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.
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.
In relativistic mechanics the time-like vector characterize the motion in spacetime with speed faster than the speed of light in vacuum c in which the line element ds2=c2dt2-dx2-dx2-dz2 is less than zero (where is infinitesimal change in time, and are infinitesimal change in space), thus the time in relativistic mechanics can instantaneously flow [1], however in quantum mechanics although the time is treated as unobservable parameter (without any Hermitian observable operator have engine-value equivalent to time) any two physical quantity described by two non-commuting observable operatorsand fulfill , the knowledge of one immediately produce the knowledge of the other [2], thus in quantum mechanics if two particles interacted in finite temporal epoch and then separated in space the gaining of knowledge by the local measurement of physical quantity runs on one them (for example the measurement of spin direction of one particle using Stern-Gerlach experiment) immediately produce the knowledge of the complementary physical quantity of the other particle (for example the opposite spin direction of the other particle), this simply called quantum entanglement the concept that so much advanced after publication of the Jon Bell’s 1964 celebrated paper [3] in which he illustrated that we can add parameters to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, and then he conclude “there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously so that such a theory could not be Lorentz invariant”. The question now what these signals that can propagate instantaneously? The answer in this paper will be the time signals field which is defined for each constituent matter particle M and at each space point P as the measure of the total length of all occupation and leaving epochs of P by M which is representing a sequence function compactly supported only at the space point occupied by it and indexed by the number of occupation epochs of P by M, thus the flow of this time signal field from the far future to near future through the present to the near past to the far past inferable by the flow of matter particles constituting the system(such as sun, moon earth and clocks hands). Thus the present will represent in this paper a local absolute feature of time signals field defined at each space point as the set of all occupation epochs of it by matter particle, however the past and future will represent relativistic non-local features of the time signal field defined at each space point as a set of all leaving epochs between each two sequential occupation epochs, so the future after one occupation epoch is representing a past of the next one. Thus according to current representation of time, the two Mc-Taggard’s A and B series of time [4] will exist together as temporal set and then the time is real, the A-series in current theory is a set of all occupation and leaving epochs of space point by the matter particle that is consisting of the present, past and future epochs, and the B-series is the set of all leaving epochs of space points between each two sequential occupation epochs which are taking position before or after the discrete occupation epochs between them and then before or after each other.
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 introduces a framework to the novel Theory of Space that seeks to unify quantum mechanics and special relativity by redefining the fourth dimension as an energy-dependent longitudinal parameter. The theory posits that quantum systems oscillate between observable three-dimensional (3D) space and the energetic fourth dimension ?p = C?, where ? = h/E is Planck?s periodic time. It offers a new explanation for quantum superposition, the measurement problem, and entanglement through random 3D projections from a 4D superposition, thus removing the necessity for observer-induced collapse theories or many-worlds interpretations. It resolves the wave particle duality by treating quantum oscillating space and compact entities (e.g., mass particles or pulsed fields) as coexisting. The Bell?s inequality violations are addressed via a fourth-dimensional locality during the oscillation, preserving 3D causality of entangled particles. The model also reinterprets relativistic effects as scale changes driven by energy and proposes a gravitational mechanism via an inward space flow proportional to energy content. A testable prediction is provided through a photon tunneling experiment, demonstrating sinusoidal probability variations. Additional prediction for no time dilation during free fall body?s is made. This framework offers a unified, realistic, and local description of quantum and relativistic phenomena, with implications for future experimental validation.
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
Since his famous discussions with Niels Bohr, Albert Einstein considered quantum entanglement (QE) as a spooky action at a distance, due to the violation of locality necessary so that two entangled particles can share this effect in an instantaneous way despite of being at a great distance from each other, i.e., not being local. In other words, a notification about the change of state in one of them could only cover the space that separates them at a speed superior to that of light, which we know is impossible according to the Theory of Relativity (TR). Besides, QE faces directly the two main pillars of Physics: TR and Quantum Theory (QT); becoming the bone of contention between both theories. Quite the contrary, in this work we will see that QE is the meeting point of both theories, so much so, that QE could be considered as the cornerstone of the Theory of Everything (TOE). Consistent with this, the entangled particles retain certain autonomy unknown to date, and in addition, they will have relativistically entangled alter-egos, which will hold the effect even when the original entangled particles are extremely separated from each other. These alter-egos can be considered as black holes (with their corresponding temperature and entropy) giving rise to a wormhole. This is possible since the locality dilates according to the Lorentz factor, which is accompanied by a contraction in the effective channel and in the temporal delay to cross that channel. All this takes place while space-time is curved (hyperspace) to generate the wormhole between both black holes. In other words, QE is a local effect of infinite range so it does not outpace the speed of light, and therefore QT is a complete theory that does not clash with TR. Finally, everything we have said has direct consequences on the link between entangled particles from the point of view of quantum communications in terms of the channel and its bandwidth, latency, capacity, robustness and security.
Since his famous discussions with Niels Bohr, Albert Einstein considered quantum entanglement (QE) as a spooky action at a distance, due to the violation of locality necessary for the state of the particle entangled with its companion to share at same a distance, in such a way that if a notification that is not local but instantaneous could only cover that space at a speed superior to that of light. The Theory of Relativity (TR) with Quantum Theory (QT) would face a direct consequence of this; turning QE into the bone of contention between both theories, which are no more than the pillars of Physics. Contrary to predictions, in this work we will see that QE is the meeting point of both theories, so much so, that QE could be considered as the cornerstone of the Theory of Everything (TOE). Consistent with this, the entangled particles retain certain autonomy unknown to date, and in addition, they have relativistically entangled alter egos, which will hold the effect even when the original entangled particles are extremely separated from each other. These alter-egos can be considered as black holes (with their corresponding temperature and entropy) giving rise to a wormhole. This is possible since the locality dilates according to the Lorentz factor, which is accompanied by a contraction in the effective channel and in the temporal delay to cross that channel. All this takes place while space-time is curved (hyperspace) to generate the wormhole between both black holes. In other words, QE is a local effect of infinite range so it does not outpace the speed of light, and therefore QT is a complete theory that does not clash with TR. Finally, everything we have said has direct consequences on the link between entangled particles from the point of view of quantum communications in terms of the channel and its bandwidth, latency, capacity, robustness and security.