Abstract
In this paper we will study for the first time how the wave-packet of a self-gravitating meso-scopic system spreads in theories beyond Einstein’s general relativity. In particular, we will consider a ghost-free infinite derivative gravity, which resolves the 1 / r singularity in the potential – such that the gradient of the potential vanishes within the scale of non-locality. We will show that a quantum wave-packet spreads faster for a ghost-free and singularity-free gravity as compared to the Newtonian case, therefore providing us a unique scenario for testing classical and quantum properties of short-distance gravity in a laboratory in the near future.
Highlights
On large distances and late times the gravitational interaction is well described by the theory of general relativity (GR) that, has been very successful since Einstein’s initial work, being tested to a very high precision in the infrared (IR) [1]
In the previous section we have found quantum spreading solutions for a self-gravitating wave-packet both in the case of infinite derivative gravity (IDG) and Newtonian self-interactions
The previous analysis holds for both cases of semi-classical and quantized gravity, in order to discuss the experimental testability of the model we need to distinguish between the two cases
Summary
On large distances and late times the gravitational interaction is well described by the theory of general relativity (GR) that, has been very successful since Einstein’s initial work, being tested to a very high precision in the infrared (IR) [1]. The most recent success of GR comes from the observation of gravitational waves from merging of binary blackholes which gave a further confirmation of its predictions [2] Despite these great achievements, our knowledge of the gravitational interaction in the ultraviolet (UV) is still very limited: suffice to say that the inverse-square law of the Newtonian potential has been tested only up to 5.6 × 10−5 m in torsion-balance experiments so far [3]. Our knowledge of the gravitational interaction in the ultraviolet (UV) is still very limited: suffice to say that the inverse-square law of the Newtonian potential has been tested only up to 5.6 × 10−5 m in torsion-balance experiments so far [3] This means that any modification from the Newtonian 1/r -fall is expected to happen in the large range of values going from the lower bound 0.004 eV to the Planck scale Mp ∼ 1019 GeV.
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