A strain tensor that couples to the Madelung stress tensor

TL;DR

This paper introduces a novel strain tensor coupled to the Madelung stress tensor, derived from frame field deformations, leading to a new constitutive law that parallels elastic and gravitational theories.

Contribution

It defines a strain tensor related to frame deformations in Madelung fluids, establishing a new constitutive law with analogies to elastic and gravitational laws.

Findings

The strain tensor is linked to frame deformations, not spatial deformations.

The constitutive law resembles elastic and Einstein gravitational laws.

Provides a new perspective on the elementary structure of Madelung fluids.

Abstract

Ordinarily, the stress tensor that one derives for a Madelung fluid is not regarded as being coupled to a strain tensor, which is consistent with the fluid hypothesis. However, based upon earlier work regarding the geometric nature of the quantum potential, one can, in fact, define a strain tensor, which is not, however, due to a deformation of a spatial region, but to a deformation of a frame field on that region. When one expresses the Madelung stress tensor as a function of the strain tensor and its derivatives, one then defines a constitutive law for the Madelung medium that might lead to a more detailed picture of its elementary structure. It is pointed out that the resulting constitutive law is strongly analogous to laws that were presented by Kelvin and Tait for the bending and torsion of elastic wires and plates, as well as the Einstein equations for gravitation if one takes the viewpoint of metric elasticity.