Entropy scale factor may explain gravity, dark matter, and the expansion of space

Abstract

The entropy scale factor (ESF) is a novel theory proposing that the scale of time and space change depending on entropy, and that this change underlies special relativity, gravity, and the expansion of space. In special relativity, as the relative velocity of objects increases, there are more possible combinations of momentum and position within the moving frame due to the uncertainty principle. This increase in possible microstates represents an increase in entropy, which can be correlated with the time dilation and length contraction of special relativity. The ESF predicts that an observer in an empty region of space taking measurements near an entropic object will measure time to run more slowly and lengths to appear longer in the direction of entropy. These changes in scale would warp of spacetime, causing gravity. For objects with low acceleration, gravity can be approximated by the time dilation component only. For a single star, this approximation predicts a gravitational field similar to that of Newtonian gravity. For a constellation of stars, the ESF predicts that gravity will be stronger than in Newtonian gravity, because time dilation is added as a scalar sum, instead of the vector sum used in Newtonian gravity. Adding fields as a scalar sum avoids the cancelling out that comes with vectors pointed in different directions, leading to increased gravitational acceleration. This effect could explain galaxy rotation dynamics and the gravitational lensing of galaxies without the need for dark matter. Additionally, the ESF would cause space to expand as the entropy of the universe increases. This is because the entropy of a spherical boundary changes only the radial dimension, so as the entropy encoded on the boundary increases time within the boundary slows down more quickly than the volume decreases. Given the constant speed of light, an observer inside such a boundary will experience the increasing volume to time ratio as the expansion of space. Accordingly, the rapid increase in entropy in the early universe would cause a rapid expansion of space, possibly explaining the homogeneity of the large-scale structure of the universe without the need for inflation. In our recent universe, the increasing rate of entropy production due to black holes may explain the accelerating expansion of space, without the need for dark energy.