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The Principle of Relativity

01 Jan 1920-
About: The article was published on 1920-01-01 and is currently open access. It has received 944 citations till now. The article focuses on the topics: Four-force & Special relativity (alternative formulations).
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TL;DR: In economics, this critique has been persistently attacked as an acceptable explanation of behavior as discussed by the authors, which has been taken various forms which include information processing limitations in computing optima from known preference or utility information, unreliable probability information about complex environmental contingencies, and the absence of a well-defined set of alternatives or consequences.
Abstract: Despite vigorous counterargument by its proponents, optimization theory has been persistently attacked as an acceptable explanation of behavior. In one form or another, these attacks repeat the oldest critique of economics; namely, the ability of agents to maximize successfully. Over the years, this critique has taken various forms which include information processing limitations in computing optima from known preference or utility information, unreliable probability information about complex environmental contingencies, and the absence of a well-defined set of alternatives or consequences, especially in an evolving world that may produce situations that never before existed. These complaints are not new to economics. Indeed, they have been present during the very intellectual sifting process that produced neoclassical optimization and general equilibrium theory. Thus, if we are to further elaborate this critique of conventional theory, the basic issue is whether there is anything new that is worthy of attention by someone well versed in standard tools and concepts. Are we simply advancing more refined or cleverly argued versions of older critiques, or extensions of them to areas not previously emphasized? Such arguments would still represent an attack on the basic rationality postulate of economics (that agents are able to maximize), but without providing a clear alternative to traditional optimization theory. However plausible these arguments might be, ultimately they must be set aside by someone desiring a theoretical understanding of behavior, unless they lead to another modeling structure whose analytical ability can be explored and compared with existing optimization theory. Another argument focuses on the desire to understand the "real" dynamic processes that actually generate observed behavior. In contrast, optimization is thought of as a surrogate theory based on false assumptions about agents' capacity to maximize. Thus, it can be defended only in terms of empirical testability, without really illuminating the underlying processes determining behavior. Nevertheless, even if this view was fully accepted, it is unlikely by itself to cause a major shift away from conventional thinking. The reason is that evolutionary processes have long ago been interpreted as one of the key mechanisms tending to produce optimizing behavior; or conversely, optimizing models will predict the behavior patterns that will survive in an evolutionary process tending to select relatively superior performance.' The latter interpretation is in fact one of the dominant justifications for standard models against the criticism of unrealistic assumptions (i.e., the surviving agents of a selection process will behave "as if" they are able to maximize).2 *Department of Economics, Brigham Young University, Provo, UT 84602. I am indebted to Axel Leijonhufvud for constant encouragement about applications to economics, and for numerous stylistic suggestions. Harold Miller helped familiarize me with a broad range of issues across the sociobiological, psychological, and behavioral science literatures. James Buchanan provided stimulating discussion about conceptual issues. I have also benefited from the advice and criticism of Armen Alchian, Ron Batchelder, Bruce Brown, Robert Clower, Daniel Friedman, Jack Hirshleifer, Kai Jeanski, Randy Johnson, Edward Leamer, Stephen Littlechild, John McCall, James McDonald, Richard Nelson, Gerald O'Driscoll, Dennis Packard, Clayne Pope, Lionello Punzo, Ezio Tarantelli, and Sidney Winter. Needless to say, these colleagues are not responsible for inadequacy in the conceptual framework or scope of ideas presented. 'See in particular Armen Alchian's well-known 1950 paper, and also Sidney Winter, 1964, 1971; Jack Hirshleifer, 1977; Richard Nelson and Winter, 1974. 2A still used reference on the "as if" point of view is Milton Friedman's 1953 paper. Some recent journal illustrations are Benjamin Klein and Keith Leffler, 1981, p. 634; Richard Posner, 1980, p. 5; Hirshleifer, 1977, p. 50; Nelson, 1981, p. 1059. The ultimate extension of this view is to claim not that agents are able to maximize (select most preferred actions), but rather that any ob-

1,193 citations

Journal ArticleDOI
TL;DR: In this article, a scalar field with a drainhole in its center is modeled as a massless, chargeless, spinless particle, whose nonrigid motions manifest themselves as gravitational phenomena.
Abstract: The Schwarzchild manifold of general relativitytheory is unsatisfactory as a particle model because the singularity at the origin makes it geodesically incomplete. A coupling of the geometry of space‐time to a scalar field φ produces in its stead a static, spherically symmetric, geodesically complete, horizonless space‐time manifold with a topological hole, termed a drainhole, in its center. The coupling is Rμν=2φ,μφ,ν; its polarity is reversed from the usual to allow both the negative curvatures found in the drainhole and the completeness of the geodesics. The scalar field satisfies the scalar wave equation □φ=0 and has finite total energy whose magnitude, expressed as a length, is comparable to the drainhole radius. On one side of the drainhole the manifold is asymptotic to a Schwarzschild manifold with positive mass parameter m, on the other to a Schwarzschild manifold with negative mass parameter m, and − m > m. The two‐sided particle thus modeled attracts matter on the one side and, with greater strength, repels it on the other. If m is one proton mass, then − m/m ≈ 1+10−19 or 1+10−39, according as the drainhole radius is close to 10−33cm or close to 10−13 cm; the ratios of total scalar fieldenergy to m in these instances are 1019 and 1039. A radially directed vector field which presents itself is interpreted, for purposes of conceptualization, as the velocity of a flowing ``substantial ether'' whose nonrigid motions manifest themselves as gravitational phenomena. When the ether is at rest, the two‐sided particle has no mass on either side, but the drainhole remains open and is able to trap test particles for any finite length of time, then release them without ever accelerating them; some it can trap for all time without accelerating them. This massless, chargeless, spinless particle can, if disturbed, dematerialize into a scalar‐field wave propagating at the wave speed characteristic of the space‐time manifold.

691 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that the k-fold suspension of a weak n-category stabilizes for k≥n+2, and its relation to stable homotopy theory was discussed.
Abstract: The study of topological quantum field theories increasingly relies upon concepts from higher‐dimensional algebra such as n‐categories and n‐vector spaces. We review progress towards a definition of n‐category suited for this purpose, and outline a program in which n‐dimensional topological quantum field theories (TQFTs) are to be described as n‐category representations. First we describe a ‘‘suspension’’ operation on n‐categories, and hypothesize that the k‐fold suspension of a weak n‐category stabilizes for k≥n+2. We give evidence for this hypothesis and describe its relation to stable homotopy theory. We then propose a description of n‐dimensional unitary extended TQFTs as weak n‐functors from the ‘‘free stable weak n‐category with duals on one object’’ to the n‐category of ‘‘n‐Hilbert spaces.’’ We conclude by describing n‐categorical generalizations of deformation quantization and the quantum double construction.

553 citations

Journal ArticleDOI
TL;DR: In this article, an inventory of the cosmic mean densities of energy associated with all known states of matter and radiation at the present epoch is presented, and a global portrait of the effects of the physical processes of cosmic evolution is presented.
Abstract: We present an inventory of the cosmic mean densities of energy associated with all the known states of matter and radiation at the present epoch. The observational and theoretical bases for the inventory have become rich enough to allow estimates with observational support for the densities of energy in some 40 forms. The result is a global portrait of the effects of the physical processes of cosmic evolution.

543 citations

Journal ArticleDOI
TL;DR: The concept of space-time representation in the brain is redefined using tensor network theory and the cerebellum acts as a predictive motor space- time metric which allows the establishment of coincidences of goal-directed movements of limbs inspace-time with external targets.

327 citations