A New Entry into Quantum Mechanics and Relativity Opened by NNRT A Turn toward Universal Physical Spacetime and the Repositioning of Hilbert Space and Observational Spacetime-Clarifying the Common Origin of Quantum and Relativistic Paradoxes
Conventional relativity places four-dimensional spacetime connected by Lorentz transformations, and fourdimensional spacetime curved by gravity, at the foundation of physical spacetime, whereas quantum mechanics places Hilbert space at the foundation of state description. As long as these two structures are simultaneously treated as fundamental realities, relativistic quantum theory and quantum gravity must begin with the problem of how a dynamically curved spacetime is to be quantized and made consistent with Hilbert-space states. Nakaza New Relativity Theory (NNRT) changes this very point of departure. NNRT takes universal time and universal three-dimensional space as physical spacetime and connects the real motions of all inertial systems by the Galilean Transformation (GT), while relocating the Lorentz transformation, time dilation, length contraction, and the gravitational metric to the observational and measurement layer obtained through electromagnetic phase. The successful mathematics and experimental values of conventional relativity are therefore retained, but the ontology in which curved and deformable four-dimensional spacetime is the unique physical spacetime is not retained. This paper uses NNRT as a new entry into quantum mechanics and repositions Hilbert space not as physical space, but as a mathematical representation space that preserves states, phases, probabilities, and correlations. Using the atomic clock as a concrete example, the paper further presents a continuous observational chain in which quantum levels generate a frequency scale and the resulting phase signal is compared between systems through relative motion and gravitational fields. Accordingly, the conventional entry point—how to quantize a physically real curved four-dimensional spacetime and incorporate it into Hilbert space—loses its premise within NNRT, and quantum theory and relativity are reconstructed as distinct representational and observational structures arising from a common universal physical spacetime. Schrödinger’s cat, EPR/Bell correlations, time dilation, length contraction, the twin problem, and the reification of the gravitational metric can then be organized as manifestations of a common ontological operation: identifying a mathematical representation with physical reality itself. The significance of this paper is therefore not to add another interpretation alongside conventional relativity, but to absorb its successful mathematics into the observational layer of NNRT and, by turning the ontological point of departure, to provide a new formulation of foundational problems that includes quantum mechanics.
Conventional relativity places four-dimensional spacetime connected by Lorentz transformations, and fourdimensional spacetime curved by gravity, at the foundation of physical spacetime, whereas quantum mechanics places Hilbert space at the foundation of state description. As long as these two structures are simultaneously treated as fundamental realities, relativistic quantum theory and quantum gravity must begin with the problem of how a dynamically curved spacetime is to be quantized and made consistent with Hilbert-space states. Nakaza New Relativity Theory (NNRT) changes this very point of departure. NNRT takes universal time and universal three-dimensional space as physical spacetime and connects the real motions of all inertial systems by the Galilean Transformation (GT), while relocating the Lorentz transformation, time dilation, length contraction, and the gravitational metric to the observational and measurement layer obtained through electromagnetic phase. The successful mathematics and experimental values of conventional relativity are therefore retained, but the ontology in which curved and deformable four-dimensional spacetime is the unique physical spacetime is not retained. This paper uses NNRT as a new entry into quantum mechanics and repositions Hilbert space not as physical space, but as a mathematical representation space that preserves states, phases, probabilities, and correlations. Using the atomic clock as a concrete example, the paper further presents a continuous observational chain in which quantum levels generate a frequency scale and the resulting phase signal is compared between systems through relative motion and gravitational fields. Accordingly, the conventional entry point—how to quantize a physically real curved four-dimensional spacetime and incorporate it into Hilbert space—loses its premise within NNRT, and quantum theory and relativity are reconstructed as distinct representational and observational structures arising from a common universal physical spacetime. Schrödinger’s cat, EPR/Bell correlations, time dilation, length contraction, the twin problem, and the reification of the gravitational metric can then be organized as manifestations of a common ontological operation: identifying a mathematical representation with physical reality itself. The significance of this paper is therefore not to add another interpretation alongside conventional relativity, but to absorb its successful mathematics into the observational layer of NNRT and, by turning the ontological point of departure, to provide a new formulation of foundational problems that includes quantum mechanics.
This paper begins with a question concerning the physical meaning of 𝑚0𝑐2 as it appears in the relativistic energy relation 𝐸2 = 𝑝2𝑐2 + 𝑚02𝑐4. The numerical relations 𝐸 = 𝑚0𝑐2 and 𝐸 = 𝛥𝑚𝑐2 are supported by precise experiments, but the ontology to which these mathematical quantities are assigned is a separate issue. This question leads directly to a reconsideration of the standard relativistic picture in which the relativistic time and relativistic length introduced by Einstein in 1905, and later geometrized as spacetime after Minkowski, are attributed to the physical world itself. The same issue appears in quantum theory. The relativistic energy–momentum relation connects to relativistic quantum-wave structures and, in the nonrelativistic regime, to Schrödinger mechanics; however, it does not follow uniquely from the mathematics that the wave function, probability, and uncertainty must be interpreted as properties of reality itself. The present paper identifies a common root of these two problems in the identification of mathematically observed quantities with reality itself. The Nakaza New Relativity Theory (NNRT) places an invariant real spacetime, consisting of universal time and universal space, as its physical basis. It does not, however, assume an absolute rest frame or an ether, and it regards all inertial frames as physically equivalent. In contrast, time, distance, phase, frequency, wavenumber, arrival time, and related quantities constructed through actual measurement are separated as quantities of measurement spacetime. The logical boundary between observational agreement and ontological identification is formulated here as the Observational–Ontological Non-Uniqueness Proposition (OONP). Taking the phase–action correspondence 𝛩 = 𝑆⁄ℏ, 𝑘𝜇(𝛩) = 𝜕𝜇𝛩, and 𝑃𝜇(𝛷) = ℏ𝑘𝜇(𝛩) as a common bridge, the dispersion structure of a single Fourier mode is organized as relativistic observation, whereas the superposition of multiple modes and Fourier duality are organized as quantum observation. In this framework, 𝛥𝑥𝛥𝑝 ≥ ℏ⁄2 is first interpreted as a bandwidth–localization constraint of a phasebased observational representation, while the Born rule, Hilbert space, and unitary evolution are retained as standard quantum mathematics in the quantum-observational layer. Furthermore, 𝑚0𝑐2 is reconstructed as the phase-invariant base scale 𝐵𝛷 = ℏ√𝜔2 − 𝑐2𝑘2 = 𝑚0𝑐2. What this paper changes is neither established mathematics nor experimental values. NNRT explicitly rejects the physical definition according to which relativistic time, relativistic length, and relativistic spacetime are properties of real time and real space themselves. It therefore proposes that these concepts be removed from the foundational description of real spacetime and be confined to the mathematics of measurement and observation.
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
The Theory of Temporal Relativity proposes a unified theoretical framework that extends Special and General Relativity into the complex domain, integrating aspects of Quantum Mechanics within a single geometrical structure. The theory introduces a generalized Hilbert-space geometry and interprets quantum states as observer-dependent, arising from complex temporal relations between reference frames. Theory of Temporal Relativity is a theoretical framework proposing a unified extension of Special and General Relativity into the complex domain, with the goal of incorporating aspects of Quantum Mechanics within a consistent geometrical model. The theory generalizes Hilbert-space geometry and relativistic invariance to complex coordinates, introducing observer-dependent descriptions of physical quantities and a reinterpretation of quantum states as complex-phase relations between reference frames. Within this model, fundamental constants such as c, G, and h are not strictly universal but can exhibit apparent local variations arising from the observer’s position in the complex spacetime manifold. These variations preserve global covariance and CPT symmetry while reconciling quantum non-locality with relativistic kinematics. The framework predicts experimentally testable effects, including measurable phase shifts in interferometric experiments, possible frequency modulations in non-inertial systems, and small local deviations of physical constants detectable in condensed-matter and gravitational contexts. The supplementary work, “Quantum Uncertainty, Planck’s Constant, and Ontological Insights from Complex Spacetime Geometry and Local Metric Deformations”, develops the principle of Temporal Relativity as a foundational element of the theory. It formalizes the connection between quantum uncertainty, metric deformations, and complex temporal structures, within an alternative logical framework (AU). This extension provides both an ontological interpretation of the wavefunction and a basis for the emergence of quantum indeterminacy from geometric causes. Together, these works present a coherent attempt to unify the relativistic and quantum domains under a single complex-geometric view of spacetime, maintaining mathematical rigor while providing clear experimental pathways for empirical validation.
Quantum mechanics came to employ complex probability amplitudes and the abstract state space known as Hilbert space because the behavior of electrons and light could not be described by the intuition of classical three-dimensional space alone. Complex numbers retain the magnitude and phase of an amplitude within a single quantity, while Hilbert space unifies linear superposition, inner products, observables, and time evolution in one mathematical framework. This made it possible to describe point-like particle detections and wave-like interference within the same theory. Yet this mathematical success also raised an ontological question: should the state structure in Hilbert space be read as physical reality itself? That question developed into long-standing debates over Schrödinger’s cat, the measurement problem, quantum entanglement, and nonlocality. This paper traces that history for a general readership and applies to quantum theory the distinction, emphasized by NNRT in relativity, between “successful mathematics” and “the physical reality of the mathematical object.” It then argues that physics remains incomplete at that stage: the next central task is to identify the physical mechanism—what acts on what, and how—that gives rise to the observed phenomena. Central thesis: Three questions must be distinguished: whether mathematics correctly describes a phenomenon, whether the mathematical structure itself is physical reality, and whether the physical mechanism producing the phenomenon is actually understood.
By expanding the research paradigm and reconciling the two binary oppositions of "relative and absolute" and "quantum and classical" in physics, a new theoretical framework that is compatible with relativity and quantum mechanics is proposed. Firstly, excavate and establish three universal axioms: Axiom 1 (consensus guarantees equal rights), Axiom 2 (objective existence independent of measurement), and Axiom 3 (universality of causality and dialectical logic), based on which to criticize the logical contradictions of existing theories. In the field of relativity, this article points out that there is a logical paradox in the explanation of "clock slowing down depends on relative motion" in special relativity (A clock is both faster and slower than B clock), and proposes a relative absolute spacetime view that "absolute motion leads to clock slowing down". By extending the Lorentz transformation, absolute motion and relative motion are unified, solving problems such as the twin paradox. At the same time, based on the prediction of the Dirac equation for negative mass matter, the "negative mass spacetime curvature paradox" is proposed, challenging Einstein's physical explanation of spacetime curvature and arguing that it is only a mathematical tool (the mathematical expression of gravity) rather than a physical reality. In the field of quantum mechanics, this article criticizes the Copenhagen interpretation for violating Axiom 2 (denying the independent eigenstates of microscopic particles). By modifying the Schrödinger equation twice (For the first time, electromagnetic potential energy was replaced with gravitational potential energy, and the Schrödinger-Tu equation was established to describe macroscopic objects such as the Earth's revolution; The second step is to convert potential energy into electromagnetic/gravitational force and derive the wave mechanics equation of classical mechanics laws, such as Newton's second law with force operator), proves that quantum and classical theories are compatible within the same mathematical framework. In the experiment, it was demonstrated through the "anti-interference electron diffraction experiment" that a strong magnetic field only changes the shape of diffraction fringes without causing them to disappear, denying the inevitability of quantum decoherence. The establishment of "generalized wave dynamics" and "relative absolute spacetime view" breaks the binary opposition of traditional theories and provides a new paradigm for the unity of relativity and quantum mechanics. The core value of these jobs lies in: In terms of theoretical innovation, reconstruct the space-time and quantum interpretation system, while retaining the original mathematical form system; In terms of experimental verification, design feasible schemes such as hollow glass disk Jones experiment and geometric optical velocimetry experiment; In terms of philosophical significance, replacing "mathematical symmetry" with "content unity" and returning to the objectivity of physical mechanisms. The research conclusion indicates that by expanding paradigms and axiomatic constraints, the contradiction between relativity and quantum mechanics can be transformed into a complementary relationship, laying the foundation for the great unity of physics theory
In general relativity, the description of spacetime relies on idealised rods and clocks, which identify a reference frame. In any concrete scenario, reference frames are associated to physical systems, which are ultimately quantum in nature. A relativistic description of the laws of physics hence needs to take into account such quantum reference frames (QRFs), through which spacetime can be given an operational meaning. Here, we introduce the notion of a spacetime quantum reference frame, associated to a quantum particle in spacetime. Such formulation has the advantage of treating space and time on equal footing, and of allowing us to describe the dynamical evolution of a set of quantum systems from the perspective of another quantum system, where the parameter in which the rest of the physical systems evolves coincides with the proper time of the particle taken as the QRF. Crucially, the proper times in two different QRFs are not related by a standard transformation, but they might be in a quantum superposition one with respect to the other.Concretely, we consider a system of N relativistic quantum particles in a weak gravitational field, and introduce a timeless formulation in which the global state of the N particles appears "frozen", but the dynamical evolution is recovered in terms of relational quantities. The position and momentum Hilbert space of the particles is used to fix the QRF via a transformation to the local frame of the particle such that the metric is locally inertial at the origin of the QRF. The internal Hilbert space corresponds to the clock space, which keeps the proper time in the local frame of the particle. Thanks to this fully relational construction we show how the remaining particles evolve dynamically in the relational variables from the perspective of the QRF. The construction proposed here includes the Page-Wootters mechanism for non interacting clocks when the external degrees of freedom are neglected. Finally, we find that a quantum superposition of gravitational redshifts and a quantum superposition of special-relativistic time dilations can be observed in the QRF.