# A New Improved Energy-Momentum Tensor and Its Possible Role in Gravity

## TL;DR

This paper introduces a novel energy-momentum tensor derived from a second-derivative Lagrangian, exploring its implications for gravity and potential experimental tests of relativistic effects.

## Contribution

It proposes a new energy-momentum tensor from a second-derivative Lagrangian and develops a gravity theory with torsion, extending Einstein-Cartan framework.

## Key findings

- The new tensor differs from canonical and symmetric tensors.
- The resulting gravity theory includes torsion-matter interactions.
- Potential for new tests of general relativistic effects.

## Abstract

Motivated by a special consideration in quantum measurement, we present a new improved energy-momentum tensor. The new tensor differs from the traditional canonical and symmetric ones, and can be derived as Nother current from a Lagrangian with second derivative. We also attempt to construct a gravitational coupling in such a way that the new energy-momentum tensor becomes the source of the gravitational field. The theory we obtain is of an Einstein-Cartan type, but derived from a minimal coupling of a Lagrangian with second-derivative, and leads to additional interaction between torsion and matter, including the scalar field. For the scalar field, the theory can also be derived in the Riemann space-time by a non-minimal coupling. Our study gives hint on more general tests of general relativistic effects.