Position measurement-induced collapse states are shown to provide a unified quantum description of diffraction of particles passing through a single slit. These states, which we here call ‘quantum location states’, are represented by the conventional rectangular wave function at the initial time of position measurement. We expand this state in terms of the position eigenstates, which in turn can be represented as a linear combination of energy eigenfunctions of the problem, using the closure property. The time-evolution of (...) the location states in the case of free particles is shown to have position probability density patterns closely resembling diffraction patterns in the Fresnel region for small times and the same in Fraunhofer region for large times. Using the quantum trajectory representations in the de Broglie–Bohm, modified de Broglie–Bohm and Floyd–Faraggi–Matone formalisms, we show that Fresnel and Fraunhofer diffractions can be described using a single expression. We also discuss how to obtain the probability density of location states for the case of particles moving in a general potential, detected at some arbitrary point. In the case of the harmonic oscillator potential, we find that they have oscillatory properties similar to that of coherent states. (shrink)

In this article, I offer the figure of the snake-bridge as (a) the coiled central metaphor in Gloria Anzaldúa’s masterpiece, Borderlands/La Frontera, (b) the interpretive bridge connecting the early (This Bridge Called My Back) middle (Borderlands) and late (Light in the Dark) periods of her oeuvre, and (c) an alternate unifying metaphor to mestizaje. My first section offers a close reading of Borderlands, locating snake-bridge in the east-west snake of the Rio Grande that queer Chicana borderlanders cross north and (...) south like snakes, while wrestling earthward with snake demons and skyward with snake goddesses. And my second section autopsies the dismembered snake-bridge in Light in the Dark, calling for a healing thereof in pursuit of a coalitional social justice politics that preserves the strengths of mestizaje without its dangers. (shrink)

Part IIb presents some of the most important theorems for stable equilibrium states that can be deduced from the four postulates of the unified theory presented in Part I. It is shown for the first time that the canonical and grand canonical distributions are the only distributions that are stable. Moreover, it is shown that reversible adiabatic processes exist which cannot be described by the dynamical equation of quantum mechanics. A number of conditions are discussed that must be (...) satisfied by the general equation of motion which is yet to be discovered. (shrink)

Part II of this three-part paper presents some of the most important theorems that can be deduced from the four postulates of the unified theory discussed in Part I. In Part IIa, it is shown that the maximum energy that can be extracted adiabatically from any system in any state is solely a function of the density operator $\hat \rho$ associated with the state. Moreover, it is shown that for any state of a system, nonequilibrium, equilibrium or stable equilibrium, (...) a unique propertyS exists which is proportional to the total energy of the system minus the maximum energy that can be extracted adiabatically from the system in combination with a reservoir. For statistically independent systems, propertyS is extensive, it is invariant during all reversible processes, and it increases during all irreversible processes. (shrink)

This part of the paper concludes the presentation of the unified theory. It is shown that the theory requires the existence of, and applies only to, irreducible quantal dispersions associated with pure or mixed states. Two experimental procedures are given for the operational verification of such dispersions. Because the existence of irreducible dispersions associated with mixed states is required by Postulate 4 of the theory, and because Postulate 4 expresses the basic implications of the second law of classical thermodynamics, (...) it is concluded that the second law is a manifestation of phenomena characteristic of irreducible quantal dispersions associated with the elementary constituents of matter. (shrink)

Although a few new results are presented, this is mainly a review article on the relationship between finite-dimensional quantum mechanics and finite groups. The main motivation for this discussion is the hidden subgroup problem of quantum computation theory. A unifying role is played by a mathematical structure that we call a Hilbert *-algebra. After reviewing material on unitary representations of finite groups we discuss a generalized quantum Fourier transform. We close with a presentation concerning position-momentum measurements (...) in this framework. (shrink)

A unified axiomatic theory that embraces both mechanics and thermodynamics is presented in three parts. It is based on four postulates; three are taken from quantum mechanics, and the fourth is the new disclosure of the existence of quantum states that are stable (Part I). For nonequilibrium and equilibrium states, the theory provides general original results, such as the relation between irreducible density operators and the maximum work that can be extracted adiabatically (Part IIa). For stable equilibrium (...) states, it shows for the first time that the canonical and grand canonical distributions are the only stable distributions (Part IIb). The theory discloses the incompleteness of the equation of motion of quantum mechanics not only for irreversible processes but, more significantly, for reversible processes (Part IIb). It establishes the operational meaning of an irreducible density operator and irreducible dispersions associated with any state, and reveals the relationship between such dispersions and the second law (Part III). (shrink)

Piercing incisively and deeply into the nature of the overlapping of the material andmental realms. Aage Petersen uncovers the reciprocal relations between quantum physics and theconcepts of metaphysics and epistemology, assessing the extent to which each has influenced theother. The author is eminently qualified to undertake this important work, which grew out of hisclose contact with Neils Bohr and his Copenhagen school during the years 1952-1962.Although themathematical formalism of quantum physics has long since been established, the question of (...) itsphysical interpretation is not yet closed, and the question of its philosophical interpretationremains in a formative state. The most widely accepted physical interpretation of the quantalformalism emerged from discussions between Bohr and Heisenberg in the winter of 1926-1927. ThisCopenhagen Interpretation centers around the relations of indeterminacy around the relations ofindeterminacy and the concept of complementarity, and was refined but not radically altered in theyears following, especially during the famous debate with Einstein on the completeness possible inthe description of events. The philosophical interpretation has proceeded along two principal lines:Bohr's emphasis on complementarity as a unifying concept, and Heisenberg's exploration of therelationship of quantum physics to the traditional categories of philosophy.To Bohr's mind, thecentral feature of human knowledge is the distinction between subject and object. The indeterminacyof the placing of the partition between instrument and system, which played so large a part inquantal description was, Bohr believed, an expression of the general relation between the knower andthe knowable. He thus sought to find relationships of complementarity in areas beyond quantumphysics.Quantum physics and traditional philosophy certainly relate enough to interact--even thoughthe effects of interaction may produce uncertain results. Heisenberg's view also emphasizes thatscience describes, not nature itself, but the interplay between nature and man, nature as affectedby man's method of questioning, thus denying the school of philosophical thought that began withDescartes' sharp separation of the World and the I.The author's investigation leads him as well tobelieve that complementarity is deeply linked to the basis of philosophy, but that the details ofthe relationship are so obscure that some other feature of quantum physics that makes amore directconnection with philosophy should be sought. He is led to choose the idea of correspondence as suchfeature. This idea played a key role in the development of the matrix version of the formalism andof the Copenhagen interpretation.Mathematically, the idea of correspondence was seen to imply thatquantal formalisms should emerge as generalizations of classical entities, that matrix mechanics wasa generalization of classical Hamiltonian mechanics. It is in this possibility of treating thetraditional categories of philosophy as limits of a more general scheme, or as analogies of a deeperorder, that the fruitfulness of the correspondence idea lies. (shrink)

Holography is a fruitful concept in modern physics. However, there is no generally accepted definition of the term, and its significance, especially as a guiding principle in quantum gravity, is rather uncertain. The present paper critically evaluates variants of the holographic principle from two perspectives: their relevance in contemporary approaches to quantum gravity and in closely related areas; their historical forerunners in the early twentieth century and the role played by past and present concepts of holography in attempts (...) to unify physics. By combining these two perspectives a certain depth of focus is gained which allows us to draw some tentative conclusions about what might be reasonable aspirations and prospects for holography in quantum gravity. By the same token, we will have a brief and critical look at wider philosophical interpretations of the term. (shrink)

This paper presents a unified theory of reality, which integrates two interdependent frameworks: Cellular Primary Consciousness Theory (CPCT) and Open and Closed Systems Theory (OCST). Although CPCT and OCST can each stand as individual theories, they are, in this work, combined to form a cohesive explanation of both the mechanics and purpose of the universe. CPCT posits that consciousness is a fundamental aspect of all life, extending to even the simplest cells, rather than being an emergent property exclusive to (...) complex neural systems. Drawing upon evidence from quantum mechanics, cell biology, and systems theory, CPCT challenges traditional views on the origins of consciousness by suggesting that awareness is a universal property present from the cellular level. OCST, which forms the second component of this unified theory, examines the nature of the universe as a closed system subject to the laws of entropy. This theory explores how the universe is moving toward maximum entropy, where meaning and contrasts dissolve. However, beyond this closed system lies the realm of an open system—a domain of infinite potential that transcends the dualities and limitations of the physical universe. This open system offers a philosophical explanation for existence and the possibility of eternal meaning. Together, these two theories provide a novel and cohesive framework that addresses both the mechanics of consciousness and the ultimate purpose of the universe. The integration of CPCT and OCST bridges scientific evidence from quantum biology and systems theory with philosophical explorations of existence, presenting a comprehensive vision of reality as both a closed physical system and an open metaphysical one. This unified theory encourages a reexamination of our place in the cosmos, suggesting that beyond the observable universe lies an infinite realm of potential where consciousness and meaning endure. (shrink)

We revise the mathematical implementation of the Dirac formulation of quantum mechanics, presenting a rigorous framework that unifies most of versions of this implementation.

We review the notion of complementarity of observables in quantum mechanics, as formulated and studied by Paul Busch and his colleagues over the years. In addition, we provide further clarification on the operational meaning of the concept, and present several characterisations of complementarity—some of which new—in a unified manner, as a consequence of a basic factorisation lemma for quantum effects. We work out several applications, including the canonical cases of position–momentum, position–energy, number–phase, as well as periodic observables (...) relevant to spatial interferometry. We close the paper with some considerations of complementarity in a noisy setting, focusing especially on the case of convolutions of position and momentum, which was a recurring topic in Paul’s work on operational formulation of quantum measurements and central to his philosophy of unsharp reality. (shrink)

In my 2013 article, “A New Theory of Free Will”, I argued that several serious hypotheses in philosophy and modern physics jointly entail that our reality is structurally identical to a peer-to-peer (P2P) networked computer simulation. The present paper outlines how quantum phenomena emerge naturally from the computational structure of a P2P simulation. §1 explains the P2P Hypothesis. §2 then sketches how the structure of any P2P simulation realizes quantum superposition and wave-function collapse (§2.1.), quantum indeterminacy (§2.2.), (...) wave-particle duality (§2.3.), and quantum entanglement (§2.4.). Finally, §3 argues that although this is by no means a philosophical proof that our reality is a P2P simulation, it provides ample reasons to investigate the hypothesis further using the methods of computer science, physics, philosophy, and mathematics. (shrink)

Sophists’ apologia. -/- Sophists were the first paid teachers ever. These ancient Greek enlighteners taught wisdom. Protagoras, Antiphon, Prodicus, Hippias, Lykophron are most famous ones. Sophists views and concerns made a unified encyclopedic system aimed at teaching common wisdom, virtue, management and public speaking. Of the contemporary “enlighters”, Deil Carnegy’s educational work seems to be the most similar to sophism. Sophists were the first intellectuals – their trade was to sell knowledge. They introduced a new type of teacher-student relationship (...) – the mutually beneficial communication on equal terms. They taught pupils how to think independently and how to persuade others, which was inseparably connected with the rise of democracy in the most advanced Greek polices. Sophists were the first to proclaim that all people are naturally equal. They put forward the idea of natural rights and social contract, working out the fundamentals of the present-day law. In addition, they developed the basics of philology, psychology, logic, and gave a scientific explanation to the origins of religions. They embodied definite positive ideals of their epoch. Sophistry flourished in the second half of the Vth through he first third of the IVth centuries B. C. The period coincides with the heyday of the entire Greek history – the so called Greek Miracle epoch. Sophists expressed some present-day concepts of Ancient Greek ideology and mentality, characteristic of its Golden Age times. The Ancient Athens of the times of Periclus were similar to the Florence of Renaissance as to the type of social structure. That is why (?) the art of eloquence (public speaking) was highly respected in Florence. The two cities had a lot of features of the present-day capitalist society, which was due to their role as the main centres of industry of their “worlds-economies”. During the subsequent Hellenic period, the Old Order was restored, based on the feudal rent recipients’ rule. The degradation of society resulted in the decline of sophistry. Sophistry represents the highest point in the evolution of Greek philosophy. It is also the most prominent school as to the novelty of its ideas. That was owing to the common propensity for innovation typical of Periclus’ Golden Age, which in its turn resulted from the establishment of the individualistic and rationalistic thinking similar to present-day mentality. Among other aspects, close attention was paid to ethnic issues; some humanistic ideas such as Master and Servant ethics and Enlightment as the primary condition of man’s freedom, received scientific grounding. The genre of philosophical dialogue was developed, as well as the rationalistic scientific gnoceology, aimed at consistently opposing any religion. Dialectics, the most outstanding achievement of the Antiquity, was also worked out by the sophists. Zeno of Helleas was one of the sophists. Democrites’ ideas were, too, quite close to dialectics. Socrates’ contemporaries regarded him ironically, as shown, for example, in the Aristophanes’ comedy “Clouds”. Nevertheless, this scholar can still be referred to as a sophist, although of somewhat weird personality. Socrates’ popularity, which came later, should be attributed to the fact that he was the first philosopher ever to have been sentenced and executed by law, rather than to any valuable scientific contributions. Sophistry as such, rather than Socrates, marks the line between pre-Socratic and post- Socratic schools. Plato, with the exception of his latest works, is considered to belong to the same philosophical school. Specifically, there are valid reasons to believe that he was paid fees by his disciples. In Plato’s Dialogues, all points of view will be proven and then disproved, so that an integral philosophical system is hard to observe. Plato’s “Idealism” is but one of the many possible theories. His ideal philosophy is a high-minded argument of wise men. As late as towards the end of his life, Plato betrayed the ideals of sophistry, turning into the world’s first proponent of totalitarianism. Sophistry is Greek classical literature. Later on, philosophy, as well as the entire Greek civilization, started to fall into decline. Over 500 subsequent years, Hellenistic-Roman scholars never came up with anything novel. The entire process of antique philosophical evolution can be subdivided into the following six stages: Phoenician (IX–VIIth centuries B. C.), archaic (VIth – the first half of IVth century B. C., classic (the epoch of sophistry: the second half of the Vth through the first decades of the IIIrd centuries B. C.), late antique (middle of the IIIrd – first decades of the VI th centuries B.C.) The fact that early in the VIth century B. C. sophistry was rejected in Athens, has a lot to do with the consequences of their defeat in Peloponnesian war, a social catastrophe. Ever since, the prevalent part of the criticism of sophistry is a criticism of sophists’ immoral ways of life and personalities, rather than the essentials of their philosophy. For instance, Aristotle’s criticism primarily concerns their pragmatism and tendency to make a profit out of teaching. However, Aristotle himself taught his disciples along similar lines, showing them how to “be able to prove both opposites”. It was Aristotle who summed up sophists’ century-long elaborations. The traditional modern interpretation of sophists as shown in Plato’s dialogues appears to be groundless. The truth of the matter is that Plato regards sophists as more serious philosophers than Socrates was. It becomes especially clear in the dialogue titled “Protagoras”, which shows the latter as gaining an undoubted victory over Socrates. Generally speaking, Plato’s works never regard sophists as weak or worthless opponents. A common opinion as to the essence of sophists’, in particular, Protagoras’s philosophy, has hitherto not been worked out. Many researchers renounce the very existence of any specific philosophical position in sophistry. The term “relativism” itself now has a bad name. However, it should be borne in mind that Protagoras doctrine emerged as a result of an attempt to get out of the ontological dead-end to which the entire Greek natural philosophy had come. To this purpose, he employed Anaxagoras’s idea about everything comprising everything, whereupon he built his physical-ontological theory, and Zeno of Helleas’s concept that all objects are such and different at the same time in the same respect. According to Protagoras’s philosophy, every object does not only seem, but is different from every other object, including human beings. Therefore, every person is his or her own measure of all other entities. The objective reality is the Ego’s relations with the outer world. Every object’s essence is defined through its interaction with ourselves. Nothing remains stagnant – every existence already contains non-existence, and vice-versa. However, the relativity of being is not to be regarded as absolute. That means, that relatively stable and therefore relatively cognizable entities do exist, among them the words we say. Doubt is not considered absolute by relativists either, which differentiates them from skeptics and agnostics. They dare to believe. Uncertainty is Godly – here, Protagoras becomes very close to the concept of apathetic theology. Gorgius shared Protagoras’s views and tried to prove them applying the same method as Zeno applied when upholding Parmenidis’s philosophy. He argued that if one accepts the opposite point of view and agrees that nothing can exist and not exist at the same time, one is bound to come to an the absurd conclusion that nothing is cognizable and nothing exists. To prove that there is a universal contradiction within the Existence itself, Protagoras and his followers in their turn put forward a number of special logical arguments, called rules of contraries, or sophisms. The most well-known of them is the Euathle’s sophism, which proves that an object can be such and different at the same time in the same respect. Generally speaking, all relationships of any entity are extraneous. The idea that all entities, including concepts, exist and do not exist at the same time, was also accepted by Plato. It should be stressed, that Plato’s philosophy as a whole is relativists’ greatest achievement. In his dispute against relativism, Aristotle put forward the main concepts of his ontology: the existence falls into the existence in possibility and the existence in reality, or substance and accidence – the ever changing “sublunary” world and the stable world of divine heavenly bodies. This division made his system self-contradictory to the point of absurd. Aristotle quite realized, that the direct disproof of relativism is hardly possible, which fact makes his criticism a mere tautology. It is very indicative in this respect that materialists, idealists and even skeptical agnostics applied the same arguments do disprove relativism. That demonstrates that the inner contradiction between any forms of “absolutism” and relativism is the most fundamental philosophical problem. Relativist ideas were repeatedly renewed throughout history, provided the social conditions were favourable. In variations, the concepts were advanced by Tzuan Tsi and ancient Chinese sophists, apostle Paul, Nicolas of Cusa, Galileo, Rene Descartes, G. Berkley, D. Hume, Ch. S. Pierce, E. Mach, A. Bogdanov, F. de Saussure, N. Bore, P. Feuerabend, U. Quain and others. However, no consistent relativist ontological system was developed after Protagoras. Meanwhile, a valid relativist theory could provide a clue to a fuller and more adequate general physical concept of the world, and to a deeper understanding of quantum mechanics. -/- Relativism as an ontological system of beliefs. -/- The relativist principle of relativity of all that exists is fundamental for the entire system of philosophy. Absolutely everything exists, but, at the same time, no existence is absolute. Anything is possible, but those entities only exist for us with which we interact this way or another, i. e., reality is interaction, “I interact – hence, I exist”. However, an overly close relationship between entities leads to non-existence – in other words, there is a certain existential optimum. For all of us, information, or perceptible heterogeneities, is real. Each of us is the center of a definite system of interactions with the world. If God is an endless Possibility, then the World is but the man’s dialogue with God. However, the ties that bind us with the world are of some definite kind, which predetermines our reality. The principle of relativity constrains itself, as any relativity is relative. On the one hand, that calls forth the Evil – caused by our own weakness. On the other hand, it makes our world relatively stable and cognizable. Generally speaking, the world is what we are. Everybody has an own Universe, but since people are fairly similar, our universes can be regarded as one Universe with common laws and regulations. It is possible for us to change the degree of objects’ existence in relation to ourselves and one another. It is equally important, though, to remain ourselves (keep following our “warrior’s path”). Since everything exists and no existence is absolute, the process of cognition should involve a criticism of everything but never a complete rebuttal of anything. The criterion of verity for any theory then is in its capacity to build itself upon a bigger number of diverse statements than in any other theory. Theoretically, all philosophies should ideally be complementary. The question of what in fact happened is meaningless unless we specify the “we”, the “where” and the “when”. The past can only exist as part of the present. When we change, our past undergoes corresponding qualitative objective changes, all of which are irreversible. The contemporary physics regards all objects of the Universe as existing for one another, which results in absurd conclusions. In fact, only what we interact with, exists. The so called “speed of light in vacuum” c is the maximum speed of direct interaction and direct exchange of signals. Specifically, at the oncoming speed c with a significant blue parallax the gamma-quantum is unable to interact with the matter. When this speed is reached, the gravitational mass of objects in relation to one another becomes equal to zero (imaginary), whereas their inertial mass equals infinity. Further acceleration will bring us into an entirely different Universe. That means that the Universe is an open system, which fact destroys all present-day cosmological models. Anything is possible in this world. Our reality is magic. Every bit of space contains a potentially limitless number of bits of other, however virtual, universes, as well as an infinite number of particles, which are still virtual for us (as postulated by quantum mechanics). In other words, there exists an infinity of different realities. With all the above in mind, the different levels of entities’ existence, in particular, of Life and Reason, should be taken into consideration. For example, to which extent a live system exists in relation to the inanimate forms of being is very indefinite, as what life is has to be determined by living creatures. An even greater compass of levels of existence can be brought about through interaction – that is the core idea of Godel’s theorem. As a result, the range of forms of existence tends towards infinity – the evolution of matter through super-intelligence will bring us up to God’s heights. A more generalized mathematical model of the physical world, including a universal operator of the co-existence of objects, can be developed based on the above considerations. The bonds between objects become weaker owing to 1) a high speed, 2) acceleration, 3) rotation, 4) strong gravity, 5) strong fields of other kinds, 6) the difference of levels of existence , 7) phase shifts. Yet, there always is an existential optimum. Such mathematical model is to operate certain non-transitive algebras. Relativist ontology assumes that the notion of “temperature” is relative, thus making it possible to ignore the Second Law of Thermodynamics. In its turn, that will allow for phase shifts. A perpetual motion machine of the second type will become a reality. Rotation could presumably be used to increase inertial and decrease gravitational mass, slowing down the time. An experimental research could shed light on the mentioned effects. (shrink)

Unified quantum logic based on unified operations of implication is formulated as an axiomatic calculus. Soundness and completeness are demonstrated using standard algebraic techniques. An embedding of quantum logic into a new modal system is carried out and discussed.

En este artículo, se atienden ciertas facetas conceptuales y experimentales del efecto Hall cuántico. Se argumenta que el mismo ofrece variados matices para la reflexión filosófica, desde la generación de entidades teóricas hasta la epistemología de la experimentación. La exposición pretende mantener cierta sensibilidad por la dinámica histórica en torno del tema, como así también por las implicaciones metrológicas de ámbitos cuánticos específicos. Dada la enorme producción científica sobre el tema, se hace un recorte a los fines de rescatar (...) algunos perfiles significativos de los fenómenos asociados con ese efecto. In this paper we address several conceptual and historical aspects of the quantum Hall effect. We argue that this effect offers a variety of perspectives for philosophical reflection, from the generation of theoretical entities to the epistemology of experimentation. The exposition attempts to maintain a certain sensitivity to the historical dynamics around the issue, considering at the same time its metrological implications for specific quantum areas. Given the vast scientific literature on the subject, a cut is made in order to rescue some meaningful profiles of the phenomena associated with this effect. (shrink)

Why did Bernhard Riemann, arguably the most original mathematician of his generation, spend the last year of life investigating the mechanism of hearing? Fighting tuberculosis and the hostility of eminent scientists such as Hermann Helmholtz, he appeared to forsake mathematics to prosecute a case close to his heart. Only sketchy pages from his last paper remain, but here we assemble some significant clues and triangulate from them to build a broad picture of what he might have been driving at. (...) Our interpretation is that Riemann was a committed idealist and from this philosophical standpoint saw that the scientific enterprise was lame without the “poetry of hypothesis”. He believed that human thought was fundamentally the dynamics of “mind-masses” and that the human mind interpenetrated, and became part of, the microscopic physical domain of the cochlea. Therefore, a full description of hearing must necessarily include the perceptual dimensions of what he saw as a single manifold. The manifold contains all the psychophysical aspects of hearing, including the logarithmic transformations that arise from Fechner’s law, faithfully preserving all the subtle perceptual qualities of sound. For Riemann, hearing was a unitary physical and mental event, and parallels with modern ideas about consciousness and quantum biology are made. A unifying quantum mechanical model for an atom of consciousness—drawing on Riemann’s mind-masses and the similar “psychons” proposed by Eccles—is put forward. (shrink)

It was in the closing year of the nineteenth century that Paul Tannery organized at an international historical congress the first international meeting devoted to the history of science. If antiquity would make a scholarly subject respectable, scholarship in the history of science must be beyond reproach; still earlier than Tannery and his colleagues in many European countries were the German historian of chemistry Kopp, and William Whewell, Master of Trinity; the eighteenth century had produced substantial works like those on (...) mathematics and astronomy of Montucla and Delambre; Isaac Vossius and others virtually take these studies back to the Renaissance and Polydore Vergil. Just as in our day such classical scholars as Heiberg, Bailey, Housman, Drachman or Peck have chosen scientific texts as their subjects, so in the past, too, learning and science have met on this common ground. Few creative mathematicians of the seventeenth century thought that attention to the writings of Euclid or Archimedes was a waste of time. (shrink)

With reference to recently proposed theoretical models accounting for reduction in terms of a unified dynamics governing all physical processes, we analyze the problem of working out a worldview accommodating our knowledge about natural phenomena. We stress the relevant conceptual differences between the considered models and standard quantum mechanics. In spite of the fact that both theories describe systems within a genuine Hilbert space framework, the peculiar features of the spontaneous reduction models limit drastically the states which are (...) dynamically stable. This fact by itself allows one to work out an interpretation of the formalism which makes it possible to give a satisfactory description of the world in terms of the values taken by an appropriately defined mass density function in ordinary configuration space. A topology based on this function and which is radically different from the one characterizing the Hilbert space is introduced, and in terms of it the idea of similarity of macroscopic situations is precisely defined. Finally, the formalism and the interpretation are shown to yield a natural criterion for establishing the psychophysical parallelism. The conclusion is that, within the considered theories and at the nonrelativistic level, one can satisfy all sensible requirements for a completely satisfactory macro-objective description of reality. (shrink)

There are, by now, many rival, sophisticated philosophical accounts of causation that qualify as ‘metaphysically reductive’. This is a good thing: these collective efforts have vastly improved our understanding of causation over the last 30 years or so. They also put us in an excellent position to reflect on some central methodological questions: What exactly is the point of offering a metaphysical reduction of causation? What philosophical scruples ought to guide the pursuit of such a reduction? Finally, how should answers (...) to these latter questions affect one’s assessment of the main contemporary approaches? That’s what we investigate in this essay. Section 1 lays out our presuppositions. Section 2 reviews a sample of philosophical accounts. Then comes the main event: Section 3 looks in detail at the foregoing methodological questions, closing with a reconsideration of our sample accounts, in light of what we’ve found. (shrink)

In-principle restrictions on the amount of information that can be gathered about a system have been proposed as a foundational principle in several recent reconstructions of the formalism of quantum mechanics. However, it seems unclear precisely why one should be thus restricted. We investigate the notion of paradoxical self-reference as a possible origin of such epistemic horizons by means of a fixed-point theorem in Cartesian closed categories due to Lawvere that illuminates and unifies the different perspectives on self-reference.

August 16, 1997 David Lewis2 has long defended an account of scientific law acceptable even to an empiricist with significant metaphysical scruples. On this account, the laws are defined to be the consequences of the best system for axiomitizing all occurrent fact. Here "best system" means the set of sentences which yields the best combination of strength of descriptive content 3 with simplicity of exposition. And occurrent facts, the facts to be systematized, are roughly the particular facts about a localized (...) space-time region that are non-modal, non-dispositional, and non-causal. Scientists providing or attempting to provide laws are plausibly seen as giving general principles that unify a body of data. Thus they organize or systematize the arrangement of occurrences. For this reason, Lewis's account has the important merits of providing contact with actual scientific practice while making sense of the standard philosophical conception that laws should be general but more than mere accidental generalizations. However, Lewis has long known about a potential problem with this account, a problem involving chance and credence.4 In a recent series of articles he, Michael Thau, and Ned Hall have developed a new formulation of the relationship between chance and credence which solves the problem. However, I will argue that these articles leave untouched and even exacerbate a closely related and more fundamental problem with the best system account, the problem of nomic necessity. Laws are supposed to be more than true; in some sense they must be true. Yet a principle's membership in the best systematization for one world seems to say nothing about its necessity, i.e., its truth at other worlds. I close by briefly describing how an alternative empiricist account may remove both problems. (shrink)

The new millennium is still very young, so it is too early to declare National Federation of Independent Business v. Sebelius1 the health law “case of the century,” but that title would not be hyperbolic. Never before have we seen a case of such monumental importance for how health care is financed and delivered in the United States. At the Supreme Court, no decision has been more closely watched and more anxiously awaited since Bush v. Gore in 2000. In the (...) balance was the fate of President Obama's signature piece of domestic legislation, one that affects nearly every aspect of the largest segment of our economy, and so is perhaps the most important piece of social legislation since the New Deal. To no one's surprise, the decision was announced at the very end of the Court's term and was split five to four.What was very surprising, however, was the Court's embrace of the tax power defense of the individual mandate. And what was outright shocking was a seven‐to‐two majority in favor of finding the Medicaid expansion unconstitutional unless states are allowed to opt out of the expansion.The case holds great significance not only for the fate of the Patient Protection and Affordable Care Act—and, thus, for the nation's health care public policy—but also for constitutional doctrine that applies much more broadly than in the health care arena. (shrink)

This book offers an original hypothesis capable of unifying evolution in the physical universe with evolution in biology; herewith it lays the conceptual foundations of ?transdisciplinary unified theory?. The rationale for the hypothesis is presented first; then the theoretical framework is outlined, and thereafter it is explored in regard to quantum physics, physical cosmology, micro- and macro-biology, and the cognitive sciences (neurophysiology, psychology, with attention to anomalous phenomena as well). The book closes with a variety of studies, both (...) by the author and his collaborators, sketching out the implications of the hypothesis in regard to brain dynamics, cosmology, the concept of space, phenomena of creativity, and the prospects for the elaboration of a mature transdisciplinary unified theory. The Foreword is written by philosopher of science Arne Naess, and the Afterword is contributed by neuroscientist Karl Pribram. (shrink)

In 1981, Takeuti introduced quantum set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed linear subspaces of a Hilbert space in a manner analogous to Boolean-valued models of set theory, and showed that appropriate counterparts of the axioms of Zermelo–Fraenkel set theory with the axiom of choice hold in the model. In this paper, we aim at unifying Takeuti’s model with Boolean-valued models by constructing models based on general (...) complete orthomodular lattices, and generalizing the transfer principle in Boolean-valued models, which asserts that every theorem in ZFC set theory holds in the models, to a general form holding in every orthomodular-valued model. One of the central problems in this program is the well-known arbitrariness in choosing a binary operation for implication. To clarify what properties are required to obtain the generalized transfer principle, we introduce a class of binary operations extending the implication on Boolean logic, called generalized implications, including even nonpolynomially definable operations. We study the properties of those operations in detail and show that all of them admit the generalized transfer principle. Moreover, we determine all the polynomially definable operations for which the generalized transfer principle holds. This result allows us to abandon the Sasaki arrow originally assumed for Takeuti’s model and leads to a much more flexible approach to quantum set theory. (shrink)

The basic evidence and doctrines of physics and astronomy are examined and found to contain a simple, consistent unitary nature. It is proposed that all physical phenomena may be better explained in terms of a single physical entity if one accepts a conceptual advancement of presently accepted doctrine. The modification postulates that the inertial mass of matter is the same entity as the virtual mass of a photon and that a circular motion of speedc is transformed into a linear motion (...) of speedc when mass is transformed into energy. The logical expansions of the modification seem to give simpler explanations for basic phenomena and the infinite and eternal nature of the universe. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Misnomer of Freud's "Seduction Theory"Hall TriplettSigmund Freud's theory of 1896 was buried without a name in 1897, less than two years after it appeared. The process by which it acquired a name, "seduction theory," and the role this name played in the history of psychoanalysis are essential parts of the legend-making in Freud's biography. The label, bestowed half a century after publication, reflected two major rhetorical transformations. (...) First, from a theory presented with highly general claims of infant sex abuse, assault, and trauma, the theory was repackaged as a theory of seduction. Second, from a theory reportedly based in actual, traumatic experience, followed by repressed memory, it was transformed into one of fantasy. The name "seduction theory" has therefore operated as a misleading, strategic misnomer for the theory that Freud published in 1896.Freud announced his theory in three publications, referred to here in order of publication as the Paris paper,1 the Berlin paper,2 and "The Aetiology of Hysteria," published in Vienna.3 In his final publication the emphasis on trauma was greatest. In the space of five pages in the Standard Edition of Freud's works he used the word "traumatic" or "traumatically" fifteen times.4 Although he was extending the traumatic memory theory that he had shared with Josef Breuer in 1895,5 he touted his new modification as "the discovery of a caput [End Page 647] Nili [source of the Nile] in neuropathology."6 Sixteen months later he would privately renounce it. The theory was resurrected in the 1980s as support for the recovered memory movement.7It is essential to recall that the issuance of scientific claims is quite different from scientific validation. Getting the name of a theory right more than a century after publication is one matter only; assessing the basis of its underlying claims raises yet another challenge, particularly when the theory has been transformed with such extensive variation as Freud's theory of 1896.Therefore, the early death of the theory, described only in private letters to Wilhelm Fliess, is critical to an understanding of the entire historical episode. It is essential also to note that when Freud published his retrospective revisions of the theory, he did not know that his contemporary letters to his intimate friend would become competing evidence of the actual events of the mid-1890s.8When Freud secretly abandoned his theory on 21 September 1897 he wrote to Fliess, "I no longer believe in my neurotica."9 Implied already is the fact that Freud's belief in his theory was all that had supported it. One of his retrospective comments unwittingly substantiates this fact. In 1914, in his "History of the Psycho-analytic Movement," he conceded that his theory "broke down under the weight of its own improbability."10Furthermore, abandoning a theory in secrecy with no public defense is itself tantamount to a confession that supporting evidence is missing. Freud had acknowledged the absence of supporting data in his Berlin paper when he stated, "In this kind of communication it is not possible to bring forward the evidence needful to support my assertions, but I hope to fulfill this obligation later in a detailed presentation."11 His claim that it was "not possible to bring forward the evidence" must be challenged. Presenting scientific evidence is always possible when one has it. Moreover, in his "later" paper, by far the longest of 1896, he evaded the presentation of "actual material," opting instead to discuss potential objections.12 He did not present a single case history of hysteria, arguing that this would have taken too much time; yet he had closed his Berlin paper with a case history of paranoia that was purportedly based in the female patient's "sexual relationship" with her brother during childhood.13 [End Page 648] This case is not persuasive, but it demonstrates Freud's eagerness in 1896 to share a case when he believed that he had one to share.The style of a live lecture in "The Aetiology of Hysteria," as though Freud were speaking to an audience of potential objectors, is highly misleading, even fictional. As he explained in his letters... (shrink)

The concepts of joint probability as implied by the Copenhagen and realist interpretations of quantum mechanics are examined in relation to (a) the rules for manipulation of probabilistic quantities, and (b) the role of the Bell inequalities in assessing the completeness of standard quantum theory. Proponents of completeness of the Copenhagen interpretation are required to accept a modification of the classical laws of probability to provide a mechanism for complementarity. A new formulation of the locality postulate is given, (...) not involving factorizability or conditional probabilities, which clarifies the role of locality in the derivation of the Bell inequalities. (shrink)

The textbook presentation of quantum mechanics, in a nutshell, is this. The physical state of any isolated system evolves deterministically in accordance with Schrödinger's equation until a "measurement" of some physical magnitude M (e.g. position, energy, spin) is made. Restricting attention to the case where the values of M are discrete, the system's pre-measurement state-vector f is a linear combination, or "superposition", of vectors f1, f2,... that individually represent states that..

In order to make scientific results relevant to practical decision making, it is often necessary to transfer a result obtained in one set of circumstances—an animal model, a computer simulation, an economic experiment—to another that may differ in relevant respects—for example, to humans, the global climate, or an auction. Such inferences, which we can call extrapolations, are a type of argument by analogy. This essay sketches a new approach to analogical inference that utilizes chain graphs, which resemble directed acyclic graphs (...) (DAGs) except in allowing that nodes may be connected by lines as well as arrows. This chain graph approach generalizes the account of extrapolation I provided in my (2008) book and leads to new insights that integrate the contributions of the other participants of this symposium. More specifically, this approach explicates the role of “fingerprints,” or distinctive markers, as a strategy for avoiding an underdetermination problem having to do with spurious analogies. Moreover, it shows how the extrapolator’s circle, one of the central challenges for extrapolation highlighted in my book, is closely tied to distinctive markers and the Markov condition as it applies to chain graphs. Finally, the approach suggests additional ways in which investigations of a model can provide information about a target that are illustrated by examples concerning nanomaterials in sunscreens and Wendy Parker’s discussion of fingerprints in climate science. (shrink)

I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way I prove versions of the recurrence theorem applicable to dynamics on linear and metric spaces, and make some comments about applications of the classical recurrence theorem in the foundations of statistical mechanics.

In a critical intervention into the bioethics debate over human enhancement, philosopher Melinda Hall tackles the claim that the expansion and development of human capacities is a moral obligation. Hall draws on French philosopher Michel Foucault to reveal and challenge the ways disability is central to the conversation. The Bioethics of Enhancement includes a close reading and analysis of the last century of enhancement thinking and contemporary transhumanist thinkers, the strongest promoters of the obligation to pursue enhancement (...) technology. With specific attention to the work of bioethicists Nick Bostrom and Julian Savulescu, the book challenges the rhetoric and strategies of enhancement thinking. These include the desire to transcend the body and decide who should live in future generations through emerging technologies such as genetic selection. Hall provides new analyses rethinking both the philosophy of enhancement and disability, arguing that enhancement should be a matter of social and political interventions, not genetic and biological interventions. Hall concludes that human vulnerability and difference should be cherished rather than extinguished. -/- This book will be of interest to academics working in bioethics and disability studies, along with those working in Continental philosophy (especially on Foucault). (shrink)

When the fuzzy indeterminacy of quantum mechanics overthrew the orderly world of Isaac Newton, Albert Einstein and Erwin Schrödinger were at the forefront of the revolution. Neither man was ever satisfied with the standard interpretation of quantum mechanics, however, and both rebelled against what they considered the most preposterous aspect of quantum mechanics: its randomness. Einstein famously quipped that God does not play dice with the universe, and Schrödinger constructed his famous fable of a cat that was (...) neither alive nor dead not to explain quantum mechanics but to highlight the apparent absurdity of a theory gone wrong. But these two giants did more than just criticize: they fought back, seeking a Theory of Everything that would make the universe seem sensible again. In Einstein’s Dice and Schrödinger’s Cat, physicist Paul Halpern tells the little-known story of how Einstein and Schrödinger searched, first as collaborators and then as competitors, for a theory that transcended quantum weirdness. This story of their quest—which ultimately failed—provides readers with new insights into the history of physics and the lives and work of two scientists whose obsessions drove its progress. Today, much of modern physics remains focused on the search for a Theory of Everything. As Halpern explains, the recent discovery of the Higgs Boson makes the Standard Model—the closest thing we have to a unified theory— nearly complete. And while Einstein and Schrödinger failed in their attempt to explain everything in the cosmos through pure geometry, the development of string theory has, in its own quantum way, brought this idea back into vogue. As in so many things, even when they were wrong, Einstein and Schrödinger couldn’t help but get a great deal right. (shrink)

The equation for the fundamental field quantity ϱ is obtained. It is Div $\rho ^\mu (\Omega _1 ) = \operatorname{h} \int {[\rho _\mu (\Omega _1 ),\rho ^\mu (\Omega _2 )]_ - \operatorname{d} \Omega _2 } $ ,where h is an arbitrary function oft andr, and [,]− is the commutator. The derivation requires the following hypotheses:(1) All of physical reality is completely described by the field ϱ.(2) Relativistic covariance of the equations governing ϱ.(3) Principle of continguous action.(4) Conservation of total amount (...) of ϱ. The equation appears to be unique. It is suggested that the physical world corresponds to ϱ being a2×2 matrix. A close correspondence between the basic equation and Maxwell's equation is displayed. The electromagnetic vector potential Aμ is identified with ε ρμ dΩ. Conservation laws on various measures of ϱ are obtained. The symmetry groups of the basic equation are derived. A preliminary attempt to connect the field ϱ to the metric is made via Einstein's gravitational equation Gμυ =KTμυ. (shrink)

The famous EPR article of 1935 challenged the completeness of quantum mechanics and spurred decades of theoretical and experimental research into the foundations of quantum theory. A crowning achievement of this research is the demonstration that nature cannot in general consist in noncontextual pre-measurement properties that uniquely determine possible measurement outcomes, through experimental violations of Bell inequalities and Kochen-Specker theorems. In this article, I reconstruct an argument from Niels Bohr’s writings that the reality of the Einstein-Planck-de Broglie relations (...) alone implies that no such properties can exist for momentum and position measurements, show how this argument responds to the challenge of EPR on general physical grounds, and advance that this reconstruction shows that and how Bohr’s “complementarity” is a view of the objective content and logic of quantum theory. (shrink)

Contrary to their predecessors, the Stoics put forward a unified notion of cause: a cause is a bodily because-of-which. Against the backdrop of Plato’s and Aristotle’s influential views, this is an original proposal. It involves the rejection of an earlier trend, according to which causes and explanations are closely associated. It also involves a pulling apart of causes and principles. And it comes with a charge against Plato and Aristotle, namely that they introduce a swarm of causes, a turba (...) causarum. (shrink)

This paper offers a theory of quotation by uniting two apparently disparate extant theories, Recanati's pragmatic theory and Washington's identity theory. Recanati draws a distinction between open and closed quotations, and contends that open quotations do not refer. Washington argues that closed quotations refer to various expression types, not just orthographic and/or phonetic types. By combining these views, this paper proposes a theory, according to which quotations, open or closed, may be tokens of semantico-physical types (i.e., meaningful expressions), and while (...) those types are mentioned (or referred to) by closed quotations, they are used in open quotations. (shrink)

Recent publications by several leading philosophers of chemistry have focused on the definition, scope, utility, and nomenclature of issues dealing with acidity and basicity. In this paper, molecular orbital theory is used to explain all acid–base reactions, concluding that the interaction of the highest occupied molecular orbital (HOMO) of one substrate, “the base,” with the lowest unoccupied molecular orbital (LUMO) of a second substrate, “the acid,” determines the reactivity of such systems. This paradigm provides an understanding of all acid–base reactions (...) as well as other reactions which, on the surface, may not seem like acid–base reactions but which have fundamental underpinnings of that kind of chemistry. Rather than being unable to determine a unified understanding of acidity and basicity as suggested in the philosophy of chemistry literature, we propose that acidity and basicity fit securely in a classification of many other reactions that, using classical chemistry knowledge, pre-quantum chemistry, would not be possible. We strongly support the use of all scientific knowledge and experience in the development of the ideas in the philosophy science. We further suggest increased interactions between philosophers of science and scientists, so that all scholars benefit from the values, knowledge, and perspectives of other disciplines. (shrink)

Lattice logic, bilattice logic, and paraconsistent quantum logic are investigated based on monosequent systems. Paraconsistent quantum logic is an extension of lattice logic, and bilattice logic is an extension of paraconsistent quantum logic. Monosequent system is a sequent calculus based on the restricted sequent that contains exactly one formula in both the antecedent and succedent. It is known that a completeness theorem with respect to a lattice-valued semantics holds for a monosequent system for lattice logic. A completeness (...) theorem with respect to a lattice-valued semantics is proved for paraconsistent quantum logic, and a completeness theorem with respect to a bilattice-valued semantics is proved for bilattice logic. Some syntactical properties, including cut-elimination and duality, are also investigated for the monosequent systems for these logics. (shrink)

A procedure is given for the transformation of quantum mechanical operator equations into stochastic equations. The stochastic equations reveal a simple correlation between quantum mechanics and classical mechanics: Quantum mechanics operates with “optimal estimations,” classical mechanics is the limit of “complete information.” In this connection, Schrödinger's substitution relationsp x → -iħ ∂/∂x, etc, reveal themselves as exact mathematical transformation formulas. The stochastic version of quantum mechanical equations provides an explanation for the difficulties in correlating quantum (...) mechanics and the theory of relativity: In physics “time” is always thought of as a numerical parameter; but in the present formalism of physics “time” is described by two formally totally different quantities. One of these two “times” is a numerical parameter and the other a random variable. This last concept of time shows all the properties required by the theory of relativity and is therefore to be considered as the relativistic time. (shrink)

A Unified Treatment of Moore's Paradox is the culmination of a decades-long engagement with Moore's paradox by the world's leading authority on the subject, the late John Williams. The book offers a comprehensive account of Moore's paradox in thought and speech, both in its comissive and omissive forms. Williams argues that Moorean absurdity comes in degrees, and shows that contrary to one tradition in the literature on Moore's Paradox, we cannot explain Moorean absurdity in speech in terms of Moorean (...) absurdity in thought, but must account for each form of absurdity in its own terms. Williams also explores the extent to which Moore's paradox may arise for attitudes other than belief, such as desire. Written with Williams' trademark clarity and wit, the book is packed with arguments bearing on a wide range of topics in epistemology, the philosophy of language, and the philosophy of mind. (shrink)

It is now well-known that Newton–Cartan theory is the correct geometrical setting for modelling the quantum Hall effect. In addition, in recent years edge modes for the Newton–Cartan quantum Hall effect have been derived. However, the existence of these edge modes has, as of yet, been derived using only orthodox methodologies involving the breaking of gauge-invariance; it would be preferable to derive the existence of such edge modes in a gauge-invariant manner. In this article, we employ (...) recent work by Donnelly and Freidel in order to accomplish exactly this task. Our results agree with known physics, but afford greater conceptual insight into the existence of these edge modes: in particular, they connect them to subtle aspects of Newton–Cartan geometry and pave the way for further applications of Newton–Cartan theory in condensed matter physics. (shrink)

Since Einstein’s failure to define a Grand Unified Theory, physicists have pursued a comprehensive theory explaining nature, a Theory of Everything. But because General Relativity, Quantum Field Theory, and Cosmology have little in common, defining one theory is an imposing task, having eluded the best scientists for ninety years. So are we close to defining a Theory of Everything? This analysis, after defining requirements, identifies four possible options for a Theory of Everything. Quotes from prominent physicists express (...) divergent views on each alternative.The leading proposal for a Theory of Everything is String Theory, which has possible issues. It requires supersymmetry, has extra compacted dimensions, and is background-dependent. A second less comprehensive theory is Loop Quantum Gravity, which emphases background-independence based on discrete quantum space. Explaining how theories define relationships between spacetime, quantum space, quantum time, and quantum gravity, positions the role of background-independence in proposed theories. If supersymmetry and extra dimensions are discovered, String Theory or a modified String Theory integrated with Loop Quantum Gravity, may be the option. Or, possibly a radically new theory might be developed. Or, as the last option considers, the answer to the question — Does a Theory of Everything exist? — may be no; if so, nature will always be a mystery. (shrink)

Quantum mechanical and molecular dynamics methods were used to analyze the structure and stability of neutral and zwitterionic configurations of the extracted active site sequence from a Burkholderia cepacia lipase, histidyl-seryl-glutamin (His86-Ser87-Gln88) and its mutated form, histidyl-cysteyl-glutamin (His86-Cys87-Gln88) in vacuum and different solvents. The effects of solvent dielectric constant, explicit and implicit water molecules and side chain mutation on the structure and stability of this sequence in both neutral and zwitterionic forms are represented. The quantum mechanics computations represent (...) that the relative stability of zwitterionic and neutral configurations depends on the solvent structure and its dielectric constant. Therefore, in vacuum and the considered non-polar solvents, the neutral form of the interested sequences is more stable than the zwitterionic form, while their zwitterionic form is more stable than the neutral form in the aqueous solution and the investigated polar solvents in most cases. However, on the potential energy surfaces calculated, there is a barrier to proton transfer from the positively charged ammonium group to the negatively charged carboxylat group or from the ammonium group to the adjacent carbonyl oxygen and or from side chain oxygen and sulfur to negatively charged carboxylat group. Molecular dynamics simulations (MD) were also performed by using periodic boundary conditions for the zwitterionic configuration of the hydrated molecules in a box of water molecules. The obtained results demonstrated that the presence of explicit water molecules provides the more compact structures of the studied molecules. These simulations also indicated that side chain mutation and replacement of sulfur with oxygen leads to reduction of molecular flexibility and packing. (shrink)