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This paper argues that a hypothetical “dark” particle (a black hole
with the reduced Planck mass and arbitrary temperature) gives a simple
explanation to the open question of dark energy and has a relic density of only
17% more than the commonly accepted value. By considering an additional near-horizon
boundary of the black hole, set by its quantum length, the black hole can
obtain an arbitrary temperature. Black-body radiation is still present and fits
as the source of the Universe’s missing energy. Support for this hypothesis is
offered by showing that a stationary solution to the black hole’s length scale
is the same if derived from a quantum analysis in continuous time, a quantum
analysis in discrete time, or a general relativistic analysis.
The thermal diffusion of a free particle is a random process and generates entropy at a rate equal to twice the particle’s temperature, (in natural units of information per second). The rate is calculated using a Gaussian process with a variance of which is a combination of quantum and classical diffusion. The solution to the quantum diffusion of a free particle is derived from the equation for kinetic energy and its associated imaginary diffusion constant; a real diffusion constant (representing classical diffusion) is shown to be . We find the entropy of the initial state is one natural unit, which is the same amount of entropy the process generates after the de-coherence time, .
In the governing thought, I find an equivalence between
the classical information in a quantum system and the integral of that system’s
energy and time, specifically , in natural units. I solve this relationship in four
ways: the first approach starts with the Schrodinger Equation and applies the
Minkowski transformation; the second uses the Canonical commutation relation;
the third through Gabor’s analysis of the time-frequency plane and Heisenberg’s
uncertainty principle; and lastly by quantizing Brownian motion within the
Bernoulli process and applying the Gaussian channel capacity. In support I give
two examples of quantum systems that follow the governing thought: namely the
Gaussian wave packet and the electron spin. I conclude with comments on the
discretization of space and the information content of a degree of freedom.