Uncertainty in measurements of distance

Baez, John C.; Olson, S. Jay

doi:10.1088/0264-9381/19/14/101

Cited by 24 publications

(23 citation statements)

References 9 publications

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“…It follows to note that the meaning β = 1/4 in our approach appears in section 3 non in an artificial way but as the maximal meaning for which Spρ(β) still stays real, according to (7) and (8). Apparently, if considering corrections of order higher than 1 on β, then members from O(β 2 ) in the formula for ρ out in (10) can give quantum corrections [22] for S semiclass BH (18) in our approach.…”

Section: Bekenstein-hawking Formulamentioning

confidence: 82%

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Quantum Mechanics at Planck's Scale and Density Matrix

Shalyt-Margolin

Suarez

2003

Int. J. Mod. Phys. D

121

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In this paper Quantum Mechanics with Fundamental Length is chosen as Quantum Mechanics at Planck's scale. This is possible due to the presence in the theory of General Uncertainty Relations. Here Quantum Mechanics with Fundamental Length is obtained as a deformation of Quantum Mechanics. The distinguishing feature of the proposed approach in comparison with previous ones, lies on the fact that here density matrix subjects to deformation whereas so far commutators have been deformed. The density matrix obtained by deformation of quantum-mechanical density one is named throughout this paper density pro-matrix. Within our approach two main features of Quantum Mechanics are conserved: the probabilistic interpretation of the theory and the well-known measuring procedure corresponding to that interpretation. The proposed approach allows to describe dynamics. In particular, the explicit form of deformed Liouville's equation and the deformed Shrödinger's picture are given. Some implications of obtained results are discussed. In particular, the problem of singularity, the hypothesis of cosmic censorship, a possible improvement of the definition of statistical entropy and the problem of information loss in black holes are considered. It is shown that obtained results allow to deduce in a simple * Phone (+375) 172 883438; e-mail: a.shalyt@mail.ru; alexm@hep.by † Phone (+375) 172 883438; e-mail: suarez@hep.by, jsuarez@mail.tut.by 1 and natural way the Bekenstein-Hawking's formula for black hole entropy in semiclassical approximation.

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Section: Bekenstein-hawking Formulamentioning

confidence: 82%

“…For instance, from an ideal experiment associated with Gravitational Field and Quantum Mechanics a lower bound on minimal length was obtained in [6], [7] and improved in [8] without using GUR to an estimate of the form ∼ L p . Let us to consider equation (3) in some detail.…”

Section: Fundamental Length and Density Matrixmentioning

confidence: 99%

Quantum Mechanics at Planck's Scale and Density Matrix

Shalyt-Margolin

Suarez

2003

Int. J. Mod. Phys. D

121

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“…The gravitational nature of macroscopic clock(-system)s is taken into account in [116], where they are commented to be expected not to exhibit quantum properties much above the Planck scale. The quantum nature of rulers of mass smaller than the Schwarzschild limit is expected [117] to be manifest at distances comparable to the Planck scale or less than one order of magnitude larger than it. The Planck-scale fluctuations (for vacuum) in measurement apparati [118] and the space range of the vacuum fluctuations in the apparati has been analyzed to be also possibly large, but subject to fine tuning.The physical passage form quantum foam to General Relativity is presented in [119] 6.…”

Section: Length Errorsmentioning

confidence: 99%

Semiclassical Length Measure from a Quantum-Gravity Wave Function

Lecian

2017

Technologies

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Abstract:The definition of a length operator in quantum cosmology is usually influenced by a quantum theory for gravity considered. The semiclassical limit at the Planck age must meet the requirements implied in present observations. The features of a semiclassical wave-functional state are investigated, for which the modern measure(ment)s is consistent. The results of a length measurement at present times are compared with the same measurement operation at cosmological times. By this measure, it is possible to discriminate, within the same Planck-length expansion, the corrections to a Minkowski flat space possibly due to classicalization of quantum phenomena at the Planck time and those due to possible quantum-gravitational manifestations of present times. This analysis and the comparison with the previous literature can be framed as a test for the verification of the time at which anomalies at present related to the gravitational field, and, in particular, whether they are ascribed to the classicalization epoch. Indeed, it allows to discriminate not only within the possible quantum features of the quasi (Minkowski) flat spacetime, but also from (possibly Lorentz violating) phenomena detectable at high-energy astrophysical scales. The results of two different (coordinate) length measures have been compared both at cosmological time and as a perturbation element on flat Minkowski spacetime. The differences for the components of the corresponding classical(ized) metric tensor have been analyzed at different orders of expansions. The results of the expectation values of a length operator in the universe at the Planck time must be comparable with the same length measurements at present times, as far as the metric tensor is concerned. The comparison of the results of (straight) length measures in two different directions, in particular, can encode the pertinent information about the parameters defining the semiclassical wavefunctional for (semiclassicalized) gravitational field.

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“…Some readers may ponder why do we need to consider a concentrated region of space. The reason is that if we allow the clock to be more massive by making it bigger, it also deteriorates its performance (see the discussion in [13] in response to [14]). …”

Section: Fundamental Limits To Realistic Clocksmentioning

confidence: 99%

Modern Space-Time and Undecidability

Gambini

Pullin

2009

Minkowski Spacetime: A Hundred Years Later

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The picture of space-time that Minkowski created in 1907 has been followed by two important developments in physics not contained in the original picture: general relativity and quantum mechanics. We will argue that the use of concepts of those theories to construct space-time implies conceptual modifications in quantum mechanics. In particular one can construct a viable picture of quantum mechanics without a reduction process that has outcomes equivalent to a picture with a reduction process. One therefore has two theories that are entirely equivalent experimentally but profoundly different in the description of reality they give. This introduces a fundamental level of undecidability in physics of a kind that has not been present before. We discuss some of the implications.

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Uncertainty in measurements of distance

Cited by 24 publications

References 9 publications

Quantum Mechanics at Planck's Scale and Density Matrix

Quantum Mechanics at Planck's Scale and Density Matrix

Semiclassical Length Measure from a Quantum-Gravity Wave Function

Modern Space-Time and Undecidability

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