Impacts of generalized uncertainty principle on black hole thermodynamics and saleckerwigner inequalities a. We will do a more general proof later, but i think it is useful to do a proof of a special case now if the proof is transparent. The generalized uncertainty principle gup has been directly applied to the motion of macroscopic test bodies on a given spacetime in order to compute corrections to the classical orbits predicted in newtonian mechanics or general relativity. This has provided the generalized uncertainty principle which modifies commutation relations shown by eq.
The functional form of the generalized uncertainty principle that we obtain agrees with the one found in string theory. Modified quantum mechanics and generalized uncertainty principle. Generalized uncertainty principle, quantum gravity and horava. In the present work the role that a generalized uncertainty principle could play in the quantization of the electromagnetic field is analyzed. Pdf a generalized uncertainty principle and sparse. An elementary proof of a basic uncertainty principle concerning pairs of representations of rsup n vectors in different orthonormal bases is provided. The statement of the generalized uncertainty principle below is followed by two proofs. In this video, i finally provederive the generalized uncertainty principle, using basic linear algebra identities such as the schwarz inequality as well as. Based on the generalized uncertainty principle gup, the researchers find that the quantum gravity affects the kleingordon equation exactly. In one dimensional case, the simplest form of the gup is represented in the context of the snyder noncommutative space2. This is called the energytime uncertainty relation. Pdf generalized uncertainty principle, extradimensions. If a is an average distance electronproton distance, the uncertainty principle informs us that the minimum electron momentum is on the order of ha. Generalized uncertainty principle and quantum electrodynamics.
Pdf generalized uncertainty principle, classical mechanics. Generalized uncertainty principle link with loop quantum gravity. These corrections generically violate the equivalence principle. Generalized gravitational uncertainty principle the existence of a minimal length based on gup introduces that t he space in hilbert space representation 29 can describe a noncomm utative. The resulting inequality is then weakened by one of two methods. Coherent states of harmonic oscillator and generalized. Hence, the kleingordon equation which is corrected by gup will be more suitable on the expression of the tunneling behavior. The uncertainty principle is related to the heisenberg algebra, and so the usual heisenberg algebra will be deformed to the generalized heisenberg. Approximation methods, spin and pauli\s priinciple.
December 1, 2006 the generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantumgravity. Studies of the socalled generalized uncertainty principle gup showed modifications in several areas of quantum mechanics. The generalized uncertainty principle proofderivation. These reasonings induce the possibility to have corrections to the heinsenberg principle in order. Then we see that the variance of qcan be written as h q2i, as shown below. The muchstudied gup form contains the momentum as the quadratic term l. Thermality of the hawking flux thermality of the hawking flux.
Generalized uncertainty principle and angular momentum. Oct 19, 2009 a meaningful prediction of various theories of quantum gravity string theory and black holes is the presence of a minimum measurable length or a maximum observable momentum. Thermodynamics of a non stationary black hole based on. The deformed algebra and therefore the form of the generalized uncertainty principle are fixed uniquely by rather simple assumptions. The uncertainty principle lies at the heart of quantum physics, and is widely. Research article horizon wavefunction of generalized. In the seminal papers on the generalized uncertainty principle gup, deformations of the uncertainty relations stem from the attempt of explaining the divergences appearing in quantum. Black holes and the generalized uncertainty principle bernard.
Quantum groups, gravity and the generalized uncertainty. Some generalizations of the heisenberg uncertainty principle. Heisenberg uncertainty principle msu pa welcome page. Applications dependent on the uncertainty principle for their operation include extremely low noise technology such as that required in. Generalized uncertainty principle, extradimensions and. Dec 28, 2018 it was previously argued that generalized uncertainty principle gup with a positive parameter removes the chandrasekhar limit. Hermitian operators, a and b with a, b 0 had compatible eigenstates, and so a. As usually assumed, the gup takes into account the gravitational uncertainty of position related to the minimum fundamental length scale in physics.
Pdf the generalized uncertainty principle and quantum. Wagner, extended uncertainty principle for rindler and cosmological horizons, epjc to appear 2019, arxiv. Uncertainty principle 2 the uncertainty principle as part of their main research program. The string theory result is reproduced expanding our result at. Introducing quantum gravity effect makes a considerable change in the density of states inside the volume of the phase space which changes the statistical and thermodynamical properties of any physical system. Asymptotic generalized extended uncertainty principle. They entered the literature as the generalized uncertainty principle gup assuming modified dispersion relation, and therefore are allowed for a wide range of applications in estimating, for example, the inflationary parameters, lorentz invariance violation. We investigate the relationship between the generalized uncertainty principle in quantum gravity and the quantum deformation of the poincar e algebra.
Proofofthe uncertaintyprinciple introduction special case. The wave function of the universe near the bigbang. The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantumgravity. The uncertainty principle in quantum mechanics is derived from the product of the uncertainties of two observables, manipulated so as to be expressed in term. This statement leads to existence of a minimal observable distance on the order of plank length lp in quantum gravity. C gravitational tests of the generalized uncertainty principle fabio scardigli 1 2 roberto casadio 0 3 0 dipartimento di fisica e astronomia, alma mater universita di bologna, via irnerio 46, 40126 bologna, italy 1 dipartimento di matematica, politecnico di milano, piazza leonardo da vinci 32, 203 milan, italy 2 department of mathematics, college of engineering, american. Pdf, the deformation parameter of the generalized uncertainty. That nifty relationship, the commutator, plays a key role. Testing generalised uncertainty principles through quantum noise. Application of the triangle inequality or by discarding the real part of a complex scalar.
We show that a deformation of the heisenberg algebra which depends on a dimensionful parameter. Here we show that the traditional uncertainty relation in fact belongs to the leading order approximation of a generalized uncertainty relation. Before proceeding further it is necessary to create the mathematical setting for the analysis. Box 220, 15453 dasman, kuwait 2 dipartimento di matematica, politecnico di milano, piazza leonardo da vinci 32, 203 milan, italy. Nov 27, 2020 the uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit of the measurement precision of incompatible observables. When we consider a quantum gravity theory, we need a fundamental distance scale of the order of the planck length l p. Uncertainty principle of the 2d affine generalized. Generalized uncertainty principle michele maggiore i. Generalized uncertainty principle, classical mechanics. Apr 08, 2020 the generalized uncertainty principle gup has been directly applied to the motion of macroscopic test bodies on a given spacetime in order to compute corrections to the classical orbits. Several approaches of the gup generalized uncertainty principle have been studied by many researchers91117. The result, slightly stronger than stated before, has a direct impact on the uniqueness property of the sparse representation of such vectors using pairs of orthonormal bases as overcomplete dictionaries.
Generalized uncertainty principle and white dwarfs redux. One way to restore the limit is by taking the gup parameter to be negative. Asymptotic generalized extended uncertainty principle mariusz p. Oct 10, 2020 the generalized uncertainty principle. Thus, we have presented an asymptotic form of the generalized extended uncertainty principle in the low energy limit given by the formula 86 which is our main achievement. As usually assumed, the gup takes into account the gravitational uncertainty of position related to the min. In quantum mechanics, the uncertainty principle also known as heisenbergs uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pairs of physical quantities of a particle, such as position, x, and momentum, p, can be predicted from initial conditions. Quantum mechanics and the generalized uncertainty principle. Article english pdf article in xml format how to cite this article scielo analytics automatic translation. The uncertainty principle lies at the heart of quantum physics, and is widely thought to be a fundamental limit on the measurement precisions of incompatible observables. Observational tests of the generalized uncertainty. The fundamental concepts of the minimal length scale and the gup are discussed and the modi.
Various frameworks of quantum gravity predict a modification in the heisenberg uncertainty principle to a socalled generalized uncertainty principle gup. Generalized uncertainty relations note that only at the very end did we make use of the specific form of the commutator. Uncertainty principle hup emerged when heisenberg 1, in a seminal paper of 1927, discussed measurement processes in quantum theory. The quantitative measure of how the combined uncertainty of measuring two variables relates to their lack of commutativity is most simply presented as a. Both proofs start by applying the schwartz inequality is to. Towards thermodynamics with generalized uncertainty principle. We study generalized uncertainty principle through the basic concepts of limit and fourier transformation and analyze both the quantum theory of gravity and string theory from the perspective of complex function theory. Here, griffiths doesnt just prove that inequality, he goes a step further and proves the general uncertainty principle for all operators. Tawfiknew varying speed of light theories joao magueijoblack holes in loop quantum gravity alejandro perezrecent citations tunnelling radiation and the microstates of a black hole influenced by the lorentz invariance violation. Nptel chemistry and biochemistry introductory quantum. Quantum mechanics and the generalized uncertainty principle jang young bang. Generalized uncertainty principle, extradimensions and holography.
The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of. Abstract the uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit of the measurement. The generalized uncertainty principle in ads space and the. This means that our result is valid in general for any two observables. A generalized uncertainty principle and sparse representation in pairs of bases michael elad and alfred m. The system has all these variables, except and tacitly its space h in. Fine structure constant, domain walls, and generalized. The generalized uncertainty principle is a consequence of incorporating a minimal length from a theory of quantum gravity. Jul 25, 2020 finally, the formalism has been extended phenomenologically to combine the result with the generalized uncertainty principle gup by virtue of deformed commutators. The nature and proof of the generalized uncertainty principle. Premontschwarz, loop black holes and the black hole uncertainty principle correspondence 20. In particular, i will focus on the application of the modified.
A generalized uncertainty principle in quantum gravity. Before proceeding further it is necessary to create the mathematical setting for. The algebraic structure of the generalized uncertainty principle measurements in quantum gravity are controlled by a generalized uncertainty principle 4. In this paper, we extend the previous works and derive the uncertainty principle for the two dimensional affine generalized fractional fourier transform 2d agfft. Dynamics of quintessence in generalized uncertainty principle.
They entered the literature as the generalized uncertainty principle gup assuming modified dispersion relation, and therefore are allowed for a wide range of applications in estimating, for example, the inflationary parameters, lorentz invariance violation, black hole thermodynamics, salekerwigner inequalities, entropic nature of. They entered the literature as the generalized uncertainty principle gup assuming modified dispersion relation, and therefore are allowed for a wide range of. Berger physics department, indiana university, bloomington, in 47405, usa dated. Carr, black holes, the generalized uncertainty principle and higher dimensions, phys. Generalized uncertainty principle, classical mechanics, and. Here it is shown that the traditional uncertainty relation in fact belongs to the leading order approximation of a generalized uncertainty relation. Garay, 1995, 2 g g gx p pt dl p 2 2 with gx and gp each of which is the uncertainty of the position and momentum of the quantum particles. Quantum wells and the generalized uncertainty principle. The uncertainty principle of the 1d case has been discussed a lot.
Gravitational tests of the generalized uncertainty principle fabio scardigli1,2,a, roberto casadio3,4,b 1 department of mathematics, college of engineering, american university of the middle east, p. In this work we discuss an alternative method that achieves the same effect. Pdf the algebraic structure of the generalized uncertainty. Generalized uncertainty principle and its implications on.
Consider a system involving a set of variables q 1, q 2, q n and their associated momenta p 1, p 2, p n. In this context, considerations from string theory 1417 and gedanken. Aug 10, 2020 the generalized uncertainty principle gup has been directly applied to the motion of macroscopic test bodies on a given spacetime in order to compute corrections to the classical orbits predicted in newtonian mechanics or general relativity. Generalized and extended uncertainty principles and their. I also revisit the black holestring phase transition, in the context of the generalized uncertainty principle. Examples of heisenberg uncertainty principle mit opencourseware.
Subplanckian black holes and the generalized uncertainty. These include, for example, tests of numberphase uncertainty relations in superconducting or quantum optics systems. Scattering in graphene quantum dots under generalized. The system has all these variables, except and tacitly its space h in praxic perspective. Generalized uncertainty principle 2 probability eigenvalue formalism where d. Bruckstein abstract an elementary proof of a basic uncertainty principle concerning pairs of representations of vectors in different orthonormal bases is provided. Uncertainty relations between two general noncommuting generalized self adjoint operators is derived in a krein space basically a hilbert space endowed with. Here we show that this mode of thought only pertains to the lowest order approximation of a generalized uncertainty principle, where the incompatibility. Generalized and extended uncertainty principles and their impact onto the hawking radiation p. They entered the literature as the generalized uncertainty principle. Two proofs of the generalized uncertainty principle. Black hole thermodynamics and the generalized uncertainty. We consider a simple quantummechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized.
The generalized uncertainty principle li 2021 annalen. Paper open access heuristic derivation of the casimir effect. Gravitational tests of the generalized uncertainty principle. So in the theory of quantum gravity the principle of uncertainty must be modified into a generalized uncertainty principle gup. The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of incompatible observables. At the end of this document i show how this special case can be generalized to include all wave functions.
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