes on in a time travel story may be a possible pattern of events in four‐dimensional space‐time with no extra time dimension; that it may be correct to regard the scattered stages of the alleged time traveler as comprising a single person; and that we may legitimately assign to those stages (...) and their surroundings a personal time order that disagrees sometimes with their order in external time. Some might concede all this, but protest that the impossibility of time travel is revealed after all when we ask not what the time traveler does, but what he could do. Finally the chapter provides time travel story about Tim and Tom. (shrink)

Multidimensional scaling of subjective color differences has shown that color stimuli are located on a hypersphere in four-dimensional space. The semantic space of color names is isomorphic with perceptual color space. A spherical four-dimensional space revealed in monkeys and fish suggests the primacy of common neuronal basis.

This work is a two-division study of twentieth century philosophies of history in Europe. Fields engaged in the study are transcendental philosophy, speculative metaphysics, theology, historiographical theory, and intellectual history. The main question concerns the historical finitude of History and its temporal horizon. The work explores the unsolved consequences of G.W.F. Hegel's Phenomenology of Spirit and Martin Heidegger's Being and Time in twentieth-century German and French philosophies of History.

About time, we have too many questions, such as the thing of the past no longer have? The future is not expected to do? Now exist? The passage of time is irreversible, it? What is eternal? Relationship with time? In this paper, the Great Perfection tradition of Tibetan Buddhism's long clearance and West Pakistan Heidegger, for example the phenomenon of school time to discuss the experience. They did not go to the concept of eternal life, but deep into the phenomenon (...) of the passage of time and experiences, reveals a new time dimension, the so-called fourth dimension of time or fourth time. This paper describes the Dzogchen tradition, the processing time of a spiritual experience, and analysis of Pakistan's four seasons Longqing concept and significance in the history of Buddhism, followed by a discussion of Heidegger's four-dimensional concept of time, and their followers on the the concept of further discussion. Finally, in conclusion, I will briefly explain the traditional four-dimensional time in these two different points in the same, and to explore possible reasons similar point. Concerning time, we have many puzzles, such as what is eternity, how it is related to the passage of time, whether the passage of time is irreversible, whether things past are no-longer, whether the future is non-predictable, whether the present exists or not, and so on. This article is an attempt to discuss such experiences of the passage of time. First, a Buddhist practice in Dzogchen tradition that deals with the experience of the passage of time will be introduced, then Longchenpa's concept of four times will be analyzed, and its significance in the history of Buddhism will also be discussed. In the following section, it will examine Heidegger's concept of four dimensional time and briefly discuss its elaboration by later philosophers. In conclusion, it will discuss the similarities and differences between the four-dimensional time theories as found in these two diverse traditions, and the possible reasons for their striking similarities. (shrink)

: Concerning time, we have many puzzles, such as what eternity is, how it is related to the passage of time, whether the passage of time is irreversible, whether things past are no longer, whether the future is non-predictable, whether or not the present exists, and so on. This article is an attempt to discuss such experiences of the passage of time. First, a Buddhist practice in the Dzogchen tradition that deals with the experience of the passage of time will (...) be introduced, then Longchenpa’s concept of four times (dus-bzhi) will be analyzed and its significance to the history of Buddhism discussed. Next, Heidegger’s concept of four-dimensional time and its elaboration by later philosophers will be discussed. It will conclude with the similarities and differences between the four-dimensional time theories as found in these two diverse traditions, and the possible reasons for their striking similarities. (shrink)

This work is a two-division study of twentieth century philosophies of history in Europe. Fields engaged in the study are transcendental philosophy, speculative metaphysics, theology, historiographical theory, and intellectual history. The main question concerns the historical finitude of History and its temporal horizon. The work explores the unsolved consequences of G.W.F. Hegel's Phenomenology of Spirit and Martin Heidegger's Being and Time in twentieth-century German and French philosophies of History.

Four-dimensionalism is the thesis that everyday objects, such as you and me, are space-time worms that persist through time by having temporal parts none of which is identical to the object itself. Objects are aggregates or sums of such temporal parts. The main virtue of fourdimensionalism is that it solves—or does away with—the problem of identity through change.1 The main charge raised against it is that it is inconsistent with the thesis according to which there is change in the (...) world.2 If this charge could be sustained, then we would need compelling arguments in support of the view that things are four-dimensional, since the view that there is no change in the world conflicts with so many of our most well-supported common-sense beliefs. In what follows, however, I want to show that, contrary to what is usually believed, fourdimensionalism does not entail a changeless world. (shrink)

This thesis is about the conceptualization of persistence of physical, middle-sized objects within the theoretical framework of the revisionary ‘B-theory’ of time. According to the B-theory, time does not flow, but is an extended and inherently directed fourth dimension along which the history of the universe is ‘laid out’ once and for all. It is a widespread view among philosophers that if we accept the B-theory, the commonsensical ‘endurance theory’ of persistence will have to be rejected. The endurance theory says (...) that objects persist through time by being wholly present at distinct times as numerically the same entity. Instead of endurantism, it has been argued, we have to adopt either ‘perdurantism’ or the ‘stage theory’. Perdurantism is the theory that objects are four-dimensional ‘space-time worms’ persisting through time by having distinct temporal parts at distinct times. The stage theory says that objects are instantaneous temporal parts (stages) of space-time worms, persisting by having distinct temporal counterparts at distinct times. In the thesis, it is argued that no good arguments have been provided for the conclusion that we are obliged to drop the endurance theory by acceptance of the B-theory. This conclusion stands even if the endurance theory incorporates the claim that objects endure through intrinsic change. It is also shown that perdurantism and the stage theory come with unwelcome consequences. -/- Paper I demonstrates that the main arguments for the view that objects cannot endure in B-time intrinsically unchanged fail. Papers II and III do the same with respect to the traditional arguments against endurance through intrinsic change in B-time. Paper III also contains a detailed account of the semantics of the tenseless copula, which occurs frequently in the debate. The contention of Paper IV is that four-dimensional space-time worms, as traditionally understood, are not suited to take dispositional predicates. In Paper V, it is shown that the stage theory needs to introduce an overabundance of persistence-concepts, many of which will have to be simultaneously applicable to a single object (qua falling under a single sortal), in order for the theory to be consistent. The final article, Paper VI, investigates the sense in which persistence can, as is sometimes suggested, be a ‘conventional matter’. It also asks whether alleged cases of ‘conventional persistence’ create trouble for the endurance theory. It is argued that conventions can only enter at a trivial semantic level, and that the endurance theory is no more threatened by such conventions than are its rivals. (shrink)

Four-dimensionalism is the thesis that everyday objects, such as you and me, are space-time worms that persist through time by having temporal parts none of which is identical to the object itself. Objects are aggregates or sums of such temporal parts. The main virtue of four-dimensionalism is that it solves—or does away with—the problem of identity through change. The main charge raised against it is that it is inconsistent with the thesis according to which there is change in (...) the world. If this charge could be sustained, then we would need compelling arguments in support of the view that things are four-dimensional, since the view that there is no change in the world conflicts with so many of our most well-supported common-sense beliefs. In what follows, however, I want to show that, contrary to what is usually believed, four-dimensionalism does not entail a changeless world. (shrink)

The present paper develops arguments for the need to formulate the basic theories of physics in terms of a six-dimensional manifold, as opposed to the four-dimensional space-time continuum of conventional theory. Employing a purely classical approach, some of the dynamical consequences of such a formulation with regard to both electrodynamics and gravitation are evaluated. The results lead to interesting implications with regard to various questions such as the occurrence and importance of superluminal particles, the existence of two (...) or more physically distinct time scales, and the variation of the gravitational coupling constant G and the law of energy conservation. The analysis also suggests a physical interpretation of the additional coordinates that occur in the metric. (shrink)

Two radically different views about time are possible. According to the first, the universe is three dimensional. It has a past and a future, but that does not mean it is spread out in time as it is spread out in the three dimensions of space. This view requires that there is an unambiguous, absolute, cosmic-wide "now" at each instant. According to the second view about time, the universe is four dimensional. It is spread out in both (...) space and time - in space-time in short. Special and general relativity rule out the first view. There is, according to relativity theory, no such thing as an unambiguous, absolute cosmic-wide "now" at each instant. However, we have every reason to hold that both special and general relativity are false. Not only does the historical record tell us that physics advances from one false theory to another. Furthermore, elsewhere I have shown that we must interpret physics as having established physicalism - in so far as physics can ever establish anything theoretical. Physicalism, here, is to be interpreted as the thesis that the universe is such that some unified "theory of everything" is true. Granted physicalism, it follows immediately that any physical theory that is about a restricted range of phenomena only, cannot be true, whatever its empirical success may be. It follows that both special and general relativity are false. This does not mean of course that the implication of these two theories that there is no unambiguous cosmic-wide "now" at each instant is false. It still may be the case that the first view of time, indicated at the outset, is false. Are there grounds for holding that an unambiguous cosmic-wide "now" does exist, despite special and general relativity, both of which imply that it does not exist? There are such grounds. Elsewhere I have argued that, in order to solve the quantum wave/particle problem and make sense of the quantum domain we need to interpret quantum theory as a fundamentally probabilistic theory, a theory which specifies how quantum entities - electrons, photons, atoms - interact with one another probabilistically. It is conceivable that this is correct, and the ultimate laws of the universe are probabilistic in character. If so, probabilistic transitions could define unambiguous, absolute cosmic-wide "nows" at each instant. It is entirely unsurprising that special and general relativity have nothing to say about the matter. Both theories are pre-quantum mechanical, classical theories, and general relativity in particular is deterministic. The universe may indeed be three dimensional, with a past and a future, but not spread out in four dimensional space-time, despite the fact that relativity theories appear to rule this out. These considerations, finally, have implications for views about the arrow of time and free will. (shrink)

Following the ideas of Poincaré, Reichenbach, and Grunbaum concerning the convention of setting up clock systems, we analyze clock systems and light propagation within the framework of four-dimensional symmetry. It is possible to construct a new four-dimensional symmetry framework incorporatingcommon time: observers in different inertial frames of reference use one and the same clock system, which is located in any one of the frames. Consequently, simultaneity has a meaning independent of position and independent of frame of (...) reference. A further consequence is that the two-way speeds of light alone are isotropic in any frame. By the choice of clock system there will be one frame in which the one-way speed of light is isotropic. This frame can be arbitrarily chosen. The difference between one-way speeds and two-way speeds of light signals is considered in detail. (shrink)

I BEGIN WITH A PUZZLE of sorts. Time is one; space is two—at least two. Time comes always already unified, one time. Thus we say “What time is it now?” and not “Which time is it now?” We do not ask, “What space is it?” Yet we might ask: “Which space are we in?”. Any supposed symmetry of time and space is skewed from the start. If time is self-consolidating—constantly gathering itself together in coherent units such as years or hours (...) or semesters or seasons— space is self-proliferating. Take, for example, the dimensionality of space. One dimension in space is represented by a point or a line, whose radically reduced format mocks the extensiveness of cosmic space. Two dimensions, as in a plane figure, also falls far short of our sense that space spreads out indefinitely far beyond the perceiving subject. Only with three dimensions do we begin to approach an adequation between the structure and the sense of space. For then the subject is surrounded by something sufficiently roomy in which to live and move. Indeed, as Aristotle, Kant, and Merleau-Ponty all remark, the three-dimensionality of space directly reflects our bodily state, that is, the fact that as upright beings three perpendicular planes implicitly meet and intersect in us. Even here, proliferation abounds: our bilateral symmetry means that each dimension is doubled: one vertical plane bifurcates into “up” and “down,” the other vertical plane into “front” and “back,” and the horizontal plane into “right” and “left.” Thus subject-centered space is triple, only to be redoubled. Further, if we think of spatiality not as body-based but as locatory—as determined by landmarks and other locales in the environment—the proliferation is more striking still. There are the four cardinal directions, which themselves split easily into the thirty two points of a compass. Nor need we be so arithmetically well-rounded. Even apart from fancy mathematical models of n –dimensional space, and recent technological instantiations of virtual space, there is no end to the number or ways in which we can be oriented in space—in accordance with what Deleuze and Guattari call “the variability, the polyvocity of directions” by which we can move in any given spatial scene. Beyond direction, however, is place. Heidegger remarks that “space has been split up into places.” The fact is that we continually find ourselves immersed in a multiplex spatial network whose nodal points are supplied by particular places. If space is infinitely large, place is indefinitely many. (shrink)

I BEGIN WITH A PUZZLE of sorts. Time is one; space is two—at least two. Time comes always already unified, one time. Thus we say “What time is it now?” and not “Which time is it now?” We do not ask, “What space is it?” Yet we might ask: “Which space are we in?”. Any supposed symmetry of time and space is skewed from the start. If time is self-consolidating—constantly gathering itself together in coherent units such as years or hours (...) or semesters or seasons— space is self-proliferating. Take, for example, the dimensionality of space. One dimension in space is represented by a point or a line, whose radically reduced format mocks the extensiveness of cosmic space. Two dimensions, as in a plane figure, also falls far short of our sense that space spreads out indefinitely far beyond the perceiving subject. Only with three dimensions do we begin to approach an adequation between the structure and the sense of space. For then the subject is surrounded by something sufficiently roomy in which to live and move. Indeed, as Aristotle, Kant, and Merleau-Ponty all remark, the three-dimensionality of space directly reflects our bodily state, that is, the fact that as upright beings three perpendicular planes implicitly meet and intersect in us. Even here, proliferation abounds: our bilateral symmetry means that each dimension is doubled: one vertical plane bifurcates into “up” and “down,” the other vertical plane into “front” and “back,” and the horizontal plane into “right” and “left.” Thus subject-centered space is triple, only to be redoubled. Further, if we think of spatiality not as body-based but as locatory—as determined by landmarks and other locales in the environment—the proliferation is more striking still. There are the four cardinal directions, which themselves split easily into the thirty two points of a compass. Nor need we be so arithmetically well-rounded. Even apart from fancy mathematical models of n –dimensional space, and recent technological instantiations of virtual space, there is no end to the number or ways in which we can be oriented in space—in accordance with what Deleuze and Guattari call “the variability, the polyvocity of directions” by which we can move in any given spatial scene. Beyond direction, however, is place. Heidegger remarks that “space has been split up into places.” The fact is that we continually find ourselves immersed in a multiplex spatial network whose nodal points are supplied by particular places. If space is infinitely large, place is indefinitely many. (shrink)

This paper presents the strongest version of a non-perdurantist four-dimensionalism: a theory according to which persisting objects are four-dimensionally extended in space-time, but not in virtue of having maximal temporal parts. The aims of considering such a view are twofold. First, to evaluate whether such an account could provide a plausible middle ground between the two main competitor accounts of persistence: three-dimensionalism and perdurantist four-dimensionalism. Second, to see what light such a theory sheds on the debate between (...) these two competitor theories. I conclude that despite prima facie reasons to suppose that non-perdurantist four-dimensionalism might be a credible alternative to either other account of persistence, ultimately the view is unsuccessful. The reasons for its failure illuminate the sometimes stagnant debate between three-dimensionalists and perdurantists, providing new reasons to prefer a perdurantist metaphysics. (shrink)