We present a quantum mechanical analysis of Bell’s approach to quantum foundations based on his hidden-variable model. We claim and try to justify that the Bell model contradicts to the Heinsenberg’s uncertainty and Bohr’s complementarity principles. The aim of this note is to point to the physical seed of the aforementioned principles. This is the Bohr’s quantum postulate: the existence of indivisible quantum of action given by the Planck constant h. By contradicting these basic principles (...) of QM, Bell’s model implies rejection of this postulate as well. Thus, this hidden-variable model contradicts not only the QM-formalism, but also the fundamental feature of the quantum world discovered by Planck. (shrink)

The purpose of this dissertation is to contribute to our understanding of scientific theory pursuit by providing a detailed case study on the development of early quantum theory, from roughly 1900 to 1916. I first elaborate on why this case should be considered an instance of piecemeal pursuit by presenting the historical quantum conjectures that were being used in different contexts. These conjectures gave varied interpretations of quantization. By comparing these conjectures, I identify a general quantum (...) class='Hi'>postulate that captures the underlying assumption common to all the cases. I argue that it is possible to consider a general postulate about quantization even when its proper application is ambiguous in a given context, and that the postulate can be separated from different elements of the framework being used to investigate it. I show that the quantum postulate can be deemed promising by analysing the support it gains using a Bayesian framework. I first defend the use of such a framework by considering the purported inconsistencies in Planck's introduction of his quantum conjecture and how we should handle these. I then explicate two cases of support for the postulate. First, I show how we can use a particular solution to the Bayesian problem of old evidence to interpret the support the quantum postulate received by accounting for phenomena that had no previous explanation. Finally, I show that the quantum postulate is also supported by a unification argument, where unification is interpreted as informational relevance between the different domains of inquiry. (shrink)

The traditional “realist” conception of physics, according to which human concepts, laws and theories can grasp the essence of a reality in our absence , seems incompatible with quantum formalism and it most fruitful interpretation. The proof rests on the violation by quantum mechanical formalism of some fundamental principles of the classical ontology. We discuss if the conception behind Einstein’s idea of a reality in our absence, could be still maintained and at which price. We conclude that (...) class='Hi'>quantum mechanical formalism is not formulated on those terms, leaving for a separated paper the discussion about the terms in which it could be formulated and the onto-epistemological implications it might have. (shrink)

It is widely held that quantum mechanics is the first scientific theory to present scientifically internal, fundamental difficulties for a realistic interpretation (in the philosophical sense). The standard (Copenhagen) interpretation of the quantum theory is often described as the inevitable instrumentalistic response. It is the purpose of the present article to argue that quantum theory doesnot present fundamental new problems to a realistic interpretation. The formalism of quantum theory has the same states—it will be argued—as the (...) formalisms of older physical theories and is capable of the same kinds of philosophical interpretation. This result is reached via an analysis of what it means to give a realistic interpretation to a theory. The main point of difference between quantum mechanics and other theories—as far as the possibilities of interpretation are concerned—is the special treatment given tomeasurement by the “projection postulate.” But it is possible to do without this postulate. Moreover, rejection of the projection postulate does not, in spite of what is often maintained in the literature, automatically lead to the many-worlds interpretation of quantum mechanics. A realistic interpretation is possible in which only the reality ofone (our) world is recognized. It is argued that the Copenhagen interpretation as expounded by Bohr is not in conflict with the here proposed realistic interpretation of quantum theory. (shrink)

The Ozawa’s intersubjectivity theorem (OIT) proved within quantum measurement theory supports the new postulate of relational quantum mechanics (RQM), the postulate on internally consistent descriptions. But from OIT viewpoint postulate’s formulation should be completed by the assumption of probability reproducibility. We remark that this postulate was proposed only recently to resolve the problem of intersubjectivity of information in RQM. In contrast to RQM for which OIT is a supporting theoretical statement, QBism is challenged by (...) OIT. (shrink)

I show that the quantum state ω can be interpreted as defining a probability measure on a subalgebra of the algebra of projection operators that is not fixed (as in classical statistical mechanics) but changes with ω and appropriate boundary conditions, hence with the dynamics of the theory. This subalgebra, while not embeddable into a Boolean algebra, will always admit two-valued homomorphisms, which correspond to the different possible ways in which a set of “determinate” quantities (selected by ω and (...) the boundary conditions) can have values. The probabilities defined by ω (via the Born rule) are probabilities over these two-valued homomorphisms or value assignments. So any universe of interacting systems, including those functioning as measuring instruments, can be modelled quantum mechanically without the projection postulate. (shrink)

Because of the measurement problem, the standard theory of quantum mechanics is at best incomplete and at worst logically inconsistent. Everett suggested that the measurement problem could be resolved by taking the linear dynamics to be a complete and accurate description of the time-evolution of every physical system. The purpose of this dissertation is to see what happens when one takes Everett's proposal seriously. This dissertation includes a discussion of the standard theory of quantum mechanics and its origins, (...) the measurement problem, Everett's relative-state formulation, the many-worlds interpretation, Albert's bare theory and its suggestive properties, and Albert and Loewer's single-mind and many-minds theories. I will show how one might construct a theory that exploits the bare theory's suggestive properties without encountering its empirical problems. (shrink)

This paper explores the status of the von Neumann-Luders state transition rule (the "projection postulate") within "real-logic" quantum logic. The entire discussion proceeds from a reading of the Luders rule according to which, although idealized in applying only to "minimally disturbing" measurements, it nevertheless makes empirical claims and is not a purely mathematical theorem. An argument (due to Friedman and Putnam) is examined to the effect that QL has an explanatory advantage over Copenhagen and other interpretations which relativize (...) truth-value assignments to experimental arrangements. Two versions of QL, the lattice-theoretic (LT) and partial-Boolean-algebra (PBA), are considered. It turns out that the projection postulate is intimately connected with the choice of conditional connective for QL. The effect of the projection postulate is obtained with the Sasaki conditional. However, this choice is found to require extra assumptions, on both the LT and PBA versions, which are either just as ad hoc as the projection postulate itself or indefensible from within the real-logic QL framework. (shrink)

This article explains why Bohr does not need to discuss the projection postulate or the "problem of measurement". Beginning with a thumbnail sketch of Bohr 's general views, it is argued that Bohr interprets the state function as giving a statistical summary of experimental outcomes. Against the objection that Bohr was too much a microrealist to endorse such an instrumentalist statistical interpretation it is suggested that he rejected the issue of microrealism as not well formed. It is shown that (...) on his statistical interpretation Bohr does not need the projection postulate or face the usual problem of measurement. (shrink)

A detailed list of postulates is formulated in an algebraic setting. These postulates are sufficient to entail the standard time evolution governed by the Schrödinger or Dirac equation. They are also necessary in a strong sense: Dropping any one of the postulates allows for other types of time evolution, as is demonstrated with examples. Some philosophical remarks hint on possible further investigations.

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)

The projection postulate is the source of a long standing controversy in the interpretation of the axiomatic foundations of quantum mechanics. In a sense which is made precise in chapter II the projection postulate is a mathematical theorem easily derivable within the mathematical framework of the theory. This theorem receives a clear and straightforward interpretation if Luders' rule is given only statistical significance. Under the assumption that an interpretation of quantum mechanics has to provide an account (...) of the process of measurement as a change on the state of individual systems, however, additional interpretive assumptions are needed in order to arrive at a satisfactory interpretation of Luders' rule. ;I show in chapter III that there are serious problems with the usual interpretation by making explicit in a quantum logical framework the concept of individual state and minimal disturbance implicit in this view. In chapter IV I show that it is possible to formulate a natural interpretation of Luders' rule as a description of 'dispersion free' state transformations within a semantic framework that takes states of individual systems to be represented by Boolean ultrafilters , as opposed to the usual approach that takes individual states to be represented by lattice ultrafilters. This lay the ground for the clarification of several interpretive issues in the foundations of quantum mechanics. It is shown that Luders' rule can be justified as a description of individual state transformations without the need of imposing additional assumptions. The derivation of Luders' rule within the semantic framework of B-states shows an important connection between interpretation that take individual state to be 'relative' to experimental situations and the statistical structure of the theory. (shrink)

I defend the projection postulate against two of Margenau's criticisms. One involves two types of nonideal measurements, measurements that disturb and measurements that annihilate. Such measurements cannot be characterized using the original version of the projection postulate. This is one of the most interesting and powerful objections to the projection postulate since most realistic measurements are nonideal, in Margenau's sense. I show that a straightforward generalization of the projection postulate is capable of handling the more realistic (...) kinds of measurements considered by Margenau. His other objection involves the EPR (Einstein-Podolsky-Rosen) situation. He suggests that there is a significant potential for violations of the no-superluminalsignals requirement of the special theory of relativity, if projections occur in this situation and others like it. He also suggests that what is paradoxical about this situation disappears if the projection postulate is rejected. I show that it is not possible to use measurements on pairs of spatially-separated systems whose states are entangled to transmit information superluminally, and generalize this result to include nonideal measurements. I also show that EPR's dilemma does not really depend on the projection postulate. (shrink)

In this paper we derive a theorem which proves that the physical interpretation implied by the first postulate of quantum mechanics is inconsistent with the orthodox formalism. In order to expose this inconsistency we will analyze how the concept of ‘physical system’ is built within classical theories through the notion of invariance and explain in what sense a vector in Hilbert space is not capable of fulfilling these same mathematical conditions. Through an analysis of the mathematical formalism we (...) derive a No Dynamical Invariance theorem which proves that, contrary to what is claimed in the first postulate, a vector in Hilbert space cannot be interpreted coherently as the state of a physical system. We conclude the paper by analyzing the consequences of the NDI theorem with respect to several ongoing debates in QM. (shrink)

Everett proposed resolving the quantum measurement problem by dropping the nonlinear collapse dynamics from quantum mechanics and taking what is left as a complete physical theory. If one takes such a proposal seriously, then the question becomes how much of the predictive and explanatory power of the standard theory can one recover without the collapse postulate and without adding anything else. Quantum mechanics without the collapse postulate has several suggestive properties, which we will consider in (...) some detail. While these properties are not enough to make it acceptable given the usual standards for a satisfactory physical theory, one might want to exploit these properties to cook up a satisfactory no-collapse formulation of quantum mechanics. In considering how this might work, we will see why any no-collapse theory must generally fail to satisfy at least one of two plausible-sounding conditions. (shrink)

The attempt to derive (rather than assume) the statistical postulate of quantum theory from the many-universes interpretation of Everett and De Witt is analyzed The many-universes interpretation is found to be neither necessary nor sufficient for the task.

The aim of this paper is to reconstruct and correct one argument in support of the symmetrization postulate in quantum mechanics. I identify the central premise of the argument as a thesis specifying a particular ontic property of quantum superpositions. The precise form of this thesis depends on some underlying assumptions of a metaphysical character. I compare the exchange degeneracy argument with alternative formal arguments for the symmetrization postulate, and I discuss the role and meaning of (...) labels in the symmetric/antisymmetric representations of the states of many particles. (shrink)

We study whether the probabilistic postulate could be derived from basic principles. Through the analysis of the Strong Law of Large Numbers and its formulation in quantum mechanics, we show, contrary to the claim of the many-worlds interpretation defenders and the arguments of some other authors, the impossibility of obtaining the probabilistic postulate by means of the frequency analysis of an ensemble of infinite copies of a single system. It is shown, though, how the standard form of (...) the probability as the square of the scalar product follows from Gleason's theorem. (shrink)

Certain modifications, by way of improvement, are proposed for the Feynman postulates in quantum mechanics. These modifications incorporate a criterion for the applicability of the principle of superposition. It is shown that the modified postulates, together with certain assumptions regarding the trajectory of a particle, lead to an expression for the position-momentum uncertainty relationship which is broadly in agreement with the conventional expression. The time-energy uncertainty relationship is, however, found to have a likely place only in the relativistic theory. (...) A criterion, in the form of a ratio involving the linear dimensions of the particle, is obtained for the validity of the classical mechanics approximation. The modified postulates are suggested to favor the statistical interpretation of quantum mechanics over the Copenhagen interpretation. (shrink)

We interpret the (formal) postulates of measurement in quantum theory in terms of measurement procedures that can be done in the laboratory (at least in principle).

In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition to account for the temporal asymmetry. In this paper, I show that the Past Hypothesis also contains enough information to simplify the quantum ontology and define a unique initial condition in such a world. First, I introduce Density Matrix Realism, the thesis that the quantum universe is described by a fundamental density matrix that represents something objective. This stands in sharp (...) contrast to Wave Function Realism, the thesis that the quantum universe is described by a wave function that represents something objective. Second, I suggest that the Past Hypothesis is sufficient to determine a unique and simple density matrix. This is achieved by what I call the Initial Projection Hypothesis: the initial density matrix of the universe is the normalized projection onto the special low-dimensional Hilbert space. Third, because the initial quantum state is unique and simple, we have a strong case for the \emph{Nomological Thesis}: the initial quantum state of the universe is on a par with laws of nature. This new package of ideas has several interesting implications, including on the harmony between statistical mechanics and quantum mechanics, the dynamic unity of the universe and the subsystems, and the alleged conflict between Humean supervenience and quantum entanglement. (shrink)

We propose the conjecture according to which the fact that quantum mechanics does not admit sharp value attributions to both members of a complementary pair of observables can be understood in the light of the symplectic reduction of phase space in constrained Hamiltonian systems. In order to unpack this claim, we propose a quantum ontology based on two independent postulates, namely the phase postulate and the quantum postulate. The phase postulate generalizes the gauge correspondence (...) between first-class constraints and gauge transformations to the observables of unconstrained Hamiltonian systems. The quantum postulate specifies the relationship between the numerical values of the observables that permit us to individualize a physical system and the symmetry transformations generated by the operators associated to these observables. We argue that the quantum postulate and the phase postulate are formally implemented by the two independent stages of the geometric quantization of a symplectic manifold, namely the prequantization formalism and the election of a polarization of pre-quantum states respectively. (shrink)

Order of information plays a crucial role in the process of updating beliefs across time. In fact, the presence of order effects makes a classical or Bayesian approach to inference difficult. As a result, the existing models of inference, such as the belief-adjustment model, merely provide an ad hoc explanation for these effects. We postulate a quantum inference model for order effects based on the axiomatic principles of quantum probability theory. The quantum inference model explains order (...) effects by transforming a state vector with different sequences of operators for different orderings of information. We demonstrate this process by fitting the quantum model to data collected in a medical diagnostic task and a jury decision-making task. To further test the quantum inference model, a new jury decision-making experiment is developed. Using the results of this experiment, we compare the quantum inference model with two versions of the belief-adjustment model, the adding model and the averaging model. We show that both the quantum model and the adding model provide good fits to the data. To distinguish the quantum model from the adding model, we develop a new experiment involving extreme evidence. The results from this new experiment suggest that the adding model faces limitations when accounting for tasks involving extreme evidence, whereas the quantum inference model does not. Ultimately, we argue that the quantum model provides a more coherent account for order effects that was not possible before. (shrink)

I briefly sketch Bohm's causal interpretation (BCI) and its solution to the measurement problem. Crucial to BCI's no-collapse account of both ideal and non-ideal measurement is the existence of particles in addition to wavefunctions. The particles in their role as the producers of the observable experimental outcomes render practical considerations, such as what observables can be reasonably measured or how to get rid of interference terms in non-ideal measurements, secondary to BCI's account of measurement. I then explain why it is (...) not easy for BCI to justify its statistical postulate. To successfully justify the postulate would be to solve the distribution problem. Two proposed deterministic solutions to this problem are only briefly set out and not discussed in detail. BCI can solve the measurement problem whether or not the distribution problem is solved. However, if the distribution problem is not solved, BCI cannot be shown to be empirically adequate. (shrink)

The standard axiomatization of quantum mechanics (QM) is not fully explicit about the role of the time-parameter. Especially, the time reference within the probability algorithm (the Born Rule, BR) is unclear. From a probability principle P1 and a second principle P2 affording a most natural way to make BR precise, a logical conflict with the standard expression for the completeness of QM can be derived. Rejecting P1 is implausible. Rejecting P2 leads to unphysical results and to a conflict with (...) a generalization of P2, a principle P3. All three principles are shown to be without alternative. It is thus shown that the standard expression of QM completeness must be revised. An absolutely explicit form of the axioms is provided, including a precise form of the projection postulate. An appropriate expression for QM completeness, reflecting the restrictions of the Gleason and Kochen-Specker theorems is proposed. (shrink)

There is an extensive philosophical literature on the interrelated issues of identity, individuality, and distinguishability in quantum systems. A key consideration is whether quantum systems are subject to a strong form of individuality termed ``haecceity'' (from the Latin for ``this-ness''). I argue that the traditional, strong form of haecceity does not apply at the quantum level, but that in order to properly account for the need for symmetrization in quantum systems, a weaker kind of haecceity must (...) be involved, which I call quantum haecceity. In the process, I also question some generally accepted tenets of the current debate, such as the idea that symmetrization of states for identical quanta must be postulated and reflects permutation invariance. Instead, I note that a perturbative Hamiltonian is required for exchange effects, which suggests that the need for symmetrization arises from specific physical conditions. (shrink)

An original quantum foundations concept of a deep learning computational Universe is introduced. The fundamental information of the Universe (or Triuniverse)is postulated to evolve about itself in a Red, Green and Blue (RGB) tricoloured stable self-mutuality in three information processing loops. The colour is a non-optical information label. The information processing loops form a feedback-reinforced deep learning macrocycle with trefoil knot topology. Fundamental information processing is driven by ψ-Epistemic Drive, the Natural appetite for information selected for advantageous knowledge. From (...) its substrate of Mathematics, the knotted information processing loops determine emergent Physics and thence the evolution of super-emergent Life (biological and artificial intelligence). RGB-tricoloured information is processed in sequence in an Elemental feedback loop (R), then an Operational feedback loop (G), then a Structural feedback loop (B) and back to an Elemental feedback loop (R), and so on around the trefoil in deep learning macrocycles. It is postulated that hierarchical information correspondence from Mathematics through Physics to Life is mapped and conserved within each colour. The substrate of Mathematics has RGB-tricoloured feedback loops which are respectively Algebra (R), Algorithms (G) and Geometry (B). In Mathematics, the trefoil macrocycle is Algebraic Algorithmic Geometry and its correlation system is a Tensor Neural Knot Network enabling Qutrit Entanglement. Emergent Physics has corresponding RGB-tricoloured feedback loops of Quantum Mechanics (R), Quantum Deep Learning (G) and Quantum Geometrodynamics(B). In Physics, the trefoil macrocycle is Quantum Intelligent Geometrodynamics and its correlation system is Quantum Darwinism. Super-emergent Life has corresponding RGB-tricoloured loops of Variation (R), Selection (G) and Heredity (B). In the evolution of Life, the trefoil macrocycle is Variational Selective Heredity and its correlation ecosystem is Darwin’s ecologically “Entangled Bank”. (shrink)

Quantum physics is believed to be the fundamental theory underlying our understanding of the physical universe. However, it is based on concepts and principles that have always been difficult to understand and controversial in their interpretation. This book aims to explain these issues using a minimum of technical language and mathematics. After a brief introduction to the ideas of quantum physics, the problems of interpretation are identified and explained. The rest of the book surveys, describes and criticises a (...) range of suggestions that have been made with the aim of resolving these problems; these include the traditional, or 'Copenhagen' interpretation, the possible role of the conscious mind in measurement, and the postulate of parallel universes. This new edition has been revised throughout to take into account developments in this field over the past fifteen years, including the idea of 'consistent histories' to which a completely new chapter is devoted. (shrink)

The reduction of a quantum mechanical wave function by the entry of a datum into the consciousness of an observer is used, in a semirealistic neurochemical model, to bring about excitation of a nerve cell in that observer's central nervous system. It is suggested that mind can induce muscular movements by choosing to note data originating from specialized elements of the nervous system. Only the freedom to note or not to note a relevant datum is postulated for the observer's (...) mind; the consequences of either choice are deterministic on the neural scale of events, so that quantum indeterminacy is consistent with physiological determinacy. The proposed mind-body coupling depends on the possibility of the biological evolution of a macroscopic device which has strikingly different neural correlates of its pure and mixed quantum states, respectively. An example of such a device is outlined in terms of components which are familiar from existing nervous systems. (shrink)

What, if anything, would be wrong with replacing the light postulate in Einstein’s 1905 formulation of special relativity with a ‘sound postulate’, stating that the speed of sound is independent of the speed of the source? After reviewing the historical reasons underlying the particular focus on light in the special theory, we consider the circumstances under which such a theory of ‘sonic relativity’ would be justified on empirical grounds. We then consider the philosophical upshots of ‘sonic relativity’ for (...) four contemporary areas of investigation in the philosophy of spacetime: global versus subsystem symmetries, dynamical versus geometrical approaches to spacetime, the possibility of a preferred frame in theories of quantum gravity, and spacetime functionalism. (shrink)

We revisit the EPR problem and make clear what is a correct comprehension of its problem. When one applies the quantum mechanics correctly, it will be shown that there is no paradox. According to these lines of thought, a quantum teleportation scheme without resort to the von Neumann projection postulate is presented.

We present a derivation of the third postulate of relational quantum mechanics from the properties of conditional probabilities. The first two RQM postulates are based on the information that can be extracted from interaction of different systems, and the third postulate defines the properties of the probability function. Here we demonstrate that from a rigorous definition of the conditional probability for the possible outcomes of different measurements, the third postulate is unnecessary and the Born’s rule naturally (...) emerges from the first two postulates by applying the Gleason’s theorem. We demonstrate in addition that the probability function is uniquely defined for classical and quantum phenomena. The presence or not of interference terms is demonstrated to be related to the precise formulation of the conditional probability where distributive property on its arguments cannot be taken for granted. In the particular case of Young’s slits experiment, the two possible argument formulations correspond to the possibility or not to determine the particle passage through a particular path. (shrink)

Question order effects are commonly observed in self-report measures of judgment and attitude. This article develops a quantum question order model (the QQ model) to account for four types of question order effects observed in literature. First, the postulates of the QQ model are presented. Second, an a priori, parameter-free, and precise prediction, called the QQ equality, is derived from these mathematical principles, and six empirical data sets are used to test the prediction. Third, a new index is derived (...) from the model to measure similarity between questions. Fourth, we show that in contrast to the QQ model, Bayesian and Markov models do not generally satisfy the QQ equality and thus cannot account for the reported empirical data that support this equality. Finally, we describe the conditions under which order effects are predicted to occur, and we review a broader range of findings that are encompassed by these very same quantum principles. We conclude that quantum probability theory, initially invented to explain order effects on measurements in physics, appears to be a powerful natural explanation for order effects of self-report measures in social and behavioral sciences, too. (shrink)

The mathematical formalism of quantum theory has been established for nearly a century, yet its physical foundations remain elusive. In recent decades, connections between quantum theory and information theory have garnered increasing attention. This study presents a physical derivation of the mathematical formalism quantum theory based on information-theoretic considerations in physical systems. We postulate that quantum systems are characterized by single independent adjustable variables. Utilizing this physical postulate along with the conservation of total probability, (...) we derive the standard Hilbert space formalism of quantum theory, including the Born probability rule. This comprehensive derivation of quantum theory offers a clear and concise physical foundation for the mathematical formalism of quantum mechanics. (shrink)

Accepted quantum description is stochastic, yet history is nonstochastic, i.e., not representable by a probability distribution. Therefore ordinary quantum mechanics is unsuited to describe history. This is a limitation of the accepted quantum theory, rather than a failing of mechanics in general. To remove the limitation, it would be desirable to find a form of quantum mechanics that describes the future stochastically and the past nonstochastically. For this purpose it proves sufficient to introduce into quantum (...) mechanics, by means of a perfected formal correspondence, certain analogs of the classical initial-condition constants. Through the restoration of such parameters at the quantum level one accomplishes a natural accommodation of time anisotropy, wave-function reduction, and “event” description by quantum mechanical equations of motion alone, without the need for extra postulates (e.g., a projection postulate). This requires a complete restructuring of quantum measurement theory. (shrink)

We give a partial answer to the question whether the Schrödinger equation can be derived from the Newtonian mechanics of a particle in a potential subject to a random force. We show that the fluctuations around the classical motion of a one dimensional harmonic oscillator subject to a random force can be described by the Schrödinger equation for a period of time depending on the frequency and the energy of the oscillator. We achieve this by deriving the postulates of Nelson’s (...) stochastic formulation of quantum mechanics for a random force depending on a small parameter. We show that the same result applies to small potential perturbations around the harmonic oscillator. We also show that the noise spectrum can be chosen to obtain the result for all oscillator frequencies for fixed mass. We discuss heuristics to generalize the result for a particle in one dimension in a potential where the motion can be described using action-angle variables. The main motivation of this paper is to provide a step for constructing a Newtonian theory which would approximately reproduce quantum mechanics both in unitary evolution and measurement regimes. (shrink)

Although the present paper looks upon the formal apparatus of quantum mechanics as a calculus of correlations, it goes beyond a purely operationalist interpretation. Having established the consistency of the correlations with the existence of their correlata, and having justified the distinction between a domain in which outcome-indicating events occur and a domain whose properties only exist if their existence is indicated by such events, it explains the difference between the two domains as essentially the difference between the manifested (...) world and its manifestation. A single, intrinsically undifferentiated Being manifests the macroworld by entering into reflexive spatial relations. This atemporal process implies a new kind of causality and sheds new light on the mysterious nonlocality of quantum mechanics. Unlike other realist interpretations, which proceed from an evolving-states formulation, the present interpretation proceeds from Feynman’s formulation of the theory, and it introduces a new interpretive principle, replacing the collapse postulate and the eigenvalue–eigenstate link of evolving-states formulations. Applied to alternatives involving distinctions between regions of space, this principle implies that the spatiotemporal differentiation of the physical world is incomplete. Applied to alternatives involving distinctions between things, it warrants the claim that, intrinsically, all fundamental particles are identical in the strong sense of numerical identical. They are the aforementioned intrinsically undifferentiated Being, which manifests the macroworld by entering into reflexive spatial relations. (shrink)

There is a consistent and simple interpretation of the quantum theory of isolated systems. The interpretation suffers no measurement problem and provides a quantum explanation of state reduction, which is usually postulated. Quantum entanglement plays an essential role in the construction of the interpretation.

Because of the conceptual difficulties it faces, quantum mechanics provides a salient example of how alternative metaphysical commitments may clarify our understanding of a physical theory and the explanations it provides. Here we will consider how postulating alternative quantum worlds in the context of Hugh Everett III’s pure wave mechanics may serve to explain determinate measurement records and the standard quantum statistics. We will focus on the properties of such worlds, then briefly consider other metaphysical options available (...) for interpreting pure wave mechanics. These reflections will serve to illustrate both the nature and the limits of naturalized metaphysics. (shrink)

In this work we attempt to confront the orthodox widespread claim, present in the philosophical and foundational debates about Quantum Mechanics (QM), that ‘superpositions are never actually observed in the lab’. In order to do so, we begin by providing a critical analysis of the famous measurement problem which, we will argue, was originated as a consequence of the strict application of the empirical-positivist requirements to subsume the quantum formalism under their specific understanding of a physical ‘theory’. In (...) particular, the ad hoc introduction of the projection postulate (or measurement rule) can be understood as the necessity of imposing a naive empiricist standpoint which presupposes that observations are self evident givens of “common sense” experience independent of metaphysical (or conceptual) presuppositions yet necessarily represented in binary terms. We then turn our attention to two “non-collapse” interpretations of QM—namely, modal and many worlds—which even though deny that the “collapse” is a real physical process retain anyhow the projection rule as a necessary axiom of the theory itself. In contraposition, following Einstein’s claim that “it is only the theory which decides what can be observed”, we propose a return to the realist representational understanding of physical theories in which ‘observation’ is not a “self evident” given of experience but something that can be only understood in the context of a theoretical (formal-conceptual) scheme. It is from this standpoint that we discuss a new non-classical conceptual representation which allows us to understand quantum phenomena in an intuitive (anschaulicht) manner. Leaving behind the projection postulate, we discuss the general physical conditions for measuring and observing quantum superpositions in the lab. (shrink)

Some mathematical theories in physics justify their explanatory superiority over earlier formalisms by the clarity of their postulates. In particular, axiomatic reconstructions drive home the importance of the composition rule and the continuity assumption as two pillars of quantum theory. Our approach sits on these pillars and combines new mathematics with a testable prediction. If the observer is defined by a limit on string complexity, information dynamics leads to an emergent continuous model in the critical regime. Restricting it to (...) a family of binary codes describing ‘bipartite systems,’ we find strong evidence of an upper bound on bipartite correlations equal to 2.82537. This is measurably different from the Tsirelson bound. The Hilbert space formalism emerges from this mathematical investigation as an effective description of a fundamental discrete theory in the critical regime. (shrink)

In this paper we review the general framework of operational probabilistic theories, along with the six axioms from which quantum theory can be derived. We argue that the OPT framework along with a relaxed version of five of the axioms, define a general information theory. We close the paper with considerations about the role of the observer in an OPT, and the interpretation of the von Neumann postulate and the Schrödinger-cat paradox.

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 wave function in quantum mechanics presents an interesting challenge to our understanding of the physical world. In this paper, I show that the wave function can be understood as four intrinsic relations on physical space. My account has three desirable features that the standard account lacks: it does not refer to any abstract mathematical objects, it is free from the usual arbitrary conventions, and it explains why the wave function has its gauge degrees of freedom, something that are (...) usually put into the theory by hand. Hence, this account has implications for debates in philosophy of mathematics and philosophy of science. First, by removing references to mathematical objects, it provides a framework for nominalizing quantum mechanics. Second, by excising superfluous structure such as overall phase, it reveals the intrinsic structure postulated by quantum mechanics. Moreover, it also removes a major obstacle to ``wave function realism.''. (shrink)