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Short Distance vs. Long Distance Physics: The Classical Limit of the Minimal Length Uncertainty Relation
High Energy Physics - Theory · Submitted 4 Apr 2002
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Comparison with observation places severe constraints on the value of the minimum length.
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The abstract, sentence by sentence
We continue our investigation of the phenomenological implications of the "deformed" commutation relations [x_i,p_j]=i hbar[(1 + beta p^2) delta_{ij} + beta' p_i p_j]. These commutation relations are motivated by the fact that they lead to the minimal length uncertainty relation which appears in perturbative string theory. In this paper, we consider the effects of the deformation on the classical orbits of particles in a central force potential. Comparison with observation places severe constraints on the value of the minimum length.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We continue our investigation of the phenomenological implications of the "deformed" commutation relations [x_i,p_j]=i hbar[(1 + beta p^2) delta_{ij} + beta' p_i p_j]. | background 0.87 | 0.55 | 0.03 | asserted 0.66 |
| s1 | These commutation relations are motivated by the fact that they lead to the minimal length uncertainty relation which appears in perturbative string theory. | background 1.00 | 0.09 | 0.03 | asserted 0.95 |
| s2 | In this paper, we consider the effects of the deformation on the classical orbits of particles in a central force potential. | contribution 0.99 | 0.87 | 0.04 | asserted 0.77 |
| s3 | Comparison with observation places severe constraints on the value of the minimum length. | result 0.94 | 0.53 | 0.68 | asserted 1.00 |
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The paper
Original abstract
We continue our investigation of the phenomenological implications of the "deformed" commutation relations [x_i,p_j]=i hbar[(1 + beta p^2) delta_{ij} + beta' p_i p_j]. These commutation relations are motivated by the fact that they lead to the minimal length uncertainty relation which appears in perturbative string theory. In this paper, we consider the effects of the deformation on the classical orbits of particles in a central force potential. Comparison with observation places severe constraints on the value of the minimum length.
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References
How the literature uses it
21 arXiv papers cite this in 27 sentences
Papers citing it · 18 sentences without a confident label
Uses its data or values 1 paper
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Then we can calculate Mercury's perihelion: [equation] also we should note observed value of the Mercury's perihelion as ( [ref] ): [equation]
Spinning particle dynamics, epicyclic frequencies, and transient QPO signatures in Schwarzschild spacetime · Constraints on the spin $s$ parameter from periastron precession. · 0.83
Compares with it 2 papers
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Our final result ([ref]) for perihelion precession perfectly coincides with the result of [ref] (Eq. 66) when $β^'=2β$.
Quantum gravity, minimum length and Keplerian orbits · Introduction · 1.00
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Their analysis used the estimated result of Mercury’s relativistic perihelion precession given by $42.980±0.002$ arcsec per century [ref] , and the GRAVITY data of the pericenter advance of the S2 star orbiting Sgr $A^*$, reporting $ζ≤0.01869$ (Mercury) and $ζ≤0.73528$ (S2 star), both consistent with our constraints.
Probing loop quantum effects through solar system experiments: observational signatures and parameter constraints · Precession of perihelia · 0.91
Cites it as background 5 papers
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Furthermore, taking the classical limit $ħ→0$, one can discuss the minimal length effects on classical systems, such as observational tests of general relativity [ref] , classical harmonic oscillator [ref] , equivalence principle [ref] , Newtonian potential [ref] , the Schrödinger-Newton equation [ref] , the weak cosmic censorship conjecture [ref] and motions of particles near a black hole horizon [ref] .
Minimal Length Effects on Motion of a Particle in Rindler Space · Introduction · 0.89
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While generalized forms of $Δp Δx ≥ħ/2$ have been discussed in the context of quantum gravity (see [ref] and references therein), we are aware of fewer such attempts [ref] regarding the TEU.
Using Neutrinos to test the Time-Energy Uncertainty Relation in an Extreme Regime · Experimental Test of the Time-Energy Uncertainty Relation with Mössbauer Neutrinos – by R. S. Raghavan · 0.89
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Regular black holes were originally proposed to avoid the singularity of ordinary black holes [ref] , which includes the well known Bardeen black hole, Hayward black hole as well as Frolov black hole [ref] .
Regular black holes with sub-Planckian curvature · Introduction · 1.00
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