Hybrid Memristor-CMOS (MeMOS) based Logic Gates and Adder Circuits

Practical memristor came into picture just few years back and instantly became the topic of interest for researchers and scientists. Memristor is the fourth basic two-terminal passive circuit element apart from well known resistor, capacitor and inductor. Recently, memristor based architectures has been proposed by many researchers. In this paper, we have designed a hybrid Memristor-CMOS (MeMOS) logic based adder circuit that can be used in numerous logic computational architectures. We have also analyzed the transient response of logic gates designed using MeMOS logic circuits. MeMOS use CMOS 180 nm process with memristor to compute boolean logic operations. Various parameters including speed, ares, delay and power dissipation are computed and compared with standard CMOS 180 nm logic design. The proposed logic shows better area utilization and excellent results from existing CMOS logic circuits at standard 1.8 V operating voltage.Comment: 10 pages, 13 figures, 5 tables, journa

Proposal for a new quantum theory of gravity

We recall a classical theory of torsion gravity with an asymmetric metric, sourced by a Nambu-Goto + Kalb-Ramond string . We explain why this is a significant gravitational theory, and in what sense classical general relativity is an approximation to it. We propose that a non-commutative generalisation of this theory (in the sense of Connes' non-commutative geometry and Adler's Trace Dynamics) is a `quantum theory of gravity'. The theory is in fact a classical matrix dynamics with only two fundamental constants -- the square of the Planck length and the speed of light, along with the two string tensions as parameters. The guiding symmetry principle is that the theory should be covariant under general coordinate transformations of non-commuting coordinates.The action for this non-commutative torsion gravity can be elegantly expressed as an invariant area integral, and represents an atom of space-time-matter. The statistical thermodynamics of a large number of such atoms yields the laws of quantum gravity and quantum field theory, at thermodynamic equilibrium. Spontaneous localisation caused by large fluctuations away from equilibrium is responsible for the emergence of classical space-time and the field equations of classical general relativity. The resolution of the quantum measurement problem by spontaneous collapse is an inevitable consequence of this process. Quantum theory and general relativity, are both seen as emergent phenomena, resulting from coarse-graining of the underlying non-commutative geometry. We explain the profound role played by entanglement in this theory: entanglement describes interaction between the atoms of space-time-matter, and indeed entanglement appears to be more fundamental than quantum theory or space-time. We also comment on possible implications for black hole entropy and evaporation, and for cosmology.Comment: v2: 32 pages, 1 figure, Section I borrows some text (overview of trace dynamics) from arXiv:1701.09132v1 [quant-ph], revised in response to reviewer comments: list of revisions appended after bibliography; accepted for publication in Zeitschrift fur Naturforschun

Space-time from collapse of the wave-function

We propose that space-time results from collapse of the wave function of macroscopic objects, in quantum dynamics. We first argue that there ought to exist a formulation of quantum theory which does not refer to classical time. We then propose such a formulation by invoking an operator Minkowski space-time on the Hilbert space. We suggest relativistic spontaneous localisation as the mechanism for recovering classical space-time from the underlying theory. Quantum interference in time could be one possible signature for operator time, and in fact may have been already observed in the laboratory, on attosecond time scales. A possible prediction of our work seems to be that interference in time will not be seen for `time slit' separations significantly larger than 100 attosecond, if the ideas of operator time and relativistic spontaneous localisation are correct.Comment: v2: 12 pages, 6 figures, clarifying remarks added, has text overlap with arXiv:1806.01297 [gr-qc], to appear in Zeitschrift f\"ur Naturforschung

General relativity, torsion, and quantum theory

We recall some of the obstacles which arise when one tries to reconcile the general theory of relativity with quantum theory. We consider the possibility that gravitation theories which include torsion, and not only curvature, provide better insight into a quantum theory of gravity. We speculate on how the Dirac equation and Einstein gravity could be thought of as limiting cases of a gravitation theory which possesses torsion.Comment: 14 pages; published in Current Science [Special Section: 100 Years of General Relativity

Nature does not play dice at the Planck scale

We start from classical general relativity coupled to matter fields. Each configuration variable and its conjugate momentum, as also space-time points, are raised to the status of matrices [equivalently operators]. These matrices obey a deterministic Lagrangian dynamics at the Planck scale. By coarse-graining this matrix dynamics over time intervals much larger than Planck time, one derives quantum theory as a low energy emergent approximation. If a sufficiently large number of degrees of freedom get entangled, spontaneous localisation takes place, leading to the emergence of classical space-time geometry and a classical universe. In our theory, dark energy is shown to be a large-scale quantum gravitational phenomenon. Quantum indeterminism is not fundamental, but results from our not probing physics at the Planck scale.Comment: v2: 8 pages; Typo corrected, Honourable mention, GRF essay contest 2020. Accepted for publication in Int. J. Mod. Phys.

Possible role of gravity in collapse of the wave-function: a brief survey of some ideas

This article is a brief survey of some approaches to implementing the suggestion that collapse of the wave function is mediated by gravity. These approaches include: a possible connection between the problem of time and problem of quantum measurement, decoherence models based on space-time uncertainty, the Schr\"{o}dinger-Newton equation, attempts to introduce gravity into collapse models such as CSL, ideas based on the black hole - elementary particle complementarity, and the possible role of a complex space-time metric.Comment: 16 pages, one figure, submitted to J. Phys. Conf. Series [proceedings of the conference DICE2014: Spacetime - Matter - Quantum Mechanics, Castiglioncello (Tuscany) September 15-19, 2014 Eds. H-T. Elze et al.

Quantum theory and the structure of space-time

We argue that space and space-time emerge as a consequence of dynamical collapse of the wave function of macroscopic objects. Locality and separability are properties of our approximate, emergent universe. At the fundamental level, space-time is non-commutative, and dynamics is non-local and non-separable.Comment: v2: 12 pages, edited version of an essay written for the FQXi essay contest (2016), minor typos in v1 corrected, to appear in Zeitschrift fur Naturforschung

A new length scale for quantum gravity

We show why and how Compton wavelength and Schwarzschild radius should be combined into one single new length scale, which we call the Compton-Schwarzschild length. Doing so offers a resolution of the black hole information loss paradox, and suggests Planck mass remnant black holes as candidates for dark matter. It also compels us to introduce torsion, and identify the Dirac field with a complex torsion field. Dirac equation, and Einstein equations, are shown to be mutually dual limiting cases of an underlying gravitation theory which involves the Compton-Schwarzschild length scale, and includes a complex torsion field.Comment: 7 pages, 1 figure; v2 - minor typo corrected, Honorable Mention in the Gravity Research Foundation 2017 Awards for Essays on Gravitatio

The problem of time and the problem of quantum measurement

Quantum theory depends on an external classical time, and there ought to exist an equivalent reformulation of the theory which does not depend on such a time. The demand for the existence of such a reformulation suggests that quantum theory is an approximation to a stochastic non-linear theory. The stochastic non-linearity provides a dynamical explanation for the collapse of the wave-function during a quantum measurement. Hence the problem of time and the measurement problem are related to each other: the search for a solution for the former problem naturally implies a solution for the latter problem.Comment: 14 pages, 4 figures, based on a talk given at Quantum Malta 2012, submitted to the volume The Forgotten Present (running title) Thomas Filk and Albrecht von Muller [Eds.

A new length scale, and modified Einstein-Cartan-Dirac equations for a point mass

We have recently proposed a new action principle for combining Einstein equations and the Dirac equation for a point mass. We used a length scale $L_{CS}$, dubbed the Compton-Schwarzschild length, to which the Compton wavelength and Schwarzschild radius are small mass and large mass approximations, respectively. Here we write down the field equations which follow from this action. We argue that the large mass limit yields Einstein equations, provided we assume wave function collapse and localisation for large masses. The small mass limit yields the Dirac equation. We explain why the Kerr-Newman black hole has the same gyromagnetic ratio as the Dirac electron, both being twice the classical value. The small mass limit also provides compelling reasons for introducing torsion, which is sourced by the spin density of the Dirac field. There is thus a symmetry between torsion and gravity: torsion couples to quantum objects through Planck's constant $\hbar$ (but not $G$) and is important in the microscopic limit. Whereas gravity couples to classical matter, as usual, through Newton's gravitational constant $G$ (but not $\hbar$), and is important in the macroscopic limit. We construct the Einstein-Cartan-Dirac equations which include the length $L_{CS}$. We find a potentially significant change in the coupling constant of the torsion driven cubic non-linear self-interaction term in the Dirac-Hehl-Datta equation. We speculate on the possibility that gravity is not a fundamental interaction, but emerges as a consequence of wave function collapse, and that the gravitational constant maybe expressible in terms of Planck's constant and the parameters of dynamical collapse models.Comment: 12 pages; this article is a follow-up of arXiv:1704.00747v2 [gr-qc]; remarks on `cubic Dirac fermions in Dirac semi-metals' added on page 7; paragraph added on page 8 to quantitatively compare spin density and mass density; references added; v3: clarifying remarks added after Eqn. (13), conclusions unchanged, references updated, published in Int. J. Mod. Phy