Repulsive gravitational effect of a quantum wave packet and experimental scheme with superfluid helium
Hongwei Xiong1,2,*()
1. Wilczek Quantum Center, Zhejiang University of Technology, Hangzhou 310023, China
2. College of Science, Zhejiang University of Technology, Hangzhou 310023, China
We consider the gravitational effect of quantum wave packets when quantum mechanics, gravity, and thermodynamics are simultaneously considered. Under the assumption of a thermodynamic origin of gravity, we propose a general equation to describe the gravitational effect of quantum wave packets. In the classical limit, this equation agrees with Newton’s law of gravitation. For quantum wave packets, however, it predicts a repulsive gravitational effect. We propose an experimental scheme using superfluid helium to test this repulsive gravitational effect. Our studies show that, with present technology such as superconducting gravimetry and cold atom interferometry, tests of the repulsive gravitational effect for superfluid helium are within experimental reach.
G. Amelino-Camelia, J. Ellis, N. E. Mavromatos, D. V. Nanopoulos, and S. Sarkar, Tests of quantum gravity from observations of γ-ray bursts, Nature 393(6687), 763 (1998)
https://doi.org/10.1038/31647
3
U. Jacob and T. Piran, Neutrinos from gamma-ray bursts as a tool to explore quantum-gravity-induced Lorentz violation, Nat. Phys. 3(2), 87 (2007)
https://doi.org/10.1038/nphys506
4
I. Pikovski, M. R. Vanner, M. Aspelmeyer, M. S. Kim, and C. Brukner, Probing Planck-scale physics with quantum optics, Nat. Phys. 8(5), 393 (2012)
https://doi.org/10.1038/nphys2262
5
R. J. Adler, H. Mueller, and M. L. Perl, A terrestrial search for dark contents of the vacuum, such as dark energy, using atom interferometry, Int. J. Mod. Phys. A 26(29), 4959 (2011)
https://doi.org/10.1142/S0217751X11054814
J. M. Bardeen, B. Carter, and S. W. Hawking, The four laws of black hole mechanics, Commun. Math. Phys. 31(2), 161 (1973)
https://doi.org/10.1007/BF01645742
See, e.g., R. G. Cai, L. M. Cao, and N. Ohta, Friedmann equations from entropic force, Phys. Rev. D 81, 061501(R) (2010)
16
T. Padmanabhan, Surface density of spacetime degrees of freedom from equipartition law in theories of gravity, Phys. Rev. D 81(12), 124040 (2010)
https://doi.org/10.1103/PhysRevD.81.124040
17
F. W. Shu and Y. G. Gong, Equipartition of energy and the first law of thermodynamics at the apparent horizon, Int. J. Mod. Phys. D 20(04), 553 (2011)
https://doi.org/10.1142/S0218271811018883
Y. F. Cai and E. N. Saridakis, Inflation in entropic cosmology: Primordial perturbations and non-Gaussianities, Phys. Lett. B 697(4), 280 (2011)
https://doi.org/10.1016/j.physletb.2011.02.020
M. A. Santos and I. V. Vancea, Entropic law of force, emergent gravity and the uncertainty principle, Mod. Phys. Lett. A 27, 1250012 (2012), arXiv: 1002.2454
https://doi.org/10.1142/S0217732312500125
26
M. R. Setare and D. Momeni, Time varying gravitational constant G via entropic force, Commum. Theor. Phys. 56(4), 691 (2011)
https://doi.org/10.1088/0253-6102/56/4/17
27
E. P. Verlinde, On the origin of gravity and the laws of Newton, J. High Energy Phys. 04, 029 (2011)
28
A. G. Riess, A. V. Filippenko, P. Challis, A. Clocchiatti, A. Diercks, P. M. Garnavich, R. L. Gilliland, C. J. Hogan, S. Jha, R. P. Kirshner, B. Leibundgut, M.M. Phillips, D. Reiss, B. P. Schmidt, R. A. Schommer, R. C. Smith, J. Spyromilio, C. Stubbs, N. B. Suntzeff, and J. Tonry, Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astron. J. 116(3), 1009 (1998)
https://doi.org/10.1086/300499
29
S. Perlmutter, G. Aldering, G. Goldhaber, R. A. Knop, P. Nugent, P. G. Castro, S. Deustua, S. Fabbro, A. Goobar, D. E. Groom, I. M. Hook, A. G. Kim, M. Y. Kim, J. C. Lee, N. J. Nunes, R. Pain, C. R. Pennypacker, R. Quimby, C. Lidman, R. S. Ellis, M. Irwin, R. G. McMahon, P. Ruiz-Lapuente, N. Walton, B. Schaefer, B. J. Boyle, A. V. Filippenko, T. Matheson, A. S. Fruchter, N. Panagia, H. J. M. Newberg, W. J. Couch, and T. S. C. Project, Measurements of Ω and Λ from 42 high-redshift supernovae, Astrophys. J. 517(2), 565 (1999)
https://doi.org/10.1086/307221
A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, Optics and interferometry with atoms and molecules, Rev. Mod. Phys. 81(3), 1051 (2009)
https://doi.org/10.1103/RevModPhys.81.1051
32
N. Poli, F. Y. Wang, M. G. Tarallo, A. Alberti, M. Prevedelli, and G. M. Tino, Precision measurement of gravity with cold atoms in an optical lattice and comparison with a classical gravimeter, Phys. Rev. Lett. 106(3), 038501 (2011)
https://doi.org/10.1103/PhysRevLett.106.038501
33
P. Cladé, S. Guellati-Khélifa, C. Schwob, F. Nez, L. Julien, and F. Biraben, A promising method for the measurement of the local acceleration of gravity using Bloch oscillations of ultracold atoms in a vertical standing wave, Europhys. Lett. 71(5), 730 (2005)
https://doi.org/10.1209/epl/i2005-10163-6
34
G. Ferrari, N. Poli, F. Sorrentino, and G. M. Tino, Longlived Bloch oscillations with Bosonic Sr atoms and application to gravity measurement at the micrometer scale, Phys. Rev. Lett. 97(6), 060402 (2006)
https://doi.org/10.1103/PhysRevLett.97.060402
35
F. Sorrentino, A. Alberti, G. Ferrari, V. V. Ivanov, N. Poli, M. Schioppo, and G. M. Tino, Quantum sensor for atomsurface interactions below 10 μm, Phys. Rev. A 79(1), 013409 (2009)
https://doi.org/10.1103/PhysRevA.79.013409
36
E. Hoskinson, Y. Sato, and R. Packard, Superfluid He4 interferometer operating near, Phys. Rev. B 74, 100509(R) (2006)
37
T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, A new generation of absolute gravimeters, Metrologia 32(3), 159 (1995)
https://doi.org/10.1088/0026-1394/32/3/004
38
G. d’Agostino, S. Desogus, A. Germak, C. Origlia, D. Quagliotti, G. Berrino, G. Corrado, V. d’Errico, and G. Ricciardi, The new IMGC-02 transportable absolute gravimeter: measurement apparatus and applications in geophysics and volcanology, Ann. Geophys. 51, 39 (2008)
39
S. Svitlov, P. Maslyk, C. Rothleitner, H. Hu, and L. J. Wang, Comparison of three digital fringe signal processing methods in a ballistic free-fall absolute gravimeter, Metrologia 47(6), 677 (2010)
https://doi.org/10.1088/0026-1394/47/6/007
40
W. A. Prothero and J. Goodkind, A superconducting gravimeter, Rev. Sci. Instrum. 39(9), 1257 (1968)
https://doi.org/10.1063/1.1683645
H. J. Paik, Superconducting tunable-diaphragm transducer for sensitive acceleration measurements, J. Appl. Phys. 47(3), 1168 (1976)
https://doi.org/10.1063/1.322699