Archive for the 'Classical Electrodynamics' Category

Feb 24 2016

Johnson–Fruechte Experiment

Produce a multiple layer wire wound coil around a roughly 2 inch diameter iron core, maybe 8 feet long. Set the cardboard tube from a roll of paper towels, on end, up on a shelf. Get as much capacitance as you can hooked up to the coil and charge up the capacitance. Aim the device at the top half of the cardboard tube, making sure the other end ‘sees’ terrestrial earth, and dump the capacitance all at once to produce a high value of current. Gravitons like to follow magnetic field lines, so one would see if the cardboard tube can be pulled over.

A software engineer across the hall from me, Jeff Johnson, who I have worked with for many years, came up with the idea of loading a lot of capacitance, and producing a high current by dumping it with one switch. The wire gauge would have to be figured out based on the current that would be produced.

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Aug 14 2011

Topology of the Vacuum

Whether we are looking at nuclear fission or the results of scattering experiments, the way spin-parity assignments are often kept in order in nature would be similar to the cause of a de Broglie wavelength.  Rotational states ratchet through the gravitational flux, with potential wells rising and falling in one of the most fundamental of quantum phenomenons that exist.

During and shortly after high flux, high velocity hadron collisions at Fermilab or the CERN LHC nevertheless, some of the scattering resonances seen may be due to a blitz through the gravitational field, not organized very well in a manner, for example, such as an electric field.  The static we typically see in Goldhaber plots generated from hadron colliding experiments may in part be due to a cascade of momentum generated through the gravitational field.

Another evidence of the gravitational field is the Bohm-Aharonov effect.  As Ryder puts it, “the Bohm-Aharonov effect owes its existence to the non-trivial topology of the vacuum, and the fact that electrodynamics is a gauge theory.  In fact, it has recently been realized that the vacuum, in gauge theories, has a rich mathematical structure, with associated physical consequences,” ([1], pg 101).

Astronomically, and for the sake of history, it is somewhat reminiscent of the luminiferous aether.

Another concept related here is that “the configuration space of the vacuum is not simply connected.” ([1], pg 102)  When we speak of ‘one loop’ consequences, we can liken it to the Cauchy integral, which Greiner calls “The surprising statement of the integral formula (4.16), namely, that it is sufficient to know a function along a closed path to determine any function value in the interior,” ([2], pg 109).  For those more willing to trust the mathematicians for pure math, the Cauchy integral formula is presented in Brown and Churchill:

f(z) = (1/2πi) ∫ (1/(s-z)) f(s) ds                     ([3], pgs 166 and 429)

With “the gauge invariance of electrodynamics” ([1], pg 97), the perfect balance of charge that exists in the near universe, – possibly the entire universe, and the quantum steps of the Coulomb force by phonon transmission, the Bohm-Aharonov effect does indeed show us that there are physical consequences to the vacuum that are non-trivial, relating to the gravitational field in which the Bohm-Aharonov test and other tests are set up and run.

As a final thought, it is probable that planar electromagnetic waves would not turn into spherical electromagnetic waves were it not for traveling through a gravitational field.

 

[1] Ryder, Lewis H., Quantum Field Theory, Second Edition, Cambridge University Press, 1996

[2] Greiner, Walter, Classical Electrodynamics, First German edition, Klassische Elektrodynamik, 1991 Verlag Harri Deutsch. 1998 Springer-Verlag New York, Inc.

[3] Brown, James Ward and Churchill, Ruel V., Complex Variables and Applications, Eighth Edition, McGraw-Hill Higher Education, 2009

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Feb 07 2011

TGF’s

Checked the Fermi mission web site for the first time in weeks.  I had been waiting a long time to get information on what the GBM has been reading, and the Fermi article from 01.10.11 finally gives some information:

http://www.nasa.gov/mission_pages/GLAST/news/fermi-thunderstorms.html

As some of you know, an explanation for terrestrial gamma-ray flashes is included in my April 2007 paper in the section entitled More on Synchronization.  The Fermi article refers to “strong electric fields” in the milliseconds before a lightning strike.  The fields result from areas of high voltage, which involve electrons in high concentration, which produce Compton scattered gravitons coming out of the earth.  The gravitons are down scattered to an energy where they are no longer gravitons, 511 keV according to the article.

The pattern of the scattered gamma rays, shown in magenta color in the article, is exactly what we would expect when gravitons are scattered in the milliseconds before a lightning strike in a TGF.

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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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Dec 23 2010

Electron Orbitals and the Lorentz Force

For an electron in an atomic orbital the magnetic part of the Lorentz force [1], F = q[E + (v x B)], deflects the electron’s path so that the electron cannot head directly toward the nucleus.  Magnetic fields produced by the nucleus essentially fight off the electron’s direct path which is due to the electrostatic part of the force.  This is one of the aids in assuring that atomic collapse does not occur.  In the vicinity of an electron orbital turn where gravitons are emitted from an electron, a planar electron arc can be assumed [2], however this is only in the tangential limit relatively far from the nucleus and there are no complete arcs in electron orbitals that are geometrically planar. 

[1] http://en.wikipedia.org/wiki/Lorentz_force

[2] http://www.fruechtetheory.com/blog/2008/07/20/spread-of-a-fermion-wave-function/

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Dec 09 2010

Field Line Curvature

Any middle school student in the free world with a true interest in science, and proper resources to learn, has noticed from diagrams in books or on the web, or with iron filings on a piece of paper with a magnet beneath, that magnetic field lines have curvature.  A local electric field between and surrounding two point charges also has curvature in the near space, except for on a line pointing directly away from the other charge.  Dr. Schombert gives us a good diagram of this on the web. [1]

The lines of a gravitational field, on the other hand, have no curvature in any instance, and “the gravitational force is entirely radial”. ([2], pg 616)  So, what is going on here?

Earlier it was mentioned that the Coulomb force may transmit “through the gravitational field in wave packets at group velocity, by phase shift and chirality” [3].  This could otherwise be stated as by phase shift and parity and, as physicists know, group velocity can be faster than the speed of light.

To extend on this concept and compare then, if a rotational component is developed in a free graviton, it is due only to Coulomb field production, and though free gravitons always travel in a straight line, neglecting lensing, when there are no charges present the rotational component of a free graviton would be zero. 

 

[1] http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec04.html

[2] Kline, Morris, Calculus, An Intuitive and Physical Approach, John Wiley and Sons, Inc., 1967, 1977; Dover (1998) unabridged republication.

[3] http://www.fruechtetheory.com/blog/2010/06/15/muonic-states/

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Mar 15 2009

Electric Charges

Published by under Classical Electrodynamics

The problem of what free charges, including nuclei, do with gravitons that arrive in a direct path has not been addressed to a great extent, though a physics PhD friend of mine has at least thought about it as relating to a free electron.  The necessity of dealing with the subject comes not only from when “energy is irretrievably radiated away by the acceleration fields” ([1], pg. 466), but also directly through electrostatics.
Let us first consider the acceleration fields.  As one example of power being radiated by an accelerated point charge, we have synchrotron radiation, the power formula for a free electron traveling near the speed of light being:
P = (2ke2γ4c) / (3r2)                      [2].
In Gaussian units, with k = 1, this becomes:
P = (2e24γ4) / (3ρ2)                   ([3], (14.31), pg 667)
In the second equation the Greek letter ρ (Rho) is used for the radius of the synchrotron accelerator, instead of r, and a β4 factor shows up which GSU left out because β = v/c is close to 1 in a synchrotron.
It could be reasoned that synchrotron radiation energy is replenished to the electron through electric and magnetic fields, by way of electric charges and currents produced by steam powered generators through the burning of hydrocarbon fuels, or nuclear fission.
Nevertheless, I do think that free charges absorb gravitons as part of the process of energy replacement when radiation is given off.  What keeps them stable is the main challenge here.  Why would they not keep absorbing gravitational energy until we end up with giant particles?  Is it gravitational pressure, in part, that keeps them at a certain charge and mass?
Fundamental charges and other ions most certainly allow gravitons to pass through, otherwise there would be scattering going on all the time and utter chaos.  Indeed, the gravitons passing through may provide conjugate wave functions that help keep the particles together.  It could be that gravity not only allows large masses to attract, but also provides for the continued existence of particle mass.
Moving on to electrostatics, the energy of a point charge is given as:
W = (ε0/2) ∫all space E2 dτ                     ([1], (2.45), pg 94),
which turns out to be infinite as Griffiths shows ([1], Sect 2.4.4, pg 95).
Here the same process of gravitons providing conjugate wave functions would be taking place, and also we may have the electric field transmitting through the gravitational field, shouldering through the gravitons in a highly relativistic sense.  The infinite energy would no longer be a mystery, though it is not really infinite because the known universe is gradually losing gravitational energy as some gravitons escape into deep space.  The result is nothing new to physicists; our galaxy is expanding at an accelerating rate.
As far as gravitational conjugate wave functions relating to conservation of charge, it has been postulated that “the average number of gravitons in an electron, in an atomic orbital at the face of the earth, could possibly be 137/2 = 68.5” [4].  Not only for electrons in atomic orbitals then, but also for free electrons, the gravitational field providing conjugate wave functions may increase the number of gravitons involved in making a fundamental charge to 137.
Considering all, in the sudden absence of a gravitational field we are presented with an alternative to sequential atomic collapse in a slowly decreasing gravitational field, which is fundamental particles simply flying apart in a high energy gamma ray burst.  Gravitons like to follow gently arcing uniform magnetic field lines, so a rotating intense magnetic field deep in space, from a neutron star for example, could produce such a phenomenon if its path intersected the path of a more conventional mass.  These are not to be confused however with lower energy gamma ray bursts, such as those that come from the earth in the milliseconds before a lightning strike, due to the Compton scattering of gravitons.
[1] Griffiths, David J., Introduction to Electrodynamics, Third Edition, c. 1999, Prentice-Hall, Inc.
[2] GSU Hyperphysics: http://hyperphysics.phy-astr.gsu.edu/hbase/particles/synchrotron.html
[3] Jackson, J. D., Classical Electrodynamics, Third Edition, c. 1999 John David Jackson, John Wiley & Sons, Inc.
[4] http://www.fruechtetheory.com/blog/2008/04/01/wave-function-transfer-2-2/
 

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