The paper takes a detailed look at a surprising new aspect of the dynamics of rigid bodies. Far from the usual consideration of rigid body theory as a merely technical chapter of classical physics, I demonstrate here that there are solutions to the conservation equations of mechanics that imply the spontaneous, unpredictable splitting of a rigid body in free rotation, something that has direct implications for the problem of causality. The paper also shows that the instability revealed in indeterminist splitting (...) processes does not depend solely on the bodies’ inertial properties but also on the number of dimensions of the physical space they inhabit. The paper concludes with a conjecture on the behavior of rigid bodies in four-dimensional space. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Four-Dimensionalism and Identity Across Time: Henry of Ghent vs. BonaventureRichard CrossModern accounts of the identity of an object across time tend to fall roughly into two basic types.Let us say that something persists ıff, somehow or other, it exists at various times; this is the neutral word. Something perdures iff it persists by having different temporal parts, or stages, at different times, though no one part of it (...) is wholly present at more than one time; whereas it endures iff it persists by being wholly present at more than one time.1On the first of these analyses, but not the second, a persistent object includes temporal parts, and persistent material substances are thus on this analysis four-dimensional objects. On the first analysis, but not on the second, time-indices are explicable in terms of temporal parts. I shall take this as the basic difference between the two views.2Both views allow us to talk of temporal order and temporal direction. I [End Page 393] shall follow the medievals and talk about succession to capture both of these claims: “The notion of succession formally consists in the notion of ‘before’ and ‘after,’”3 and I take it that talk of “before” and “after” entails both order and direction.4 Medieval accounts of identity across time are, however, in some ways more obscure than the two modern ones just described. The medievals tend to associate all temporal succession with temporal extension: an object x has temporal succession if and only if x is temporally extended (and thus includes temporal parts).5 The medievals also (correctly, I believe) tend to suppose that substances—unlike (say) processes—do not have temporal parts.6 Thus, by the end of the thirteenth century the schoolmen commonly [End Page 394] distinguish permanent objects from successive objects. Permanent objects do not, and successive objects do, have temporal parts.7 Successive objects are processes; the class of permanent objects was generally held to include not only God, but also angels, material substances, and static accidents (i.e., accidents which do not entail any sort of process).8Given these claims, there is a problem to be faced in giving an account of the identity of, say, a material substance across time. But it is not the problem we would face. Our problem, post-Hume, is to explain the relevant (explanatory) continuity requirements for identity across time. The medievals’ problem is rather different. They do not need to specify general continuity requirements, because for them there is a very real sense in which substances—and indeed all permanent objects—lack temporal extension and, therefore, any sort of temporal succession at all. The problem for the medievals is thus to explain how substances can persist at all, rather than exist merely fleetingly.9In what follows, I will examine two thirteenth-century solutions to this problem. The first is a radical one: simply to deny the standard claim that substances lack temporal parts. This view will thus bear some resemblance to what we would label four-dimensionalism. The second solution I will examine represents one of the more successful attempts to defend the standard thirteenth-century line that substances lack temporal parts. This solution goes some way towards allowing succession (and time-indexing) without appealing to temporal parts.To understand the debate, we need to keep in mind that the medievals—following Aristotle—talk of the temporality of an object in terms of its being [End Page 395] measured by time. Confusingly, they might speak of a substance’s being measured in one sort of way, and its accidental properties’ being measured in another. Thus, by the end of the thirteenth century it was often claimed that the duration of a substance is measured not by time but by the aevum—the durational measure of objects lacking temporal parts—while some of a substance’s accidental properties could be measured by time. (I will explain in detail below how time and the aevum were understood.) On this view, the temporality of an object’s properties is not sufficient cause for positing the temporality of the object. There are acceptable and unacceptable ways of understanding... (shrink)

”The last remnant of physical objectivity of space-time” is disclosed 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 autonomous degrees of freedom of the gravitational field, which represent -as it were -the ontic part of the metric field. The physical role of the epistemic part is likewise clarified as embodying the unavoidable non-inertial aspects of GR. At the end the philosophical import of the Hole Argument (...) is substantially weakened and in fact the Argument itself dis-solved, while a specific four-dimensional holistic and structuralist view of space-time emerges, including elements common to the tradition of both substantivalism and relationism. The observables of our models undergo real temporal change: this gives new evidence to the fact that statements like the frozen-time character of evolution, as other ontological claims about GR, are model dependent. (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)

The process of a four-dimensional conversion and/or transformation strives in helping the leadership of an organisation, especially such as the church, with practical ways that may lead to the development of an effective leadership by observing the four important aspects of human spirituality as elaborated on in the article. The spiritual, intellectual, moral and socio-political dimensions of the transformation can be catered for so that the complete inner being of humans, as well as their social and political (...) attitudes and behaviours, can equally be transformed to maximum spiritual, personal and socio-political profitability. Mutombo-Mukendi demonstrates that the need for a spiritual leadership that can contribute to an effective transformation of Africa is dire, both for the church and the larger community. The real challenge is how to develop such leadership. This article provides intentional and practical ways that may lead to the development of the needed leadership. Four-dimensional transformation of people can be planned and carried out both in the church arena and in the surrounding communities. Skills development and transfer can also take place when skilled people from the church work with unskilled people from the community. (shrink)

This paper defends the view of continuants as 'four-dimensional worms' against an argument of Geach's. This is to the effect that if continuants are four-dimensional worms then their stages either do, or do not, fall under the very general terms satisfied by the continuants themselves (a stage of a man either is, or is not, a man); but that either alternative is untenable. I try to show how the former alternative may be defended by appealing to (...) some of Geach's own ideas about identity; then go on to defend the four-dimensionalist view from a criticism of it by Mellor, and finish with an account of the intuitive distinction between process and continuant terms. (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)

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.

The typical Four-Dimensionalist metaphysics will posit the existence of many entities with thinking temporal parts. To determine which of these entities are persons, Hud Hudson relies upon an exclusion principle that withholds the label “person” from objects possessing any parts that don’t contribute to thought. Thus the human animal can’t be identified with the human person because it initially consists of mindless embryonic temporal parts. Since even normal adult human animals have parts such as hair and nails that don’t (...) appear to contribute to the production of thought, Hudson argues that the person is to be found “beneath the skin” of the animal. This chapter contests this claim of the non-identity of the human person and human animal while still operating with Hudson’s assumptions that we persist in virtue of temporal parts, that composition is unrestricted, and that there cannot be any persons embedded within larger persons. (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)

I offer a clear conception of a temporal part that does not make the existence of temporal parts implausible. This can be done if (and only if) we think of physical objects as four dimensional, The fourth dimension being time. Unless we are willing to deny the existence of most spatial parts, Or willing to accept the possibility of coincident entities, Or accept something even more implausible, We should accept the existence of temporal parts.

This book presents original translations and a penetrating analysis of hymns from the Rg Veda, the earliest literary document of the Indian tradition. For many years the Rg Veda has been a source of interest and inspiration to Western readers. Composed in the predawn of recorded history it narrates the struggle of the Aryans as they tried to unify the world around them by sharing a common vision.

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.

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.

Carroll shaped the corporate social responsibility discourse into a four-dimensional pyramid framework, which was later adapted to corporate citizenship and sustainability approaches. The four layers of the pyramid—structured from foundation to apex as economic, legal, ethical, and philanthropic responsibilities—drew considerable managerial attention. An important criticism of the economic foundation of the Carroll pyramid concerns the identification and ordering of the four dimensions, which are inadequately justified theoretically. The authors of this article propose an alternative approach that (...) builds on the public value concept, which integrates a microfoundation of psychological research into basic human needs. Drawing on their Swiss Dialogue process, the authors argue that a four-dimensional pyramid does have heuristic value for managers. The advantage of this alternative pyramid logic is that it may be contingently adapted to different cultural contexts, because it allows adaptive internal reordering. (shrink)

The paper argues that four-dimensionalism is incompatible with the existence of additively cumulative properties, including mass, volume, and electrical charge. These properties add up over disjoint objects: for example, the mass of a whole composed of two disjoint objects is a sum of the individual masses of the objects. The difficulty with such properties for four-dimensionalism stems from the way this theory makes persistence depend on the existence of disjoint objects at disjoint times. I consider various possible responses (...) to this difficulty and conclude that they all fail. (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)

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)

In this paper we present definitions of different four-dimensional (4D) geometric quantities (Clifford multivectors). New decompositions of the torque N and the angular momentum M (bivectors) into 1-vectors Ns, Nt and Ms, Mt, respectively, are given. The torques Ns, Nt (the angular momentums Ms, Mt), taken together, contain the same physical information as the bivector N (the bivector M). The usual approaches that deal with the 3D quantities $\varvec{E,\,B,\,F,\,L,\,N}$ etc. and their transformations are objected from the viewpoint of (...) the invariant special relativity (ISR). In the ISR, it is considered that 4D geometric quantities are well-defined both theoretically and experimentally in the 4D spacetime. This is not the case with the usual 3D quantities. It is shown that there is no apparent electrodynamic paradox with the torque, and that the principle of relativity is naturally satisfied, when the 4D geometric quantities are used instead of the 3D quantities. (shrink)

We explore the mathematical structure and the physical implications of a general four-dimensional symmetry framework which is consistent with the Poincaré—Einstein principle of relativity for physical laws and with experiments. In particular, we discuss a four-dimensional framework in which all observers in different frames use one and the same grid of clocks. The general framework includes special relativity and a recently proposed new four-dimensional symmetry with a nonuniversal light speed as two special simple cases. (...) The connection between the properties of light propagation and the convention concerning clock systems is also discussed, and is seen to be nonunique within the four-dimensional framework. (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)

Author argues that the implicit bias against theism is part of a larger pattern of ignoring the realm of illusion and related products of culture. In response, each psychologist must develop an integrated theory that incorporates four dimensions of human experience: intrapersonal, interpersonal, impersonal, and transpersonal. 2012 APA, all rights reserved).

This book presents original translations and a penetrating analysis of hymns from the Rg Veda, the earliest literary document of the Indian tradition. For many years the Rg Veda has been a source of interest and inspiration to Western readers. Composed in the predawn of recorded history it narrates the struggle of the Aryans as they tried to unify the world around them by sharing a common vision.

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)

Are shapes of objects intrinsic to them? The issue has been intensely debated. Special relativity (SR) adds a new dimension to it by relativizing three-dimensional (3D) shapes not just to times, but to times-in-frames. Arguably, however, such relativized spatial shapes are mere perspectival representations of an invariant, hence intrinsic, four-dimensional (4D) shape of an object in Minkowski spacetime. In a recent note, Matthew Davidson questions the intrinsicality of 4D shapes in SR. I show that his conclusion and (...) the reasoning behind it are in error. (shrink)

We discuss quantum electrodynamics within the framework of a new four-dimensional symmetry in which the concept of time, the propagation of light, and the transformation property of many physical quantities are drastically different from those in special relativity. However, they are consistent with experiments. The new framework allows for natural developments of additional concepts. Observers in different frames may use the same grid of clocks, located in any one of the frames, and hence have a universal time.

This study compares college students with other adults in terms of the Muncy–Vitell (1992) consumer ethics scale. Further, the study updates the Muncy–Vitell consumer ethics scale with modifications that include rewording and the addition of new items. These new items can be grouped into three distinct categories – (1) downloading/buying counterfeit goods, (2) recycling/environmental awareness and (3) doing the right thing/doing good. The study also compares these two groups in terms of their attitude toward business. Results show that there is (...) indeed a significant difference between these two groups in terms of ethical perceptions, but not in terms of the “recycling” items and the “doing good” items. There was also little difference between the groups in terms of their attitude toward business indicating that attitude toward business does not explain their different ethical perspectives. (shrink)

We show the existence of Lorentz invariant Berry phases generated, in the Stueckelberg–Horwitz–Piron manifestly covariant quantum theory (SHP), by a perturbed four dimensional harmonic oscillator. These phases are associated with a fractional perturbation of the azimuthal symmetry of the oscillator. They are computed numerically by using time independent perturbation theory and the definition of the Berry phase generalized to the framework of SHP relativistic quantum theory.

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)

This paper presents the topological arrangements in four geometrical figures of modal propositions and their derivative relations by means of Peirce's gamma graphs and their rules of transformation. The idea of arraying the gamma graphs in a geometric and symmetrical order comes from Peirce himself who in a manuscript drew two cubes in which he presented the derivative relations of some gamma graphs. Therefore, Peirce's insights of a topological order of gamma graphs are extended here backwards from the cube (...) to the line and the square; and then forwards from the cube to the four-dimensional polyhedron. (shrink)

The law of gravitational attraction is a window on three formal approaches to laws of nature based on Lorentz-invariance: Poincaré’s four-dimensional vector space (1906), Minkowski’s matrix calculus and spacetime geometry (1908), and Sommerfeld’s 4-vector algebra (1910). In virtue of a common appeal to 4-vectors for the characterization of gravitational attraction, these three contributions track the emergence and early development of four-dimensional physics.