Abstract
We consider a hypothesis in which classical space-time emerges from information exchange (interactions) between quantum fluctuations in the gravity theory. In this picture, a line element would arise as a statistical average of how frequently particles interact, through an individual rate dt ∼ 1/ft and spatially interconnecting rates dl ∼ c/f . The question is if space-time can be modelled consistently in this way. The ansatz would be opposite to the standard treatment of space-time as insensitive to altered physics at event horizons (disrupted propagation of information) but by extension relate to the connection of space-time to entanglement (interactions) through the gauge/gravity duality. We make a first, rough analysis of the implications this type of quantization would have on the classical structure of flat space-time, and of what would be required of the interactions. Seeing no obvious reason for why the origin would be unrealistic, we comment on expected effects in the presence of curvature.
Highlights
A line element would arise as a statistical average of how frequently particles interact, through an individual rate dt ∼ 1/ft and spatially interconnecting rates dl ∼ c/f
Equilibrated quantum interactions must have a Gaussian fall-off to capture the relations of Euclidean geometry, which coincides with trivial particle diffraction for Gaussian apertures
A line element would arise as a statistical average of how frequently particles interact, through an individual rate dt ∼ 1/ft and interconnecting rates dl ∼ c/f
Summary
Emergence of space-time can occur in different ways (see section 1.6 for a comparison with some examples) but to allow for as rich a dynamics at the quantum level as possible we choose not to define that physics in relation to the observed space-time physics. If an obstacle describing a surface extending only through a fraction of the region is placed within the region, an information origin of space-time would mean a bending of the light rays around the surface edges, relative to the reference frame set by the vacuum behaviour This would happen since the surface would describe an ‘insulating’ surface (using the temperature analogy) in terms of the interactions present, which would be cut off in one space dimension along the surface (the object). The pair of relative geometry metric and reference frame metric represent metrics general relativity does not distinguish between, where a space-time originating in information exchange would do so, i.e. in agreement with different physics being observed (in terms of particle paths) for the two distinct scenarios (obstacles vs not). The notion of directions and angles imparted on passing particles would be that of the lines in figure 1 instead of lines of constant value of (x, y)
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