Past and Future Blurring at Fundamental Length Scale

Neves, M. J.; Farina, C.; Cougo-Pinto, M. V.

doi:10.1103/physrevlett.105.211601

Cited by 5 publications

(15 citation statements)

References 33 publications

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“…The claim of Ref. [33] about the size of the nonlocal effects in κ-Minkowski is rejected by our analysis. Rather than an in-principle untestable Planckian fuzzyness, our κ-deformed Pauli-Jordan function is nonzero outside of the light-cone over a region of size ∼ L p L, i.e., the geometric average of the Planck length and the distance from the origin.…”

Section: Discussioncontrasting

confidence: 79%

“…In [38], available online, we produced an animation showing ∆ κ PJ in the plane δx 1 − δx 0 , zooming away from the origin. [33], where the 'blurry' region has the same thickness everywhere; the boost in the size of our nonlocal effect is apparent.…”

Section: Noncommutative Light-conementioning

confidence: 66%

“…If the spatial coordinate z 1 and the temporal one z 0 have uncertainties of the same order of magnitude, they will be of the order of L p z 1 . 4 For macroscopic distances, this is a colossal boost in the size of the effect, with respect to what was proposed in [33].…”

Section: Introductionmentioning

confidence: 80%

“…A more rigorous strategy is to use Quantum Field Theory (QFT) on κ-Minkowski. Reference [33] is highly significant in this context: by analyzing the retarded and advanced Green functions the authors are able to study their causality properties. Their conclusions are diametrically opposite to those of the advocates of (2) or (3): the light-cone is blurred over a region of Planckian size, independently of the distance from the origin.…”

Section: Introductionmentioning

confidence: 99%

“…The analysis of [33] is definitely a step further from arbitrarily postulating a relation of the kind (2) or ( 3), but it relies on an inadequate assumption: the deformed Casimir of κ-Minkowski is simply promoted to a nonlinear wave operator on a space of commutative functions, and its Green functions are calculated by inverting classical partial differential equations. Again, this approach will yield different results in different Hopf-algebra bases.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Light cone in a quantum spacetime

Mercati

Sergola

2018

Physics Letters B

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Noncommutative spacetimes are a proposed effective description of the low-energy regime of Quantum Gravity. Defining the microcausality relations of a scalar quantum field theory on the κ-Minkowski noncommutative spacetime allows us to define for the first time a notion of light-cone in a quantum spacetime. This allows us to reach two conclusions. First, the majority of the literature on κ-Minkowski suggests that this spacetime allows superluminal propagation of particles. The structure of the light-cone we introduced allows to rule this out, thereby excluding the possibility of constraining the relevant models with observations of in-vacuo dispersion of Gamma Ray Burst photons. Second, we are able to reject a claim made in [Phys. Rev. Lett. 105, 211601 (2010)], according to which the light-cone of the κ-Minkowski spacetime has a 'blurry' region of Plancklength thickness, independently of the distance of the two events considered. Such an effect would be hopeless to measure. Our analysis reveals that the thickness of the region where the notion of timelike and spacelike separations blurs grows like the square root of the distance. This magnifies the effect, e.g. in the case of cosmological distances, by 30 orders of magnitude.

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Section: Discussioncontrasting

confidence: 79%

Section: Noncommutative Light-conementioning

confidence: 66%

Section: Introductionmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Light cone in a quantum spacetime

Mercati

Sergola

2018

Physics Letters B

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Quantum causality in κ-Minkowski and related constraints

Franco

Hersent

Maris

et al. 2023

Class. Quantum Grav.

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We study quantum causal structures in 1+1 κ-Minkowski space-time described by a Lorentzian Spectral Triple whose Dirac operator is built from a natural set of twisted derivations of the κ-Poincaré algebra. We show that the Lorentzian Spectral Triple must be twisted to accommodate the twisted nature of the derivations. We exhibit various interesting classes of causal functions, including an analog of the light-cone coordinates. We show in particular that the existence of a causal propagation between two pure states, the quantum analogs of points, can exist provided quantum constraints, linking the momentum and the space coordinate, are satisfied. One of these constraints is a quantum analog of the speed of light limit.

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Pauli-Jordan function and scalar field quantization in κ -Minkowski noncommutative spacetime

Mercati

Sergola

2018

Phys. Rev. D

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We study a complex free scalar field theory on a noncommutative background spacetime called κ-Minkowski. In particular we address the problem of second quantization. We obtain the algebra of creation and annihilation operators in an explicitly covariant way. Our procedure does not use canonical/Hamiltonian formulations, which turn out to be ill-defined in our context. Instead we work in a spacetime covariant way by introducing a noncommutative Pauli-Jordan function. This function is obtained as a generalization of the ordinary, commutative, one by taking into account the constraints imposed by the symmetries of our noncommutative spacetime. The Pauli-Jordan function is later employed to study the structure of the light cone in κ-Minkowski spacetime, and to draw conclusions on the superluminal propagation of signals.

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Past and Future Blurring at Fundamental Length Scale

Cited by 5 publications

References 33 publications

Light cone in a quantum spacetime

Light cone in a quantum spacetime

Quantum causality in κ-Minkowski and related constraints

Pauli-Jordan function and scalar field quantization in κ -Minkowski noncommutative spacetime

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