On the Semiclassical Approach of the Heisenberg Uncertainty Relation in the Strong Gravitational Field of Static Blackhole (original) (raw)
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Gravitational effects on the Heisenberg Uncertainty Principle: A geometric approach
Results in Physics
The Heisenberg Uncertainty Principle (HUP) limits the accuracy in the simultaneous measurements of the position and momentum variables of any quantum system. This is known to be true in the context of non-relativistic quantum mechanics. Based on a semiclassical geometric approach, here we propose an effective generalization of this principle, which is well-suited to be extended to general relativity scenarios as well. We apply our formalism to Schwarzschild and de Sitter spacetime, showing that the ensuing uncertainty relations can be mapped into well-known deformations of the HUP. We also infer the form of the perturbed metric that mimics the emergence of a discrete spacetime structure at Planck scale, consistently with the predictions of the Generalized Uncertainty Principle. Finally, we discuss our results in connection with other approaches recently appeared in the literature.
Some aspects of gravitational quantum mechanics
General Relativity and Gravitation, 2006
String theory, quantum geometry, loop quantum gravity and black hole physics all indicate the existence of a minimal observable length on the order of Planck length. This feature leads to a modification of Heisenberg uncertainty principle. Such a modified Heisenberg uncertainty principle is referred as gravitational uncertainty principle(GUP) in literatures. This proposal has some novel implications on various domains of theoretical physics. Here, we study some consequences of GUP in the spirit of Quantum mechanics. We consider two problem: a particle in an one-dimensional box and momentum space wave function for a "free particle". In each case we will solve corresponding perturbational equations and compare the results with ordinary solutions. PACS: 03.65.-w, 04.60.-m , 42.50.Nn
On Gravity and the Uncertainty Principle
Modern Physics Letters A, 1999
Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons. As we show here the gravitational interaction of the photon and the particle being observed modifies the uncertainty principle with an additional term. From the modified or gravitational uncertainty principle it follows that there is an absolute minimum uncertainty in the position of any particle, of order of the Planck length. A modified uncertainty relation of this form is a standard result of superstring theory, but the derivation given here is based on simpler and rather general considerations with either Newtonian gravitational theory or general relativity theory.
Incompatibility between Einstein's General Relativity and Heisenberg's Uncertainty Principle
2018
Are General Relativity and Quantum Mechanics incompatible? Each in their world, that of the infinitely large and that of the infinitely small, they did not seem to interfere as long as they avoided each other. However, it is their fundamental oppositions that prevent the scientific community from achieving a unification of physics. The proposal of this paper is to provide a mathematical proof of incompatibility, beyond the fact that they have fundamentally different principles, between the foundations of General Relativity and Quantum Mechanics, namely the deformation of the space-time geometry and the Uncertainty Principle. It will thus be possible to provide an absolute limitation in establishing a unifying theory of physics, if any. Moreover, while respecting the conditions fixed by the Uncertainty Principle, it will be tempted to determine with accuracy and simultaneity, the position and the speed of a non-relativistic particle, by application of relativistic principles and bypassing the problems raised by such an operation. The Uncertainty Principle as stated by Werner Heisenberg will be then, in the light of observations made on the measurement of the time dilatation and in accordance with its own terms, refuted by the present.
The Generalized Uncertainty Principle and Quantum Gravity Phenomenology
2010
In this article we examine a Generalized Uncertainty Principle which differs from the Heisenberg Uncertainty Principle by terms linear and quadratic in particle momenta, as proposed by the authors in an earlier paper. We show that this affects all Hamiltonians, and in particular those which describe low energy experiments. We discuss possible observational consequences. Further, we also show that this indicates that space may be discrete at the fundamental level.
Classical and Quantum Gravity, 2020
After a critical overview of the Generalized Uncertainty Principle (GUP) applied to compact objects, we propose a texture of Heisenberg uncertainty principle in curved spacetimes (CHUP). CHUP allows to write down physically motivated STUR (spacetime uncertainty relations) in a generic background for a non commutative spacetime in terms of tetrad variables. In order to study possible quantum effects for compact astrophysical objects as white dwarf, neutron stars and black holes, an expression for quantum fluctuations is outlined. As a result, contrary to GUP-based claims, we found no evidence for quantum effects concerning equilibrium equation and critical mass Mc for white dwarf and neutron stars. Conversely, our expression for CHUP confirms that general relativistic effects strongly reduce the OppenheimerVolkoff Newtonian limit for very compact astrophysical objects as neutron stars. In particular, we found that for a degenerate relativistic ∗s.viaggiu@unimarconi.it and viaggiu@axp...
Research Gate, 2023
This paper presents a reinterpretation of Heisenberg’s uncertainty principle (HUP) as a common fundamental principle of both Quantum mechanisms (QM) and General relativity (GR). Contrarily to the mainstream opinion in modern physics, this paper mathematically demonstrates that QM & GR are in fact reciprocally compatible (as the two “faces” of the same “coin”, a so-called physical monad), because having this profound direct connection two each other via time discreteness (TD), which TD is mathematically implied by both GR & HUP via the same common Planck units derived from GR and re-used in this reformulation of HUP in terms of Planck time. A future plausible TOE will surely and firmly stand on this reformulation of HUP based on Planck units derived directly from GR. The main implications of this newly discovered GR-QM compatibility will be discussed in a future version of this paper. #DONATIONS. Anyone can donate for dr. Dragoi’s independent research and original music at: www.paypal.com/donate/?hosted\_button\_id=AQYGGDVDR7KH2
Generalized uncertainty principle and corpuscular gravity
The European Physical Journal C, 2019
We show that the implications of the generalized uncertainty principle (GUP) in the black hole physics are consistent with the predictions of the corpuscular theory of gravity, in which a black hole is conceived as a Bose-Einstein condensate of weakly interacting gravitons stuck at the critical point of a quantum phase transition. In particular, we compute such characteristic thermodynamic quantities as the temperature and the evaporation rate of a black hole. By comparing the results obtained in the two scenarios, we are able to estimate the GUP deformation parameter β, which turns out to be of order unity, in agreement with the expectations of some models of string theory. We also comment on the sign of β, exploring the possibility of having a negative deformation parameter when a corpuscular quantum description of the gravitational interaction is assumed to be valid. 1 Throughout the paper, we work with the units c = k B = 1, where k B is the Boltzmann constant, andh = 1. The Planck length is defined as p = √h G, while the Planck mass as m p =h/ p .
Astrophysics and Space Science, 2012
By using the null tetrad and the 't Hooft brickwall model, the quantum entropies of a Reissner-Nordström black hole due to the Weyl neutrino, electromagnetic, massless Rarita-Schwinger and gravitational fields for the sourcefree case are investigated from a generalized uncertainty principle. The divergence structure for the entropy is demonstrated. In addition to the usual linearly and logarithmically divergent terms, additional quadratic, cubic, biquadratic and other higher order divergences exist near the event horizon in the entropy, which not only depend on the black hole characteristics but also on the spin fields and the gravitational interactions. The terms describe the contribution of the quantum fields to the entropy and the effects of the generalized uncertainty principle on it. If the smallest length scale is taken into account, the contribution of the gravitational interactions to the entropy is found to be a part of the dominant term and very important, and therefore it can not be neglected.
Analysis of some classical and quantum aspects of black holes
2019
El objetivo de la presente tesis es profundizar en diversos aspectos de la fisica de los agujeros negros. Tanto en lo que respecta a sus caracteristicas constitutivas fundamentales, su "estructura" interna, como a la posibilidad de observar o detectar mediante observaciones astrofisicas ciertos efectos producto de su dinamica.Por un lado, hemos seguido las ideas de Dvali, Gomez et al. quienes han sugerido la posibilidad de que un agujero negro sea un condensado de Bose—Einstein de gravitones debilmente interactuantes. En nuestro caso hemos estudiado la existencia de este tipo de soluciones sobre diferentes metricas de agujero negro (Schwarzschild y Reissner— Nordstrom) que actuarian como potencial confinante para dichos condensados. Un parametro necesario para ello, es el equivalente a un potencial quimico que debe ser incorporado a la relatividad general. Cabe destacar que la solucion encontrada puede ser interpretada como la funcion de campo medio del condensado. Ademas ...