The general view is that all fundamental physical laws should be formulated within the framework given by quantum mechanics (QM). In a sense, QM therefore has the character of a metaphysical theory. Consequently, if it is possible to derive QM from more basic principles, these principles should be of general, philosophical nature. Here, we derive the formalism of QM from well-motivated epistemic principles. A key assumption is that a physical theory that relies on entities or distinctions that are unknowable in principle gives rise to wrong predictions. First, an epistemic formalism is developed, using concepts like knowledge and potential knowledge, identifying a physical state
S with the potential knowledge of the physical world. It is demonstrated that QM emerges from this formalism. However, Hilbert spaces, wave functions and probabilities are defined in certain well-defined observational contexts only. This means that the epistemic formalism is broader than QM. In the fundamental layer of description, the physical state
S is a subset of a state space
S={Z}, such that
S always contains many elements
Z. These elements correspond to unattainable states of complete knowledge of the world. The evolution of
S cannot be determined in terms of the individual evolution of the elements
Z, unlike the evolution of an ensemble in classical phase space. The evolution of
S is described in terms of sequential time
n∈N, which is updated according to
n→n+1 each time an event occurs, each time potential knowledge changes. Sequential time
n can be separated from relational time
t, which describes distances between events in space-time. There is an entire space-time associated with each
n, in which
t represents the knowledge at sequential time
n about the temporal relations between present and past events.
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical principles underlying the theory, we rigorously construct a discrete model of quantum mechanics. Kets are names, or labels which categorise states of matter but do not directly describe them. The principle of superposition is seen as a definitional truism in the categorisation of states. This resolves the measurement problem of quantum mechanics by attributing the collapse of the wave function to information. The probability interpretation has a natural meaning in which the configuration of interacting particles plays the role of a hidden variable. The model supports a form of relativistic quantum field theory which does not depend on quantisation or second quantisation from classical mechanics. Continuous laws of wave mechanics are found in a discrete metaphysic which does not involve waves. Classical law is the expected behaviour of many elementary particles. The constraints on the theory are sufficient to establish that particles are point-like entities with specific properties found in nature. Newton's first law and conservation of momentum are established from the principle of homogeneity. Maxwell's equations are derived from the simple interaction in which a Dirac particle emits or absorbs a photon. Feynman rules are calculated for the discrete theory and differ from the standard rules by the removal of the ultraviolet divergence and the use of proper loop integrals. They give finite and unambiguous results.
Quantum Mechanics is a successful model to describe physical phenomena. We show that a simple set of postulates about the description of objects in Nature allows the derivation of the principles of QM, transforming this theory into a deductive approach to Physics. The main postulate is: Objects are described as energy distributions in Space–Time. 1 Quantum Mechanics from START It is universally accepted that Quantum Mechanics is a successful model to describe physical phenomena, in particular of the electronic structure of atoms, molecules and solids. As such it has been reformulated in several different forms (see for example: Nine formulations of quantum mechanics, Daniel F. Styer et al. [15]). The aim of the present paper is to show that a simple set of postulates about the description of objects in Nature allows the derivation of the principles of QM, transforming this theory into a deductive approach to Physics. In our approach the main postulate is: Objects are described as energy distributions in Space–Time. The theory is in fact a systematic mathematical analysis of this postulate and of other general considerations about action, energy–momentum and the role of the theory as a useful description of Nature. The paper also shows the fundamental and basic status of Density Functional Theory, also contained in our approach. The initial mathematical structure is a geometric (quadratic form based) union of space, time and action. In physics bundles of trajectories are used to describe the objects of nature: distribution of heights over a surface, a real object is described as a bundle of space-time trajectories, here we use a description as a bundle of action valves in space-time (energy densities in space following light-like lines). The author is fully aware that the presentation is strongly guided by the knowledge of the usual computational approach to study atoms, molecules and condensed matter electronic structure.
Despite its power as the conceptual basis for a huge range of physical phenomena in atomic and subatomic physics, quantum mechanics still suffers from a lack of clarity regarding the physical meaning of its fundamental theoretical concepts, such as those of quantum state and of quantum theoretical quantities or variables , dealt with by the known mathematical-theoretical rules. These concepts have generally been considered as not giving a direct description of physical systems, for they do not correspond to what is usually understood by `physical states' or `physical properties', notably characterized by definite numerical values such as those obtained from measurement. The situation has been tentatively expressed in terms of various `interpretations', conceived not only with regard to the physical meanings of mathematical quantities, but also in connection with philosophical statements about `physical reality'. The question of whether or not quantum theoretical quantities describe definite physical systems existing in nature has therefore generally been considered as beyond the possibilities of physics, because of the definitions that are commonly taken for `physical state' and `physical quantity'. We sketch the main ideas on this problem and propose a possible way out of the puzzle, in terms of an extension of the meaning given to the concepts of the physical state and physical quantity of a system, which would allow one, without any theoretical change in quantum mechanics, to speak consistently of real quantum systems as having definite physical properties .
Abstract Addressing the epistemological dilemmas regarding the "a priori absolute spacetime container" and the "subjective observer effect" in classical physics and modern quantum mechanics, this study proposes Resistance-Anchored Realism (RAT). The theory first reviews and deconstructs the core theoretical disputes in traditional physics: on the one hand, the classical paradigm treats three-dimensional space and the continuous real time axis () as a priori containers, which logically violates the principle of background independence inherent to physical interactions and gives rise to contradictions in the arrow of time and entropy increase, such as Loschmidt's Paradox; on the other hand, traditional quantum observer theories, such as the Copenhagen interpretation, attributing wave function collapse to subjective factors or ill-defined classical-quantum boundaries" leading to mystical misinterpretations of quantum non-locality and action-at-a-distance. To this end, this study reconstructs three major theoretical achievements: Deconstruction of Spacetime Protocols: Reconstructs macroscopic continuous space and continuous time as "topological classification and distance reduction protocols" used by macroscopic probe systems when processing multi-point interaction correlations. Defines the irreversible closed loop of "Action Operator Resistance Operator " as the minimum endogenous time unit (Interaction Round ), proves that the continuous time domain is an algebraic total order forcibly projected from a sequence of discrete non-commuting operators, and explains thermodynamic entropy increase based on Landauer's Principle as the inerasability of the interface "resistance log," thereby self-consistently resolving the classical time paradox. Reconstruction of the Quantum Measurement Interface: Rejects the "conscious participation" hypothesis and redefines measurement as an intervention process in which a macroscopic probe applies irreversible physical action to a microscopic non-local field. Proves that "wave function collapse" is not the physical contraction of a spatial entity, but the irreversible convergence of the probability distribution of the potential resistance spectrum on the interface, where the operator's eigenvalues represent the strict impedance quota yielded by the resistance field; simultaneously deconstructs quantum entanglement as multi-point projections of a single underlying non-local entity in regions where the spatial protocol fails. Deduction Beyond Local Protocols: Analyzes the self-referential epistemological closed loop of local electromagnetic probes measuring -phenomena via speed-of-light hardware, reconstructing the speed of light as the maximum refresh rate (Ticker Rate) of the electromagnetic probe interface; deduces non-local/topological action mechanisms based on the conjecture, providing a theoretical framework and falsifiable predictions for physical interactions that bypass traditional three-dimensional spatial manifold rendering pathways. This theory achieves a high-dimensional unification of "objective resistance reality" and "spacetime/causal protocolity," driving physics and epistemology away from "a priori entity/truth anchoring" and toward "dynamic resistance/feedback anchoring."
A physical theory, in the narrow sense of the word, is a logical structure based on assumptions and definitions which permits one to predict the outcome of a maximum number of different experiments on the basis of a minimum number of postulates. One usually desires the postulates to be as self-evident as possible; one demands simplicity, beauty, and even elegance. A physical theory seems to have only a finite lifetime. Newtonian mechanics was replaced by relativistic mechanics, thermodynamics by statistical mechanics, classical by quantum mechanics. There is a logical order in theoretical physics. Indeed, such an order is necessary if the endeavor of theoretical physics is to be meaningful and is to succeed in the direction of more and more general axiomatic deductive systems. The relationship between classical and quantum mechanics is especially interesting. The chapter also presents an overview of the key concepts discussed in this book.