Friday, April 11, 2014

How does the vacuum take a limit to zero?

The issue came up in one the grand announcements that space inflated faster than light can sample. So I looked, naturally, and began wondering how the vacuum of space takes an integral to zero in the limit?  Evidently the vacuum knows a zero when it sees one?  Not possible in any quantum solution that I know of. I can see the vacuum bouncing around a limit of 10E-5 relative to (3/2)**108*(1/2+sqrt()5)/2)**91.  But if it goes beyond that error, the vacuum will reset the quantum structure. The variation of that action cannot be zero, ever. Absent any action, there is no equalization of the sample rate.The vacuum has a band limit.

Think of it this way. -iLog(i) when i is zero.  Quantum noise is a bit high.

When the phase elements of the vacuum start deviating from their natural sample rate, they beat against each other, they are stuck with their relaxation  moments,  the packed nulls fall apart, and the system converts to free space until the sample rates are realigned to the Plank integer.

Derivation of Einstein's field equations

Suppose that the full action of the theory is given by the Einstein–Hilbert term plus a term \mathcal{L}_\mathrm{M} describing any matter fields appearing in the theory.
S = \int \left[ {1 \over 2\kappa} \, R + \mathcal{L}_\mathrm{M} \right] \sqrt{-g} \, \mathrm{d}^4 x
The action principle then tells us that the variation of this action with respect to the inverse metric is zero, yielding

\begin{align}
0 & = \delta S \\
  & = \int 
         \left[ 
            {1 \over 2\kappa} \frac{\delta (\sqrt{-g}R)}{\delta g^{\mu\nu}} + 
            \frac{\delta (\sqrt{-g} \mathcal{L}_\mathrm{M})}{\delta g^{\mu\nu}}
         \right] \delta g^{\mu\nu}\mathrm{d}^4x \\
  & = \int 
        \left[ 
           {1 \over 2\kappa} \left( \frac{\delta R}{\delta g^{\mu\nu}} +
             \frac{R}{\sqrt{-g}} \frac{\delta \sqrt{-g}}{\delta g^{\mu\nu} } 
            \right) +
           \frac{1}{\sqrt{-g}} \frac{\delta (\sqrt{-g} \mathcal{L}_\mathrm{M})}{\delta g^{\mu\nu}} 
        \right] \delta g^{\mu\nu} \sqrt{-g}\, \mathrm{d}^4x.
\end{align}

How to plot?

Anyway, this is a moment to bring up the issue of plotting.  I need to write out scaled up version of the complete sequence to a file and use a stronger plotting package.  We should be able to run the quantizer to its limit and actually zero in on the fine details of the periodic table, for example.  That is where I am.

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