Large-scale nonlocality in “doubly special relativity” with an energy-dependent speed of light

Schützhold, Ralf; Unruh, W. G.

doi:10.1134/1.1633311

Cited by 45 publications

(69 citation statements)

References 28 publications

(52 reference statements)

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“…It is still unclear why the latter nonlinear momenta should be the physically measured ones and there is a rich literature now devoted to the interpretation of DSR in momentum space. Such an interpretation should hopefully clarify some of the problems pointed out in the recent literature [38].…”

Section: B Deformed Special Relativitymentioning

confidence: 99%

Modified dispersion relations from the renormalization group of gravity

Girelli¹,

Liberati²,

Percacci³

et al. 2007

Class. Quantum Grav.

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We show that the running of gravitational couplings, together with a suitable identification of the renormalization group scale can give rise to modified dispersion relations for massive particles. This result seems to be compatible with both the frameworks of effective field theory with Lorentz invariance violation and deformed special relativity. The phenomenological consequences depend on which of the frameworks is assumed. We discuss the nature and strength of the available constraints for both cases and show that in the case of Lorentz invariance violation, the theory would be strongly constrained.

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Section: B Deformed Special Relativitymentioning

confidence: 99%

Modified dispersion relations from the renormalization group of gravity

Girelli¹,

Liberati²,

Percacci³

et al. 2007

Class. Quantum Grav.

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“…This effect, first noticed in Ref. [24] is the characteristic trait of the so-called relative locality [25,26]. The space-time resulting in such a way from the automaton dynamics is not "objective", in the sense that events that coincide for one observer may not for another boosted observer.…”

mentioning

confidence: 99%

“…For the present purpose without loss of generality we focus on the easiest d = 1 dimensional case. As for any DSR model, it turns out that the spacetime emerging from the automaton exhibits relative locality, namely the phenomenon according to which the coincidence of two events is observer-dependent [24][25][26].arXiv:1310.6760v1 [quant-ph] …”

mentioning

confidence: 99%

“…[24], interpreting physically the coordinates (x, t) in terms of the mean position x at time t of a restricted class of states that can be interpreted as moving particles, namely narrow-band Gaussian wavepackets moving at the group-velocity. In this construction points in space-time are regarded as crossing points of the trajectories of two particles (such points have an "extension" due to the Gaussian profile).…”

mentioning

confidence: 99%

“…Under the action of the deformed boost L D β a functionf (ω, k) transforms aŝ f (ω, k) =f (ω (ω, k), k (ω, k)) and, following an ansatz due to Schützhold et al [24], one can express the boosted function in the variables t, x by conjugating the boost L D β with the Fourier transform F [29] i. e.…”

mentioning

confidence: 99%

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Doubly special relativity from quantum cellular automata

Bibeau-Delisle¹,

Bisio²,

D’Ariano³

et al. 2015

EPL

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It is shown how a Doubly-Special Relativity model can emerge from a quantum cellular automaton description of the evolution of countably many interacting quantum systems. We consider a onedimensional automaton that spawns the Dirac evolution in the relativistic limit of small wave-vectors and masses (in Planck units). The assumption of invariance of dispersion relations for boosted observers leads to a non-linear representation of the Lorentz group on the (ω, k) space, with an additional invariant given by the wave-vector k = π/2. The space-time reconstructed from the (ω, k) space is intrinsically quantum, and exhibits the phenomenon of relative locality.The existence of a fundamental scale of length or mass, which can be identified with the Planck scale, is a ubiquitous feature of quantum gravity models [1][2][3][4][5][6][7]. The appearance of the minimum length P = G/c 3 is the result of combining the fundamental constants that characterize physical theories describing different scales: (quantum mechanics), c (special relativity), and G (gravity). The so-called Planck length P is commonly regarded as the threshold below which the intuitive description of space-time breaks down, and new phenomenology is expected. A natural hypothesis is that quantum features become crucial in determining the structure of space-time below the Planck scale, leading to a radical departure from the traditional geometric concepts. This perspective makes one wonder about the fate of Lorentz symmetry at the Planck scale. A possible way of tackling this question is to consider a theory with two observerindependent scales, the speed of light and the Planck length, as proposed in the models of Doubly-Special Relativity (DSR) [8][9][10][11][12][13]. All the DSR models share the feature of a non-linear deformation of the Poincaré symmetry that eventually leads to a modification of the quadratic invariantSuch deformed kinematics are especially interesting since they provide new phenomenological predictions, e. g. wavelength dependence of the speed of light and a modified threshold for particle creation in collision processes. Evidences for a violation of the Lorentz energymomentum dispersion relation (1) have recently been sought in astrophysics, see e. g. the thresholds for ultrahigh-energy cosmic rays [14,15], and in cold-atom experiments [16].A recent approach to a Planck scale description of physical kinematics is that of quantum cellular automata (QCAs) [17][18][19][20][21]. The QCA generalizes the notion of cellular automaton of von Neumann [22] to the quantum case, with cells of quantum systems interacting with a finite numer of neighbors via a unitary operator describing the single step evolution [23]. We assume that each cell x of the lattice corresponds to the local value ψ(x) of a quantum field whose dynamics is described by a QCA. From this perspective the usual quantum field evolution should emerge as a large scale approximation of the automaton dynamics occurring at an hypothetical discrete Planck scale. In Ref.[17] a QCA-cal...

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Lorentz Breaking Effective Field Theory and Observational Tests

Liberati

2013

Lecture Notes in Physics

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Analogue models of gravity have provided an experimentally realizable test field for our ideas on quantum field theory in curved spacetimes but they have also inspired the investigation of possible departures from exact Lorentz invariance at microscopic scales. In this role they have joined, and sometime anticipated, several quantum gravity models characterized by Lorentz breaking phenomenology. A crucial difference between these speculations and other ones associated to quantum gravity scenarios, is the possibility to carry out observational and experimental tests which have nowadays led to a broad range of constraints on departures from Lorentz invariance. We shall review here the effective field theory approach to Lorentz breaking in the matter sector, present the constraints provided by the available observations and finally discuss the implications of the persisting uncertainty on the composition of the ultra high energy cosmic rays for the constraints on the higher order, analogue gravity inspired, Lorentz violations.

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Large-scale nonlocality in “doubly special relativity” with an energy-dependent speed of light

Cited by 45 publications

References 28 publications

Modified dispersion relations from the renormalization group of gravity

Modified dispersion relations from the renormalization group of gravity

Doubly special relativity from quantum cellular automata

Lorentz Breaking Effective Field Theory and Observational Tests

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