Quantum uncertainty in doubly special relativity

Cortés, José Luis; Gamboa, J.

doi:10.1103/physrevd.71.065015

Cited by 225 publications

(213 citation statements)

References 37 publications

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“…4 Now, modified uncertainty relations can be traced back, formally, to modified commutators. And the DSR variables obey modified commutation relations [20]. This appears to support our claim about the phenomenological character of energy and momentum used in DSR -the variables E and p. If one were able to remove the additional uncertainty due to gravity, one would end up with standard Heisenberg relations, and standard commutation relations, for the variables ǫ and π.…”

Section: Physical Origin Of the Modificationssupporting

confidence: 74%

Interpreting doubly special relativity as a modified theory of measurement

2005

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In this article we develop a physical interpretation for the deformed (doubly) special relativity theories (DSRs), based on a modification of the theory of measurement in special relativity. We suggest that it is useful to regard the DSRs as reflecting the manner in which quantum gravity effects induce Planck-suppressed distortions in the measurement of the "true" energy and momentum. This interpretation provides a framework for the DSRs that is manifestly consistent, non-trivial, and in principle falsifiable. However, it does so at the cost of demoting such theories from the level of "fundamental" physics to the level of phenomenological models -models that should in principle be derivable from whatever theory of quantum gravity one ultimately chooses to adopt.

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Section: Physical Origin Of the Modificationssupporting

confidence: 74%

Interpreting doubly special relativity as a modified theory of measurement

2005

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“…(1) Commutators and inequalities similar to (1) and (2) were proposed and derived respectively in [2][3][4][5][6][7][8][9]. These in turn imply a minimum measurable length and a maximum measurable momentum -the latter following from the assumption that ∆p characterizes the maximum momentum of a particle as well [10], and also from the fact that DSR predicts such an maximum (to the best of our knowledge, (1) and (2) are the only forms which imply both) ∆x ≥ (∆x) min ≈ α 0 ℓ P l…”

Section: Introductionmentioning

confidence: 99%

Proposal for testing quantum gravity in the lab

2011

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Attempts to formulate a quantum theory of gravitation are collectively known as quantum gravity. Various approaches to quantum gravity such as string theory and loop quantum gravity, as well as black hole physics and doubly special relativity theories predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg Uncertainty Principle to a so-called generalized uncertainty principle (GUP). We have proposed a GUP consistent with string theory, black hole physics and doubly special relativity theories and have showed that this modifies all quantum mechanical Hamiltonians. When applied to an elementary particle, it suggests that the space that confines it must be quantized, and in fact that all measurable lengths are quantized in units of a fundamental length (which can be the Planck length). On the one hand, this may signal the breakdown of the spacetime continuum picture near that scale, and on the other hand, it can predict an upper bound on the quantum gravity parameter in the GUP, from current observations. Furthermore, such fundamental discreteness of space may have observable consequences at length scales much larger than the Planck scale. Because this influences all the quantum Hamiltonians in an universal way, it predicts quantum gravity corrections to various quantum phenomena. Therefore, in the present work we compute these corrections to the Lamb shift, simple harmonic oscillator, Landau levels, and the tunneling current in a scanning tunneling microscope.

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“…These include optomechanical interactions [22], gravitational bar detectors [6], nanodiamond interferometry [23], and direct measurements on a harmonic oscillator [24]. Several different forms of the GUP have been proposed in the literature [5,[13][14][15][16][17]. A general form of the GUP, expressed in terms of an inequality and in terms of a deformed commutator, is given, to O(γ 2 ), by…”

Section: Introductionmentioning

confidence: 99%

Amplified transduction of Planck-scale effects using quantum optics

et al. 2017

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The unification of quantum mechanics and gravity remains as one of the primary challenges of present-day physics. Quantum-gravity-inspired phenomenological models offer a window to explore potential aspects of quantum gravity including qualitatively new behaviour that can be experimentally tested. One such phenomenological model is the generalized uncertainty principle (GUP), which predicts a modified Heisenberg uncertainty relation and a deformed canonical commutator. It was recently shown that optomechanical systems offer significant promise to put stringent experimental bounds on such models. In this paper, we introduce a scheme to increase the sensitivity of these experiments with an extended sequence of pulsed optomechanical interactions. We also analyze the effects of optical phase noise and optical loss and present a strategy to mitigate such deleterious effects.

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Quantum uncertainty in doubly special relativity

Cited by 225 publications

References 37 publications

Interpreting doubly special relativity as a modified theory of measurement

Interpreting doubly special relativity as a modified theory of measurement

Proposal for testing quantum gravity in the lab

Amplified transduction of Planck-scale effects using quantum optics

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