Abstract We propose a special relativistic framework for quantum mechanics. It is based on introducing a Hilbert space for events. Events are taken as primitive notions (as customary in relativity), whereas quantum systems (e.g. fields and particles) are emergent in the form of joint probability amplitudes for position and time of events. Textbook relativistic quantum mechanics and quantum field theory can be recovered by dividing the event Hilbert spaces into space and time (a foliation) and then conditioning the event states onto the time part. Our theory satisfies the full Lorentz symmetry as a ‘geometric’ unitary transformation, and possesses relativistic observables for space (location of an event) and time (position in time of an event).
Abstract We propose a special relativistic framework for quantum mechanics. It is based on introducing a Hilbert space for events. Events are taken as primitive notions (as customary in relativity), whereas quantum systems (e.g. fields and particles) are emergent in the form of joint probability amplitudes for position and time of events. Textbook relativistic quantum mechanics and quantum field theory can be recovered by dividing the event Hilbert spaces into space and time (a foliation) and then conditioning the event states onto the time part. Our theory satisfies the full Lorentz symmetry as a ‘geometric’ unitary transformation, and possesses relativistic observables for space (location of an event) and time (position in time of an event).
A physical theory is proposed that obeys both the principles of special relativity and of quantum mechanics. Time and space are treated on exactly the same footing, namely as quantum mechanical observables on a Hilbert space. The theory is not based upon Lagrangian or Hamiltonian mechanics and cannot be formulated within the framework of unitary dynamics. As a most important aspect, the theory breaks with the concept of a continuously flowing time in favour of a discrete jump process in spacetime. All physical statements are formulated in terms of detector events rather than particle states. The physical object under consideration is a spinless particle in empty space. Yet the theory also accounts for particle-antiparticle pair creation and annihilation, and is therefore not a single-particle theory in the strict sense. The Maxwell equations are derived as a straightforward consequence of some fundamental commutation relations. In the non-relativistic limit, and in the limit of infinitely small time uncertainties, one obtains the familiar Schr\\"odinger equation of a spinless particle exposed to an external electromagnetic field.
Abstract The phase space of a relativistic system can be identified with the future tube of complexified Minkowski space. As well as a complex structure and a symplectic structure, the future tube, seen as an eight-dimensional real manifold, is endowed with a natural positive-definite Riemannian metric that accommodates the underlying geometry of the indefinite Minkowski space metric, together with its symmetry group. A unitary representation of the 15-parameter group of conformal transformations can then be constructed that acts upon the Hilbert space of square-integrable holomorphic functions on the future tube. These structures are enough to allow one to put forward a quantum theory of phase-space events. In particular, a theory of quantum measurement can be formulated in a relativistic setting, based on the use of positive operator valued measures, for the detection of phase-space events, hence allowing one to assign probabilities to the outcomes of joint space-time and four-momentum measurements in a manifestly covariant framework. This leads to a localization theorem for phase-space events in relativistic quantum theory, determined by the associated Compton wavelength.
A physical theory is proposed that obeys both the principles of special relativity and of quantum mechanics. As a key feature, the laws are formulated in terms of quantum events rather than of particle states. Temporal and spatial coordinates of a quantum event are treated on equal footing, namely as self-adjoint operators on a Hilbert space. The theory is not based upon Lagrangian or Hamiltonian mechanics, and breaks with the concept of a continuously flowing time. The physical object under consideration is a spinless particle exposed to an external potential. The theory also accounts for particle-antiparticle pair creation and annihilation, and is therefore not a single-particle theory in the usual sense. The Maxwell equations are derived as a straightforward consequence of certain fundamental commutation relations. In the non-relativistic limit and in the limit of vanishing time uncertainty, the Schrödinger equation of a spinless particle exposed to an external electromagnetic field is obtained.
In special relativity, time and space are transformed according to the Lorentz transformation. Relativistic quantum mechanics is quantum mechanics that is consistent with special relativity. Nevertheless, relativistic quantum mechanics is only an approximation to a fully self-consistent relativistic theory of known particle interactions because it does not describe cases where the number of particles changes. In special relativity, mass can emerge from energy, which is not possible in quantum mechanics based on the conservation of probability. Dirac proposed the equation named after him to solve the difficulty encountered in the Klein-Gordon equation stemmed from the fact that it is a second-order differential equation in time.
Abstract The conceptual unification of quantum mechanics and relativity remains one of the central challenges of modern theoretical physics. While quantum theory successfully describes microscopic phenomena through probabilistic wave dynamics and field quantization, relativity establishes the geometric structure of space-time and the causal organization of physical events. Despite extensive progress in quantum field theory and relativistic quantum frameworks, foundational tensions persist regarding locality, causality, and coherence. This study presents a conceptual and structural analysis of quantum field coherence within relativistic space-time. Rather than focusing on specific unification proposals, we examine the compatibility conditions between quantum coherence, relativistic causality, and space-time structure. Particular attention is given to field-based interpretations of quantum states, entanglement propagation limits, and covariance requirements. The analysis synthesizes perspectives from relativistic quantum field theory, conceptual foundations of quantum measurement, and geometric interpretations of space-time. We argue that coherence phenomena can be understood as structurally constrained by relativistic causal order, without requiring violation of space-time locality. The aim of this article is to clarify foundational relationships between quantum coherence and relativistic structure through a conceptual framework that integrates field-theoretic and geometric viewpoints.
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.