Gravitational bar detectors set limits to Planck-scale physics on macroscopic variables

Abstract

Different approaches to quantum gravity, such as string theory 1,2 and loop quantum gravity, as well as doubly special relativity 3 and gedanken experiments in black-hole physics 4-6 , all indicate the existence of a minimal measurable length 7,8 of the order of the Planck length, L p = √h G/c 3 = 1.6 × 10 −35 m. This observation has motivated the proposal of generalized uncertainty relations, which imply changes in the energy spectrum of quantum systems. As a consequence, quantum gravitational effects could be revealed by experiments able to test deviations from standard quantum mechanics 9-11 , such as those recently proposed on macroscopic mechanical oscillators 12. Here we exploit the sub-millikelvin cooling of the normal modes of the ton-scale gravitational wave detector AURIGA, to place an upper limit for possible Planck-scale modifications on the ground-state energy of an oscillator. Our analysis calls for the development of a satisfactory treatment of multi-particle states in the framework of quantum gravity models. General relativity and quantum physics are expected to merge at the Planck scale, defined by distances of the order of ∼ L p and/or extremely high energies of the order of ∼ E p = ch/L p = 1.2 × 10 19 GeV. Therefore, present approaches to test quantum gravitational effects are mainly focused on highenergy astronomical events 13-15 , which allowed stringent limits to the predicted breaking of Lorentz invariance at the Planck scale to be put in place 16. On the other hand, the emergence of a minimal length scale can result in relevant consequences also for low-energy quantum mechanics experiments. The Heisenberg relation states that the uncertainties in the measurements of a position x and its conjugate momentum p are related by x p ≥h/2; that is, the position and the momentum of a particle cannot be determined simultaneously with arbitrarily high accuracy. However, an arbitrarily precise measurement of only one of the two observables, say position, is still possible at the cost of our knowledge about the other (momentum), a fact that is obviously incompatible with the existence of a minimal observable distance. This consideration motivates the introduction of generalized Heisenberg uncertainty principles 1-7. As a consequence, an alternative way to check quantum gravitational effects would be to perform high-sensitivity measurements of the uncertainty relation,

Amplified transduction of Planck-scale effects using quantum optics

“…One route to finding such a theory is through the study of phenomenological models, which can motivate conceptual and experimental studies of the interplay between quantum mechanics and general relativity [1][2][3]. Experimental bounds on a variety of such models have been obtained, both from the observed validity of quantum mechanics in a variety of systems and from studies focussed on experimentally testing for such phenomena [4][5][6][7][8][9]. Although, thus far, there has been no experimental evidence of any modifications to quantum mechanics or general relativity.…”

“…In the last few years, several schemes to test the GUP have been proposed. 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].…”

Gravitational tests of the generalized uncertainty principle

“…From more theoretical shores, the discussion has therefore landed on the ground of experimental predictions about the size of these modifications, and several experiments have been proposed to test GUPs in the laboratory. Among the more elaborated proposals are those, for example, of the groups of Brukner, Cerdonio, and Bonaldi [17][18][19]. a e-mail: fabio@phys.ntu.edu.tw b e-mail: casadio@bo.…”

Minimal length in quantum gravity and gravitational measurements

“…The upper bounds on the parameter α 0 have been calculated in [13] and it was proposed that GUP may introduce an intermediate length scale between Planck scale and electroweak scale. Recent proposals suggested that these bounds can be measured using quantum optics techniques in [16] and using gravitational wave techniques [17,18] which may be considered as a milestone in quantum gravity phenomenology. In a series of papers, various phenomenological implications of the new model of GUP were investigated [19][20][21][22][23][24].…”