Limits...
Probing deformed commutators with macroscopic harmonic oscillators.

Bawaj M, Biancofiore C, Bonaldi M, Bonfigli F, Borrielli A, Di Giuseppe G, Marconi L, Marino F, Natali R, Pontin A, Prodi GA, Serra E, Vitali D, Marin F - Nat Commun (2015)

Bottom Line: Quantum mechanically, this concept is associated with a nonzero minimal uncertainty in position measurements, which is encoded in deformed commutation relations.As recently proposed, low-energy mechanical oscillators could allow to reveal the effect of a modified commutator.The direct check against a model of deformed dynamics substantially lowers the previous limits on the parameters quantifying the commutator deformation.

View Article: PubMed Central - PubMed

Affiliation: 1] Physics Division, School of Science and Technology, University of Camerino, via Madonna delle Carceri 9, Camerino (MC) I-62032, Italy [2] INFN, Sezione di Perugia, Via A. Pascoli, Perugia I-06123, Italy.

ABSTRACT
A minimal observable length is a common feature of theories that aim to merge quantum physics and gravity. Quantum mechanically, this concept is associated with a nonzero minimal uncertainty in position measurements, which is encoded in deformed commutation relations. In spite of increasing theoretical interest, the subject suffers from the complete lack of dedicated experiments and bounds to the deformation parameters have just been extrapolated from indirect measurements. As recently proposed, low-energy mechanical oscillators could allow to reveal the effect of a modified commutator. Here we analyze the free evolution of high-quality factor micro- and nano-oscillators, spanning a wide range of masses around the Planck mass mP (≈ 22 μg). The direct check against a model of deformed dynamics substantially lowers the previous limits on the parameters quantifying the commutator deformation.

No MeSH data available.


Related in: MedlinePlus

Upper limits to the deformed commutator.The parameter β0 quantifies the deformation to the standard commutator between position and momentum, or the scale  below which new physics could come into play. Full symbols reports its upper limits obtained in this work, as a function of the mass. Red dots: from the dependence of the oscillation frequency from its amplitude; magenta stars: from the third harmonic distortion. In the former data set, for the intermediate mass range (10–100 μg), we report the results obtained with two different oscillators. Light blue shows the area below the electroweak scale, dark blue the area that remains unexplored. Dashed lines report some previously estimated upper limits, obtained in mass ranges outside this graph (as indicated by the arrows). Green: from high-resolution spectroscopy on the hydrogen atom, considering the ground state Lamb shift (upper line)21 and the 1S–2S level difference (lower line)22. Magenta: from the AURIGA detector1011. Yellow: from the lack of violation of the equivalence principle39. The vertical line corresponds to the Planck mass (22 μg).
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f3: Upper limits to the deformed commutator.The parameter β0 quantifies the deformation to the standard commutator between position and momentum, or the scale below which new physics could come into play. Full symbols reports its upper limits obtained in this work, as a function of the mass. Red dots: from the dependence of the oscillation frequency from its amplitude; magenta stars: from the third harmonic distortion. In the former data set, for the intermediate mass range (10–100 μg), we report the results obtained with two different oscillators. Light blue shows the area below the electroweak scale, dark blue the area that remains unexplored. Dashed lines report some previously estimated upper limits, obtained in mass ranges outside this graph (as indicated by the arrows). Green: from high-resolution spectroscopy on the hydrogen atom, considering the ground state Lamb shift (upper line)21 and the 1S–2S level difference (lower line)22. Magenta: from the AURIGA detector1011. Yellow: from the lack of violation of the equivalence principle39. The vertical line corresponds to the Planck mass (22 μg).

Mentions: For a more accurate and specific bound, we focus on the model described by Equations 7 and 8. The values and uncertainties in β and β0 are obtained from b and from the third harmonic distortion, using the oscillator parameters (namely, its mass and frequency). In Table 1 we summarize our results for the different upper limits, given at the 95% confidence level. The results for β0 are also displayed in Fig. 3 as a function of the oscillator mass, and compared with some previously existing limits. We have achieved a significant improvement, by many orders of magnitude, working on systems with disparate mass scales and considering different measured observables.


Probing deformed commutators with macroscopic harmonic oscillators.

Bawaj M, Biancofiore C, Bonaldi M, Bonfigli F, Borrielli A, Di Giuseppe G, Marconi L, Marino F, Natali R, Pontin A, Prodi GA, Serra E, Vitali D, Marin F - Nat Commun (2015)

Upper limits to the deformed commutator.The parameter β0 quantifies the deformation to the standard commutator between position and momentum, or the scale  below which new physics could come into play. Full symbols reports its upper limits obtained in this work, as a function of the mass. Red dots: from the dependence of the oscillation frequency from its amplitude; magenta stars: from the third harmonic distortion. In the former data set, for the intermediate mass range (10–100 μg), we report the results obtained with two different oscillators. Light blue shows the area below the electroweak scale, dark blue the area that remains unexplored. Dashed lines report some previously estimated upper limits, obtained in mass ranges outside this graph (as indicated by the arrows). Green: from high-resolution spectroscopy on the hydrogen atom, considering the ground state Lamb shift (upper line)21 and the 1S–2S level difference (lower line)22. Magenta: from the AURIGA detector1011. Yellow: from the lack of violation of the equivalence principle39. The vertical line corresponds to the Planck mass (22 μg).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4557370&req=5

f3: Upper limits to the deformed commutator.The parameter β0 quantifies the deformation to the standard commutator between position and momentum, or the scale below which new physics could come into play. Full symbols reports its upper limits obtained in this work, as a function of the mass. Red dots: from the dependence of the oscillation frequency from its amplitude; magenta stars: from the third harmonic distortion. In the former data set, for the intermediate mass range (10–100 μg), we report the results obtained with two different oscillators. Light blue shows the area below the electroweak scale, dark blue the area that remains unexplored. Dashed lines report some previously estimated upper limits, obtained in mass ranges outside this graph (as indicated by the arrows). Green: from high-resolution spectroscopy on the hydrogen atom, considering the ground state Lamb shift (upper line)21 and the 1S–2S level difference (lower line)22. Magenta: from the AURIGA detector1011. Yellow: from the lack of violation of the equivalence principle39. The vertical line corresponds to the Planck mass (22 μg).
Mentions: For a more accurate and specific bound, we focus on the model described by Equations 7 and 8. The values and uncertainties in β and β0 are obtained from b and from the third harmonic distortion, using the oscillator parameters (namely, its mass and frequency). In Table 1 we summarize our results for the different upper limits, given at the 95% confidence level. The results for β0 are also displayed in Fig. 3 as a function of the oscillator mass, and compared with some previously existing limits. We have achieved a significant improvement, by many orders of magnitude, working on systems with disparate mass scales and considering different measured observables.

Bottom Line: Quantum mechanically, this concept is associated with a nonzero minimal uncertainty in position measurements, which is encoded in deformed commutation relations.As recently proposed, low-energy mechanical oscillators could allow to reveal the effect of a modified commutator.The direct check against a model of deformed dynamics substantially lowers the previous limits on the parameters quantifying the commutator deformation.

View Article: PubMed Central - PubMed

Affiliation: 1] Physics Division, School of Science and Technology, University of Camerino, via Madonna delle Carceri 9, Camerino (MC) I-62032, Italy [2] INFN, Sezione di Perugia, Via A. Pascoli, Perugia I-06123, Italy.

ABSTRACT
A minimal observable length is a common feature of theories that aim to merge quantum physics and gravity. Quantum mechanically, this concept is associated with a nonzero minimal uncertainty in position measurements, which is encoded in deformed commutation relations. In spite of increasing theoretical interest, the subject suffers from the complete lack of dedicated experiments and bounds to the deformation parameters have just been extrapolated from indirect measurements. As recently proposed, low-energy mechanical oscillators could allow to reveal the effect of a modified commutator. Here we analyze the free evolution of high-quality factor micro- and nano-oscillators, spanning a wide range of masses around the Planck mass mP (≈ 22 μg). The direct check against a model of deformed dynamics substantially lowers the previous limits on the parameters quantifying the commutator deformation.

No MeSH data available.


Related in: MedlinePlus