arXiv subjects

Abhishek Majhi

Publications and source records attributed to Abhishek Majhi.

At least 19 recordsLinked to original sources

arXiv2024

The Undecidable Charge Gap and the Oil Drop Experiment

Decision problems in physics have been an active field of research for quite a few decades resulting in some interesting findings in recent years. However, such research investigations are based on a priori knowledge of theoretical computer science and the technical jargon of set theory. Here, I discuss a particular, but a significant, instance of how decision problems in physics can be realized without such specific prerequisites. I expose a hitherto unnoticed contradiction, that can be posed as a decision problem, concerning the oil drop experiment and thereby resolve it by refining the notion of ``existence'' in physics. This consequently leads to the undecidability of the charge spectral gap through the notion of ``undecidable charges" which is in tandem with the completeness condition of a theory as was stated by Einstein, Podolsky and Rosen in their seminal work. Decision problems can now be realized in connection to basic physics, in general, rather than quantum physics, in particular, as per some recent claims.

physics.gen-ph↗

arXiv2023

Unprovability of First Maxwell's Equation in Light of EPR's Completeness Condition -- A Computational Approach from Logico-linguistic Perspective

Maxwell's verbal statement of Coulomb's experimental verification of his hypothesis, concerning force between two electrified bodies, is suggestive of a modification of the respective computable expression on logical grounds. This modification is in tandem with the completeness condition for a physical theory, that was stated by Einstein, Podolsky and Rosen in their seminal work. Working with such a modification, I show that the first Maxwell's equation, symbolically identifiable as ``$\vec{\nabla}\cdot\vec{E}=ρ/ε_0$'' from the standard literature, is {\it unprovable}. This renders Poynting's theorem to be {\it unprovable} as well. Therefore, the explanation of `light' as `propagation of electromagnetic energy' comes into question on theoretical grounds.

physics.gen-ph↗

arXiv2023

Scientific value of the quantum tests of equivalence principle in light of Hilbert's sixth problem

In his sixth problem, Hilbert called for an axiomatic approach to theoretical physics with an aim to achieve precision and rigour in scientific reasoning, where logic and language (semantics) of physics play the pivotal role. It is from such a point of view, we investigate the scientific value of the modern experiments to perform quantum tests of equivalence principle. Determination of Planck constant involves the use of acceleration due to gravity of the earth $(g)$ that results in the force on a test mass. The equivalence between inertial mass and gravitational mass of a test object is assumed in the process of logically defining $g$ from the relevant hypotheses of physics. Consequently, if Planck constant is used as input in any experiment (or in the associated theory that founds such an experiment) that is designed to test the equivalence between inertial and gravitational mass, then it is equivalent to establish a scientific truth by implicitly assuming it i.e. a tautology. There are several notable examples which plague the frontiers of current scientific research which claim to make quantum test of equivalence principle. We question the scientific value of such experiments from Hilbert's axiomatic point of view. This work adds to the recently reported semantic obstacle in any axiomatic attempt to put "quantum" and "gravity" together, albeit with an experimental tint.

physics.hist-ph↗

arXiv2022

Cauchy's Logico-Linguistic Slip, the Heisenberg Uncertainty Principle and a Semantic Dilemma Concerning "Quantum Gravity"

The importance of language in physics has gained emphasis in recent times, on the one hand through Hilbert's views that concern formalism and intuition applied for outer inquiry, and on the other hand through Brouwer's point of view that concerns intuition applied for inner inquiry or, as I call, self-inquiry. It is to demonstrate the essence of such investigations, especially self-inquiry (inward intuition), I find it compelling to report that a careful analysis of Cauchy's statements for the definition of derivative, as applied in physics, unveils the connection to the Heisenberg uncertainty principle as a condition for the failure of classical mechanics. Such logico-linguistic, or semantically driven, self-inquiry of physics can provide new insights to physicists in the pursuit of truth and reality, for example, in the context of Schroedinger equation. I point out an explicit dilemma that plagues the semantics of physics, as far as general relativity and quantum mechanics are concerned, which needs to be taken into account during any attempt to pen down a theory of "quantum gravity".

physics.gen-ph↗

arXiv2021

Logic, Philosophy and Physics: a critical commentary on the dilemma of categories

I provide a critical commentary regarding the attitude of the logician and the philosopher towards the physicist and physics. The commentary is intended to showcase how a general change in attitude towards making scientific inquiries can be beneficial for science as a whole. However, such a change can come at the cost of looking beyond the categories of the disciplines of logic, philosophy and physics. It is through self-inquiry that such a change is possible, along with the realization of the essence of the middle that is otherwise excluded by choice. The logician, who generally holds a reverential attitude towards the physicist, can then actively contribute to the betterment of physics by improving the language through which the physicist expresses his experience. The philosopher, who otherwise chooses to follow the advancement of physics and gets stuck in the trap of sophistication of language, can then be of guidance to the physicist on intellectual grounds by having the physicist's experience himself. In course of this commentary, I provide a glimpse of how a truthful conversion of verbal statements to physico-mathematical expressions unravels the hitherto unrealized connection between Heisenberg uncertainty relation and Cauchy's definition of derivative that is used in physics. The commentary can be an essential reading if the reader is willing to look beyond the categories of logic, philosophy and physics by being `nobody'.

physics.gen-ph↗

arXiv2021

A logico-linguistic inquiry into the foundations of physics: Part I

Physical dimensions are {\it not numbers}, but used as {\it numbers} to perform dimensional analysis by the physicist. The law of excluded middle falls short of explaining the contradictory meanings of the same symbols. The statements like ``$r\to 0$'', ``$q\to 0$'', used by the physicist, are inconsistent on dimensional grounds because ``$r$'', ``$q$'' represent {\it quantities} with physical dimensions of $[L], [Q]$ respectively and ``$0$'' represents just a number devoid of physical dimension. Consequently, the involvement of the statement ``$\lim_{q\to 0}$, where $q$ is the test charge'' in the definition of electric field leads to either circular reasoning or a contradiction regarding the experimental verification of the smallest charge in the Millikan-Fletcher oil drop experiment. Considering such issues as problematic, by choice, I make an inquiry regarding the basic language in terms of which physics is written, with an aim of exploring how truthfully the verbal statements can be converted to the corresponding physico-mathematical expressions (involving physical dimensions). Necessarily I demonstrate the meaning of the terms ``self inquiry'', ``middle way'', ``dependent origination'', ``emptiness/relational existence'', which signify the basic tenets of Buddhism. In light of this, I explain my view of ``definition''; the relation among quantity, physical dimension and number; the logico-linguistic fallacy of ``zero quantity''; difference between unit and unity. I present a critical analysis of the definitions of electric field due to Maxwell and Jackson. A postulate regarding the existence of charges becomes necessary which, however, resolves the contradiction regarding the oil drop experiment. This work is an appeal for the dissociation of the categorical disciplines of logic and physics and on the large, a fruitful merger of Eastern philosophy and Western science.

physics.gen-ph↗

arXiv2020

Note on $SU(2)$ isolated horizon

We point out that the symplectic structure, written in terms of the Sen-Ashtekar-Immirzi-Barbero variables, of a spacetime admitting an isolated horizon as the inner boundary, involves a positive constant parameter, say $σ$, if $γ\neq\pm i$, where $γ$ is the Barbero-Immirzi parameter. The parameter $σ$ represents the rescaling freedom that characterizes the equivalence class of null generators of the isolated horizon. We reiterate the fact that the laws of mechanics associated with the isolated horizon does not depend on the choice of $σ$ and, in particular, while one uses the value of standard surface gravity as input, that does not fix $σ$ to a particular value. This fact contradicts the claims made in certain parts of the concerned literature that we duly refer to. We do the calculations by taking Schwarzschild metric as an example so that the contradiction with the referred literature, where similar approaches were adopted, becomes apparent. The contribution to the symplectic structure that comes from the isolated horizon, diverges for $σ^2=(1+γ^2)^{-1}$, implying that the rescaling symmetry of the isolated horizon is violated for any real $γ$. Since the quantum theory of $SU(2)$ isolated horizon in the LQG framework exists only for real values of $γ$, it is founded on this flawed classical setup. Nevertheless, if the flaw is ignored, then two different viewpoints persist in the literature for entropy calculation. We highlight the main features of those approaches and point out why one is logically viable and the other is not.

gr-qc↗

arXiv2019

Variation of rest mass scale in a gravitational field

I argue that an angular momentum scale is necessary to explain energy-momentum propagation along a single null geodesic, the scale being known as Planck's constant $(h)$. If $h$ and $c$ (the velocity of light in vacuum), are considered to be given fundamental (constant) scales in local measurements, then the rest mass scale varies exactly inversely as the time scale varies in two different locally flat regions of a curved spacetime. As the time scale variation gives rise to gravitational redshift, the rest mass scale variation leads to a change in the Compton length scale associated with an elementary particle. I suggest an experiment for the MICROSCOPE satellite and report the expected outcome.

gr-qc↗

arXiv2018

Expectation of primordial gravity waves generated during inflation

The inflationary paradigm is extremely successful regarding predictions of temperature anisotropies in the CMB. However, inflation also makes predictions for a CMB B-mode polarization, which has not been detected. Moreover, the standard inflationary paradigm is unable to accommodate the evolution from the initial state, which is assumed to be symmetric, into a non-symmetric aftermath. In Phys. Rev. D 96, 101301(R), we show that the incorporation of an element capable of explaining such a transition drastically changes the prediction for the shape and size of the B-mode spectrum. In particular, employing a realistic objective collapse model in a well-defined semiclassical context, we find that, while predictions of temperature anisotropies are nor altered (with respect to standard predictions), the B-mode spectrum gets strongly suppressed--in accordance with observations. Here we present an in-depth discussion of that analysis, together with the details of the calculation.

gr-qc↗

arXiv2018

Singularity from star collapse, torsion and asymptotic safety of gravity

A star of mass greater than a critical mass is believed to undergo gravitational collapse to form a singularity, owing to Hawking-Penrose singularity theorem which is based on the Raychaudhuri equation in the absence of torsion. We argue that the spin-aspect of matter can lead to the evasion of singularity, caused by its mass-aspect, via torsion in asymptotically safe gravity.

gr-qc↗

arXiv2018

An area rescaling ansatz and black hole entropy from loop quantum gravity

Considering the possibility of `renormalization' of the gravitational constant on the horizon, leading to a dependence on the level of the associated Chern-Simons theory, a rescaled area spectrum is proposed for the non-rotating black hole horizon in loop quantum gravity. The statistical mechanical calculation leading to the entropy provides a unique choice of the rescaling function for which the Bekenstein-Hawking area law is yielded without the need to choose the Barbero-Immirzi parameter $(γ)$. $γ$ is determined by studying the limit in which the `renormalized' gravitational constant on the horizon asymptotically approaches the `bare' value. Unlike the usual, much criticized, practice of choosing $γ$ just for the sake of the entropy matching the area law, its value is now rather determined by a physical consistency requirement.

gr-qc↗

arXiv2017

Reassessing the link between B-modes and inflation

We reevaluate the predictions of inflation regarding primordial gravity waves, which should appear as B-modes in the CMB, in light of the fact that the standard inflationary paradigm is unable to account for the transition from an initially symmetric state into a non-symmetric outcome. We show that the incorporation of an element capable of explaining such a transition dramatically alters the prediction for the shape and size of the B-mode spectrum. In particular, we find that by adapting a realistic objective collapse model to the situation at hand, the B-mode spectrum gets strongly suppressed with respect to the standard prediction. We conclude that the failure to detect B-modes in the CMB does not rule-out the simplest inflationary models.

gr-qc↗

arXiv2017

Non-extensive Statistical Mechanics and Black Hole Entropy From Quantum Geometry

Using non-extensive statistical mechanics, the Bekenstein-Hawking area law is obtained from microstates of black holes in loop quantum gravity, for arbitrary real positive values of the Barbero-Immirzi parameter$(γ)$. The arbitrariness of $γ$ is encoded in the strength of the "bias" created in the horizon microstates through the coupling with the quantum geometric fields exterior to the horizon. An experimental determination of $γ$ will fix this coupling, leaving out the macroscopic area of the black hole to be the only free quantity of the theory.

gr-qc↗

arXiv2017

Field dynamics on the trapping horizon in Vaidya spacetime

In this article, we shed some light on the field theoretic aspect of the spherically symmetric trapping horizon in Vaidya spacetime. The effective field equations are that of a Chern-Simons theory coupled to bulk sources through two different couplings, one is purely geometric and the other is matter dependent. This is an effective generalization of the equilibrium horizon scenario where the Chern-Simons theory is coupled to the bulk geometry through a constant matter-independent coupling. Further, we note that the field equations pulled-back to a cross-section of the horizon is inadequate to manifest the nature of the horizon. Hence, contrary to the usual practice, the evolution equation needs to be considered at least while passing on to the quantum theory.

gr-qc↗

arXiv2016

Energy spectrum of black holes : a new view

Energy of a black hole is usually quantized by invoking some area quantization scheme after expressing the energy in terms of the horizon area. However, in this approach one has to quantize the local and asymptotic energy of the black hole separately and the two results do not manifest any physical correspondence with each other. Here, as opposed to this practice, we find the unique energy spectrum of black holes by adopting a top-down approach. The physical links among the underlying quantum theory, statistical mechanics and thermodynamics of the black hole horizon play the central role in determining the energy spectrum. The energy spectrum that we obtain, explicitly reveals the correspondence between asymptotic and local observations through the presence of the surface gravity of the horizon as a parameter in the spectrum, rather than being expressed as a function of area and consequently getting quantized in the usual approach. Thus, our result presents a new view as far as black hole energy quantization is concerned. The calculations are performed using the quantum geometric description of black hole horizons as laid down by loop quantum gravity.

gr-qc↗

arXiv2016

Conformal blocks on a 2-sphere with indistinguishable punctures and implications on black hole entropy

The dimensionality of the Hilbert space of a Chern-Simons theory on a 3-fold, in the presence of Wilson lines carrying spin representations, had been counted by using its link with the Wess-Zumino theory, with level $k$, on the 2-sphere with points (to be called punctures) marked by the piercing of the corresponding Wilson lines and carrying the respective spin representations. It is shown, in the weak coupling (large $k$) limit, the formula decouples into two characteristically distinct parts; one mimics the dimensionality of the Hilbert space of a collection of non-interacting spin systems and the other is an effective overall correction contributed by all the punctures. The exact formula yield from this counting has been shown earlier to have resulted from the consideration of the punctures to be distinguishable. We investigate the same counting problem by considering the punctures to be indistinguishable. Although the full formula remains undiscovered, nonetheless, we are able to impose the relevant statistics for indistinguishable punctures in the approximate formula resulting from the weak coupling limit. As an implication of this counting, in the context of its relation to that of black hole entropy calculation in quantum geometric approach, we are able to show that the logarithmic area correction, with a coefficient of $-3/2$, that results in this method of entropy calculation, in independent of whether the punctures are distinguishable or not.

gr-qc↗

arXiv2016

Proof of Bekenstein-Mukhanov ansatz in loop quantum gravity

A simple proof of Bekenstein-Mukhanov(BM) ansatz is given within the loop quantum gravity(LQG) framework. The macroscopic area of an equilibrium black hole horizon indeed manifests a linear quantization. The quantum number responsible for this discreteness of the macroscopic area has a physical meaning in the LQG framework, unlike the ad hoc one that remained unexplained in BM ansatz.

gr-qc↗

arXiv2016

Thermodynamic partition function from quantum theory for black hole horizons in loop quantum gravity

We establish the link between the thermodynamics and the quantum theory of black hole horizons through the construction of the thermodynamic partition function, partly based on some physically plausible arguments, by beginning from the description of quantum states of the horizon, considering loop quantum gravity(LQG) as the underlying theory. Although, the effective `thermalized\rq{} form of the partition function has been previously used in the literature to study the effect of thermal fluctuations of the black hole horizon, nonetheless the direct link to any existing quantum theory (which is here taken to be LQG), especially a derivation of the partition function from the quantum states of the horizon, appears to be hitherto absent. This work is an attempt to bridge this small, but essential, gap that appears to be present between the existing literature of quantum theory and thermodynamics of black holes. Further, it may be emphasized that this work is {\it only} concerned with the {\it metric independent} approaches to black hole thermodynamics.

gr-qc↗