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Why Different Infinities Are Really Equal

ABSTRACT: Assuming different infinities are unequal leads to strange and counter-intuitive mathematical results such as Ramanujan's ...

Friday, July 1, 2016

Derive the Field Equations From the Uncertainty Principle

Heisenberg's Uncertainty Principle is General Relativity in disguise. Let me show you. Begin with the Uncertainty Principle. The variables are momentum (p), position (x), Planck's constant (h-bar).  Work through equations 1 through 3 below to get 4.  Notice how an increase in p causes a decrease in x and vice versa.  Somehow this seems eerily familiar.

At 5 and 6 below, we do a dimensional analysis and see the terms are all numbers divided by a line squared (L^-2). The field equations are formatted this way. Notice the "curved space" is an increase in the change in momentum (p) and a decrease in the change in space (x). The new variables are Newton's constant (G or Gn), volume (V), light speed (c), energy (E).

With equations 7-9 we derive Einstein's field equations featuring Einstein's tensor (Gij) and the energy-stress tensor (Tij). Oh ... and let's not forget 8pi.

Now let's derive the other Uncertainty Principle ... you know ... the one with energy and time?

Now, just for fun, let's go back to equation 5 and, from there, derive a quasi-Schrodinger/Einstein equation, which features the Hamiltonian energy (H) the Greek letter psi, the metric tensor (gij), and N for a large number of particles. To get a little gravity, you need a huge number (N).

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