Comments on "On the Origin of Gravity and the Laws of Newton", by Erik Verlinde

Abstract

We argue that the relativistic Unruh temperature cannot be associated with the bits on the screen, in the form considered by Verlinde. The acceleration $a$ is a scalar quantity (the modulus of the acceleration four vecor) and not a vector. When the mass $m$ approaches the holographic screen, viewed as a stretched horizon, the shift $\Delta x$ from Verlinde's Eq. (3.15) becomes $c^{2}/a$ and the entropy variation equals $(1/2) k_{B} \Delta N$, in accordance with Gao's calculations. Using the Heisenberg Principle we show that the energy on the causal horizon (viewed as a holographic screen) of an inertial observer is proportional to its radius, as for a black hole.