Gravitation, Entropy & the Mandelbrot Set

Abstract

The fundamental forces are often seen, in Physics, to arise in the context of symmetries and symmetry groups. Perhaps the reason we lack a full unification of gravitation with the other forces is that gravity results from a fundamental asymmetry instead. Some assert that gravitation is different from the strong and weak nuclear forces and electromagnetism, and should not be considered a fundamental force, but should rather be seen as a residual of the other forces. Jacobson wrote that gravity appears to be a consequence of thermodynamic entropy. Verlinde and Padmanabhan further developed entropic theories of gravity. This work shows that both Newton’s gravitation and Einstein’s equations can arise from entropic considerations. But is the basis for dissipative processes found in pure Mathematics? The Mandelbrot Set reproduces the Verhulst dynamic and further displays the monotonic progress of entropy. Furthermore; it is maximally asymmetrical along the real axis – exhibiting fundamental asymmetry. This paper asserts that M is the missing link for gravity theorists, because it is asymmetrical on the whole but contains many exact symmetries. M therefore reveals a natural balance between preserved and broken symmetry, which illustrates how symmetry-breaking is essential to the Physics of gravitation.