Special Relativity at the Quantum Scale

International Journal of Theoretical Physics, 1993

We propose a unified description of the known forces. We formulate a quantum relativistic spacetime as a (directed) graph of causal arrows with indefinite Hilbert metric, whose physical meaning is given. The simplest graph whose quantum relativity supports conservation of energy-momentum also supports a semidirect product of the cyclic groups2 and3 and the four-group2 2. We call these lattice degrees of freedom (permutational) twain, trine, and spin. Quantized2 2 becomes LorentzSpin(4). Gauged, the energy-momentum and spin groups lead to gravity and torsion, and twain and trine lead toSU 2 andSU 3. We infer that color is actually trine, and thez component of isospin is twain.

It has been shown that the Lorentz transformations in special relativity can be derived in terms of the principle of relativity and certain properties of space and time such as homogeneity. In this paper, we argue that the free Schrodinger equation in quantum mechanics may also be regarded as a consequence of the homogeneity of space and time and the principle of relativity when assuming linearity of time evolution.

International Journal of Theoretical Physics, 1984

A quantum relativity theory formulated in terms of Davis' quantum relativity principle is outlined. The first task in this theory as in classical relativity theory is to model space-time, the arena of natural processes. It is shown that the quantum space-time models of Banai introduced in another paper is formulated in terms of Davis' quantum relativity. The recently proposed classical relativistic quantum theory of Prugovečki and his corresponding classical relativistic quantum model of space-time open the way to introduce, in a consistent way, the quantum space-time model (the quantum substitute of Minkowski space) of Banai proposed in the paper mentioned. The goal of quantum mechanics of quantum relativistic particles living in this model of space-time is to predict the rest mass system properties of classically relativistic (massive) quantum particles (“elementary particles”). The main new aspect of this quantum mechanics is that provides a true mass eigenvalue problem, and that the excited mass states of quantum relativistic particles can be interpreted as elementary particles. The question of field theory over quantum relativistic model of space-time is also discussed. Finally it is suggested that “quarks” should be considered as quantum relativistic particles.

The possibility that quantum mechanics is foundationally the same as classical theories in explaining phenomena in space and time is postulated. Such a view is motivated by interpreting the experimental violation of Bell inequalities as resulting from questions of geometry and algebraic representation of variables, and thereby the structure of space, rather than realism or locality. While time remains Euclidean in the proposed new structure, space is described by Projective geometry. A dual geometry facilitates description of a physically real quantum particle trajectory. Implications for the physical basis of Bohmian mechanics is briefly examined, and found that the hidden variables pilot-wave model is local. Conceptually, the consequence of this proposal is that quantum mechanics has common ground with relativity as ultimately geometrical. This permits the derivation of physically meaningful quantum Lorentz transformations. Departure from classical notions of measurability is discussed.

We argue that special relativity, instead of quantum theory, should be radically reformulated to resolve inconsistencies between those two theories. A new relativistic transformation recently-proposed renders physical laws form-invariant via transformation of physical quantities, instead of space-time coordinates. This new perspective on relativistic transformation provides an insight into the very meaning of the principle of relativity. The principle of relativity means that the same physical laws hold in all inertial frames, rather than their mathematical formulas are Lorentz-covariant under the Lorentz transformation of space-time coordinates. The space-time concept underlying this new relativistic transformation is Newtonian absolute space and absolute time. With this new perspective, quantum theory becomes compatible with the principle of relativity. A new theory of relativistic quantum mechanics is formulated. The new relativistic quantum mechanics thus obtained maintains the ...

Abstract The fundamental relation between space and time is motion expressed as the ratio of space over time for motion in space and the ratio of time over space for motion in time. This indicates that space and time are co-existent reciprocal aspects of motion. While inseparable and interdependent both space and time have distinct geometric properties. There are two fundamental quantum holographic interference patterns which most closely exemplify these structural properties. These are separately identified and defined consistent with the space-time reciprocal relationship. Quantum time potentials and space time networks are defined. The first network consists of two interacting quantum time potentials forming a space-time network whereby space is an emergent feature; there being an inverse structure with inverse properties. The phenomenon of mass and force are emergent features from the various permutations of interconnections between nodes within this space-time network. The resulting structure implies the existence of a coordinate system where each node represents coordinates defined by the rays from each pole. The coordinates form an information field and indicate that space and time ARE information, The connections between the nodes are determined by pre-mathematical connection algorithms indicating the underlying mechanism of creation. Further properties of the space-time network are identified and reveal underlying mechanisms to account for elusive and anomalous physical phenomenon including non-locality, quantum entanglement and quantum gravity.

2014

One of the most important open questions in physics is the possibility of reconciliation, and perhaps unification, between quantum theory and relativity theory. Here I show that a relativity theory without the Lorentz Invariance Principle, termed Complete Relativity, reconciles with quantum mechanics at significant meeting points: It explains the quantum criticality at the Golden Ratio. More importantly, it confirms with Planck's energy. These results are quite astounding, given the fact that Complete Relativity, like Special Relativity, is a deterministic model of the dynamics of moving bodies. An application of the theory to cosmology, discussed in a recent paper, revealed that it yields definitions of dark matter and dark energy, and predicts the contents of the universe with impressive accuracy. Taken together, these results raise the exciting possibility that physics at the quantum scale, and at the cosmological scale, are the two faces of one coin: The coin of relativity.

The intrinsic unification of the quantum theory and relativity has been discussed here in the light of the last developments. Such development is possible only on the way of the serious deviation from traditional assumptions about a priori spacetime structure and the Yang-Mills generalization of the well known U (1) Abelian gauge symmetry of the classical electrodynamics. In fact, more general gauge theory should be constructed. Formally we deal with the quantum version of the gauge theory of the deformable bodies-the gauge theory of the deformable quantum state. More physically this means that the distance between quantum states is strictly defined value whereas the distance between bodies (particle) is an approximate value, at best. Thereby, all well known solid frames and clocks even with corrections of special relativity should be replaced by the flexible and anholo-nomic quantum setup. Then Yang-Mills arguments about the spacetime coordinate dependence of the gauge unitary rotations should be reversed on the dependence of the spacetime structure on the gauge transformations of the flexible quantum setup. One needs to build " inverse representation " of the unitary transformations by the intrinsic dynamical spacetime transformations. In order to achieve such generalization one needs the general footing for gauge fields and for " matter fields ". Only fundamental pure quantum degrees of freedom like spin, charge, hyper-charges, etc., obey this requirement. One may assume that they correspond some fundamental quantum motions in the manifold of the unlocated quantum states (UQS's). Then " elementary particles " will be represented as a dynamical process keeping non-linear coherent superposition of these fundamental quantum motions.

In this paper, I have studied the properties of atomic and molecular world along with general and special theories of relativity. This is an attempt to merge Gravity into the standard model in order to complete the Grand Unification Theory. The merger of gravity into the other forces i.e. electromagnetic, strong and weak nuclear forces should be well defined and in the boundaries of Gauge Group theory. The Lorentz transformations used in the theory too are invariant under SU(2) type of space. The relative force exerted on two separate quantum systems is also discussed along with Dark matter and Dark energy at a quantum level. I have also tried to solve the Ba-nach-Tarski theorem by applications of Heisenbergs Uncertainty principle in the later part of the paper. Detailed particle Chirality in standard model is redefined to fit in the criterion of operators used in the same process. Possible existence of a new quasi particle is also included in the paper along with its properties.

Foundations of Physics, 2021

The true nature of space and time has been a topic of natural philosophy, passed down since the presocratic era. In modern times reflection has particularly been inspired by the physical theories of Newton and Einstein and, more recently, by the quest for a theory of quantum gravity. In this paper we want to specify the idea that material systems and their spatio-temporal distances emerge from quantum-events. We will show a mechanism, by which quantum-events induce a metric field between material systems, which is governed by Einstein's equation including a cosmological constant.