Special Relativity in a Discrete Quantum Universe

EPL (Europhysics Letters), 2015

It is shown how a Doubly-Special Relativity model can emerge from a quantum cellular automaton description of the evolution of countably many interacting quantum systems. We consider a onedimensional automaton that spawns the Dirac evolution in the relativistic limit of small wave-vectors and masses (in Planck units). The assumption of invariance of dispersion relations for boosted observers leads to a non-linear representation of the Lorentz group on the (ω, k) space, with an additional invariant given by the wave-vector k = π/2. The space-time reconstructed from the (ω, k) space is intrinsically quantum, and exhibits the phenomenon of relative locality.

Modern Physics Letters A, 2004

Contrary to what is often stated, a fundamental spacetime discreteness need not contradict Lorentz invariance. A causal set's discreteness is in fact locally Lorentz invariant, and we recall the reasons why. For illustration, we introduce a phenomenological model of massive particles propagating in a Minkowski spacetime which arises from an underlying causal set. The particles undergo a Lorentz invariant diffusion in phase space, and we speculate on whether this could have any bearing on the origin of high energy cosmic rays.

arXiv (Cornell University), 2021

An argument is presented that if a theory of quantum gravity is physically discrete at the Planck scale and the theory recovers General Relativity as an approximation, then, at the current stage of our knowledge, causal sets must arise within the theory, even if they are not its basis. We show in particular that an apparent alternative to causal sets, viz. a certain sort of discrete Lorentzian simplicial complex, cannot recover General Relativistic spacetimes in the appropriately unique way. For it cannot discriminate between Minkowski spacetime and a spacetime with a certain sort of gravitational wave burst.

Annals of Physics, 2015

We present a quantum cellular automaton model in one space-dimension which has the Dirac equation as emergent. This model, a discrete-time and causal unitary evolution of a lattice of quantum systems, is derived from the assumptions of homogeneity, parity and time-reversal invariance. The comparison between the automaton and the Dirac evolutions is rigorously set as a discrimination problem between unitary channels. We derive an exact lower bound for the probability of error in the discrimination as an explicit function of the mass, the number and the momentum of the particles, and the duration of the evolution. Computing this bound with experimentally achievable values, we see that in that regime the QCA model cannot be discriminated from the usual Dirac evolution. Finally, we show that the evolution of one-particle states with narrow-band in momentum can be efficiently simulated by a dispersive differential equation for any regime. This analysis allows for a comparison with the dynamics of wave-packets as it is described by the usual Dirac equation. This paper is a first step in exploring the idea that quantum field theory could be grounded on a more fundamental quantum cellular automaton model and that physical dynamics could emerge from quantum information processing. In this framework, the discretization is a central ingredient and not only a tool for performing non-perturbative calculation as in lattice gauge theory. The automaton model, endowed with a precise notion of local observables and a full probabilistic interpretation, could lead to a coherent unification of an hypothetical discrete Planck scale with the usual Fermi scale of high-energy physics.

Journal of High Energy Physics, 2004

A common misconception is that Lorentz invariance is inconsistent with a discrete spacetime structure and a minimal length: under Lorentz contraction, a Planck length ruler would be seen as smaller by a boosted observer. We argue that in the context of quantum gravity, the distance between two points becomes an operator and show through a toy model, inspired by Loop Quantum Gravity, that the notion of a quantum of geometry and of discrete spectra of geometric operators, is not inconsistent with Lorentz invariance. The main feature of the model is that a state of definite length for a given observer turns into a superposition of eigenstates of the length operator when seen by a boosted observer. More generally, we discuss the issue of actually measuring distances taking into account the limitations imposed by quantum gravity considerations and we analyze the notion of distance and the phenomenon of Lorentz contraction in the framework of "deformed (or doubly) special relativity" (DSR), which tentatively provides an effective description of quantum gravity around a flat background. In order to do this we study the Hilbert space structure of DSR, and study various quantum geometric operators acting on it and analyze their spectral properties. We also discuss the notion of spacetime point in DSR in terms of coherent states. We show how the way Lorentz invariance is preserved in this context is analogous to that in the toy model. * [email protected]

Foundations of Physics, 2015

After leading to a new axiomatic derivation of quantum theory, the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles (linearity, unitarity, locality, homogeneity, isotropy, and minimality of dimension), the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements (unmanageable by quantum field theory), solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how from the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs.

The General Science Journal, 2023

Leaving aside the fact that special relativity is a theory built on the infinitist spacetime continuum, and that this spacetime continuum is inconsistent (see paper 3 of this series), here it will be proved that special relativity is not compatible with discrete space and time. Therefore, the relativistic inertial length contractions and inertial time dilations could be only apparent, as is apparent the continuous motion in a film, or the refractive deformations; or even motion in a discrete universe. It also happens that the relativistic Lorentz factor, which is crucial in the Lorentz Transformation, coincides with the conversion factor between the continuous and the discrete versions of Pythagoras Theorem.

PLoS ONE, 2014

It has been suggested that the space-time structure as described by the theory of special relativity is a macroscopic manifestation of a more fundamental quantum structure (pre-geometry). Efforts to quantify this idea have come mainly from the area of abstract quantum logic theory. Here we present a preliminary attempt to develop a quantum formulation of special relativity based on a model that retains some geometric attributes. Our model is Feynman's "checker-board" trajectory for a 1-D relativistic free particle. We use this model to guide us in identifying (1) the quantum version of the postulates of special relativity and (2) the appropriate quantum "coordinates". This model possesses a useful feature that it admits an interpretation both in terms of paths in space-time and in terms of quantum states. Based on the quantum version of the postulates, we derive a transformation rule for velocity. This rule reduces to the Einstein's velocity-addition formula in the macroscopic limit and reveals an interesting aspect of time. The 3-D case, time-dilation effect, and invariant interval are also discussed in term of this new formulation. This is a preliminary investigation; some results are derived, while others are interesting observations at this point.

2013

Developing Planck scale physics requires addressing problem of time, quantum reduction, determinism and continuum limit. In this article on the already known foundations of quantum mechanics, a set of proposals of dynamics is built on fully constrained discrete models: 1) Self-Evolution-Flow of time in the phase space in a single point system, 2) Local Measurement by Local Reduction through quantum diffusion theory, quantum diffusion equation is rederived with different assumptions, 3) Quantum Evolution of a MultiPoint Discrete Manifold of systems through a foliation chosen dynamically, and 4) Continuum Limit, and Determinism are enforced by adding terms and averaging to the action. The proposals are applied to the various physical scenarios such as: 1) Minisuperspace reduced cosmology of isotropic and homogenous universe with scalar field, 2) Expanding universe with perturbation, and 3) Newtonian universe. Ways to experimentally test the theory is discussed. This article is a further revision of its previous revision.

Recent mathematical evidence suggests that the structure and dynamics of gravitational objects can be described using the wave equation in the form of the Schrödinger equation; thus suggesting an underlining symmetry across large and subatomic/atomic scales of the physical universe. However, the current accepted theoretical frameworks across said scales of the physical universe are incompatible. This publication proposes that the philosophical assumptions concerning the concept time in quantum theory and general relativity, as constituting the major barrier in reconciling the two discordant frameworks. In both quantum theory and general relativity, time is presumed to be a dimension, in which events occur, with the time dimension interpreted as asymmetric. This publication proposes a novel theoretical framework, which redefines time, and resolves the discordancy between quantum theory and general relativity. The suggestive idea is proposed that the concept time in the physical universe (termed, physical time) should be defined as the measure of the magnitude of change in the location of a demarcated physical structure (for example, a clock) within a non-discrete compressible fluid physical universe, which is an enclosed structure (a closed ball). Consequently, physical time and length are not just related, but are in fact one and the same, as both measure the magnitude of change in location within the non-discrete compressible fluid. Matter and vacuum, along with all other constituents of the physical universe are manifestations of differential “specific energy” densities, due to compressions and rarefactions within the non-discrete compressible fluid. Demarcation (detection, interaction, or wavefunction collapse) and analysis of the dynamics of said demarcated physical structures within the non- discrete compressible fluid system is governed by the framework of the Wheeler-Feynman-Cramer-Mead transactional (quantum handshake) theory, wherein energy exchange is restricted to supersymmetric partner-wavefunctions termed, “bosons” and “fermions” (which are fundamental demarcated structures) resulting in the manifestation of the “quantum” phenomena. Consequently, the nature and dynamics of demarcated physical structures (for example, clocks, particles) within the non-discrete compressible fluid system is termed an emergent equilibrium state, and is accurately model one-dimensionally as a longitudinal wave (compression wave) and analyzed using the wave equation and perturbation theory methods in a novel theoretical framework, termed, “equilibrium theory”.