We investigate the meaning of the wavefunction by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wavefunction. In a realistic interpretation, the wavefunction of a quantum system can be taken as a description of either a physical field or the ergodic motion (...) of a particle. The essential difference between a field and the ergodic motion of a particle lies in the property of simultaneity; a field exists throughout space simultaneously, whereas the ergodic motion of a particle exists throughout space in a time-divided way. If the wavefunction is a physical field, then the mass and charge density will be distributed in space simultaneously for a charged quantum system, and thus there will exist gravitational and electrostatic self-interactions of its wavefunction. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus the wavefunction cannot be a description of a physical field but a description of the ergodic motion of a particle. For the later there is only a localized particle with mass and charge at every instant, and thus there will not exist any self-interaction for the wavefunction. Which kind of ergodic motion of particles then? It is argued that the classical ergodic models, which assume continuous motion of particles, cannot be consistent with quantum mechanics. Based on the negative result, we suggest that the wavefunction is a description of the quantum motion of particles, which is random and discontinuous in nature. On this interpretation, the square of the absolute value of the wavefunction not only gives the probability of the particle being found in certain locations, but also gives the probability of the particle being there. We show that this new interpretation of the wavefunction provides a natural realistic alternative to the orthodox interpretation, and its implications for other realistic interpretations of quantum mechanics are also briefly discussed. (shrink)
The meaning of the wavefunction and its evolution are investigated. First, we argue that the wavefunction in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wavefunction gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wavefunction of an isolated system obeys the free Schrödinger equation due (...) to the requirements of spacetime translation invariance and relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wavefunction. A discrete model of energy-conserved wavefunction collapse is proposed and shown consistent with existing experiments and our macroscopic experience. Besides, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and other dynamical collapse theories, and briefly discuss the issues of unifying quantum mechanics and relativity. (shrink)
We show that the physical meaning of the wavefunction can be derived based on the established parts of quantum mechanics. It turns out that the wavefunction represents the state of random discontinuous motion of particles, and its modulus square determines the probability density of the particles appearing in certain positions in space.
This article analyzes the implications of protective measurement for the meaning of the wavefunction. According to protective measurement, a charged quantum system has mass and charge density proportional to the modulus square of its wavefunction. It is shown that the mass and charge density is not real but effective, formed by the ergodic motion of a localized particle with the total mass and charge of the system. Moreover, it is argued that the ergodic motion (...) is not continuous but discontinuous and random. This result suggests a new interpretation of the wavefunction, according to which the wavefunction is a description of random discontinuous motion of particles, and the modulus square of the wavefunction gives the probability density of the particles being in certain locations. It is shown that the suggested interpretation of the wavefunction disfavors the de Broglie-Bohm theory and the many-worlds interpretation but favors the dynamical collapse theories, and the random discontinuous motion of particles may provide an appropriate random source to collapse the wavefunction. (shrink)
It is shown that Uffink's attempt to protect the interpretation of the wavefunction against protective measurements fails due to several errors in his arguments.
I argue that the wavefunction ontology for quantum mechanics is an undesirable ontology. This ontology holds that the fundamental space in which entities evolve is not three-dimensional, but instead 3N-dimensional, where N is the number of particles standardly thought to exist in three-dimensional space. I show that the state of three-dimensional objects does not supervene on the state of objects in 3N-dimensional space. I also show that the only way to guarantee the existence of the appropriate mental (...) states in the wavefunction ontology has undesirable metaphysical baggage: either mind/body dualism is true, or circumstances which we take to be logically possible turn out to be logically impossible.While our theory can be extended formally in a logically consistent way by introducing the concept of a wave in a 3N-dimensional space, it is evident that this procedure is not really acceptable in a physical theory... (Bohm 1957, 117). (shrink)
Two different concepts of distinguishability are often mixed up in attempts to derive in quantum mechanics the (anti)symmetry of the wavefunction from indistinguishability of identical particles. Some of these attempts are analyzed and shown to be defective. It is argued that, although identical particles should be considered as observationally indistinguishable in (anti)symmetric states, they may be considered to be conceptually distinguishable. These two notions of (in)distinguishability have quite different physical origins, the former one being related to observations (...) while the latter has to do with the preparation of the system. (shrink)
The following introduction offers a broad survey of the history of quantum physics. It then outlines the position of each contributor in this Special Focus Section concerning the collapse of the quantum wavefunction and defines three important terms (Hilbert space, Schrödinger’s cat, and decoherence) used in discussing this topic.
Scientific endeavour has often tried to localize superior cerebral functions either in areas like the ones described by Broca as being those connected with language in the left hemisphere, or in the huge array of the hundred billion of interconnected neurons. But in this last case the coined description of the grandmother neuron, tends to show humorously that hopes have fallen short of their target.Along the same lines, the specific timing of electric neural activity is known to take place around (...) a few milliseconds, which seems to be insufficient to account for the high potential speed necessary to sustain the very massive and complex process which is involved in mental activity. (shrink)
We investigate the validity of the field explanation of the wavefunction by analyzing the mass and charge density distributions of a quantum system. It is argued that a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wavefunction. This is also a consequence of protective measurement. If the wavefunction is a physical field, then the mass and charge density (...) will be distributed in space simultaneously for a charged quantum system, and thus there will exist a remarkable electrostatic self-interaction of its wavefunction, though the gravitational self-interaction is too weak to be detected presently. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus we conclude that the wavefunction cannot be a description of a physical field. In the second part of this paper, we further analyze the implications of these results for the main realistic interpretations of quantum mechanics, especially for de Broglie-Bohm theory. It has been argued that de Broglie-Bohm theory gives the same predictions as quantum mechanics by means of quantum equilibrium hypothesis. However, this equivalence is based on the premise that the wavefunction, regarded as a Ψ-field, has no mass and charge density distributions, which turns out to be wrong according to the above results. For a charged quantum system, both Ψ-field and Bohmian particle have charge density distribution. This then results in the existence of an electrostatic self-interaction of the field and an electromagnetic interaction between the field and Bohmian particle, which contradicts both the predictions of quantum mechanics and experimental observations. Therefore, de Broglie-Bohm theory as a realistic interpretation of quantum mechanics is probably wrong. Lastly, we suggest that the wavefunction is a description of some sort of ergodic motion (e.g. random discontinuous motion) of particles, and we also briefly analyze the implications of this suggestion for other realistic interpretations of quantum mechanics including many-worlds interpretation and dynamical collapse theories. (shrink)
It is shown that the superposed wavefunction of a measuring device, in each branch of which there is a definite measurement result, does not correspond to many mutually unobservable but equally real worlds, as the superposed wavefunction can be observed in our world by protective measurement.
We investigate the implications of protective measurement for de Broglie-Bohm theory, mainly focusing on the interpretation of the wavefunction. It has been argued that the de Broglie-Bohm theory gives the same predictions as quantum mechanics by means of quantum equilibrium hypothesis. However, this equivalence is based on the premise that the wavefunction, regarded as a Ψ-field, has no mass and charge density distributions. But this premise turns out to be wrong according to protective measurement; (...) a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wavefunction. Then in the de Broglie-Bohm theory both Ψ-field and Bohmian particle will have charge density distribution for a charged quantum system. This will result in the existence of an electrostatic self-interaction of the field and an electromagnetic interaction between the field and Bohmian particle, which not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Therefore, the de Broglie-Bohm theory as a realistic interpretation of quantum mechanics is problematic according to protective measurement. Lastly, we briefly discuss the possibility that the wavefunction is not a physical field but a description of some sort of ergodic motion (e.g. random discontinuous motion) of particles. (shrink)
What is quantum mechanics about? The most natural way to interpret quantum mechanics realistically as a theory about the world might seem to be what is called wavefunction ontology: the view according to which the wavefunction mathematically represents in a complete way fundamentally all there is in the world. Erwin Schroedinger was one of the first proponents of such a view, but he dismissed it after he realized it led to macroscopic superpositions (if the (...)wavefunction evolves in time according to the equations that has his name). The Many-Worlds interpretation1 accepts the existence of such macroscopic superpositions but takes it that they can never be observed. Superposed objects and superposed observers split together in different worlds of the type of the one we appear to live in. For these who, like Schroedinger, think that macroscopic superpositions are a problem, the common wisdom is that there are two alternative views: "Either the wavefunction, as given by the Schroedinger equation, is not everything, or is not right" [Bell 1987]. The deBroglie-Bohm theory, now commonly known as Bohmian Mechanics, takes the first option: the description provided by a Schroedinger-evolving wavefunction is supplemented by the information provided by the configuration of the particles. The second possibility consists in assuming that, while the wavefunction provides the complete description of the system, its temporal evolution is not given by the Schroedinger equation. Rather, the usual Schroedinger evolution is interrupted by random and sudden "collapses". The most promising theory of this kind is the GRW theory, named after the scientists that developed it: Gian Carlo Ghirardi, Alberto Rimini and Tullio Weber.. It seems tempting to think that in GRW we can take the wavefunction ontologically seriously and avoid the problem of macroscopic superpositions just allowing for quantum jumps. In this paper we will argue that such "bare" wavefunction ontology is not possible, neither for GRW nor for any other quantum theory: quantum mechanics cannot be about the wavefunction simpliciter. That is, we need more structure than the one provided by the wavefunction. As a response, quantum theories about the wavefunction can be supplemented with structure, without taking it as an additional ontology. We argue in reply that such "dressed-up" versions of wavefunction ontology are not sensible, since they compromise the acceptability of the theory as a satisfactory fundamental physical theory. Therefore we maintain that: 1- Strictly speaking, it is not possible to interpret quantum theories as theories about the wavefunction; 2- Even if the wavefunction is supplemented by additional non-ontological structures, there are reasons not to take the resulting theory seriously. Moreover, we will argue that any of the traditional responses to the measurement problem of quantum mechanics (Bohmian mechanics, GRW and Many-Worlds), contrarily to what commonly believed, share a common structure. That is, we maintain that: 3- All quantum theories should be regarded as theories in which physical objects are constituted by a primitive ontology. The primitive ontology is mathematically represented in the theory by a mathematical entity in three-dimensional space, or space-time. (shrink)
We give a new argument supporting a gravitational role in quantum collapse. It is demonstrated that the discreteness of space-time, which results from the proper combination of quantum theory and general relativity, may inevitably result in the dynamical collapse of thewave function. Moreover, the minimum size of discrete space-time yields a plausible collapse criterion consistent with experiments. By assuming that the source to collapse the wavefunction is the inherent random motion of particles described by the (...) class='Hi'>wavefunction, we further propose a concrete model of wavefunction collapse in the discrete space-time. It is shown that the model is consistent with the existing experiments and macroscopic experiences. (shrink)
Recently we have given proof of two theorems characterizing the Clifford algebra. By using such two theorems we have reformulated the well known von Neumann postulate on quantum measurements giving evidence of the algebraic manner in which quantum wavefunction collapse of quantum mechanics happens. In the present paper we introduce logic in Clifford algebra interpreting its idempotents as logical statements. Using the previously mentioned theorems we demonstrate that the two basic foundations of quantum mechanics, as the indeterminism (...) and the quantum interference, do not arise from physics itself but from logic. We advance the principles that there are levels of our reality in which we lose our possibility of unconditionally define the truth. At this level of reality we cannot separate matter per se from the basic foundations of the logic that we use to describe it. This logical relativism does not characterize classical mechanics but quantum physics. According to Y. F. Orlov, at quantum level the truths of logical statements about dynamic variables become dynamic variables themselves. (shrink)
For a long time it was believed that it was impossible to be realist about quantum mechanics. It took quite a while for the researchers in the foundations of physics, beginning with John Stuart Bell [Bell 1987], to convince others that such an alleged impossibility had no foundation. Nowadays there are several quantum theories that can be interpreted realistically, among which Bohmian mechanics, the GRW theory, and the many-worlds theory. The debate, though, is far from being over: in what respect (...) should we be realist regarding these theories? Two diff erent proposals have been made: on the one hand, there are those who insist on a direct ontological interpretation of the wavefunction as representing physical bodies, and on the other hand there are those who claim that quantum mechanics is not really about the wavefunction. In this paper we will present and discuss one proposal of the latter kind that focuses on the notion of primitive ontology. (shrink)
A simple quantum model describing the onset of time is presented. This is combined with a simple quantum model of the onset of space. A major purpose is to explore the interpretational issues which arise. The state vector is a superposition of states representing different “instants.” The sample space and probability measure are discussed. Critical to the dynamics is state vector collapse: it is argued that a tenable interpretation is not possible without it. Collapse provides a mechanism whereby the universe (...) size, like a clock, is narrowly correlated with the quantized time eigenvalues. (shrink)
This paper presents a new Symmetrical Interpretation (SI) of relativistic quantum mechanics which postulates: quantum mechanics is a theory about complete experiments, not particles; a complete experiment is maximally described by a complex transition amplitude density; and this transition amplitude density never collapses. This SI is compared to the Copenhagen Interpretation (CI) for the analysis of Einstein’s bubble experiment. This SI makes several experimentally testable predictions that differ from the CI, solves one part of the measurement problem, resolves some inconsistencies (...) of the CI, and gives intuitive explanations of some previously mysterious quantum effects. (shrink)
Experiments are described, using electroencephalography (EEG) and simple tests of performance, which support the hypothesis that collapse of a quantum field is of importance to the functioning of the brain. The theoretical basis of our experiments is derived from Penrose (1989) who suggested that conscious decision-making is a manifestation of the outcome of quantum computation in the brain involving collapse of some relevant wavefunction. He also proposed that collapse of any wavefunction depends on a (...) gravitational criterion. As different brain areas are known to subserve different functions, we argue that `Penrose collapse' must occur in a particular brain area when performing a task that uses it. Further, taking an EEG from the area should amplify the gravitational prerequisite for collapse, so affecting task performance. There are no non-quantum theories which could lead one to expect that taking an EEG could directly affect task performance by subjects. The results of both pilot and main experiments indicated that task performance was indeed influenced by taking an EEG from relevant brain areas. Control experiments suggested that the influence was quantum mechanical in origin, and was not due to any experimental artefact. The results are statistically significant and merit attempts at replication in an independent laboratory, preferably with more sophisticated equipment than was available to us. (shrink)
I critically evaluate Bickle’s version of scientific theory reduction. I press three main points. First, a small point, Bickle modifies the new wave account of reduction developed by Paul Churchland and Clifford Hooker by treating theories as set-theoretic structures. But that structuralist gloss seems to lose what was distinctive about the Churchland-Hooker account, namely, that a corrected theory must be specified entirely by terms and concepts drawn from the basic reducing theory. Set-theoretic structures are not terms or concepts but (...) the structures that they describe. Second, and more serious, a familiar problem for classical positivist account of reduction resurfaces within this newest wave of thinking, namely, commitment to property identities and inter-theoretic bridge laws (a problem I discussed at more length in "Collapse of the New Wave"). Indeed, this problem is exacerbated by Bickle’s conciliatory treatment of property plasticity, since he is willing to grant that a large number of special science terms denote multiply realized properties, at least if realistically construed. Still, in the end, Bickle sidesteps the reduction of properties by appealing to Hooker’s "function-to-structure token reduction." This is an interesting move with an intriguing concept of reduction. But problems remain. For, third, Bickle and Hooker's function-to-structure token reduction is actually a guised form of eliminative materialism. But that should be unacceptable since the position extends well beyond any modest revisionism for suspect items from a folk theory, say, in folk psychology or folk biology. Instead, it applies to functional terms and concepts employed throughout well-developed and explanatorily successful sciences. (shrink)
A general conceptual framework for large-scale neocortical dynamics based on data from many laboratories is applied to a variety of experimental designs, spatial scales, and brain states. Partly distinct, but interacting local processes (e.g., neural networks) arise from functional segregation. Global processes arise from functional integration and can facilitate (top down) synchronous activity in remote cell groups that function simultaneously at several different spatial scales. Simultaneous local processes may help drive (bottom up) macroscopic global dynamics observed with electroencephalography (EEG) (...) or magnetoencephalography (MEG). A local/global dynamic theory that is consistent with EEG data and the proposed conceptual framework is outlined. This theory is neutral about properties of neural networks embedded in macroscopic fields, but its global component makes several qualitative and semiquantitative predictions about EEG measures of traveling and standing wave phenomena. A more general “metatheory” suggests what large-scale quantitative theories of neocortical dynamics may be like when more accurate treatment of local and nonlinear effects is achieved. The theory describes the dynamics of excitatory and inhibitory synaptic action fields. EEG and MEG provide large-scale estimates of modulation of these synaptic fields around background levels. Brain states are determined by neuromodulatory control parameters. Purely local states are dominated by local feedback gains and rise and decay times of postsynaptic potentials. Dominant local frequencies vary with brain region. Other states are purely global, with moderate to high coherence over large distances. Multiple global mode frequencies arise from a combination of delays in corticocortical axons and neocortical boundary conditions. Global frequencies are identical in all cortical regions, but most states involve dynamic interactions between local networks and the global system. EEG frequencies may involve a “matching” of local resonant frequencies with one or more of the many, closely spaced global frequencies. Key Words: binding problem; cell assemblies; coherence; EEG; limit cycles; neocortical dynamics; pacemakers; phase locking; spatial scale; standing waves; synchronization. Footnotes1 The relationship between the synaptic action fields proposed in the target article and cell assemblies is clarified with Figure R1 (p. 416) of the Response. (This figure was not available to Commentators. (shrink)
A new theory for basic function in the nervous system has recently been proposed (Dempsher, J., 1979a, 1979b; 1980, 1981). The major basic themes of the new theory are as follows: (1) There are two fundamental units of structure and function, the fibre or conducting mechanism, and the neurocentre, where nervous system function as we know it takes place. (2) The nerve impulse is regarded as a mathematical event. The mathematics is the result of a prescribed fusion (...) of energy and matter. (3) Nervous system function everywhere in the nervous system is mathematical. In the fibre, the prescribed fusion of energy and matter results in a number. In the neurocentre, the prescribed fusion of energy and matter results in a mathematical function. Basic function in the nervous system everywhere requires a transformation of a nerve impulse in the fibre into a nerve impulse in the neurocentre with opposing properties: The nerve impulse in the fibre is confined to the fibre; cannot sum with another nerve impulse; can travel long distances with constant form and velocity; curvature in space and time are not significant features; and it is regarded as a number. On the other hand, the nerve impulse in the neurocentre is confined to the neurocentre; can sum with other nerve impulses; cannot travel long distances - even in a very short distance, it changes form; curvature in space and time is a very significant feature; and it is regarded as a mathematical function.The approach to determine how one form of the nerve impulse is transformed into the other at the input region is based on two of the differences listed above: (1) The nerve impulse in the fibre cannot sum with another nerve impulse in the fibre, whereas in the neurocentre, several nerve impulses sum to form a larger nerve impulse. (2) The nerve impulse in the fibre is regarded as a number, in the neurocentre, it is regarded as a mathematical function. The commonality of (1) and (2) is that the properties defining the nerve impulse in the fibre are associated with the property ofdiscreteness, whereas, the properties defining the nerve impulse in the neurocentre are associated with the property ofcontinuousness. Thus, the basic theme of unification of function at the input region of the neurocentre is the transformation of a phenomenon with the property of discreteness into a phenomenon with the property of continuousness. The solution to this transformation is approached from two directions:biologic andmathematical. In the biologic approach, the unit element of the nerve impulse in the fibre terminations (as.u. as a wave of energy, a spike in the classical theory) fuses with a. calcium-binding protein causing the release of Ca++. The calcium ions then combine with another protein. Associated with the second reaction is a conformational change in the Ca++-protein complex and the unit element in the neurocentre, bs.u., is emitted. Individual bs.u. then fuse with acetylcholine; summation occurs andwave b is emitted. In the mathematical approach, the nerve impulse as a number, is partitioned into two numbers with a precise rule relating these two numbers. One possibility suggested is that the number can be regarded as the value of a trigonometric function. This value then gives rise to an angle with sides related in a ratio or proportionality fashion — a relationship with the property of continuousness, as contrasted with that of a single number, discreteness. Both biologic and mathematical approaches are united so as to suggest that the mathematical (trigonometric) function arose as the result of a fusion of energy (as.u. as a wave of energy) and the calcium-binding protein as matter; following this reaction, bs.u., with opposing properties, is emitted. (shrink)
The purpose of this paper is to present a bio-physical basis of mathematics. The essence of the theory is that function in the nervous system is mathematical. The mathematics arises as a result of the interaction of energy (a wave with a precise curvature in space and time) and matter (a molecular or ionic structure with a precise form in space and time). In this interaction, both energy and matter play an active role. That is, the interaction results (...) in a change in form of both energy and matter. There are at least six mathematical operations in a simple synaptic region. It is believed the form of both energy and matter are specific, and their interaction is specific, that is, function in most of the nervous system is stereotyped. It is suggested that mathematics be taken out of the mind and placed where it belongs — in nature and the synaptic regions of the nervous system; it results in both places from a precise interaction between energy (in a precise form) and matter (in a precise structure). (shrink)
It is argued that some elusive “entropic” characteristics of chemical bonds, e.g., bond multiplicities (orders), which connect the bonded atoms in molecules, can be probed using quantities and techniques of Information Theory (IT). This complementary perspective increases our insight and understanding of the molecular electronic structure. The specific IT tools for detecting effects of chemical bonds and predicting their entropic multiplicities in molecules are summarized. Alternative information densities, including measures of the local entropy deficiency or its displacement relative to the (...) system atomic promolecule, and the nonadditive Fisher information in the atomic orbital resolution(called contragradience ) are used to diagnose the bonding patterns in illustrative diatomic and polyatomic molecules. The elements of the orbital communication theory of the chemical bond are briefly summarized and illustrated for the simplest case of the two -orbital model. The information-cascade perspective also suggests a novel, indirect mechanism of the orbital interactions in molecular systems, through “bridges” (orbital intermediates), in addition to the familiar direct chemical bonds realized through “space”, as a result of the orbital constructive interference in the subspace of the occupied molecular orbitals. Some implications of these two sources of chemical bonds in propellanes, π-electron systems and polymers are examined. The current –density concept associated with the wave-function phase is introduced and the relevant phase -continuity equation is discussed. For the first time, the quantum generalizations of the classical measures of the information content, functionals of the probability distribution alone, are introduced to distinguish systems with the same electron density, but differing in their current(phase) composition. The corresponding information/entropy sources are identified in the associated continuity equations. (shrink)
A generally ignored feature of Aristotle’s famous function argument is its reliance on the claim that practitioners of the crafts (technai) have functions: but this claim does important work. Aristotle is pointing to the fact that we judge everyday rational agency and agents by norms which are independent of their contingent desires: a good doctor is not just one who happens to achieve his personal goals through his work. But, Aristotle argues, such norms can only be binding on individuals (...) if human rational agency as such is governed by objective teleological norms. . (shrink)
The function of a trait token is usually defined in terms of some properties of other (past, present, future) tokens of the same trait type. I argue that this strategy is problematic, as trait types are (at least partly) individuated by their functional properties, which would lead to circularity. In order to avoid this problem, I suggest a way to define the function of a trait token in terms of the properties of the very same trait token. To (...) able to allow for the possibility of malfunctioning, some of these properties need to be modal ones: a function of a trait is to do F just in case its doing F would contribute to the inclusive fitness of the organism whose trait it is. Function attributions have modal force. Finally, I explore whether and how this theory of biological function could be modified to cover artifact function. (shrink)
I argue that there are at least four different ways in which the term ‘function’ is used in connection with the study of living organisms, namely: (1) function as (mere) activity, (2) function as biological role, (3) function as biological advantage, and (4) function as selected effect. Notion (1) refers to what an item does by itself; (2) refers to the contribution of an item or activity to a complex activity or capacity of an organism; (...) (3) refers to the value for the organism of an item having a certain character rather than another; (4) refers to the way in which a trait acquired and has maintained its current share in the population. The recognition of a separate notion of function as biological advantage solves the problem of the indeterminate reference situation that has been raised against a counterfactual analysis of function, and emphasizes the importance of counterfactual comparison in the explanatory practice of organismal biology. This reveals a neglected problem in the philosophy of biology, namely that of accounting for the insights provided. (shrink)
I clarify some of the details of the modal theory of function I outlined in Nanay (2010): (a) I explicate what it means that the function of a token biological trait is fixed by modal facts; (b) I address an objection to my trait type individuation argument against etiological function and (c) I examine the consequences of replacing the etiological theory of function with a modal theory for the prospects of using the concept of biological (...) class='Hi'>function to explain mental content. (shrink)
Function theorists routinely speculate that a viable function theory will be equally applicable to biological traits and artifacts. However, artifact function has received only the most cursory scrutiny in its own right. Closer scrutiny reveals that only a pluralist theory comprising two distinct notions of function--proper function and system function--will serve as an adequate general theory. The first section describes these two notions of function. The second section shows why both notions are necessary, (...) by showing that attempts to do away with one of them fail. This demonstration draws on examples from the artifactual realm to motivate major points of the argument. The third section is an outline of artifact function. It confirms the conclusions of the second section, and also begins the task of describing some of the special features of artifact function needing accommodation within the general theory. (shrink)
The survival enhancing propensity (SEP) account has a crucial role to play in the analysis of proper function. However, a central feature of the account, its specification of the proper environment to which functions are relativized, is seriously underdeveloped. In this paper, I argue that existent accounts of proper environment fail because they either allow too many or too few characters to count as proper functions. While SEP accounts retain their promise, they are unworkable because of their inability to (...) specify this important feature. However, I suggest that this problem can be overcome by the application of a new strategy for specifying proper environment that is grounded in the operation of natural selection and I conclude by offering a first approximation of such an account. (shrink)
In ‘A modal theory of function’, I gave an argument against all existing theories of function and outlined a new theory. Karen Neander and Alex Rosenberg argue against both my negative and my positive claim. My aim here is not merely to defend my account from their objections, but to (a) very briefly point out that the new account of etiological function they propose in response to my criticism cannot avoid the circularity worry either and, more importantly, (...) to (b) highlight, and attempt to make precise, an important feature of my modal theory that may have been understated in the original paper – that function attributions depend on the explanatory project at hand. (shrink)
Conscious mental states are states we are in some way aware of. I compare higher-order theories of consciousness, which explain consciousness by appeal to such higher-order awareness (HOA), and first-order theories, which do not, and I argue that higher-order theories have substantial explanatory advantages. The higher-order nature of our awareness of our conscious states suggests an analogy with the metacognition that figures in the regulation of psychological processes and behaviour. I argue that, although both consciousness and metacognition involve higher-order psychological (...) states, they have little more in common. One thing they do share is the possibility of misrepresentation; just as metacognitive processing can misrepresent one’s cognitive states and abilities, so the HOA in virtue of which one’s mental states are conscious can, and sometimes does, misdescribe those states. A striking difference between the two, however, has to do with utility for psychological processing. Metacognition has considerable benefit for psychological processing; in contrast, it is unlikely that there is much, if any, utility to mental states’ being conscious over and above the utility those states have when they are not conscious. (shrink)
What is the biological function of perception? I hold perception, especially visual perception in humans, has the biological function of accurately representing the environment. Tyler Burge argues this cannot be so in Origins of Objectivity (Oxford, 2010), for accuracy is a semantical relationship and not, as such, a practical matter. Burge also provides a supporting example. I rebut the argument and the example. Accuracy is sometimes also a practical matter if accuracy partly explains how perception contributes to survival (...) and reproduction. (shrink)
In this paper I put forward a new micro realistic, fundamentally probabilistic, propensiton version of quantum theory. According to this theory, the entities of the quantum domain - electrons, photons, atoms - are neither particles nor fields, but a new kind of fundamentally probabilistic entity, the propensiton - entities which interact with one another probabilistically. This version of quantum theory leaves the Schroedinger equation unchanged, but reinterprets it to specify how propensitons evolve when no probabilistic transitions occur. Probabilisitic transitions occur (...) when new "particles" are created as a result of inelastic interactions. All measurements are just special cases of this. This propensiton version of quantum theory, I argue, solves the wave/particle dilemma, is free of conceptual problems that plague orthodox quantum theory, recovers all the empirical success of orthodox quantum theory, and at the same time yields as yet untested predictions that differ from those of orthodox quantum theory. (shrink)
Even if all of the content of conscious experience is encoded in the brain, there is a considerable difference between the view that consciousness does independent processing and the view that it does not. If all processing is done by the brain, then conscious experience is unnecessary and irrelevant to behavior. If consciousness performs a function, then its association with particular aspects of brain processing reflect its functional use in determining behavior. However, if consciousness does perform a function, (...) it cannot be described entirely by known physical laws. Rather, even if the content of conscious experience follows physical encoding in the brain, consciousness must then be governed in part by a principle which is different from any known physical principle. (shrink)
A recent rethinking of the early history of Quantum Mechanics deemed the late 1920s agreement on the equivalence of Matrix Mechanics and Wave Mechanics, prompted by Schrödinger's 1926 proof, a myth. Schrödinger supposedly failed to prove isomorphism, or even a weaker equivalence (“Schrödinger-equivalence”) of the mathematical structures of the two theories; developments in the early 1930s, especially the work of mathematician von Neumann provided sound proof of mathematical equivalence. The alleged agreement about the Copenhagen Interpretation, predicated to a large (...) extent on this equivalence, was deemed a myth as well. In response, I argue that Schrödinger's proof concerned primarily a domain-specific ontological equivalence, rather than the isomorphism or a weaker mathematical equivalence. It stemmed initially from the agreement of the eigenvalues of Wave Mechanics and energy-states of Bohr's Model that was discovered and published by Schrödinger in his first and second communications of 1926. Schrödinger demonstrated in this proof that the laws of motion arrived at by the method of Matrix Mechanics are satisfied by assigning the auxiliary role to eigenfunctions in the derivation of matrices (while he only outlined the reversed derivation of eigenfunctions from Matrix Mechanics, which was necessary for the proof of both isomorphism and Schrödinger-equivalence of the two theories). This result was intended to demonstrate the domain-specific ontological equivalence of Matrix Mechanics and Wave Mechanics, with respect to the domain of Bohr's atom. And although the mathematical equivalence of the theories did not seem out of the reach of existing theories and methods, Schrödinger never intended to fully explore such a possibility in his proof paper. In a further development of Quantum Mechanics, Bohr's complementarity and Copenhagen Interpretation captured a more substantial convergence of the subsequently revised (in light of the experimental results) Wave and Matrix Mechanics. I argue that both the equivalence and Copenhagen Interpretation can be deemed myths if one predicates the philosophical and historical analysis on a narrow model of physical theory which disregards its historical context, and focuses exclusively on its formal aspects and the exploration of the logical models supposedly implicit in it. (shrink)
Functional hypotheses about animal signalling often refer to mental states of the sender or the receiver. Mental states are functional categorizations of neurophysiological states. Functional questions about animal signals are intertwined with causal questions. This interrelationship is illustrated in regard to avian distraction displays. In purposive signalling, the sender has a goal of influencing the behavior of the receiver. Purposive signalling is innovative if the sender's goal is unrelated to the biological function of the signal. This may be the (...) case in some instances of false alarm calling. Biological functionalism differs from philosophical functionalism in its concept of identity and in the specification of relevant inputs and outputs. (shrink)
A recent rethinking of the early history of Quantum Mechanics deemed the late 1920s agreement on the equivalence of Matrix Mechanics and Wave Mechanics, prompted by Schrödinger’s 1926 proof, a myth. Schrödinger supposedly failed to achieve the goal of proving isomorphism of the mathematical structures of the two theories, while only later developments in the early 1930s, especially the work of mathematician John von Neumman (1932) provided sound proof of equivalence. The alleged agreement about the Copenhagen Interpretation, predicated to (...) a large extent on this equivalence, was deemed a myth as well. If such analysis is correct, it provides considerable evidence that, in its critical moments, the foundations of scientific practice might not live up to the minimal standards of rigor, as such standards are established in the practice of logic, mathematics, and mathematical physics, thereby prompting one to question the rationality of the practice of physics. In response, I argue that Schrödinger’s proof concerned primarily a domain-specific ontological equivalence, rather than the isomorphism. It stemmed initially from the agreement of the eigenvalues of Wave Mechanics and energy-states of Bohr’s Model that was discovered and published by Schrödinger in his First and Second Communications of 1926. Schrödinger demonstrated in this proof that the laws of motion arrived at by the method of Matrix Mechanics could be derived successfully from eigenfunctions as well (while he only outlined the reversed derivation of eigenfunctions from Matrix Mechanics, which was necessary for the proof of isomorphism of the two theories). This result was intended to demonstrate the domain-specific ontological equivalence of Matrix Mechanics and Wave Mechanics, with respect to the domain of Bohr’s atom. And although the full-fledged mathematico-logical equivalence of the theories did not seem out of the reach of existing theories and methods, Schrödinger never intended to fully explore such a possibility in his proof paper. In a further development of Quantum Mechanics, Bohr’s complementarity and Copenhagen Interpretation captured a more substantial convergence of the subsequently revised (in light of the experimental results) Wave and Matrix Mechanics. I argue that both the equivalence and Copenhagen Interpretation can be deemed myths if one predicates the philosophical and historical analysis on a narrow model of physical theory which disregards its historical context, and focuses exclusively on its formal aspects and the exploration of the logical models supposedly implicit in it. (shrink)
Humans possess two nonverbal systems capable of representing numbers, both limited in their representational power: the first one represents numbers in an approximate fashion, and the second one conveys information about small numbers only. Conception of exact large numbers has therefore been thought to arise from the manipulation of exact numerical symbols. Here, we focus on two fundamental properties of the exact numbers as prerequisites to the concept of EXACT NUMBERS : the fact that all numbers can be generated by (...) a successor function and the fact that equality between numbers can be defined in an exact fashion. We discuss some recent findings assessing how speakers of Munduruc (an Amazonian language), and young Western children (3-4 years old) understand these fundamental properties of numbers. (shrink)
The Dirac δ function has solid roots in nineteenth century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac’s discovery by over a century, and illuminating the nature of Cauchy’s infinitesimals and his infinitesimal definition of δ.
Analyzing the ancient Greek point of view concerning anger, shame and justice and a very modern one, one can see, that anger has a regulative function, but shame does as well. Anger puts the other in his place, thereby regulating hierarchies. Shame regulates the social relations of recognition. And both emotions also have an evaluative function, because anger evaluates a situation with regard to a humiliation; shame, with regard to a misdemeanor. In addition, attention has to be paid (...) to the correct molding of these emotions and the correct ways of using them in rearing to be good or just (i.e., in personality formation. (shrink)
This volume collects many of the major essays of feminist theory of the past forty years. The essays included here are those which have made key contributions to feminist theory during this period and which have generated extensive discussion. The volume organizes these essays historically, so as to provide a sense of the major turning points in feminist theory. Beginning with those essays which have provoked widespread discussion in the early days of the second wave, the volume then presents (...) essays which have been central to major discussions since that time. The essays present the complex relationship between feminism and Marxism, the second wave's "gynocentric turn," the theoretical elaboration of differences among women, and the essentialist debate, as these have occupied the attention of feminist theorists. Through this collection, the reader is able to gain a sense of the diverse directions feminist theory has taken over the past forty years, where feminist theory stands at the moment, and the questions which are just now beginning to emerge. (shrink)
In this paper, I examine metaphysical aspects in the neuroeconomics debate. I propose that part of the debate can be better understood by supposing two metaphysical stances, mechanistic and functional. I characterize the two stances, and discuss their relations. I consider two models of framing, in order to illustrate how the features of mechanistic and functional stances figure in the practice of the sciences of individual decision making.
The objective of this paper is to show that, instead of quantum probabilities, wave packets are physically real. First, Cartwright's recent argument for the reality of quantum probabilities is criticized. Then, the notion of ‘physically real’ is precisely defined and the difference between wave functions and quantum probabilities clarified. Being thus prepared, some strong reasons are discussed for considering the wave packet to be physically real. Finding the reasons inconclusive, I explain how the Aharonov—Bohm effect delivers the (...) final punch. I conclude that wave packets are the quantum objects that underlie the indeterministic quantum processes and have the propensity of displaying probabilistic (or indeterministic) behavior. (shrink)
Drawing on Christopher Boorse's Biostatistical Theory (BST), Norman Daniels contends that a genuine health need is one which is necessary to restore normal functioning – a supposedly objective notion which he believes can be read from the natural world without reference to potentially controversial normative categories. But despite his claims to the contrary, this conception of health harbors arbitrary evaluative judgments which make room for intractable disagreement as to which conditions should count as genuine health needs and therefore which needs (...) should be met. I begin by offering a brief summary of Boorse's BST, the theory to which Daniels appeals for providing the conception of health as normal functioning upon which his overall distributive scheme rests. Next, I consider what I call practical objections to Daniels's use of Boorse's theory. Finally I recount Elseljin Kingma's theoretical objection to Boorse's BST and discuss its impact on Daniels's overall theory. Though I conclude that Boorse's view, so weakened, will no longer be able to sustain the judgments which Daniels's theory uses it to reach, in the end, I offer Daniels an olive branch by briefly sketching an alternative strategy for reaching suitably objective conclusions regarding the health and/or disease status of various conditions. (shrink)
We argue that human consciousness may be a property of single electron in the brain. We suppose that each electron in the universe has at least primitive consciousness. Each electron subjectively “observes” its quantum dynamics (energy, momentum, “shape” of wavefunction) in the form of sensations and other mental phenomena. However, some electrons in neural cells have complex “human” consciousnesses due to complex quantum dynamics in complex organic environment. We discuss neurophysiological and physical aspects of this hypothesis and (...) show that: (1) single chemically active electron has enough informational capacity to “contain” the richness of human subjective experience; (2) quantum states of some electrons might be directly influenced by human sensory data and have direct influence upon human behavior in real brain; (3) main physical and philosophical drawbacks of “conventional” “quantum theories of consciousness” may be solved by our hypothesis without much changes in their conceptual basis. We do not suggest any “new physics”, and our neuroscientific assumptions are similar to those used by other proponents of “quantum consciousness”. However, our hypothesis suggests radical changes in our view on human and physical reality. (shrink)
We analyze the possible implications of spacetime discreteness for the special and general relativity and quantum theory. It is argued that the existence of a minimum size of spacetime may explain the invariance of the speed of light in special relativity and Einstein’s equivalence principle in general relativity. Moreover, the discreteness of spacetime may also result in the collapse of the wavefunction in quantum mechanics, which may provide a possible solution to the quantum measurement problem. These interesting (...) results might have some important implications for a complete theory of quantum gravity. (shrink)
Features of consciousness difficult to understand in terms of conventional neuroscience have evoked application of quantum theory, which describes the fundamental behavior of matter and energy. In this paper we propose that aspects of quantum theory (e.g. quantum coherence) and of a newly proposed physical phenomenon of quantum wavefunction "self-collapse"(objective reduction: OR -Penrose, 1994) are essential for consciousness, and occur in cytoskeletal microtubules and other structures within each of the brain's neurons. The particular characteristics of microtubules suitable (...) for quantum effects include their crystal-like lattice structure, hollow inner core, organization of cell function and capacity for information processing. We envisage that conformational states of microtubule subunits (tubulins) are coupled to internal quantum events, and cooperatively interact (compute) with other tubulins. We further assume that macroscopic coherent superposition of quantum-coupled tubulin conformational states occurs throughout significant brain volumes and provides the global binding essential to consciousness. We equate the emergence of the microtubule quantum coherence with pre-conscious processing which grows (for up to 500 milliseconds) until the mass-energy difference among the separated states of tubulins reaches a threshold related to quantum gravity. According to the arguments for OR put forth in Penrose (1994), superpositioned states each have their own space-time geometries. When the degree of coherent mass-energy difference leads to sufficient separation of space-time geometry, the system must choose and decay (reduce, collapse) to a single universe state. In this way, a transient superposition of slightly differing space-time geometries persists until an abrupt quantum classical reduction occurs. Unlike the random, "subjective reduction"( SR, or R) of standard quantum theory caused by observation or environmental entanglement, the OR we propose in microtubules is a self-collapse and it results in particular patterns of microtubule-tubulin conformational states that regulate neuronal activities including synaptic functions. (shrink)
In this paper I argue that we can solve the interpretation problem of quantum mechanics and the question of ontology of Quantum Field Theory on the basis of simple metaphysical position: The connection of the phase space with the ancient Theory of Logi of Beings, which is, by giving ontological meaning to the entities which "live" at the phase space, the Hamiltonian or Lagrangian formalism. There is a physical subject of such functions and it is the logos of a being. (...) Therefore we can refer to the logical space as the total sum of logi of being. The result of this position is that we can attribute to the wavefunction a physical meaning, a special case of logos of a being and also give an ontological meaning at a quantum field. The developed metaphysical scheme can interpret the quantum paradoxes, by using the commonly accepted mathematical formalism. It can also interpret certain issues of Quantum Field Theory, although further study of this topic is necessary. (shrink)
In a recent Analysis article, Quentin Smith argues that classical theism is inconsistent with certain consequences of Stephen Hawking's quantum cosmology.1 Although I am not a theist, it seems to me that Smith's argument fails to establish its conclusion. The purpose of this paper is to show what is wrong with Smith's argument. According to Smith, Hawking's cosmological theory includes what Smith calls "Hawking's wavefunction law." Hawking's wavefunction law (hereafter, "HL") apparently has, among its (...) consequences, the following claim. (1) The unconditional probability that a universe like this one - i.e., a universe with the metric hij and matter field Φ - should begin to exist is 95%.2 Smith then argues that the theist who accepts HL must also accept that the following sentence was once true.3.. (shrink)
Question #2: How many dimensions does space have, according to quantum mechanics? If quantum mechanics were a true theory of the world, then the answer to Question #2 would be the same as the answer to Question #1. But quantum mechanics is not true, and so the answers need not be the same.
Age-old battle lines over the puzzling nature of mental experience are shaping a modern resurgence in the study of consciousness. On one side are the long-dominant "physicalists" who view consciousness as an emergent property of the brain's neural networks. On the alternative, rebellious side are those who see a necessary added ingredient: proto-conscious experience intrinsic to reality, perhaps understandable through modern physics (panpsychists, pan-experientialists, "funda-mentalists"). It is argued here that the physicalist premise alone is unable to solve completely the difficult (...) issues of consciousness and that to do so will require supplemental panpsychist/pan-experiential philosophy expressed in modern physics. In one scheme proto-conscious experience is a basic property of physical reality accessible to a quantum process associated with brain activity. The proposed process is Roger Penrose's "objective reduction" (OR), a self-organizing "collapse" of the quantum wavefunction related to instability at the most basic level of space-time geometry. In the Penrose- Hameroff model of "orchestrated objective reduction" (Orch OR), OR quantum computation occurs in cytoskeletal microtubules within the brain's neurons. The basic thesis is that consciousness involves brain activities coupled to a self-organizing ripples in fundamental reality. (shrink)
The concept of temporal flow has been attacked both on the grounds that it is logically incoherent, and on the grounds that it conflicts with the theory of relativity. I argue that the charge of incoherence cannot be made to stick: McTaggart's argument commits the fallacy of equivocation, and arguments deployed by Smart and others turn out to be question-begging. But objections arising from relativity, so I claim, have considerably more force than Lucas acknowledges. Moreover, the idea of equating the (...) cosmic time which arises in general relativistic cosmology with a metaphysically preferred space-time foliation, founders on the fact that the Friedmann models are idealisations. Finally, Lucas may be right in claiming that dynamical wave-function collapse, provided it does not propagate superluminally, will define a preferred foliation. But it is arguable that this consideration, so far from supporting Lucas's position, is grounds for rejecting collapse interpretations of quantum mechanics. (shrink)
The literature on physicalism often fails to elucidate, I think, what the word physical in physical ism precisely means. Philosophers speak at times of an ideal set of fundamental physical facts, or they stipulate that physical means non-mental , such that all fundamental physical facts are fundamental facts pertaining to the non-mental. In this article, I will probe physicalism in the very much tangible framework of quantum mechanics. Although this theory, unlike “ideal physics” or some “final theory of non-mentality”, is (...) an incomplete theory of the world, I believe this analysis will be of value, if for nothing else, at least for bringing some taste of physical reality, as it were, back to the debate. First, I will introduce a broad characterization of the physicalist credo. In Sect. 2, I will provide a rather quick review of quantum mechanics and some of its current interpretations. In Sect. 3, the notion of quantum non-separability will be analyzed, which will facilitate a discussion of the wavefunction ontology in Sect. 4. In Sects. 5 and 6, I will explore competing views on the implications of this ontology. In Sect. 7, I will argue that the prior results, based on a thoroughly realist interpretation of quantum mechanics, support only a weak version of non-reductive physicalism. (shrink)
GRW Theory postulates a stochastic mechanism assuring that every so often the wavefunction of a quantum system is `hit', which leaves it in a localised state. How are we to interpret the probabilities built into this mechanism? GRW theory is a firmly realist proposal and it is therefore clear that these probabilities are objective probabilities (i.e. chances). A discussion of the major theories of chance leads us to the conclusion that GRW probabilities can be understood only as (...) either single case propensities or Humean objective chances. Although single case propensities have some intuitive appeal in the context of GRW theory, on balance it seems that Humean objective chances are preferable on conceptual grounds because single case propensities suffer from various well know problems such as unlimited frequency tolerance and lack of a rationalisation of the principal principle. (shrink)
What ontology does realism about the quantum state suggest? The main extant view in contemporary philosophy of physics is wave-function realism . We elaborate the sense in which wave-function realism does provide an ontological picture, and defend it from certain objections that have been raised against it. However, there are good reasons to be dissatisfied with wave-function realism, as we go on to elaborate. This motivates the development of an opposing picture: what we call (...) spacetime state realism , a view which takes the states associated to spacetime regions as fundamental. This approach enjoys a number of beneficial features, although, unlike wave-function realism, it involves non-separability at the level of fundamental ontology. We investigate the pros and cons of this non-separability, arguing that it is a quite acceptable feature, even one which proves fruitful in the context of relativistic covariance. A companion paper discusses the prospects for combining a spacetime-based ontology with separability, along lines suggested by Deutsch and Hayden. (shrink)
The Copenhagen interpretation, which informs the textbook presentation of quantum mechanics, depends fundamentally on the notion of ontological wave-particle duality and a viewpoint called “complementarity.” In this paper, Bohr's own interpretation is traced in detail and is shown to be fundamentally different from and even opposed to the Copenhagen interpretation in virtually all its particulars. In particular, Bohr's interpretation avoids the ad hoc postulate of wavefunction ‘collapse' that is central to the Copenhagen interpretation. The strengths and (...) weakness of both interpretations are summarized. ‡I thank Edward Mackinnon, Henry Folse, and Greg Anderson for valuable comments on the penultimate draft. The final responsibility for the paper rests with the author. †To contact the author, please write to: Bhaktivedanta Institute, 2334 Stuart Street, Berkeley, CA; e-mail: rgomatam@bvinst.edu. I have been unable to achieve a sharp formulation of Bohr's principle of complementarity despite much effort I have expended on it. (Einstein 1949, 674) While imagining that I understand the position of Einstein, as regards the EPR correlations, I have very little understanding of his principal opponent, Bohr. (Bell 1987, 155) Niels Bohr brain-washed a generation of physicists into believing that the problem had been solved fifty years ago. (Gell-Mann 1979, 29) Every sentence I say must be understood not as an affirmation, but as a question. (Niels Bohr, quoted in Jammer 1966, 175) Bohr's interpretation has never been fully clarified. It needs an interpretation itself, and only that will be its defense. (Weizsäcker 1971, 25). (shrink)
Schrödinger’s first proposal for the interpretation of quantum mechanics was based on a postulate relating the wavefunction on configuration space to charge density in physical space. Schrödinger apparently later thought that his proposal was empirically wrong. We argue here that this is not the case, at least for a very similar proposal with charge density replaced by mass density. We argue that when analyzed carefully, this theory is seen to be an empirically adequate many-worlds theory and not (...) an empirically inadequate theory describing a single world. Moreover, this formulation—Schrödinger’s first quantum theory—can be regarded as a formulation of the many-worlds view of quantum mechanics that is ontologically clearer than Everett’s. (shrink)
Relativistic quantum theories are equipped with a background Minkowski spacetime and non-relativistic quantum theories with a Galilean space-time. Traditional investigations have distinguished their distinct space-time structures and have examined ways in which relativistic theories become sufficiently like Galilean theories in a low velocity approximation or limit. A different way to look at their relationship is to see that both kinds of theories are special cases of a certain five-dimensional generalization involving no limiting procedures or approximations. When one compares them, striking (...) features emerge that bear on philosophical questions, including the ontological status of the wavefunction and time reversal invariance. (shrink)
Bohmian mechanics and the Ghirardi-Rimini-Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wavefunction, whereas the latter implements spontaneous collapses of the wavefunction by a nonlinear and stochastic modification of Schrödinger's equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about 'matter' moving in space, represented by either particle trajectories, fields on space-time, (...) or a discrete set of space-time points. The role of the wavefunction then is to govern the motion of the matter. (shrink)
Bohmian mechanics, which is also called the de Broglie-Bohm theory, the pilot-wave model, and the causal interpretation of quantum mechanics, is a version of quantum theory discovered by Louis de Broglie in 1927 and rediscovered by David Bohm in 1952. It is the simplest example of what is often called a hidden variables interpretation of quantum mechanics. In Bohmian mechanics a system of particles is described in part by its wavefunction, evolving, as usual, according to Schrödinger's (...) equation. However, the wavefunction provides only a partial description of the system. This description is completed by the specification of the actual positions of the particles. The latter evolve according to the.. (shrink)
We present a theory of discontinuous motion of particles in continuous space-time. We show that the simplest nonrelativistic evolution equation of such motion is just the Schroedinger equation in quantum mechanics. This strongly implies what quantum mechanics describes is discontinuous motion of particles. Considering the fact that space-time may be essentially discrete when considering gravity, we further present a theory of discontinuous motion of particles in discrete space-time. We show that its evolution will naturally result in the dynamical collapse process (...) of the wavefunction, and this collapse will bring about the appearance of continuous motion of objects in the macroscopic world. (shrink)
Bohmian mechanics and the Ghirardi–Rimini–Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wavefunction, whereas the latter implements spontaneous collapses of the wavefunction by a nonlinear and stochastic modification of Schrödinger's equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about matter moving in space, represented by either particle trajectories, fields on space-time, (...) or a discrete set of space-time points. The role of the wavefunction then is to govern the motion of the matter. Introduction Bohmian Mechanics Ghirardi, Rimini, and Weber 3.1 GRWm 3.2 GRWf 3.3 Empirical equivalence between GRWm and GRWf Primitive Ontology 4.1 Primitive ontology and physical equivalence 4.2 Primitive ontology and symmetry 4.3 Without primitive ontology 4.4 Primitive ontology and quantum state Differences between BM and GRW 5.1 Primitive ontology and quadratic functionals 5.2 Primitive ontology and equivariance A Plethora of Theories 6.1 Particles, fields, and flashes 6.2 Schrödinger wave functions and many-worlds The Flexible WaveFunction 7.1 GRWf without collapse 7.2 Bohmian mechanics with collapse 7.3 Empirical equivalence and equivariance What is a Quantum Theory without Observers? CiteULike Connotea Del.icio.us What's this? (shrink)
The renewed interest in the foundations of quantum statistical mechanics in recent years has led us to study John von Neumann’s 1929 article on the quantum ergodic theorem. We have found this almost forgotten article, which until now has been available only in German, to be a treasure chest, and to be much misunderstood. In it, von Neumann studied the long-time behavior of macroscopic quantum systems. While one of the two theorems announced in his title, the one he calls the (...) “quantum H-theorem,” is actually a much weaker statement than Boltzmann’s classical H-theorem, the other theorem, which he calls the “quantum ergodic theorem,” is a beautiful and very non-trivial result. It expresses a fact we call “normal typicality” and can be summarized as follows: For a “typical” finite family of commuting macroscopic observables, every initial wavefunction ψ0 from a micro-canonical energy shell so evolves that for most times t in the long run, the joint probability distribution of these observables obtained from ψ is close to.. (shrink)
We study the possible connection between self-consciousness and quantum process. It is shown that the self-consciousness function can help to measure the collapse time of wavefunction under some condition, while the usual physical device without self-consciousness can't. Furthermore, we show that the observer with self-consciousness can distinguish the definite state and the superposition of definite states under some stronger condition. This provides a practical physical method to differentiate man and machine, and will also help to find (...) the possible existence of self-consciousness in the animal kingdom. We finally give some further discussions about these new results. (shrink)
We discuss two recent attempts two solve Schrodinger's cat paradox. One is the modal interpretation developed by Kochen, Healey, Dieks, and van Fraassen. It allows for an observable which pertains to a system to possess a value even when the system is not in an eigenstate of that observable. The other is a recent theory of the collapse of the wavefunction due to Ghirardi, Rimini, and Weber. It posits a dynamics which has the effect of collapsing (...) the state of macroscopic systems. We argue that the modal interpretation cannot account for non-accurate measurements and that both accounts have the consequence that in ordinary measurement situations (including the situation of Schrodinger's cat) the observables that ends up well defined are not quite the ones that we want to be well defined. (shrink)
Onc of thc problems of quantnun cosmology follows from thc fact that thc Hamiltonian H of classical general relativity equals zero. Quantizing canonically in thc Schrodinger picture, thc Schrodinger equation for thc wavefunction *1* of thc universe is thcreforc thc so-called Whcelc:r—DeWitt..
The renewed interest in the foundations of quantum statistical mechanics in recent years has led us to study John von Neumann’s 1929 article on the quantum ergodic theorem. We have found this almost forgotten article, which until now has been available only in German, to be a treasure chest, and to be much misunderstood. In it, von Neumann studied the long-time behavior of macroscopic quantum systems. While one of the two theorems announced in his title, the one he calls the (...) “quantum H-theorem,” is actually a much weaker statement than Boltzmann’s classical H-theorem, the other theorem, which he calls the “quantum ergodic theorem,” is a beautiful and very non-trivial result. It expresses a fact we call “normal typicality” and can be summarized as follows: For a “typical” finite family of commuting macroscopic observables, every initial wavefunction ψ0 from a micro-canonical energy shell so evolves that for most times t in the long run, the joint probability distribution of these observables obtained from ψt is close to their micro-canonical distribution. (shrink)
The Ghirardi–Rimini–Weber (GRW) theory of spontaneous wavefunction collapse is known to provide a quantum theory without observers, in fact two different ones by using either the matter density ontology (GRWm) or the flash ontology (GRWf). Both theories are known to make predictions different from those of quantum mechanics, but the difference is so small that no decisive experiment can as yet be performed. While some testable deviations from quantum mechanics have long been known, we provide here something (...) that has until now been missing: a formalism that succinctly summarizes the empirical predictions of GRWm and GRWf. We call it the GRW formalism. Its structure is similar to that of the quantum formalism but involves different operators. In other words, we establish the validity of a general algorithm for directly computing the testable predictions of GRWm and GRWf. We further show that some well-defined quantities cannot be measured in a GRWm or GRWf world. (shrink)
I maintain that quantum mechanics is fundamentally about a system of N particles evolving in three-dimensional space, not the wavefunction evolving in 3N-dimensional space.
Faculty Of Philosophy, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands m.k.d.schouten{at}uvt.nl' + u + '@' + d + ''//--> This paper inquires into the nature of intertheoretic relations between psychology and neuroscience. This relationship has been characterized by some as one in which psychological explanations eventually will fall away as otiose, overthrown completely by neurobiological ones. Against this view it will be argued that it squares poorly with scientific practices and empirical developments in the cognitive neurosciences. We (...) analyse a case from research on visual perception, which suggests a much more subtle and complex interplay between psychology and neuroscience than a complete take-over of the former by the latter. In the case of vision, cross-theory influences between psychology and neuroscience go back and forth, resulting in refinement in both disciplines. We interpret this case study as showing that: (1) Mutual co-evolution of psychological and neurobiological theories, exemplifying persisting top-down influences from psychology, is a more empirically adequate way to describe psychoneural theory relations than a view on co-evolution, favoured by reductionists, which regards the cross-theory contributions from psychology as merely heuristically useful with no enduring influence on neurobiological theorizing; (2) In research on vision, discovering (or hypothesizing) the neural basis of functions vindicates psychological approaches, it does not eliminate them; (3) Current work on vision shows that many perceptual phenomena must be understood in terms of dynamical interactions between an observer and his/her environment. Therefore, we argue that internalist characterizations of the visual system must be supplemented with externalist accounts that address these reciprocal observer-environment interactions involved in vision. Such processes seem quite different from (internal) cellular and molecular ones, and as such seem to lie outside the scope of neuroscientific inquiry. We conclude that psychoneural reduction or elimination is implausible as a meta-theoretical prediction of theory choice in empirical work. Instead, this case study of vision shows that both psychology and neuroscience contribute to, and complement one another in the study of visual perception. Psychoneural reductionism 1.1 Introduction 1.2 New Wave Reductionism 1.3 NWR and psychology: three characteristics of psychoneural reductionism 1.4 NWR and the problem of mutual feedback 1.4.1 The ?Mere Heuristics? claim 1.4.2 The disappearance of psychology as an irrelevant historical accident 1.5 Summary: three claims of NWR on psychoneural reduction Vision: a case study 2.1 Introduction 2.1.1 Three opposing claims 2.1.2 Psychology and neuroscience of vision: the orthodoxy 2.2 Testing claim 1: vanishing heuristics or persisting influences? 2.2.1 From what and where to perception and action 2.2.2 Real co-evolution: more than vanishing heuristics 2. (shrink)
In the May 15, 1935 issue of Physical Review Albert Einstein co-authored a paper with his two postdoctoral research associates at the Institute for Advanced Study, Boris Podolsky and Nathan Rosen. The article was entitled “Can Quantum Mechanical Description of Physical Reality Be Considered Complete?” (Einstein et al. 1935). Generally referred to as “EPR”, this paper quickly became a centerpiece in the debate over the interpretation of the quantum theory, a debate that continues today. The paper features a striking case (...) where two quantum systems interact in such a way as to link both their spatial coordinates in a certain direction and also their linear momenta (in the same direction). As a result of this “entanglement”, determining either position or momentum for one system would fix (respectively) the position or the momentum of the other. EPR use this case to argue that one cannot maintain both an intuitive condition of local action and the completeness of the quantum description by means of the wavefunction. This entry describes the argument of that 1935 paper, considers several different versions and reactions, and explores the ongoing significance of the issues they raise. (shrink)
We discuss the content and significance of John von Neumann’s quantum ergodic theorem (QET) of 1929, a strong result arising from the mere mathematical structure of quantum mechanics. The QET is a precise formulation of what we call normal typicality, i.e., the statement that, for typical large systems, every initial wavefunction ψ0 from an energy shell is “normal”: it evolves in such a way that |ψt ψt| is, for most t, macroscopically equivalent to the micro-canonical density matrix. (...) The QET has been mostly forgotten after it was criticized as a dynamically vacuous statement in several papers in the 1950s. However, we point out that this criticism does not apply to the actual QET, a correct statement of which does not appear in these papers, but to a different (indeed weaker) statement. Furthermore, we formulate a stronger statement of normal typicality, based on the observation that the bound on the deviations from the average specified by von Neumann is unnecessarily coarse and a much tighter (and more relevant) bound actually follows from his proof. (shrink)
Bohmian mechanics is arguably the most naively obvious embedding imaginable of Schr¨ odinger’s equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wavefunction ψ its configuration (...) is typically random, with probability density ρ given by |ψ|2, the quantum equilibrium distribution. It also turns out that the entire quantum formalism, operators as observables and all the rest, naturally emerges in Bohmian mechanics from the analysis of “measurements.” This analysis reveals the status of operators as observables in the description of quantum phenomena, and facilitates a clear view of the range of applicability of the usual quantum mechanical formulas. (shrink)
The Copenhagen interpretation, which informs the textbook presentation of quantum mechanics, depends fundamentally on the notion of ontological wave-particle duality and a viewpoint called “complementarity”. In this paper, Bohr’s own interpretation is traced in detail and is shown to be fundamentally different from and even opposed to the Copenhagen interpretation in virtually all its particulars. In particular, Bohr’s interpretation avoids the ad hoc postulate of wavefunction ‘collapse’ that is central to the Copenhagen interpretation. The strengths and (...) weakness of both interpretations are summarized. (shrink)
In a recent paper, David Albert has suggested that no quantum theory can yield a description of the world unfolding in Minkowski spacetime. This conclusion is premature; a natural extension of Stein's notion of becoming in Minkowski spacetime to accommodate the demands of quantum nonseparability yields such an account, an account that is in accord with a proposal which was made by Aharonov and Albert but which is dismissed by Albert as a ‘mere trick’. The nature of such an account (...) is clarified by an extension to a relativistic quantum context of David Lewis' picture of objective chances evolving in time. 1 Introduction 2 Classical relativistic becoming 3 Relativistic quantum becoming, without collapse 4 Relativistic quantum becoming, with collapse 5 Objective chance, conditional probability, and definite properties 6 The nature of the wavefunction 7 Conclusion. (shrink)
Atheists have tacitly conceded the field to theists in the area of philosophical cosmology, specifically, in the enterprise of explaining why the universe exists. The theistic hypothesis is that the reason the universe exists lies in God’s creative choice, but atheists have not proposed any reason why the universe exists. I argue that quantum cosmology proposes such an atheistic reason, namely, that the universe exists because it has an unconditional probability of existing based on a functional law of nature. This (...) law of nature (“the wavefunction of the universe”) is inconsistent with theism and implies that God does not exist. I criticize the claims of Alston, Craig, Deltete and Guy, Oppy and Plantinga that theism is consistent with quantum cosmology. (shrink)
Quantum philosophy, a peculiar twentieth-century malady, is responsible for most of the conceptual muddle plaguing the foundations of quantum physics. When this philosophy is eschewed, one naturally arrives at Bohmian mechanics, which is what emerges from Schrodinger's equation for a nonrelativistic system of particles when we merely insist that 'particles' means particles. While distinctly non-Newtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wavefunction. The quantum formalism emerges when measurement (...) situations are analyzed according to this theory. When the quantum formalism is regarded as arising in this way, the paradoxes and perplexities so often associated with quantum theory simply evaporate.Bohr's ... approach to atomic problems ... is really remarkable. He is completely convinced that any understanding in the usual sense of the word is impossible. Therefore the conversation is almost immediately driven into philosophical questions, and soon you no longer know whether you really take the position he is attacking, or whether you really must attack the position he is defending. (shrink)
The paper points out that the modern formulation of Bohm’s quantum theory known as Bohmian mechanics is committed only to particles’ positions and a law of motion. We explain how this view can avoid the open questions that the traditional view faces according to which Bohm’s theory is committed to a wave-function that is a physical entity over and above the particles, although it is defined on configuration space instead of three-dimensional space. We then enquire into the status (...) of the law of motion, elaborating on how the main philosophical options to ground a law of motion, namely Humeanism and dispositionalism, can be applied to Bohmian mechanics. In conclusion, we sketch out how these options apply to primitive ontology approaches to quantum mechanics in general. (shrink)
In a recent paper [1], O. F. de Alcantara Bonfim, J. Florencio, and F. C. S´ a Barreto claim to have found numerical evidence of chaos in the motion of a Bohmian quantum particle in a double square-well potential, for a wavefunction that is a superposition of five energy eigenstates. But according to the result proven here, chaos for this motion is impossible. We prove in fact that for a particle on the line in a superposition of (...) n + 1 energy eigenstates, the Bohm motion x(t) is always quasiperiodic, with (at most) n frequencies. This means that there is a function F (y1, . . . , yn) of period 2π in each of its variables and n frequencies ω1, . . . , ωn such that x(t) = F (ω1t, . . . , ωnt). The Bohm motion for a quantum particle of mass m with wavefunction ψ = ψ(x, t), a solution to Schrödinger’s equation, is defined by.. (shrink)
Features of consciousness difficult to understand in terms of conventional neuroscience have evoked application of quantum theory, which describes the fundamental behavior of matter and energy. In this paper we propose that aspects of quantum theory (e.g. quantum coherence) and of a newly proposed physical phenomenon of quantum wavefunction "self-collapse"(objective reduction: OR -Penrose, 1994) are essential for consciousness, and occur in cytoskeletal microtubules and other structures within each of the brain's neurons. The particular characteristics of microtubules suitable (...) for quantum effects include their crystal-like lattice structure, hollow inner core, organization of cell function and capacity for information processing. We envisage that conformational states of microtubule subunits (tubulins) are coupled to internal quantum events, and cooperatively interact (compute) with other tubulins. We further assume that macroscopic coherent superposition of quantum-coupled tubulin conformational states occurs throughout significant brain volumes and provides the global binding essential to consciousness. We equate the emergence of the microtubule quantum coherence with pre-conscious processing which grows (for up to 500 milliseconds) until the mass-energy difference among the separated states of tubulins reaches a threshold related to quantum gravity. According to the arguments for OR put forth in Penrose (1994), superpositioned states each have their own space-time geometries. When the degree of coherent massenergy difference leads to sufficient separation of space-time geometry, the system must choose and decay (reduce, collapse) to a single universe state. In this way, a transient superposition of slightly differing space-time geometries persists until an abrupt quantum classical reduction occurs. Unlike the random, "subjective reduction"(SR, or R) of standard quantum theory caused by observation or environmental entanglement, the OR we propose in microtubules is a self-collapse and it results in particular patterns of microtubule-tubulin conformational states that regulate neuronal activities including synaptic functions. Possibilities and probabilities for post-reduction tubulin states are influenced by factors including attachments of microtubule-associated proteins (MAPs) acting as "nodes"which tune and "orchestrate"the quantum oscillations.. (shrink)
The question of how to interpret spontaneous collapse theories of quantum mechanics is an open one. One issue involves what link one should use to go from wavefunction talk to talk of ordinary macroscopic objects. Another issue involves whether that link should be taken ontologically seriously. In this paper, I ague that the link should be taken ontologically seriously; I argue against an ontology consisting solely of the wavefunction. I then consider three possible links: (...) the fuzzy link, the accessible mass density link, and the mass density simpliciter link. I show that the first two links have serious anomalies which render them unacceptable. I show that the mass density simpliciter link, in contrast, is viable. (shrink)
The basic purpose of this essay, the first of an intended pair, is to interpret standard von Neumann quantum theory in a framework of iterated measure algebraic truth for mathematical (and thus mathematical-physical) assertions — a framework, that is, in which the truth-values for such assertions are elements of iterated boolean measure-algebras (cf. Sections 2.2.9, 5.2.1–5.2.6 and 5.3 below).The essay itself employs constructions of Takeuti's boolean-valued analysis (whose origins lay in work of Scott, Solovay, Krauss and others) to provide a (...) metamathematical interpretation of ideas sometimes considered disparate, heuristic, or simply ill-defined: the collapse of the wavefunction, for example; Everett's many worlds'-construal of quantum measurement; and a natural product space of contextual (nonlocal) hidden variables. (shrink)
GRW models of the physical world are criticized in the literature for involving wavefunction "tails" that allegedly create fatal interpretive problems and even compromise standard arithmetic. I find such objections both unfair and misguided. But not all is well with the GRW approach. One complaint I articulate in this paper does not have to do with tails as such but with the specific way in which past physical structures linger forever in the total GRW wave (...) class='Hi'>function. By pushing the total proposal towards either the "Many Worlds" approach or the Bohmian approach, this feature diminishes extant GRW claims to preferability. I suggest, however, that the problem here is just an artifact of the particular and ultimately optional genre of collapse mechanism chosen by GRW. (shrink)
In his long 1957 paper, “The Theory of the Universal WaveFunction”, Hugh Everett III made some significant preliminary steps towards the application and generalization of Shannon’s information theory to quantum mechanics. In the course of doing so, he conjectured that, for a given wavefunction on a compound space, the Schmidt decomposition maximises the correlation between subsystem bases. This is proved here.
For time-independent fields the Aharonov-Bohm effect has been obtained by idealizing the coordinate space as multiply-connected and using representations of its fundamental homotopy group to provide information on what is physically identified as the magnetic flux. With a time-dependent field, multiple-connectedness introduces the same degree of ambiguity; by taking into account electromagnetic fields induced by the time dependence, full physical behavior is again recovered once a representation is selected. The selection depends on a single arbitrary time (hence the so-called holonomies (...) are not unique), although no physical effects depend on the value of that particular time. These features can also be phrased in terms of the selection of self-adjoint extensions, thereby involving yet another question that has come up in this context, namely, boundary conditions for the wavefunction. (shrink)
governed by Newtonian laws. In standard quantum mechanics only the wavefunction or the results of measurements exist, and to answer the question of how the classical world can be part of the quantum world is a rather formidable task. However, this is not the case for Bohmian mechanics, which, like classical mechanics, is a theory about real objects. In Bohmian terms, the problem of the classical limit becomes very simple: when do the Bohmian trajectories look Newtonian?
We argue that genuine biological autonomy, or described at human level as free will, requires taking into account quantum vacuum processes in the context of biological teleology. One faces at least three basic problems of genuine biological autonomy: (1) if biological autonomy is not physical, where does it come from? (2) Is there a room for biological causes? And (3) how to obtain a workable model of biological teleology? It is shown here that the solution of all these three problems (...) is related to the quantum vacuum. We present a short review of how this basic aspect of the fundamentals of quantum theory, although it had not been addressed for nearly 100 years, actually it was suggested by Bohr, Heisenberg, and others. Realizing that the quantum mechanical measurement problem associated with the “collapse” of the wavefunction is related, in the Copenhagen Interpretation of quantum mechanics, to a process between self-consciousness and the external physical environment, we are extending the issue for an explanation of the different processes occurring between living organisms and their internal environment. Definitions of genuine biological autonomy, biological aim, and biological spontaneity are presented. We propose to improve the popular two-stage model of decisions with a biological model suitable to obtain a deeper look at the nature of the mind-body problem. In the newly emerging picture biological autonomy emerges as a new, fundamental and inevitable element of the scientific worldview. (shrink)
Classical physics is about real objects, like apples falling from trees, whose motion is governed by Newtonian laws. In standard quantum mechanics only the wavefunction or the results of measurements exist, and to answer the question of how the classical world can be part of the quantum world is a rather formidable task. However, this is not the case for Bohmian mechanics, which, like classical mechanics, is a theory about real objects. In Bohmian terms, the problem of (...) the classical limit becomes very simple: when do the Bohmian trajectories look Newtonian? (shrink)
