Archive for January, 2011

Jan 15 2011

Permittivity of Free Space

It is interesting, to say the least, the way some of the constants of physics mix and match.  There are lots of examples of this in text books and on web sites, including this one, so there is no point in reiterating any now which do not relate specifically to this entry.

Some constants, nevertheless, turn out not to be constants, including the permittivity of free space, termed ε0.  At the surface of the earth, and at any point not far enough away to discern a difference, we have ε0 = 8.85 x 10-12 C2/(N-m2) when measured in a vacuum.  One of the ways in which the permittivity of free space relates to other physical entities is in the makeup of the Coulomb constant, k = 1/(4πε0), which is then also not really a constant in all locations, the difference relating to the local density of gravitons.

The speed of light in a vacuum can be written as: c = sqrt(k/km) = 1/sqrt(ε0 µ0) = 2.998 x 108 m/s, which is a constant throughout the universe.  One may be tempted to say then that µ0 is an inverse function to ε0 when evaluated at a given point, except that this is so unlikely with present understanding so as to be unimaginable.  Along with the constancy of the speed of light in a vacuum in any reference frame, the fact that it equals 1/sqrt(ε0 µ0) in our locale can remain somewhat of a mystery.

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Jan 12 2011

Gradient of a Scalar Potential

In Thomas’ Calculus we find the definition: “If F is a vector field defined on D and F = del f for some scalar function f on D, then f is called a potential function for F.” ([1], pg 921)

Kaplan states that the “gravitational field is the gradient of the scalar f = kMm/r” ([2], Prob. 4, pg 180), which for General Relativity is indeed the case.  With gamma ray energy exchange however, the scalar is f = k1M/r, in form much like the scalar potential k2q/r with electrodynamics.  This tells us that both gravitational and Coulomb forces are of independent action, and the corresponding fields are gradients of scalar potentials, which can be considered as more evidence for unification.

The vector fields we are looking at have units of N/kg for gravity, and of course E = N/C for an electric field.  A gravitational field calculation is most applicable when the object in the field is small compared to, or far away from, the source of the field, such as Jupiter compared to the sun.

Aside from the King James Version of the Bible, Wilfred Kaplan’s Advanced Calculus is still my favorite book.  By the way, we used Thomas’ Calculus book at the University of Wisconsin in 1976 and 1977.


[1] Thomas, George B., as revised by Weir, Maurice D. and Hass, Joel, Thomas’ Calculus, Twelfth Edition, Addison-Wesley of Pearson Education, Inc., 2010, 2005, 2001

[2] Kaplan, Wilfred, Advanced Calculus, Fifth Edition, Addison-Wesley of Pearson Education, Inc., 2003

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Jan 05 2011

Bubble Spectrum

Published by under Astrophysics

There is a graph of Brightness vs. Energy (GeV) at the lower left of the image at the following NASA Fermi web site, relating to the same discovery I have been writing about recently, and one that has been fascinating to a great number of scientists:

I just thought it was interesting to see that the “Bubble spectrum” in magenta color has a pointer at what could be 313 MeV.  The brightness rises markedly from that point which is where we would expect gravitons to reside.  Once peaked in brightness, the spectrum rises to much higher energies which, if it were not that we are very far away from the bubbles, could indicate that energies are adding.

We know from laser calculations and uses that energy from coherent light waves do add.  As an example, the gravitons coming off the sun, at the surface of the sun, would be so concentrated so as to create somewhat of a laser field.  The earth, of course, is of a size and at a distance from the sun where the gravitons help sustain life rather than damage biological function.

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