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.
What does not satisfy me in that theory [quantum mechanics], from the standpoint of principle, is its attitude towards that which appears to me to be the programmatic aim of all physics: the complete description of any (individual) real situation (as it supposedly exists irrespective of any act of observation or substantiation). Albert Einstein, Reply to Criticisms [This] implies the impossibility of any sharp separation between the behaviour of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear . In fact, the individuality of the typical quantum effects finds its proper expression in the circumstance that any attempt of subdividing the phenomena will demand a change in the experimental arrangement introducing new possibilities of interaction between objects and measuring instruments which in principle cannot be controlled. Consequently, evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomena exhausts the possible information about the objects. Indeed the finite interaction between object and measuring agencies conditioned by the very existence of the quantum of action entails – because of the impossibility of controlling the reaction of the object on the measuring instruments, if these are to serve their purpose – the necessity of a final renunciation of the classical idea of causality and a radical revision of our attitude towards the problem of physical reality. […]
Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates. Here we introduce an axiomatization approach to quantum mechanics which is very similar to special theory of relativity derivation. The core idea is that a composed system obeys the same laws of nature as its components. This leads to a Jordan-Lie algebraic formulation of quantum mechanics. The starting assumptions are minimal: the laws of nature are invariant under time evolution, the laws of nature are invariant under tensor composition, the laws of nature are relational, together with the ability to define a physical state (positivity). Quantum mechanics is singled out by a fifth experimentally justified postulate: nature violates Bell inequalities.
We demonstrate two points: 1) the formalism of quantum mechanics can be understood simply as a structure for the expression of the physical notion that not all observables can have values simultaneously; 2) the specific uncertainty relations can be derived (rigorously) by combination of the invariance principle with a general uncertainty relation based only on the existence of unspecified pairs of conjugate observables. For this purpose, we present a formulation of quantum mechanics based strictly on the invariance principle and a “weak” statement of the uncertainty principle that asserts only the existence of incompatible (conjugate) observables without specifying which observables are incompatible. We go on to show that the invariance principle can be used to develop the equations of motion of the theory, including the Klein-Gordon and Schrodinger equations.
The aim of the research is to develop a dialectical relational-event ontology (DREO), that is, a second-order metaphysical framework designed to resolve the fundamental problems of the philosophy of quantum physics: wave-particle dualism and the irreducible pluralism of interpretations. The scientific novelty of the article lies in the following: for the first time, not just another interpretation of quantum mechanics is proposed, but a meta-framework that dialectically sublates the pluralism of interpretations itself and demonstrates their systemic unity; the category of a "relational event" is introduced as a fundamental unit of being, which marks a transition from substantial metaphysics (debates on the individuality of objects) to a metaphysics of becoming; wave-particle dualism is interpreted not as ontological (two entities) and not as epistemological (N. Bohr's complementarity principle), but as a dialectical contradiction sublated in the concept of "relational potentiality" – a structure of possibilities actualized depending on the perspective; the complementarity of wave and particle for the first time receives ontological status – it is a mode of existence of quantum reality itself as a "pulsation" between modes of actualization; a new model of scientific rationality is substantiated – dialectical pluralism – where truth is not a property of an individual proposition but a property of the entire system of perspectives taken in their dialectical unity, which fundamentally distinguishes DREO from contextual quantum realism (CQR), which remains within the static opposition of "rule – application" and epistemological perspectivism. The key results of the study are the following ideas: a relational event (rather than an object or a relation in itself) is recognized as the fundamental unit of being – a discrete act of transition from the potential to the actual in a specific context of interaction; "particle" and "wave" are interpreted as two extreme, mutually exclusive and simultaneously complementary types of actualization of a single structure of potencies in different perspectives; the multiplicity of incompatible but empirically equivalent interpretations of quantum mechanics is shown not as a flaw in the theory, but as a logical consequence of the relational structure of reality, which requires a multitude of complementary perspectives for its adequate expression. Thus, the century-old opposition between objectivism and relativism in the philosophy of science is removed.