Narrow Results

Assuming the equipartition of energy to hold on a holographic sphere, Erik Verlinde demonstrated that Newton’s gravity follows as an entropic force. Some comments are in place about Verlinde’s assumptions in his derivation. It is pointed out that the holographic principle allows for freedom up to a free scale factor in the choice of Planck scale area while leading to classical gravity. Similarity of this free parameter with the Immirzi parameter of loop quantum gravity is discussed. We point out that the equipartition of energy is inbuilt into the holographic principle and, therefore, need not be assumed from the outset.

The Immirzi parameter of loop quantum gravity is a one-parameter ambiguity of the theory whose precise interpretation is not universally agreed upon. It is an inherent characteristic of the quantum theory as it appears in the spectra of geometric operators, despite being irrelevant at the classical level. The parameter’s appearance in the area and volume spectra to the same power as the Planck area suggest that it plays a role in determining the fundamental length scale of space. In fact, a consistent interpretation is that it represents a constant rescaling of the kinematical spatial geometry. An interesting realization is that promoting the Immirzi parameter to be a general conformal transformation leads to a system which can be identified as analogous to the linking theory of shape dynamics. A three-dimensional gravitational gauge connection is then constructed within the linking theory in a manner analogous to loop quantum gravity, thereby facilitating the application of the established procedure of loop quantization.

The following sections are included:

• Introduction

• Modified, Unambiguous Coupling Procedure

• References