Optical simulations of gravitational effects in the Newton–Schrödinger system



Some predictions of Einstein’s theory of general relativity (GR) still elude observation, hence analogous systems, such as optical set-ups, have been suggested as platforms for emulating GR phenomena. GR is inherently nonlinear: for example, the curvature of space is induced by masses whose dynamics is also affected by the curved space they themselves induce. But, thus far all GR emulation experiments with optical systems have reproduced only linear dynamics. Here, we study gravitational effects with optical wavepackets under a long-range nonlocal thermal nonlinearity. This system is mathematically equivalent to the Newton–Schrödinger model proposed to describe the gravitational self-interaction of quantum wavepackets. We emulate gravitational phenomena by creating interactions between a wavepacket and the gravitational potential of a massive star, observing gravitational lensing, tidal forces and gravitational redshift and blueshift. These wavepackets interact in the curved space they themselves induce, exhibiting complex nonlinear dynamics arising from the interplay between diffraction, interference and the emulated gravitational effects.

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Figure 1: Experimental settings and results.
Figure 2: Simulations and experiments showing the trajectories of the beam accelerating away from the ‘star’ and the deformation of its structure, unravelling the effect of tidal forces.
Figure 3: Using the inhomogeneous geodesic equation to model the trajectories of the beam accelerating away from the ‘star’ and the tidal forces acting on it.
Figure 4: Experimental observations of redshift and blueshift.


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We thank A. Ori for valuable discussions that considerably contributed to our work, and A. Arie and I. Dolev for letting us use their phase masks for generating the accelerating beams. R. Bekenstein gratefully acknowledges the support of the Adams Fellowship Program of the Israel Academy of Sciences and Humanities, and a fellowship from the Israel Ministry of Science and Technology. This research was also supported by the ICore Excellence centre ‘Circle of Light’ and the Binational USA-Israel Science Foundation BSF.

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All authors contributed significantly to this work.

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Correspondence to Rivka Bekenstein.

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Bekenstein, R., Schley, R., Mutzafi, M. et al. Optical simulations of gravitational effects in the Newton–Schrödinger system. Nature Phys 11, 872–878 (2015). https://doi.org/10.1038/nphys3451

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