Thursday, September 24, 2009

The Secrets of the Einstein Equations

The Einstein equations represent a mind boggling ten equation tensor that interrelates curvature of space, Newtonian gravity, General Relativity and the energy-stress tensor.  If there was a symbol that described the daunting task of creating a hyperdrive, it would be this equation.  It appeared in both movies, The Day the Earth Stood Still.  What was daunting to the human mind was just a puzzle to the advanced aliens.

With hints from mysterious places of my mind, I began to see what the equations meant.  On the left side, there were all of the terms that described curvature.  On the right side, there was the energy-stress tensor multiplied or scaled by 1/c^4.  Let me put this in layperson's terms.  Think of the energy-stress tensor as money.  It is the money you have to pay for the curvature you want.  Similarly, it is the money you will have to pay if you have curvature.  If I move the 1/c^4 to the left side, I discover that, for the curvature I want, the speed of light drives up the energy-stress by c^4.   Now, imagine that someone hands you a tiny ball.  They tell you that this ball is  universe that is tightly rolled up; it has a speed of light of c, and it's going to overcome the superforce that keeps it small, in about ten seconds.  Then, this person vanishes to a safe place, leaving you with a universe in your hand that is about to go Big Bang in ten seconds.   After about 7 seconds of cursing about your hard life, and how its about to be cut short by a universe that is going to explode in 3 seconds, you get to experience first hand (no pun intended), the meaning of curvature as it relates to space.  3...2...1...Oh Crap!!!  In a blinding flash of light, you realize that curvature is the opposite of flatness.  For  a tiny exploding universe that is destined to become platonically flat, it took an incomprehensible amount of energy to squeeze it down into a tiny ball that would fit inside of your hand.  In fact, one of the terms of the Einstein equations is R, which represents the radius of the ball.  When the ball escaped its Superforce bonds, the stress-energy could easily be mistaken for an infinite amount of energy.  That energy is going to escape in the fastest and easiest way that it can.  In my opinion, for the first few femtoseconds, the quickest and easiest way to expend energy was to burn higher dimensional physics into the tiny universe itself.  I say this for two reason.  First, energy will expand faster if it has more dimensions to do it in.  Second, quantum mechanics itself can be describes as 52(???) platonically flat dimensions of Minowski space.  But the etching of these 52 dimensions only lasted briefly, long enough to etch a Planck constant, h = 6.6e-34J-s into the fabric of space-time itself.  If the speed of light had been larger, there would have been more energy put into etching the Planck constant, and it would have been larger.  For the first few fempt seconds, the Planck constant of the brane absorbs the incredibly intense energy caused by the near infinite curvature. For universes that formed in a similar way with much larger speeds of light, the Planck constant is larger. The Planck constant is a familiar QM constant. For a frequency of light, f, the photon of that light will carry an energy packet of E=hf. The speed of light helps to determine the relationship between distance and time for a particular universe. The speed of light, c = wavelength * frequency. The wavelength establishes relative separation. The frequency establshishes relative time. Quantum Mechanics can be described mathematically as a Minowski 52 flat dimensional field. The scale of its effect is determined by the Planck constant. For a universe with a Plance constant of 10^6, the quantum universe would be visual to us. Space and momentum would be intermixed; as would energy and time. The various hyperspaces permit this interesting property. This is what allows the particle-space concept.

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