This work presents a speculative theoretical model for a novel quantum gate inspired by the properties of tachyons, hypothetical particles associated with speeds greater than that of light. The research proposes the Tachyonic Phase Gate (TPG), a quantum gate based on non-Hermitian dynamics and PT symmetry, exploring how a tachyonic field could modify quantum states in ways inaccessible to conventional quantum gates. The article develops a description of the mathematical and conceptual architecture of the TPG, including its dynamic behavior, transitions between different physical phases, and effects on the states of individual qubits and entangled systems. A tachyonic entanglement gate for two qubits is also introduced, and potential connections with phenomena such as closed time-curves, relativistic causality, and advanced computational complexity are analyzed. Furthermore, the work compares TPG with standard quantum computing gates, showing that this approach could formally extend traditional models of quantum operations to non-unitary regimes inspired by imaginary mass physics and PT-symmetric systems. The study emphasizes that tachyons lack experimental evidence and that the proposed framework is explicitly speculative. However, some mathematical elements related to non-Hermitian dynamics and PT symmetry do have experimental support in modern optical systems, making the work a conceptual exploration of possible future extensions of quantum computing and theoretical physics.
This work presents a speculative theoretical model for a novel quantum gate inspired by the properties of tachyons, hypothetical particles associated with speeds greater than that of light. The research proposes the Tachyonic Phase Gate (TPG), a quantum gate based on non-Hermitian dynamics and PT symmetry, exploring how a tachyonic field could modify quantum states in ways inaccessible to conventional quantum gates. The article develops a description of the mathematical and conceptual architecture of the TPG, including its dynamic behavior, transitions between different physical phases, and effects on the states of individual qubits and entangled systems. A tachyonic entanglement gate for two qubits is also introduced, and potential connections with phenomena such as closed time-curves, relativistic causality, and advanced computational complexity are analyzed. Furthermore, the work compares TPG with standard quantum computing gates, showing that this approach could formally extend traditional models of quantum operations to non-unitary regimes inspired by imaginary mass physics and PT-symmetric systems. The study emphasizes that tachyons lack experimental evidence and that the proposed framework is explicitly speculative. However, some mathematical elements related to non-Hermitian dynamics and PT symmetry do have experimental support in modern optical systems, making the work a conceptual exploration of possible future extensions of quantum computing and theoretical physics.
Unifying quantum mechanics and special relativity, the Dirac equation describes the behaviour of relativistic quantum particles, including imaginary-mass particles with faster-than-light speeds (e.g., tachyon). However, experimental searches for such particles remain negative so far. Fortunately, there are possibilities to investigate the relativistic quantum effects by quantum simulations using a controllable system. However, these simulations are mostly explored in closed physical systems that hinders the demonstration of imaginary-mass particles, whereas the general open framework would promise more possibilities in quantum simulations. Here, we reveal that the dynamic behaviors of imaginary-mass particles can be mapped to the transfer of wave packet in a non-Hermitian silicon optical lattice. We experimentally demonstrate a super-divergent dynamics of tachyon that travels faster than massless particles (e.g., photon). Besides, our simulation suggests another kind of imaginary-mass particles that have rarely been explored, which show non-divergent behaviors with imaginary energy. It is the first experimental quantum simulation being able to observe the imaginary-mass particles that have never been experimentally verified. Our work provides a fully controllable and extensible platform to investigate relativistic quantum phenomena at a chip-scale level, which would inspire more insightful explorations in quantum effects with non-Hermiticity.
This work is a revised version (Version 2) of a previous paper by the author, presented in a manner intended to emphasize more clearly the connection between its epistemological postulates and the subsequent development of its formalism. Several modifications have been introduced, and new sections have been added. As in the first version, the study concerns the physical interpretation of the imaginary quantities that arise in the formulation of superluminal relativity (including complex coordinates, velocities, angles, charges, and masses). In this framework, the kinematics of tachyons is analyzed, and the nature of the imaginary velocities appearing therein is examined. Furthermore, it is shown that a physical interpretation of the complex quantities (masses and charges) occurring both in quantum mechanics and in superluminal relativity is indeed possible. In this context, the complex nature of the electric charge is investigated, with particular attention to its divisibility. It is demonstrated that singular fractions of the electric charge exist whose squared values coincide with the observed quark charges. Within the same conceptual framework, the physical nature of a complex mass is also explored. It is shown that the imaginary component of such a mass implies that its gravitational field intensity behaves as a wave, propagating with the velocity of the wave associated with the particle itself. It is further demonstrated that the corresponding wavelength coincides with that given by the De Broglie relation, and that the resulting wave equation—second order in both spatial and temporal coordinates—is compatible with the Klein–Gordon wave equation. This constitutes a significant indication of the physical character of the associated wave and suggests an alternative interpretation to the orthodox probabilistic view of quantum mechanics.
Two statements in physics are frequently conflated: that nothing can travel faster than light, and that two entangled particles behave as if "instantaneously" connected regardless of their separation. This paper addresses both questions together: whether a faster-than-light particle could exist and, if so, whether it would count as matter; and whether quantum entanglement actually violates the light-speed limit. Starting from the energy–velocity relation of special relativity, it is shown that massive particles cannot reach the speed of light, and the properties of hypothetical tachyons (imaginary mass, absence of a rest frame and violation of causality) are examined. Using the singlet state, the non-separability, reduced state and correlation properties of entanglement are derived, and the quantum violation of the CHSH inequality up to 2√2 is computed. Finally, via the no-signaling theorem, it is shown that entanglement produces non-local correlations without permitting superluminal communication. In conclusion, nature accommodates non-local correlations without allowing any object to travel faster than light.
Abstract Parity-time-reversal (PT) symmetric quantum mechanics promotes the increasing research interest of non-Hermitian (NH) systems for the theoretical value, novel properties, and links to open and dissipative systems in various areas. Recently, anti-PT–symmetric systems and their featured properties have started to be investigated. In this work, we develop the PT and anti-PT symmetry to PT-arbitrary-phase symmetry (or PT- φ symmetry) for the first time, being analogous to bosons, fermions and anyons. It can also be seen as a complex extension of the PT symmetry, unifying the PT and anti-PT symmetries and having intermediate properties between them. Many of the established concepts and mathematics in the PT-symmetric system are still compatible. We mainly investigate quantum simulation of this novel NH system in two dimensions in detail and discuss for higher-dimensional cases in general using the linear combinations of unitaries in the scheme of duality quantum computing, enabling implementations and experimental investigations of novel properties on both small quantum devices and near-term quantum computers.
We investigate the spinor solutions, the spectrum and the symmetry properties of a matrix-valued wave equation whose plane-wave solutions satisfy the superluminal (tachyonic) dispersion relation , where E is the energy, is the spatial momentum and m is the mass of the particle. The equation reads (iγ μ ∂ μ − γ 5 m )ψ = 0, where γ 5 is the fifth current. The tachyonic equation is shown to be invariant and invariant. The tachyonic Hamiltonian breaks parity and is non-Hermitian but fulfils the pseudo-Hermitian property , where P is the parity matrix and is the full parity transformation. The energy eigenvalues and eigenvectors describe a continuous spectrum of plane-wave solutions (which correspond to real eigenvalues for ) and evanescent waves, which constitute resonances and anti-resonances with complex-conjugate pairs of resonance eigenvalues (for ). In view of additional algebraic properties of the Hamiltonian which supplement the pseudo-Hermiticity, the existence of a resonance energy eigenvalue E implies that E *, − E and − E * also constitute resonance energies of H 5 . This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Quantum physics with non-Hermitian operators'.
It has been predicted that particles with imaginary mass, called tachyons, would be able to travel faster than the speed of light. There has not been any experimental evidence for tachyons occurring naturally. Here, we propose how to experimentally simulate Dirac tachyons with trapped ions. Quantum measurement on a Dirac particle simulated by a trapped ion causes it to have an imaginary mass so that it may travel faster than the effective speed of light. We show that a Dirac tachyon must have spinor-motion correlation in order to be superluminal. We also show that it exhibits significantly more Klein tunneling than a normal Dirac particle. We provide numerical simulations of realistic ion systems and show that our scheme is feasible with current technology.