ATON is a hopefully evolving classification theory. It aspires to unify knowledge around numbers and prefers naive methods. Some of the older posts are wrong but I'll keep them for the sake of continuity.

Tuesday, March 27, 2007

Time and pressure

Time displays thermodynamic aspects. Consider the triplets;

{Time, Matter, Space}
{Pressure, Temperature, Volume}

The P-T-V triplet are related to each other by the famous equation of ideal gas; PV = NkT, where N is the number of particles, k is the Boltzmann constant.

Time stops at the event horizon of a black hole. The entropy of a black hole is proportional to it's area; S = k(c^3)A / 4G(hb), where c is speed of light, hb is Planck's constant. This equation contains all the goodies. Black holes are the boundaries of space-matter-time, so they must contain it. It also includes the Boltzmann's constant k, and makes the link to thermodynamics pretty explicit. The great surprise of this equation was that the entropy is proportional to the area A. Time slows down in gravity, and eventually stops at the most intense gravity gradient; the even horizon of a black hole.

Gravity works as if space-time is squishing out it's contents towards less pressure, since space-time dilate in gravity. A gravity field is like a 3D hill's surface of a 4D volume (a normal hill's surface is 2D). We feel the squeeze down of gravity by the counter pressure of the earth. Thus space-time is has strong thermodynamic aspects. {Matter, Temperature} correspondence makes sense since matter is equivalent to energy. {Space, Volume} correspondence is obvious. Thus we get {Time, Pressure} correspondence implied. As we well know, pressure cookers shorten the time of cooking. Sounds funny I know, but I think this fact reflects the correspondence quite well, since pressure increases the event density in time.

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