Frank Arntzenius presents a series of radical new ideas about the structure of space and time. Space, Time, and Stuff is an attempt to show that physics is geometry: that the fundamental structure of the physical world is purely geometrical structure. Along the way, he examines some non-standard views about the structure of spacetime and its inhabitants, including the idea that space and time are pointless, the idea that quantum mechanics is a completely local theory, the idea that antiparticles are (...) just particles travelling back in time, and the idea that time has no structure whatsoever. The main thrust of the book, however, is that there are good reasons to believe that spaces other than spacetime exist, and that it is the existence of these additional spaces that allows one to reduce all of physics to geometry. Philosophy, and metaphysics in particular, plays an important role here: the assumption that the fundamental laws of physics are simple in terms of the fundamental physical properties and relations is pivotal. Without this assumption one gets nowhere. That is to say, when trying to extract the fundamental structure of the world from theories of physics one ignores philosophy at one's peril! (shrink)

In this article it is presented the idea that quantum electrodynamics has to be seen as a theoretical upgrade of classical electrodynamics and the theory of relativity, that permits an extension of classical theory in the description of phenomena, that while being clearly related to the conceptual framework of the classical theory – the description of matter, radiation, and their interaction – cannot be properly addressed from the classical theory. In this way quantum electrodynamics would not be a fundamental theory, (...) and principally, we could not consider classical electrodynamics as contained in the quantum theory and being recovered from it by some sort of limiting procedure. (shrink)

DRAFT of my book on Realistic Empiricism. The book revives the neutral monism of Mach, James, and Russell and applies the updated view to the problem of redefining physicalism, explaining the origins of sensation, and the problem of deriving extended physical objects and systems from an ontology of events.

Extension is probably the most general natural property. Is it a fundamental property? Leibniz claimed the answer was no, and that the structureless intuition of extension concealed more fundamental properties and relations. This paper follows Leibniz's program through Herbart and Riemann to Grassmann and uses Grassmann's algebra of points to build up levels of extensions algebraically. Finally, the connection between extension and measurement is considered.

An overview of the problem of constructing extension combinatorially from qualities cum dispositional powers. In the model recommended here, Grassmann's algebra provides the combinatorial structure while Machian elements give the content.

The paper is about the physical theories which result when one identifies points in phase space related by symmetries; with applications to problems concerning gauge freedom and the structure of spacetime in classical mechanics.

I will discuss only one of the several entwined strands of the philosophy of space and time, the question of the relation between the nature of motion and the geometrical structure of the world.1 This topic has many of the virtues of the best philosophy of science. It is of long-standing philosophical interest and has a rich history of connections to problems of physics. It has loomed large in discussions of space and time among contemporary philosophers of science. Furthermore, there (...) is, I think, widespread agreement that recent insights here have lead to a genuine deepening of our understanding. (shrink)

The physicist's conception of space-time underwent two major upheavals thanks to the general theory of relativity and quantum mechanics. Both theories play a fundamental role in describing the same natural world, although at different scales. However, the inconsistency between them emerged clearly as the limitation of twentieth-century physics, so a more complete description of nature must encompass general relativity and quantum mechanics as well. The problem is a theorists' problem par excellence. Experiment provide little guide, and the inconsistency mentioned above (...) is an important problem which clearly illustrates the intermingling of philosophical, mathematical, and physical thought. In fact, in order to unify general relativity with quantum field theory, it seems necessary to invent a new mathematical framework which will generalise Riemannian geometry and therefore our present conception of space and space-time. Contemporary developments in theoretical physics suggest that another revolution may be in progress, through which a new kind of geometry may enter physics, and space-time itself can be reinterpreted as an approximate, derived concept. The main purpose of this article is to show the great significance of space-time geometry in predetermining the laws which are supposed to govern the behaviour of matter, and further to support the thesis that matter itself can be built from geometry, in the sense that particles of matter as well as the other forces of nature emerges in the same way that gravity emerges from geometry. Scientific research is not a process of steady accumulation of absolute truths, which has culminated in present theories, but rather a much more dynamic kind of process in which there are no final theoretical concepts valid in unlimited domains. (David Bohm). (shrink)

This collection, with essays by Graham H. Bird, Jaakko Hintikka, Ilkka Niiniluoto, Jan Wolenski, will interest graduate students of the philosophy of language ...

This excellent, semi-technical account includes a review of classical physics (origin of space and time measurements, Ptolemaic and Copernican astronomy, laws of motion, inertia, and more) and coverage of Einstein’s special and general theories of relativity, discussing the concept of simultaneity, kinematics, Einstein’s mechanics and dynamics, and more.

This paper briefly review a current trend in neuroscience aiming to combine neurophysiological and physical concepts in order to understand the emergence of spatio-temporal patterns within brain activity by which brain constructs knowledge from multiple streams of information. The authors further suggest that the meanings, which subjectively are experienced as thoughts or perceptions can best be described objectively as created and carried by large fields of neural activity within the operational architectonics of brain functioning.

Seeking to derive the manifestly qualitative world of objects and entities without recourse to fundamental categoricity or qualitativity, I offer an account of how higher-order categorical properties and objects may emerge from a pure-power base. I explore the possibility of ‘fields’ whose fluctuations are force-carrying entities, differentiated with respect to a micro-topology of curled-up spatial dimensions. Since the spacetime paths of gauge bosons have zero ‘spacetime interval’ and no time-like extension, I argue that according them the status of fundamental entities (...) would support a pure-power ontology. Such entities, circulating within self-sustaining micro-topological ‘networks’, feasibly maintain definite spatial configurations of conserved physical quantities, including energy-momentum. Perceived as time-like and massy, and representing fermionic entities, they give rise to the manifest world. (shrink)

David Albert (2000) and Barry Loewer (2007) have argued that the temporal asymmetry of our concept of causal influence or control is grounded in the statistical mechanical assumption of a low-entropy past. In this paper I critically examine Albert's and Loewer's accounts.

The remarkable connections between gravity and thermodynamics seem to imply that gravity is not fundamental but emergent, and in particular, as Verlinde suggested, gravity is probably an entropic force. In this paper, we will argue that the idea of gravity as an entropic force is debatable. It is shown that there is no convincing analogy between gravity and entropic force in Verlinde’s example. Neither holographic screen nor test particle satisfies all requirements for the existence of entropic force in a thermodynamics (...) system. As a result, there is no entropic force in the gravity system. Furthermore, we show that the entropy increase of the screen is not caused by its statistical tendency to increase entropy as required by the existence of entropic force, but in fact caused by gravity. Therefore, Verlinde’s argument for the entropic origin of gravity is problematic. In addition, we argue that the existence of a minimum size of spacetime, together with the Heisenberg uncertainty principle in quantum theory, may imply the fundamental existence of gravity as a geometric property of spacetime. This provides a further support for the conclusion that gravity is not an entropic force. (shrink)

The early history of the attempts to unify quantum theory with the general theory of relativity is depicted through the work of the under--appreciated Italo-Brazilian physicist Gleb Wataghin, who is responsible for many of the ideas that the quantum gravity community is entertaining today.

Vacuum (leer, frei) bezeichnete bis zum 19. Jahrhundert allein den körperlosen Raum. Unter dem Einfluss physikalischer (Feld-) Theorien meint der Terminus inzwischen diejenige residuale physische Entiät, die einen vorgegebenen Raum ausfüllt bzw. im Prinzip ausfüllen würde, nachdem alles, was mit physikalischen Mitteln entfernt werden kann, aus dem Raum entfernt wurde. Theorien über das V. sind daher eng mit Theorien über die Struktur des Raumes, die Bewegung, die physikalischen Gegenstände und deren Wechselwirkungen verbunden. In der Quantentheorie bezeichnet V. den Zustand niedrigster (...) Energie (Grundzustand) eines Systems. (shrink)

A true Turing machine (TM) requires an infinitely long paper tape. Thus a TM can be housed in the infinite world of Newtonian spacetime (the spacetime of common sense), but not necessarily in our world, because our world-at least according to our best spacetime theory, general relativity-may be finite. All the same, one can argue for the "existence" of a TM on the basis that there is no such housing problem in some other relativistic worlds that are similar ("close") to (...) our world. But curiously enough-and this is the main point of this paper-some of these close worlds have a special spacetime structure that allows TMs to perform certain Turing unsolvable tasks. For example, in one kind of spacetime a TM can be used to solve first-order predicate logic and the halting problem. And in a more complicated spacetime, TMs can be used to decide arithmetic. These new computers serve to show that Church's thesis is a thoroughly contingent claim. Moreover, since these new computers share the fundamental properties of a TM in ordinary operation (e.g. intuitive, finitely programmed, limited in computational capability), a computability theory based on these non-Turing computers is no less worthy of investigation than orthodox computability theory. Some ideas about this new mathematical theory are given. (shrink)

We consider the question of the manner of the internalization of the geometry and topology of physical space in the mind, both the mechanism of internalization and precisely what structures are internalized. Though we will not argue for the point here, we agree with the long tradition which holds that an understanding of this issue is crucial for addressing many metaphysical and epistemological questions concerning space.

Owing to intensive development of the theory of self-organization of complex systems called also synergetics, profound changes in our notions of time occur. Whereas at the beginning of the 20th century, natural sciences, by picking up the general spirit of Einstein's theory of relativity, consider a geometrization as an ideal, i.e. try to represent time and force interactions through space and the changes of its properties, nowadays, at the beginning of the 21st century, time turns to be in the focus (...) of attention. It turns to be possible to represent space through time, because synergetics shows that historical and evolutionary stages of development of a complex structure can be found now, in its present spatial configuration. A whole series of paradoxical notions, such as “the influence of the future upon the present”, a “possibility of touching of a rather remote future today”, “availability of the past and the future now, in praesenti”, “irreversibility and elements of reversibility in the course of evolutionary processes in time”, “discrete unites, quanta of time”, appear in synergetics. (shrink)

Today a change is imperative in approaching global problems: what is needed is not arm-twisting and power politics, but searching for ways of co-evolution in the complex social and geopolitical systems of the world. The modern theory of self-organization of complex systems provides us with an understanding of the possible forms of coexistence of heterogeneous social and geopolitical structures at different stages of development regarding the different paths of their sustainable co-evolutionary development. The theory argues that the evolutionary channel to (...) the observed increasing complexity is extremely narrow and only certain discrete spectra of relatively stable self-maintained structures are feasible in complex systems. There exists a restricted set of ways of assembling a complex evolutionary whole from diverse parts. The law of nonlinear synthesis of complex structures reads: the integration of structures in more complex ones occurs due to the establishment of a common tempo of their evolution. On the basis of the theory, we can see not only desirable but also attainable futures. (shrink)

Thinking about time travel is an entertaining way to explore how to understand time and its location in the broad conceptual landscape that includes causation, fate, action, possibility, experience, and reality. It is uncontroversial that time travel towards the future exists, and time travel to the past is generally recognized as permitted by Einstein’s general theory of relativity, though no one knows yet whether nature truly allows it. Coherent time travel stories have added flair to traditional debates over the metaphysical (...) status of the past, the reality of temporal passage, and the existence of free will. Moreover, plausible models of time travel and time machines can be used to investigate the subtle relation between space-time structure and causality. -/- It surveys some philosophical issues concerning time travel and should serves as a quick introduction. It includes a new and improved way to define a time machine. (shrink)

Extending on an earlier paper [Found. Phys. Ltt., 16(4) 343–355, (2003)], it is argued that instants of time and the instantaneous (including instantaneous relative position) do not actually exist. This conclusion, one which is also argued to represent the correct solution to Zeno’s motion paradoxes, has several implications for modern physics and for our philosophical view of time, including that time and space cannot be quantized; that contrary to common interpretation, motion and change are compatible with the “block” universe and (...) relativity; and that time, space, and space-time too, cannot exist. Instead, motion and change become the major players. (shrink)

John Norton has recently argued that Newtonian gravitation theory (at least as applied to cosmological contexts where one envisions the possibility of a homogeneous mass distribution throughout all of space) is inconsistent. I am not convinced. Traditional formulations of the theory may seem to break down in cases of the sort Norton considers. But the difficulties they face are only apparent. They are artifacts of the formulations themselves, and disappear if one passes to the so-called "geometrized" formulation of the theory.

Quantum Mechanics, and apparently its successors, claim that there are minimum quantities by which objects can differ, at least in some situations: electrons can have various “energy levels” in an atom, but to move from one to another they must jump rather than move via continuous variation: and an electron in a hydrogen atom going from -13.6 eV of energy to -3.4 eV does not pass through states of -10eV or -5.1eV, let along -11.1111115637 eV or -4.89712384 eV.

Paradoxes have long been a driving force in philosophy. They compel us to think more clearly about what we otherwise take for granted. In Antiquity, Zeno insisted that a runner could never complete the course because he’d first need to go half way, and then half way again; and so on indefinitely. Zeno also argued that matter could not be infinitely divisible, else it would be made of parts of no size at all. Even infinitely many nothings combined still measure (...) nothing. These simple thoughts forced us to develop ever more careful and sophisticated accounts of space, time, motion, continuity and measure and modern versions of these paradoxes continue to vex us. (shrink)

Metaphysicians of space and time are fond of talking about objects being present at, wholly present at, or existing at certain times, or occupying certain regions of space, or even regions of space-time. Take, for example, this famous set of definitions due to Mark Johnston and David Lewis: Let us say that something persists, iff, 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. (Lewis 1986, p. 202) A great deal of debate has been conducted in this terminology: debates about whether anything does endure or perdure; about the ontology of temporal parts; about whether it makes sense to apply this kind of thinking to space, as well as to time (we can ask, for example, the analogous questions whether things are extended by being entended, or pertended); about whether it can be applied to space-time, and if so, to relativistic space-time. These debates have been fruitful, but cursed with a certain amount of imprecision. People sometimes talk past each.. (shrink)

The mapping of numbers onto space is fundamental to measurement and to mathematics. Is this mapping a cultural invention or a universal intuition shared by all humans regardless of culture and education? We probed number-space mappings in the Mundurucu, an Amazonian indigene group with a reduced numerical lexicon and little or no formal education. At all ages, the Mundurucu mapped symbolic and nonsymbolic numbers onto a logarithmic scale, whereas Western adults used linear mapping with small or symbolic numbers and logarithmic (...) mapping when numbers were presented nonsymbolically under conditions that discouraged counting. This indicates that the mapping of numbers onto space is a universal intuition and that this initial intuition of number is logarithmic. The concept of a linear number line appears to be a cultural invention that fails to develop in the absence of formal education. (shrink)

In recent years, the branching spacetime (BST) interpretation of quantum mechanics has come under study by a number of philosophers, physicists and mathematicians. This paper points out some implications of the BST interpretation for two areas of quantum physics: (1) quantum gravity, and (2) stochastic interpretations of quantum mechanics.

In this paper, I explore the feasibility of a realistic interpretation of the quantum mechanical path integral - that is, an interpretation according to which the particle actually follows the paths that contribute to the integral. I argue that an interpretation of this sort requires spacetime to have a branching structure similar to the structures of the branching spacetimes proposed by previous authors. I point out one possible way to construct branching spacetimes of the required sort, and I ask whether (...) the resulting interpretation of quantum mechanics is empirically testable. (shrink)

A material simple is a material object that has no proper parts. Some philosophers have argued for the possibility of extended simples. Some have even argued for the possibility of heterogeneous simples or simples that have intrinsic variations across their surfaces. There is a puzzle, though, that is meant to show that extended, heterogeneous simples are impossible. Although several plausible responses have been given to this puzzle, I wish to reopen the case against extended, heterogeneous simples. In this paper, I (...) briefly canvass responses to this puzzle which may be made in defense of extended, heterogeneous simples. I then present a new version of this puzzle which targets simples that occupy atomic yet extended regions of space. It seems that none of the traditional responses can be used to successfully save this particular kind of extended simple from the new puzzle. I also consider some non-traditional defenses of heterogeneous extended simples and argue that they too are unsuccessful. Finally, I will argue that a substantial case can be made against the possibility of extended heterogeneous simples of any kind. (shrink)

Poincaré's claim that Euclidean and non-Euclidean geometries are translatable has generally been thought to be based on his introduction of a model to prove the consistency of Lobachevskian geometry and to be equivalent to a claim that Euclidean and non-Euclidean geometries are logically isomorphic axiomatic systems. In contrast to the standard view, I argue that Poincaré's translation thesis has a mathematical, rather than a meta-mathematical basis. The mathematical basis of Poincaré's translation thesis is that the underlying manifolds of Euclidean and (...) Lobachevskian geometries are homeomorphic. Assuming as Poincaré does that metric relations are not factual, it follows that we can rewrite a physical theory using Euclidean geometry as one using Lobachevskian geometry and express the same facts. (shrink)

Questo volumetto conclude il confronto fra la speculazione bruniana e la tradizione del pensiero aristotelico. Ora Giordano Bruno considera le obiezioni della tradizione aristotelica all'esistenza di un corpo universale infinito in movimento interno (creativo e dialettico) infinito. Demolendo e disgregando le premesse dell'impostazione aristotelica la riflessione di Giordano Bruno ridetermina e riqualifica le tradizionali nozioni di spirito e di materia, innovandole in radice e sospingendole verso una rivoluzionarietà, capace di mantenere sempre uniti l'aspetto teoretico e il momento pratico della riflessione (...) e del pensiero. (shrink)

Amidst many discussions on super-valuational algebras and their philosophical applications — on which I was writing my dissertation — Hans and I once paused to ponder the mystical experience of the square. I mean A Square, the hero of Flatland. I mean that perfectly two-dimensional being, with no depth whatsoever, citizen of an equally two-dimensional depthless world, who one day had the good fortune of receiving a visit from a Sphere. What's more, he had the fortune of being able to (...) visit, albeit briefly, the undreamt-of three-dimensional world his guest came from — which is to say, our three-dimensional world. He visited and experienced our world before falling back for all eternity into the total flatness of .. (shrink)