Canonical Reduction for Dilatonic Gravity in 3+1 Dimensions

What is it about?

From minimal assumptions of analytic continuation and conformal transformations, Mann and Ross had derived a General Relativity (GRT) formulation which introduced the addition of a particle called a 'dilaton' that ensured that a 'd+1' theory would ensure the correct Newtonian limit in 'd' spatial dimensions, as shown by T. Ohta. Herein, we show the '3+1' version of theory, with the right choice of coordinate and gauge conditions in a ADM prescription yields a dilaton field governed by a Logarithmic Schrödinger Equation (logSE). The coefficient of the log term vanishes in the far-field i.e. flat space. Thus, we get part of quantum mechanics from GRT itself. The logSE is also seen in Superfluids and has been proposed as a model for the Higgs field. This paper provides a key piece in a proposed solution to the century-old problem of trying to reconcile General Relativity (GRT) with Quantum Theory.

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Photo by Iván Díaz on Unsplash

Photo by Iván Díaz on Unsplash

Why is it important?

From minimal assumptions of analytic continuation and conformal transformations, Mann and Ross had derived a General Relativity (GRT) formulation which introduced the addition of a particle called a 'dilaton' that ensured that a 'd+1' theory would ensure the correct Newtonian limit in 'd' spatial dimensions, as shown by T. Ohta. Herein, we show the '3+1' version of theory, with the right choice of coordinate and gauge conditions in a ADM prescription yields a dilaton field governed by a Logarithmic Schroedinger Equation (logSE). The coefficient of the log term vanishes in the far-field i.e. flat space. Thus, we get part of quantum mechanics from GRT itself. The logSE is also seen in Superfluids and has been proposed as a model for the Higgs field. This paper provides a key piece in a proposed solution to the century-old problem of trying to reconcile General Relativity (GRT) with Quantum Theory.

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