Bemerkung zur Quantentheorie des Laue-Effektes

Bronstein, M.

doi:10.1007/bf01331724

Cited by 12 publications

(21 citation statements)

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“…The minimal length can be incorporated by modifying the standard Heisenberg uncertainty principle, which we call as the generalized uncertainty principle or GUP. The relation between the minimal length and gravity was shown first in [6,7] and later in [8]. Along with the theoretical models there is a very strong signature of the existence of the GUP in the gedanken experiments as well.…”

Section: Introductionmentioning

confidence: 95%

“…where x and p are the position and momentum operators of the mechanical oscillator following the usual commutation relation, [x, p] = ih. We can break the Hamiltonian (7) as…”

Section: Noise Spectrum In the Gup Frameworkmentioning

confidence: 99%

“…The exact expression of the second term, δx(τ )x 0 (0) in equation ( 42) is given by equation (74) in appendix A.3. Now using equations ( 41) and (74) in equation ( 29), we can get the correlation function of the positions at different times over the modified Hamiltonian (7) in presence of the GUP corrections, containing both the linear and quadratic terms in momentum uncertainty. In this paper we want to investigate the effect of GUP in the power spectrum of an optomechanical system.…”

Section: Noise Spectrum In the Gup Frameworkmentioning

confidence: 99%

“…In this paper we want to investigate the effect of GUP in the power spectrum of an optomechanical system. After getting the correlation function over the modified Hamiltonian (7) we can now calculate the power spectrum S PF (ω) using equation (28). To do this, we substitute equations ( 41) and (42) in equation ( 28), to get…”

Section: Noise Spectrum In the Gup Frameworkmentioning

confidence: 99%

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Probing the generalized uncertainty principle through quantum noises in optomechanical systems

Sen

Bhattacharyya

Gangopadhyay

2022

Class. Quantum Grav.

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In this work we have considered a simple mechanical oscillator interacting with a single mode optical field inside a cavity in the generalized uncertainty principle framework (GUP). Our aim is to calculate the modified noise spectrum and observe the effects of the GUP. The commutation relation that we have considered has an extra linear order momentum term along with a quadratic order term. Confronting our theoretical results with the observational results, we observe that we get a much tighter bound on the GUP parameters from the noise spectrum using the values of the system parameters from different experiments.

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Section: Introductionmentioning

confidence: 95%

“…where x and p are the position and momentum operators of the mechanical oscillator following the usual commutation relation, [x, p] = ih. We can break the Hamiltonian (7) as…”

Section: Noise Spectrum In the Gup Frameworkmentioning

confidence: 99%

Section: Noise Spectrum In the Gup Frameworkmentioning

confidence: 99%

Section: Noise Spectrum In the Gup Frameworkmentioning

confidence: 99%

See 2 more Smart Citations

Probing the generalized uncertainty principle through quantum noises in optomechanical systems

Sen

Bhattacharyya

Gangopadhyay

2022

Class. Quantum Grav.

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“…On the other hand, as it was first argued by Bronstein [1] there is the smallest possible distance in quantum gravity, the Planck length, beyond which measurements are not possible. The argument relies on non-perturbative effects such as black hole formation and could be described only within a non-perturbative quantum theory of gravity absent to the date.…”

Section: Introductionmentioning

confidence: 98%

Quantum Analysis of BTZ Black Hole Formation Due to the Collapse of a Dust Shell

2020

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We perform Hamiltonian reduction of a model in which 2 + 1 dimensional gravity with negative cosmological constant is coupled to a cylindrically symmetric dust shell. The resulting action contains only a finite number of degrees of freedom. The phase space consists of two copies of ADS2—both coordinate and momentum space are curved. Different regions in the Penrose diagram can be identified with different patches of ADS2 momentum space. Quantization in the momentum representation becomes particularly simple in the vicinity of the horizon, where one can neglect momentum non-commutativity. In this region, we calculate the spectrum of the shell radius. This spectrum turns out to be continuous outside the horizon and becomes discrete inside the horizon with eigenvalue spacing proportional to the square root of the black hole mass. We also calculate numerically quantum transition amplitudes between different regions of the Penrose diagram in the vicinity of the horizon. This calculation shows a possibility of quantum tunneling of the shell into classically forbidden regions of the Penrose diagram, although with an exponentially damped rate away from the horizon.

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Intrinsic measurement errors for the speed of light in vacuum

Braun

Schneiter

Fischer

2017

Class. Quantum Grav.

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The speed of light in vacuum, one of the most important and precisely measured natural constants, is fixed by convention to c = 299792458 m/s. Advanced theories predict possible deviations from this universal value, or even quantum fluctuations of c. Combining arguments from quantum parameter estimation theory and classical general relativity, we here establish rigorously the existence of lower bounds on the uncertainty to which the speed of light in vacuum can be determined in a given region of space-time, subject to several reasonable restrictions. They provide a novel perspective on the experimental falsifiability of predictions for the quantum fluctuations of space-time.

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Bemerkung zur Quantentheorie des Laue-Effektes

Abstract: Phys. 22, 193, 1924. In dar letzten Arbeit zaigt Herr Wentzel, dall dam Grundbegriffe der Wellentheorie, dem Begriff der Phase, eine quantentheoretisehe Umdeutung gegeben sein kann.

Cited by 12 publications

References 0 publications

Probing the generalized uncertainty principle through quantum noises in optomechanical systems

Probing the generalized uncertainty principle through quantum noises in optomechanical systems

Quantum Analysis of BTZ Black Hole Formation Due to the Collapse of a Dust Shell

Intrinsic measurement errors for the speed of light in vacuum

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