Foundations of a Universal Theory of Relativity

In this presentation, I will summarize the present status of the developments with a Universal Theory of Relativity . Some general challenges to be overcome will also be discussed.

We discuss here the significance of the generalization of the newtonian concept of force by that of a transformation of a certain Standard Borel Space of cardinality c of the continuum as the "cause" behind motions of material bodies that are representable as Borel measurable subsets of this space. This generalization forms the basis for a Universal Theory of Relativity in which, importantly, the fundamental physical constants can only arise from mutual relationships of the so-defined physical bodies. This Universal Relativity also has the potential to explain the quantum nature of the physical world.

arXiv (Cornell University), 2021

Quantum information theorists have created axiomatic reconstructions of quantum mechanics (QM) that are very successful at identifying precisely what distinguishes quantum probability theory from classical and more general probability theories in terms of information-theoretic principles. Herein, we show how one such principle, Information Invariance & Continuity, at the foundation of those axiomatic reconstructions maps to "no preferred reference frame" (NPRF, aka "the relativity principle") as it pertains to the invariant measurement of Planck's constant h for Stern-Gerlach (SG) spin measurements. This is in exact analogy to the relativity principle as it pertains to the invariant measurement of the speed of light c at the foundation of special relativity (SR). Essentially, quantum information theorists have extended Einstein's use of NPRF from the boost invariance of measurements of c to include the SO(3) invariance of measurements of h between different reference frames of mutually complementary spin measurements via the principle of Information Invariance & Continuity. Consequently, the "mystery" of the Bell states that is responsible for the Tsirelson bound and the exclusion of the no-signalling, "superquantum" Popescu-Rohrlich joint probabilities is understood to result from conservation per Information Invariance & Continuity between different reference frames of mutually complementary qubit measurements, and this maps to conservation per NPRF in spacetime. If one falsely conflates the relativity principle with the classical theory of SR, then it may seem impossible that the relativity principle resides at the foundation of non-relativisitic QM. In fact, there is nothing inherently classical or quantum about NPRF. Thus, the axiomatic reconstructions of QM have succeeded in producing a principle account of QM that reveals as much about Nature as the postulates of SR.

Advances in Quantum Chemistry, 2008

Quo Vadis Quantum Mechanics?, 2005

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.

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.

1996

We put forward a framework, inspired by recent axiomatic and opera- tional approaches to generalized quantum theories, wherein we investigate the possibility of unifying quantum theories and relativity theories. The framework concentrates on a detailed analysis of a general construction of reality, that can be used in both, quantum and relativity theories. By means of this construction of reality we clarify some well known conceptual problems that stand in the way for a conceptual uniflcation of quantum and relativity theories on a more profound physical level than the purely mathematical algebraic level on which now uniflcation attempts are in- vestigated. More speciflcally we concentrate on the problem of 'what is physical reality' in quantum and relativity theories.

We consider inertial physical systems in which signals about physical measurements conducted in one reference frame are transmitted to a receiver moving with relative constant velocity v, by an information carrier with a constant velocity v_c with respect to the transmitter's rest frame. To render the model relevant to reality, we assume v_c> v. We make no other assumptions. For systems of this type, we derive the relativistic time, distance, mass, and energy transformations, relating measurements transmitted by the information sender, to the corresponding information registered at the receiver. The sender and receiver need not be human or animate observers. The resulting relativistic terms are beautiful and simple. They are functions only of the normalized velocity β = v/v_c , implying they are scale independent with respect to the velocity of the information carrier, and to the mass and spatial dimensions of the observed bodies. The model's scale independence renders it applicable for all physical systems, irrespective of their size, and the velocity of the information carrier used in the system. For β << 1, all the derived transformations reduce to Galileo-Newton physics. The derived transformations disobey the Lorentz invariance principle. The time transformation predicts relativistic time dilation for distancing bodies and time contraction for approaching bodies. The distance transformation predicts relativistic length contraction for approaching bodies and length extension for distancing bodies. The mass transformation is inversely proportional to the distance transformation, implying an increase in relativistic mass density for approaching bodies and a decrease of mass density for distancing bodies, due to respective length contraction or extension along the body's travel path. For distancing bodies, the relativistic kinetic energy as a function of β displays a monotonic pattern, with a unique maximum at β = Φ, where Φ is the golden ratio (≈ 0.618). At sufficiently high normalized velocities, the relativistic extension can maintain spatial locality between distanced particles, suggesting quantum entanglement is not "spooky," because it is a proximal action. For the special case of v_c = c, where c is the velocity of light, application of the proposed model yields new important insights and results and reproduces several important predictions of Special Relativity, General Relativity, observationally based ΛCDM models, and quantum theory. The model makes excellent predictions for the Michelson-Morley's "null" result, the relativistic lifetime of decaying muons, the Sagnac effect, and the neutrino velocities reported by OPERA and other collaborations. Application of the model to cosmology, without alteration or addition of free parameters, is successful in accounting for several cosmological findings, including the pattern of recession velocity predicted by inflationary theories, the amounts of matter and dark energy in various segments of redshift, reported in recent ΛCDM cosmologies, the GZK energy suppression phenomenon, and the radius of gravitational black holes. More interestingly, we show that the model, despite being deterministic and local, reproduces the predictions of quantum theory for key quantum phenomena, including matter-wave duality, quantum criticality, quantum entanglement, and the formation of Bose-Einstein condensate. The multiplicity and range of the proposed epistemic model predictions suggests that for inertial systems, mere comparison between physical observations taken at the rest of reference and the information received about the same measurement from another moving reference frame is a potent tool for extracting the laws of nature as they are revealed to us. Put metaphorically, we contend that the hidden secrets of the book of Nature often disclose themselves by leaving fingerprints on the book's cover. From observing the fingerprints, humans and other beings can reconstruct information valuable for their survival.