In this paper we shall develop a hidden-beable theory which not only reproduce all the predictions of quantum mechanics but also gives an objective-ontological derivations to all postulates that give the foundation of the quantum mechanics. This is done by assuming that the state of a single system can be described completely by two complementary irreducible primitive realities: First is system's position and orientation which serve as local and explicit beables, and second is a new, hidden and global beable named "system's imaginability". System's imaginability is defined as degree of imagination attached to the system that it "could have" other states than it actually has. It is thus of ontological nature which refers to a single system, replacing the conventional epistemological concept of probability which tells the relative frequency of occurrence of various events in an ensemble of systems. We then derive a dynamical equation from which neglecting subquantum fluctuations of the order of \\hbar^2 will lead to the Schrodinger equation in configuration space. An objective measurement theory without observer is then developed, by introducing a new notion of "a controllable apparatus". The superposition principle, Dirac-von Neumann projection postulate and Born's probability rule will be given an objective derivation. Finally we shall prove that the new dynamics fits Einstein's locality postulate in a very simple manner.
In this paper we shall develop a hidden-beable theory which not only reproduce all the predictions of quantum mechanics but also gives an objective-ontological derivations to all postulates that give the foundation of the quantum mechanics. This is done by assuming that the state of a single system can be described completely by two complementary irreducible primitive realities: First is system's position and orientation which serve as local and explicit beables, and second is a new, hidden and global beable named "system's imaginability". System's imaginability is defined as degree of imagination attached to the system that it "could have" other states than it actually has. It is thus of ontological nature which refers to a single system, replacing the conventional epistemological concept of probability which tells the relative frequency of occurrence of various events in an ensemble of systems. We then derive a dynamical equation from which neglecting subquantum fluctuations of the order of \hbar^2 will lead to the Schrodinger equation in configuration space. An objective measurement theory without observer is then developed, by introducing a new notion of "a controllable apparatus". The superposition principle, Dirac-von Neumann projection postulate and Born's probability rule will be given an objective derivation. Finally we shall prove that the new dynamics fits Einstein's locality postulate in a very simple manner.
We have developed a new dynamical theory that describes deterministic phenomena of very large scale of matter and the seemingly indeterministic experimental results on very small scale of matter in equal footing. This is done by introducing a new non-local ontological quantity, namely matter's knowledge on its own local position-beable. The matter's knowledge is given uniquely by a new non-local beable called "imaginability". The latter is an ontological concept giving a degree of imagination that the matter "could have" state than it actually has, replacing the conventional epistemological concept of probability. The classical objective notion of trajectories are given a new spirit. The classical mechanics turns out to its special case, whereas the Schrodinger's equation is recovered by neglecting sub-quantum fluctuations of the order of hbar2. All the quantum mechanical results on spectrum of energy is confirmed. Furthermore, the Dirac-Von Newmann projection postulate is given a physical objective mechanism in term of a single experiment, and the Born's probability rule is given a derivation. Finally we show that our dynamical theory can be considered as a combination between the classical mechanics and the thermodynamics had it applies to a single particle.
The axiomatic foundations of quantum mechanics, while operationally successful, obscure the underlying physical reality. This work introduces a mechanical topological ontology intended to provide a causal basis for the theory. We propose a single postulate: that a fundamental fermion is the 0-dimensional boundary of a 1-dimensional, massive, string-like object topologically anchored to a dynamic vacuum field. From this postulate, we argue that the core structures of single-particle relativistic quantum mechanics can be understood as derivable theorems. First, we construct the object’s state space by identifying two independent, binary properties—a local, vibrational/topological duality (spin) and a global, orientational duality (matter/antimatter)—whose tensor product naturally yields the 4-component Dirac spinor. Second, we show that the requirement of relativistic consistency uniquely determines the algebraic operators (gamma matrices and their Clifford algebra) and the lowest-order dynamical law, leading to the Dirac equation as a theorem of consistency. Third, we demonstrate that the non-relativistic Schrödinger and Pauli equations emerge as its correct low-energy limits, where the quantum potential V (x) is identified with a local variation in the object’s rest mass. Finally, we argue that the foundational tenets of quantum measurement—the spin-1/2 property, the probabilistic Born rule, and the correlations of entanglement—can be reframed as necessary consequences of the object’s intrinsic topology and interaction mechanics. This framework thus offers a path toward demoting the axioms of quantum theory to derivable theorems, aiming to resolve its long-standing paradoxes by providing a clear and coherent physical picture.
A history of the discovery of quantum mechanics and paradoxes of its interpretation is reconsidered from the modern point of view of quantum stochastics and information. It is argued that in the orthodox quantum mechanics there is no place for quantum phenomenology such as events. The development of quantum measurement theory, initiated by von Neumann, and Bell's conceptual critics of hidden variable theories indicated a possibility for resolution of this crisis. This can be done by divorcing the algebra of the dynamical generators and an extended algebra of the potential (quantum) and the actual (classical) observables. The latter, called beables, form the center of the algebra of all observables, as the only visible (macroscopic) observables must be compatible with any hidden (microscopic) observable. It is shown that within this approach quantum causality can be rehabilitated within an extended quantum mechanics (eventum mechanics) in the form of a superselection rule for compatibility of the consistent histories with the statistically predictable future. The application of this rule in the form of the nondemolition principle leads to the statistical inference of the von Neumann projection postulate, and also to the more general quantum information dynamics for instantaneous events, spontaneous localizations (i.e. quantum jumps), and state diffusions (i.e. continuous trajectories). This gives a dynamical solution, in the form of a Dirac boundary value problem and reduced filtering equations, of the notorious decoherence and measurement problems which was tackled unsuccessfully by many famous mathematicians and physicists starting with von Neumann, Schroedinger and Bohr.
Abstract This paper develops a metaphysical interpretation of quantum probability under the title Distributed Presence (DP). The central claim is that quantum probabilities should not be understood as measures of ignorance, nor merely as formal devices for predicting measurement outcomes, but as expressions of an objective mode of being: a system’s structured distribution of presence across mutually available channels of realization. On this view, a quantum system prior to measurement is neither fully actual in one determinate outcome nor reducible to a set of hidden definite properties. Rather, it exists in a non-binary mode, articulated by normalized presence fractions associated with the possible outcomes defined by a given interaction context. The Born rule is accordingly not replaced, but reinterpreted: the standard probability assignment is read as the operational expression of an underlying ontological distribution. The paper argues that this framework provides a unified reading of several familiar quantum features. Superposition is understood as a real distribution of presence rather than as epistemic indeterminacy; measurement is interpreted as single-channel actualization rather than as the physical destruction of alternatives; wave-particle duality is recast as the relation between distributed structure and localized realization; and quantum randomness is treated as intrinsic yet structurally constrained. The proposal remains fully compatible with the standard Hilbert-space formalism and introduces no hidden variables, additional collapse dynamics, or many-world branching. Its aim is interpretive rather than revisionary. Beyond its relevance to the foundations of quantum theory, DP is advanced as a contribution to the ontology of probability more broadly. It seeks to show how probability may be objective, physically meaningful, and ontologically basic without collapsing into determinism on the one hand or epistemicism on the other. In that sense, the paper offers a realist, single-world, structurally articulated account of quantum chance.
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for assigning outcome probabilities (Born's rule) and the post-measurement state-update rule, can be deduced from the other quantum postulates, often referred to as "unitary quantum mechanics", and the assumption that ensembles on finite-dimensional Hilbert spaces are characterized by finitely many parameters. This is achieved by taking an operational approach to physical theories, and using the fact that the manner in which a physical system is partitioned into subsystems is a subjective choice of the observer, and hence should not affect the predictions of the theory. In contrast to other approaches, our result does not assume that measurements are related to operators or bases, it does not rely on the universality of quantum mechanics, and it is independent of the interpretation of probability.
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for assigning outcome probabilities (Born's rule) and the post-measurement state-update rule, can be deduced from the other quantum postulates, often referred to as unitary quantum and the assumption that ensembles on finite-dimensional Hilbert spaces are characterised by finitely many parameters. This is achieved by taking an operational approach to physical theories, and using the fact that the manner in which a physical system is partitioned into subsystems is a subjective choice of the observer, and hence should not affect the predictions of the theory. In contrast to other approaches, our result does not assume that measurements are related to operators or bases, it does not rely on the universality of quantum mechanics, and it is independent of the interpretation of probability.