A model of a three-dimensional quantum vacuum as a fundamental arena is introduced where time measured with clocks is only a mathematical parameter, namely the numerical order of changes and the most fundamental physical properties are the energy density and statereduction (RS) processes (of creation-annihilation of quantum particles). This model introduces interesting perspectives in the interpretation of quantum mechanics and has the merit to see the quantum behaviour of matter and gravity as two different aspects of the same source.
A model of a three-dimensional quantum vacuum as a fundamental arena is introduced where time measured with clocks is only a mathematical parameter, namely the numerical order of changes and the most fundamental physical properties are the energy density and statereduction (RS) processes (of creation-annihilation of quantum particles). This model introduces interesting perspectives in the interpretation of quantum mechanics and has the merit to see the quantum behaviour of matter and gravity as two different aspects of the same source.
Most physicists today still conceptualize time as a part of the physical space in which material objects move, although time has never been observed and measured as a part of the space. The concept of time here presented is that time measured with clocks is merely the numerical order of material change, i.e. motion in a three-dimensional space. In special relativity the Minkowskian four-dimensional space-time can be replaced with a three-dimensional space where time does not represent a fourth coordinate of space but must be considered merely as a mathematical quantity measuring the numerical order of material changes. By quantum entanglement the three-dimensional space is a medium of a direct information transfer between quantum particles. Numerical order of non-local correlations between subatomic particles in EPR-type experiments and other immediate quantum processes is zero in the sense that the three-dimensional space acts as an immediate information medium between them.
In the special theory of relativity, space and time are intrinsically linked and united into one manifold called ‘space-time’. The three coordinates x1, x2 and x3 are spatial, the fourth coordinate x4 is temporal. Godel’s idea according to which x4 is spatial too is coherent. In the fourth coordinate x4 = ict, time t is only a component. Mathematical time t is only an element of x4 and represents physical time that is run of clocks in timeless cosmic space. Time t that we gain with clocks is a quantity which describes the numerical order of material changes. Clocks are reference systems for measuring frequency, speed and numerical order of material changes. Time is not part of space. Space itself is timeless. This insight introduces new perspectives in the interpretation of Einstein-Podolsky-Rosen (EPR) experiment — subatomic particles move only into space and not into space-time, and are instantaneously connected through space which functions as an immediate information medium between them. Bohm’s approach introduces the idea that non-local correlations between subatomic particles are linked to the space-like action of quantum potential but is not time-symmetric. To interpret the time-reverse of a quantum process in a correct way (and thus also of the instantaneous communication between subatomic particles), a symmetry in time in quantum mechanics is needed, a symmetrized reformulation of Bohmian mechanics is suggested and its perspectives with regard to the arena of quantum processes are analyzed.
The universe we live in is both strange and interesting. This strangeness comes about because, at the most fundamental level, the universe is governed by the laws of quantum mechanics. This is the most spectacularly accurate and powerful theory ever devised, one that has given us insights into many aspects of the world, from the structure of matter to the meaning of information. This textbook provides a comprehensive account of all things quantum. It starts by introducing the wavefunction and its interpretation as an ephemeral wave of complex probability, before delving into the mathematical formalism of quantum mechanics and exploring its diverse applications, from atomic physics and scattering, to quantum computing. Designed to be accessible, this volume is suitable for both students and researchers, beginning with the basics before progressing to more advanced topics.
A case study of quantum mechanics is investigated in the framework of the philosophical opposition “mathematical model – reality”. All classical science obeys the postulate about the fundamental difference of model and reality, and thus distinguishing epistemology from ontology fundamentally. The theorems about the absence of hidden variables in quantum mechanics imply for it to be “complete” (versus Einstein’s opinion). That consistent completeness (unlike arithmetic to set theory in the foundations of mathematics in Gödel’s opinion) can be interpreted furthermore as the coincidence of model and reality. The paper discusses the option and fact of that coincidence it its base: the fundamental postulate formulated by Niels Bohr about what quantum mechanics studies (unlike all classical science). Quantum mechanics involves and develops further both identification and disjunctive distinction of the global space of the apparatus and the local space of the investigated quantum entity as complementary to each other. This results into the analogical complementarity of model and reality in quantum mechanics. The apparatus turns out to be both absolutely “transparent” and identically coinciding simultaneously with the reflected quantum reality. Thus, the coincidence of model and reality is postulated as necessary condition for cognition in quantum mechanics by Bohr’s postulate and further, embodied in its formalism of the separable complex Hilbert space, in turn, implying the theorems of the absence of hidden variables (or the equivalent to them “conservation of energy conservation” in quantum mechanics). What the apparatus and measured entity exchange cannot be energy (for the different exponents of energy), but quantum information (as a certain, unambiguously determined wave function) therefore a generalized law of conservation, from which the conservation of energy conservation is a corollary. Particularly, the local and global space (rigorously justified in the Standard model) share the complementarity isomorphic to that of model and reality in the foundation of quantum mechanics. On that background, one can think of the troubles of “quantum gravity” as fundamental, direct corollaries from the postulates of quantum mechanics. Gravity can be defined only as a relation or by a pair of non-orthogonal separable complex Hilbert space attachable whether to two “parts” or to a whole and its parts. On the contrary, all the three fundamental interactions in the Standard model are “flat” and only “properties”: they need only a single separable complex Hilbert space to be defined.
Abstract Quantum mechanics and relativity are extraordinarily successful mathematical theories, yet their conventional physical interpretations rely on substantially different conceptual frameworks. The Theory of Space (TS) proposes a fourth dimension defined by the Planck-related interval, with interpreted as a longitudinal dimension associated with energy (cτ), rather than as the conventional Minkowski spacetime interval. This fourth dimension does not coexist continuously with the observable three spatial dimensions as a conventional four-dimensional manifold. Instead, TS proposes an oscillatory existence between observable 3D presence and a non-observable fourth-dimensional phase. Through this oscillation, the quantum system undergoes repeated dimensional projection into observable 3D, with individual eigenstates manifested probabilistically while the underlying quantum state continues to evolve. Within this framework, phenomena including measurement, the Born rule, the arrow of time, entropy, entanglement, tunneling, and Bell-type correlations acquire a common physical interpretation. Heisenberg uncertainty and non-commutativity are interpreted as consequences of physical parameters associated with different phases of the dimensional oscillation and therefore not simultaneously manifested within the same 3D instance. TS further distinguishes between the quantum system’s spatial component and its compact physical entity. Their coexistence within the complete system provides a proposed physical basis for quantum interference and phase-dependent phenomena, including the double-slit experiment and the path-integral description of quantum evolution. As an extension of the model, TS proposes that the periodic displacement and replacement of quantum space generate a pulsed inward spatial flow. This mechanism provides a possible basis for a quantized gravitational interaction and suggests that gravitational energy may be represented by a positive contribution. Related developments, including spiral spatial flows, follow naturally from the same dimensional-oscillation mechanism. The Theory of Space therefore seeks to provide a common conceptual framework for quantum, relativistic, and gravitational phenomena without replacing the established mathematical equations that successfully reproduce experimental observations. The present work develops this framework and invites critical examination of its assumptions, physical implications, and potential experimental consequences. Keywords: relativity; Lorentz transformation; quantum superposition; quantum superposition; collapse; entanglement; quantum gravity