We have shown in a previous article by Olivi-Tran and Gauthier [1] that Heisenberg's uncertainty principle is only an approximation be- cause time can only be equal to zero at the beginning of the constitution of the universe: the Big Bang. Indeed time is related to the local radius of curvature and to the total radius of curvature of the universe for a given location. Moreover, we have shown (see Olivi-Tran's reference [2]) that time has the dimension of a length. So if our three dimensional universe is embedded in a four dimensional universe where the fourth dimension is related to time, it is possible to define a 'universal' system of coordinate (x,y,z,t) for which the precise location of a given object is possible. With these hypothesis, it is possible to make a measure simultaneously on two different locations in the four dimensional space. The EPR paradox comes from the fact that it would not be possible to have two entangled states at two different locations without having to overcome the speed of light to carry information from one particle to the other to which it is intricate. We will see by a simple calculation that the state 'entangled' is only transient as the time is not the same for different locations in our three dimensional universe.
This paper focuses on the reason behind the entanglement phenomena, which is still an unknown fundamental question. It argues that while two entangled particles are separated in the 3D space the flow of information between them is instantaneous through the 4D space. The fourth dimension of space has the unit of measurement of length like the other three space dimensions. We shall call it Q, from the word quatre (four) in French. Its magnitude is equal to the invariant proper time τ times the speed of light c. Q = cτ. Each point in the 4D space corresponds to an event. Distances between events in the four-dimensional space can be computed using the Pythagoras theorem. It is argued that time t as measured by clock in our 3D space times the speed of light gives the length of the position vector of an event in the 4D space. At time t, when an observation is made at one of the entangled particles, the length of the position vectors of both entangled particles, sharing the same wave function, in 4D space are equal to t times the speed of light, i.e., ct. The time t is also the same for all the points on the line connecting the two events in the 3D space. Consequently, the length of the position vectors of all the points on the line connecting the two events in the 3D space is equal to ct in the 4D space. The corresponding points in the 4D space make an arc of equidistance to the origin. It is conjectured that the flow of information between the two entangled particles through this arc in the 4D space is not carried by energy or mass particles. It is, therefore, not bound by the time nor the speed of light constraint in 4D space and is instantaneous.
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.
The EPR paradox appears when measurement results of some properties of two distantly entangled particles are correlated in a way that cannot be explained classically, and apparently violate locality. The resolution of the paradox depends on one’s interpretation of quantum mechanics. Explanations from quantum mechanics remain commonplace today, but they fail to explain the EPR (Einstein, Podolsky and Rosen) paradox totally in a way than can be accepted by the whole community. Here, we present a simple resolution to this paradox in which the uncertainty in the energy of the two-particle system is reduced by its lack of interaction during the journey so that the uncertainty in time becomes greater than the time they have been separating. Consequently, the present and past become indistinguishable because when we measure an observable in the system its value is the same as if the two particle were still together or very close. It is also argued that the destruction of information as the present and past become identical should release heat by Landauer’s principle, and this might make this proposal testable.
Two problems with the Einstein-Podolsky-Rosen argument originate from the difficult-to-explain continual dismissal of Minkowski’s demonstration that the concept of spacetime represents a real four-dimensional world and is not just a mathematical space. The uncritical employment of the traditional three-dimensional language to the description of this argument leads (e.g., in its Bohm's version) to those problems: (1) due to the collapse of the common wavefunction of the constituents 1 and 2 of a disintegrated system, caused by the measurement of 1's spin (event
E1), and due the conservation of the total spin, 2's spin is \textit{instantaneously} determined (event
E2), which in three-dimensional language inescapably means that
E2 is \textit{caused} by
E1 (using merely a different word -- `correlation' -- does not explain anything in three-dimensional language); (2) events
E1 and
E2 are simultaneous \textit{only} for an observer
A, who was at rest with respect to the disintegrated system, and therefore the total spin is not conserved for arbitrarily large periods of time for all observers in relative motion with respect to
A and there exists a class of observers
B for whom event
E2 occurs \textit{before}
E1, which demonstrates the inadequacy of the fundamental implicit assumption that the physical world is three-dimensional. When the reality of spacetime is explicitly recognized, (1) the paradoxes of the non-conservation of the total spin and that
E2 happens before
E1 for observers
B do not arise (because there is no `before' and `after' in spacetime) and the statement that there is a correlation between
E1 and
E2 makes a perfect sense, and (2) a spacetime model of the quantum object can then be considered (by also taking into account the non-fully-realized experimental fact that the quantum object \textit{actually} exists everywhere where its wavefunction is different from zero) in order to address the fundamental incompleteness of quantum mechanics -- that it deals not with the quantum object itself, but only with its states. The paper ends with a discussion of a prediction by the proposed spacetime model of the electron that can be tested experimentally probably by the quadratic Stark effect.
This preprint develops a new framework in which quantum tunneling is interpreted as a transient leap into a higher (4D) spatial dimension. In this view, tunneling does not involve traversal through a classical barrier but rather a geometric shortcut made possible by temporary access to an extended dimension. The paper identifies four key mechanisms that arise naturally in a 4D tunneling model: (1) dimensional leap, (2) time curvature, (3) retrocausality as perceived by 3D observers, and (4) a block-universe connection in which events appear reordered when projected back into 3+1 spacetime. The framework proposes that tunneling time anomalies, apparent superluminality, and non-local correlations may all emerge from this higher-dimensional geometry rather than from probabilistic paradoxes within 3D quantum mechanics. The model is constructed to be falsifiable in principle through precision tunneling-time experiments and correlations in condensed-matter systems. This work serves as a conceptual foundation for understanding tunneling as a geometric phenomenon embedded in extended spacetime structure.
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