Psychological momentum (PM) is thought to be a force that influences judgment, emotion, and performance. Based on a review of the extant literature, we elucidate two distinct approaches that researchers have adopted in their study of PM: the input-centered approach and the output-centered approach. Consistent with the input-centered approach, we conceptualize PM as a process whereby temporal and contextual PM-like stimuli (i.e., perceptual velocity, perceptual mass, perceptual historicity, and perceptually interconnected timescales)—initially perceived as an impetus—are extrapolated to imagined future (...) outcomes through mental simulation. In turn, and consistent with the output-centered approach, we posit that mental simulation elicits experiential (e.g., perceptual, cognitive, emotional) and behavioral states that govern goal pursuit, and that the pursuit of goals further influences perceptions of self, environment, and action quality. In all, we suggest that PM is interdependently linked to perceptions and behaviors in the sense that PM both influences and is influenced by changes in self-perceptions, environmental perceptions, and behavior, and we conclude by linking the PM construct to recent work on prospection. (shrink)

In the metaphor of behavioral momentum, the rate of a free operant in the presence of a discriminative stimulus is analogous to the velocity of a moving body, and resistance to change measures an aspect of behavior that is analogous to its inertial mass. An extension of the metaphor suggests that preference measures an analog to the gravitational mass of that body. The independent functions relating resistance to change and preference to the conditions of reinforcement may be construed as (...) convergent measures of a single construct, analogous to physical mass, that represents the effects of a history of exposure to the signaled conditions of reinforcement and that unifies the traditionally separate notions of the strength of learning and the value of incentives. Research guided by the momentum metaphor encompasses the effects of reinforcement on response rate, resistance to change, and preference and has implications for clinical interventions, drug addiction, and self-control. In addition, its principles can be seen as a modern, quantitative version of Thorndike's (1911) Law of Effect, providing a new perspective on some of the challenges to his postulation of strengthening by reinforcement. Key Words: behavioral momentum; clinical interventions; drug addiction; preference; reinforcement; resistance to change; response strength; self-control. (shrink)

Nevin & Grace's behavioral-momentum model accommodates a large body of data. This commentary highlights some experimental findings that the model does not always predict. The model does not consistently predict resistance to change when response-independent food is delivered simultaneously with response-contingent food, when drugs are used as response disrupters, and when responding is reinforced under single rather than multiple schedules of reinforcement.

The method of projection is applied to a relativistic field theory of fermions interacting with a nonlinear scalar field, specifically the Friedberg-Lee soliton model. Projection is effected by operating on a localized “bag” state with the translation operator exp (iP·Z), and integrating overZ. The resulting state is an eigenstate of zero momentum. The energy and the expectation value of other physical operators can be expressed as Gaussian moments of the Hamiltonian or the physical operator times powers of the (...) class='Hi'>momentum operator taken with respect to the bag state. Renormalization in the one-loop approximation is discussed in detail for the boson sector, and briefly for the fermion sector. The method can be tested for convergence against nonexpansion techniques. The latter, however, cannot so easily handle distortion of the Bose modes or the distortion of the Dirac sea. (shrink)

The notions of ``motion'' and ``conserved quantities'', if applied to extended objects, are already quite non-trivial in Special Relativity. This contribution is meant to remind us on all the relevant mathematical structures and constructions that underlie these concepts, which we will review in some detail. Next to the prerequisites from Special Relativity, like Minkowski space and its automorphism group, this will include the notion of a body in Minkowski space, the momentum map, a characterisation of the habitat of globally (...) conserved quantities associated with Poincare symmetry -- so called Poincare charges --, the frame-dependent decomposition of global angular momentum into Spin and an orbital part, and, last not least, the likewise frame-dependent notion of centre of mass together with a geometric description of the Moeller Radius, of which we also list some typical values. (shrink)

Behavioral momentum theory has evolved within the realm of operant conditioning. The thought-provoking momentum metaphor equates the strength of an operant response with its resistance to change and preference (i.e., choice) for that response over other available responses. Whereas baseline response rate (velocity in the metaphor) is assumed to be largely influenced by the response-reinforcer contingency, resistance to change and preference are assumed to reflect an intervening variable called behavioral mass, which is determined primarily by the stimulus-reinforcer relationship. (...) This invites the question of how well the momentum metaphor applies to the stimulus-reinforcer relationships of traditional Pavlovian paradigms. Presumably, a correspondence exists between behavioral mass and the notion of associative strength in the associative learning literature. Although response rate has little meaning in the trialwise structure of classical (i.e., Pavlovian) conditioning, response probability or magnitude might be regarded metaphorically as velocity. Momentum theory suggests that resistance to change (e.g., extinction) is a better indicator of associative strength than is response probability or magnitude. Therefore, variables that strengthen Pavlovian learning should influence resistance to extinction of conditioned responding in a similar manner. Moreover, it is important to assess momentum theory outside of strictly operant paradigms, particularly because in clinical settings many common disorders (e.g., phobias) and their therapies (e.g., cue exposure) are thought to be classically conditioned. (shrink)

The present thesis considers, in the light of Heisenberg's interpretation of the uncertainty formulas, the conditions necessary for the derivation of the quantitative statement or law of momentum conservation. The result of such considerations is a contradiction between the formalism of quantum physics and the asserted consequences of Heisenberg's interpretation. This contradiction decides against Heisenberg's interpretation of the uncertainty formulas on upholding that the formalism of quantum physics is both consistent and complete, at least insofar as the statement of (...) momentum conservation can be proved within this formalism. A few comments are also included on Bohr's “complementarity interpretation” of the formalism of quantum physics. A suggestion, based on a statistical mode of empirical testing of the “uncertainty” formulas, does not give rise to any such contradiction. (shrink)

Nevin & Grace invoke a behavioral metaphor from the physics of momentum. The idealized assumptions they invoke are argued to translate to behavior only in the limited case of steady-state, constant-probability VI responding. Rather than further refine this limit case, mathematical models should be applied to generalizations of the limit case itself, broadening our understanding of behavioral processes.

The nucleon spin problem raises experimental and theoretical questions regarding the contribution of the orbital angular momentum of the quarks to the total spin of the nucleon. In this article we examine the commutation relationships of various operators that contribute to the total angular momentum of the nucleon. We find that the sum of the orbital plus gluon field angular momenta should satisfy the angular momentum commutators, at least up to the one-loop level. This, requirement on the (...) sum of these operators imposes a non-trivial restriction on the form of the color electric and magnetic fields. This is similar to the magnetic monopole/electric charge system where it is only the sum of the orbital plus field angular momentum that satisfies the correct commutation relationships. (shrink)

The constructs of behavioral mass in research on the momentum of operant behavior and associative strength in Pavlovian conditioning have some interesting parallels, as suggested by Savastano & Miller. Some recent findings challenge the strict separation of operant and Pavlovian determiners of response rate and resistance to change in behavioral momentum, renewing the need for research on the interaction of processes that have traditionally been studied separately. Relatedly, Furedy notes that some autonomic responses may be refractory to conditioning, (...) but a combination of operant contingencies and enriched Pavlovian stimulus-reinforcer relations may prove effective. (shrink)

The present research examines psychological momentum (PM), a perceived force that lay intuition suggests influences performance. PM theory is proposed to account for how momentum perceptions arise, and four studies demonstrate the influence of lay intuitions about PM on expectations regarding performance outcomes. Study 1 establishes that individuals share intuitions about the types of events that precipitate PM, and Study 2 finds that defeating a rival increases momentum perception. Study 3 provides evidence for the lay belief that (...) as more PM accumulates during a prior task, there should be more residual momentum left to carry over to a subsequent task, and Study 4 finds that an individual whose PM is interrupted is expected to have greater difficulty completing a task than is an individual whose steady progress is interrupted. Discussion focuses on linkages between PM and related constructs. (shrink)

The Desarguesian nature of angular-momentum theory is illustrated by drawing correspondences between relations satisfied by then-j symbols and various collinearity properties of the appropriate diagrams. No examples of Pappus' theorem have been found. A relation is suggested between the operations of angular-momentum theory and Hilbert's constructions for the addition and multiplication of points on a line.

We have analyzed many discrimination learning difficulties as reflecting multiple stimulus control topographies (SCTs). Nevin & Grace's analysis offers new variables to consider in the design of stimulus-control shaping procedures and cross-setting generalization of newly established behavior. A multiple-SCT perspective also suggests that fixed-trial discrimination procedures may offer advantages for reconciling momentum theory and partial reinforcement extinction effects.

One goal of environmental ethics is to recommend changes to patterns of human life so as to bring inhabited landscapes into line with a vision of the good. However, the complex intertwining of nature and culture in inhabited landscapes makes this project much more difficult, complicating ethical judgment and limiting the efficacy of ethical action. Technological momentum, a model introduced by historian Thomas P. Hughes to describe the development of complex technological systems, can shed some light on these difficulties. (...) The process of metropolitan growth in the United States will serve to illustrate the consequences of technological momentum for environmental ethics and policy. (shrink)

I describe how relativistic field theory generalizes the paradigm property of material systems, the possession of mass, to the requirement that they have a mass–energy–momentum density tensor T µ associated with them. I argue that T µ does not represent an intrinsic property of matter. For it will become evident that the definition of T µ depends on the metric field g µ in a variety of ways. Accordingly, since g µ represents the geometry of spacetime itself, the properties (...) of mass, stress, energy, and momentum should not be seen as intrinsic properties of matter, but as relational properties that material systems have only in virtue of their relation to spacetime structure. (shrink)

In reply to the comments on our target article, we address a variety of issues concerning the generality of our major findings, their relation to other theoretical formulations, and the metaphor of behavioral momentum that inspired much of our work. Most of these issues can be resolved by empirical studies, and we hope that the ideas advanced here will promote the analysis of resistance to change and preference in new areas of research and application.

Metaphors “highlight and hide” different aspects of phenomena. A behavioral economic metaphor for excessive consumption highlights the contextual features of behavioral-environment relations. Can the behavioral momentum metaphor generate a representation of context that is at least as useful as that generated by behavioral economics? Maybe, maybe not; or maybe a mixed metaphor will do a better job than either alone.

The mental representation of brief temporal durations, when assessed in standard laboratory conditions, is highly accurate. Here we show that adding or subtracting temporal durations systematically results in strong and opposite biases, namely over-estimation for addition and under-estimation for subtraction. The difference with respect to a baseline temporal reproduction task changed across durations in an operation-specific way and survived correcting for the effect due to operation sign alone, indexing a reliable signature of arithmetic processing on time representation. A second experiment (...) replicated these findings with a different set of stimuli. This novel behavioral marker conceptually mirrors in the time domain the representational momentum found with motion, whereby the estimated spatial position of a visual target is displaced in the direction of motion itself. This momentum effect in temporal arithmetic suggests a striking analogy between time processing and visuospatial processing, which might index the presence of common computational principles. (shrink)

We show that in the presence of the torsion tensor \, the quantum commutation relation for the four-momentum, traced over spinor indices, is given by \. In the Einstein–Cartan theory of gravity, in which torsion is coupled to spin of fermions, this relation in a coordinate frame reduces to a commutation relation of noncommutative momentum space, \, where U is a constant on the order of the squared inverse of the Planck mass. We propose that this relation replaces (...) the integration in the momentum space in Feynman diagrams with the summation over the discrete momentum eigenvalues. We derive a prescription for this summation that agrees with convergent integrals: \^s}\rightarrow 4\pi U^{s-2}\sum _{l=1}^\infty \int _0^{\pi /2} d\phi \frac{\sin ^4\phi \,n^{s-3}}{[\sin \phi +U\varDelta n]^s}\), where \}\) and \ does not depend on p. We show that this prescription regularizes ultraviolet-divergent integrals in loop diagrams. We extend this prescription to tensor integrals. We derive a finite, gauge-invariant vacuum polarization tensor and a finite running coupling. Including loops from all charged fermions, we find a finite value for the bare electric charge of an electron: \. This torsional regularization may therefore provide a realistic, physical mechanism for eliminating infinities in quantum field theory and making renormalization finite. (shrink)

Behavioral momentum is a useful metaphor reminding us that with constant conditions, ongoing behavior – in the form of response rate – would be expected to remain constant. But despite an impressive array of behavioral experiments, the concept has not yet been applied in a way that would make it useful as a general behavioral law.

We discuss the question of linear momentum conservation when an atom coupled to a laser field enters into a state which is not an eigenstate of the linear momentum. Such a situation happens in the recently demonstrated laser cooling of atoms by velocity selective coherent population trapping. We show that this process can be understood as a filtering of the atomic state by the laser field taken as a classical measuring apparatus. In a different approach, the laser field (...) can be taken as a quantized system; then the filtering process leads to an “entangled state” of the atom and the field. (shrink)

We examine the possible role played by field angular momentum in two systems of vastly different sizes: (i) the nucleon and (ii) highly magnetic white dwarf stars. For the nucleon we study the restrictions on the nucleon's structure that arise from the requirement that the total field angular (spin, orbital and field angular momentum) should satisfy the standard angular momentum commutation relationship. For the magnetic white dwarfs we argue that the magnetic field may alter the statistics of (...) some fraction of the white dwarf's electrons from fermionic to bosonic. This would effect the stars structure, giving it a smaller than expected radius, and a lower than expected temperature. In some extreme cases one could imagine that this effect could lead to the collapse of the white dwarf into a neutron star despite being below the Chandreshekar limit. (shrink)

two dimensions, quantum radiation production is incompatible with a conserved and traceless T„,. We therefore resolve an ambiguity in our expression for Tr„, regularized by a geodesic point-separation procedure.

We show that the spread of momentum can be broken up into two terms, one that depends only on the change in amplitude and the other which depends only on the deviations of current from the average momentum. We present a method for measuring the relative contributions of each and interpret each contribution in terms of local quantities. A generalization for arbitrary operators is given. For the case of the Hamiltonian, the local value of energy is shown to (...) yield the quantum potential as defined by Bohm. (shrink)

The goal of therapy is often to increase the momentum (persistence) of self-control behaviors. Determining how best to accomplish this goal necessitates conducting behavioral momentum research under a wider variety of conditions.

The rigorous equivalence of the Schrödinger and Heisenberg pictures requires that one uses Born–Jordan quantization in place of Weyl quantization. We confirm this by showing that the much discussed “ angular momentum dilemma” disappears if one uses Born–Jordan quantization. We argue that the latter is the only physically correct quantization procedure. We also briefly discuss a possible redefinition of phase space quantum mechanics, where the usual Wigner distribution has to be replaced with a new quasi-distribution associated with Born–Jordan quantization, (...) and which has proven to be successful in time-frequency analysis. (shrink)

Pérez Laraudogoitia (1996) presented an isolated system of infinitely many particles with infinite total mass whose total classical energy and momentum are not necessarily conserved in some particular inertial frame of reference. With a more generalized model Atkinson (2007) proved that a system of infinitely many balls with finite total mass may evolve so that its total classical energy and total relativistic energy and momentum are not conserved in any inertial frame of reference, and yet concluded that its (...) total classical momentum is necessarily conserved. Contrary to this conclusion of Atkinson, I show that Atkinson's model has a solution in which the total momentum fails to be conserved in every inertial frame of reference. This result, combined with Atkinson's, demonstrates that both classical and relativistic mechanics allow the energy and momentum of a system of infinitely many components to fail to be conserved in every inertial frame of reference. (shrink)

From the known coordinate representation of these operators, a unified treatment of the abstract operators for curvilinear coordinates and their canonically conjugate momenta is given for systems in three dimensions. A configuration representation, corresponding to classical configuration space, exists in which description is simplified; the three-dimensional ket space factors into a direct product of one-dimensional spaces. Four cases are examined, according to the range of the continuous curvilinear coordinate. In addition to normalization of momentum eigenstates to the Kronecker delta (...) for finite range of coordinate and normalization to the Dirac delta for range on the entire real axis, normalization occurs to δ (or δ+) for range on the positive (or negative) part of the real axis. The domain of Hermiticity of curvilinear coordinate and conjugate momentum operators in each case is the entire three-dimension ket space. The fundamental commutation relations hold in all representations. Statements to the contrary for the radial and azimuth coordinates in spherical polar coordinates are seen to be erroneous. (shrink)

By means of a Clebsch representation which differs from that previously applied to electromagnetic field theory it is shown that Maxwell's equations are derivable from a variational principle. In contrast to the standard approach, the Hamiltonian complex associated with this principle is identical with the generally accepted energy-momentum tensor of the fields. In addition, the Clebsch representation of a contravariant vector field makes it possible to consistently construct a field theory based upon a direction-dependent Lagrangian density (it is this (...) kind of Lagrangian density that may arise when developing the Finslerian extension of general relativity). The corresponding field equations are proved to be independent of any gauge of Clebsch potentials. The law of energy-momentum conservation of the field appears to be covariant and integrable in a rather wide class of direction-dependent Lagrangian densities. (shrink)

A sentence's meaning may depend on the state of motion of the speaker. I argue that this context-sensitivity blocks the inference from special relativity to four-dimensionalism.

It has been known for many years that the matrix representation of the one-dimensional position-momentum commutator calculated with the position and momentum matrices in a finite basis is not proportional to the diagonal matrix, contrary to what one expects from the continuous-space commutator. This discrepancy has correctly been ascribed to the incompleteness of any finite basis, but without the details of exactly why this happens. Understanding why the discrepancy occurs requires calculating the position, momentum, and commutator matrix (...) elements in the continuous position basis, in which all are generalized functions. The reason for the discrepancy is revealed by replacing the generalized functions with sequences approaching them as their parameter approaches zero. Besides explaining the discrepancy in the discrete and continuous models, this investigation finds an unusual double-peaked sequence for the Dirac delta function. (shrink)

We compute the energy tensor and the energy-momentum tensor for electrodynamics coupled to the current of a charged scalar field and for electrodynamics coupled tothe current of a Dirac spinor field, without using the equations of motion.

The paper begins with a proposal for a reconstruction of three major statements of the traditional Marxian version of historical materialism. The general concept of an adaptive mechanism is introduced to explain how, in the Marxian sense, several parts of the superstructure are to be thought of as determined by the economic base. The paper proceeds by asking whether the classical type of economic determination is valid not only for precapitalist and capitalist societies, but for socialist societies as well. An (...) answer in the negative is given. The author tries to outline a type of historical materialism which takes into account the autonomous role of political institutions and social relations as determinants in socialist societies. (shrink)

Stemming from our energy localization hypothesis that energy in general relativity is localized in the regions of the energy-momentum tensor, we had devised a test with the classic Eddington spinning rod. Consistent with the localization hypothesis, we found that the Tolman energy integral did not change in the course of the motion. This implied that gravitational waves do not carry energy in vacuum, bringing into question the demand for the quantization of gravity. Also if information is conveyed by the (...) waves, the traditional view that information transfer demands energy is challenged. Later, we showed that the “body” angular momentum changed at a rate indicating that the moment of inertia increased to higher order, contrary to traditional expectations. We consider the challenges facing the development of a localized expression for the total angular momentum of the body including the contribution from gravity. We find that Komar's expression does not lead to an adequate formulation of localized angular momentum. (shrink)

A theoretical and experimental search for the so-called Weyssenhof behavior of a spinning particle, due to the noncollinearity of its velocity and momentum, has been undertaken. Z-independent solutions of Maxwell's equations had previously been produced with a nonzeros z component of the Poynting vector; indeed, Imbert emphasized that the spatial exponential damping of Fresnel's evanescent wave would entail a nonzero value for the integral ε εs z dx dy. Excellent experimental verifications of this point have been obtained by Imbert. (...) Besides having noz component of their momentum, the energy-momentum quanta inside Fresnel's evanescent wave have typical tachyon properties, the imaginary character of theiry component (normal to the reflecting surface) entailing that (in units such thatc=1) theirx component islarger than the energy quanta. Imbert is now planning experiments to test these interesting properties. Thus, the two main aspects of noncollinearity of velocity and momentum of spinning particles would be displayed. (shrink)

A common reducible representation space of the Lie algebras su and su is equipped with two different types of scalar products. The representation bases are labeled by the azimuthal and magnetic quantum numbers. The generators of su are the x-, y- and z-components of the orbital angular momentum operator. The representation of each of these Lie algebras is unitary with respect to only one of the scalar products. To each positive magnetic quantum number a family of the su-Barut–Girardello coherent (...) states is associated. The normalization and resolution of the identity condition for the coherent states are realized in two different approaches, i.e. the unitary and the non-unitary approaches. For the coherent states of the non-unitary case we calculate the uncertainty relation for the Hermitian x- and y-components of the angular momentum operator. While the unitary case leads to the known uncertainty relation for the Hermitian x- and y-components of su Lie algebra. (shrink)

The aim of this paper is to contribute to the clarification of concepts usually found in books on quantum mechanics, aided by knowledge from the field of the theory of operators in Hilbert space. Frequently the basic distinction between bounded and unbounded operators is not established in books on quantum mechanics. It is repeatedly overlooked that the condition for an unbounded operator to be symmetric (Hermitian) is not sufficient to make it self-adjoint. To make things worse, nearly all operators in (...) quantum mechanics are unbounded. Often one finds statements such as: For any linear operator A we can write a Hermitian operator HA=(A+A+)/2, where Hermitian is thought to mean self-adjoint. Along these lines, self-adjointness of the momentum operator in generalized coordinates, taken from that expression, is questioned. In particular, the redescription in terms of spherical polar coordinates and its implications for the eventual loss of self-adjointness of the momenta conjugate to them are studied. (shrink)

There exist different kinds of averaging of the differences of the energy–momentum and angular momentum in normal coordinates NC(P) which give tensorial quantities. The obtained averaged quantities are equivalent mathematically because they differ only by constant scalar dimensional factors. One of these averaging was used in our papers [J. Garecki, Rep. Math. Phys. 33, 57 (1993); Int. J. Theor. Phys. 35, 2195 (1996); Rep. Math. Phys. 40, 485 (1997); J. Math. Phys. 40, 4035 (1999); Rep. Math. Phys. 43, (...) 397 (1999); Rep. Math. Phys. 44, 95 (1999); Ann. Phys. (Leipzig) 11, 441 (2002); M.P. Dabrowski and J. Garecki, Class. Quantum. Grar. 19, 1 (2002)] giving the canonical superenergy and angular supermomentum tensors. In this paper we present another averaging of the differences of the energy–momentum and angular momentum which gives tensorial quantities with proper dimensions of the energy–momentum and angular momentum densities. We have called these tensorial quantities “the averaged relative energy–momentum and angular momentum tensors”. These tensors are very closely related to the canonical superenergy and angular supermomentum tensors and they depend on some fundamental length L > 0. The averaged relative energy–momentum and angular momentum tensors of the gravitational field obtained in the paper can be applied, like the canonical superenergy and angular supermomentum tensors, to coordinate independent analysis (local and in special cases also global) of this field. Up to now we have applied the averaged relative energy–momentum tensors to analyze vacuum gravitational energy and momentum and to analyze energy and momentum of the Friedman (and also more general, only homogeneous) universes. The obtained results are interesting, e.g., the averaged relative energy density is positive definite for the all Friedman and other universes which have been considered in this paper. (shrink)