Emergent spacetime and the origin of gravity

Abstract

We present an exposition on the geometrization of the electromagnetic force. We show that, in noncommutative (NC) spacetime, there always exists a coordinate transformation to locally eliminate the electromagnetic force, which is precisely the Darboux theorem in symplectic geometry. As a consequence, the electromagnetism can be realized as a geometrical property of spacetime like gravity. We show that the geometrization of the electromagnetic force in NC spacetime is the origin of gravity, dubbed as the emergent gravity. We discuss how the emergent gravity reveals a novel, radically different picture about the origin of spacetime. In particular, the emergent gravity naturally explains the dynamical origin of flat spacetime, which is absent in Einstein gravity. This spacetime picture turns out to be crucial for a tenable solution of the cosmological constant problem.

Dark Energy and Dark Matter from Emergent Gravity Picture

“…P [2,3]. An important point is that the fluctuations over the coherent vacuum (3) should be subject to the spacetime uncertainty relation since the NC Coulomb branch satisfies the Heisenberg algebra.…”

“…Hence let us consider the vacuum fluctuations whose IR fluctuations have a macroscopic wavelength L H = M −1 H . Having this in mind, one can estimate the energy scale of the Liouville energy-momentum tensor (16) by observing that the vacuum fluctuations represented by F µν (y) are not localized but extended to a macroscopic scale L H [2,3]. Actually the vacuum fluctuation energy…”

“…When considering the fact that the fluctuations are random in nature and we are living in the (3+1)-dimensional spacetime, the ratio of the repulsive and attractive components will end in 3 4 : 1 4 = 75 : 25 and this ratio curiously coincides with the dark composition of our current Universe [3]. Note that the dark energy in (19) sets the current Hubble parameter H 0 = c L H and the Hubble parameter induces a characteristic acceleration scale a 0 = cH 0 = c 2 L H . Since the dark matter is the third of the dark energy, the dark matter will give rise to the attractive acceleration scale a 0 3 = c 2 3L H .…”

“…But it is not yet understood what matter is from the emergent gravity picture although a tough idea was suggested in [1][2][3]. So we simply assume the matter fields that obey the law of Standard Model.…”

Quantum gravity from noncommutative spacetime

“…Of course, the Standard Model does not have such kind of gauge fields, but we will see later that the desired vector fields arise from the electromagnetic fields living in noncommutative spacetime [4][5][6][7]. Thus, the noncommutative spacetime will allow a novel unification between electromagnetism and Einstein gravity in a completely different context from the Kaluza-Klein unification.…”