Fruechte Gravity Theory Blog

It occurred to me only today, while studying from Kenneth Krane’s Introductory Nuclear Physics, that it would take pulsed magnetic fields to focus gravitons on space debris or an enemy satellite.  The way magnetic field lines fan out from a pole of a dipole magnet would make the concept otherwise unworkable.  Since protons in the CERN LHC travel very close to the speed of light, that part of the technology would already be available.  There is no cross product in this case, apart from creating the magnetic field pulses.  As far as aiming and tracking accurately and effectively from the ground, one in my position can only guess that this technology is available also.

In an earlier entry it was lamented how some physicists seem to make a transition from special to general relativity as though the two are somehow linked.  I don’t know if the Wikipedia article on Albert Einstein was written by a physicist, however it goes one step further and gets relativity completely mixed up.  It calls Einstein “a German born theoretical physicist who discovered the theory of general relativity effecting a revolution in physics.” [1]

For young people studying math and science, please note that it was special relativity that advanced physics by a giant leap, not general relativity.  In a recent article on CERN’s startup of the Large Hadron Collider after a 10-week shutdown, Robert Evans of Reuters, and the Toronto Sun, got it right when it was said:

“New Physics, the motto of the LHC, refers to knowledge that will take research beyond the “Standard Model” of how the universe works that emerged from the work of Albert Einstein and his 1905 Theory of Special Relativity.” [2]

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

[2] http://www.torontosun.com/news/world/2011/02/21/17353401.html

The “Fermi Sky Blog” can be reached from the Fermi main web page [1], though I guess it doesn’t hurt to note the direct link here [2].

In the “Fermi LAT weekly report N. 138 … 2011.January.24 – 2011.January.30”, we find the following:  “3C 454.3 fairly bright for all the week, with daily flux between 2.5e-6 and 6.4e-6.”  This type of report has been a fairly common format in the Fermi Sky Blog, with flux levels often being very low, from sources so far away that it leaves one quite impressed with the technology and analysis methods whatever they may be.

Noteworthy is that “Fluxes are in the unit of photons/cm²/s above 100 MeV. All errors are statistical only.”  Gravity is at 313 MeV and, as has been said many times before, the LAT seems designed to measure gravity as one of its main purposes.  The designers would not have had to know how gravity works; they would only have had to know the typical frequency range of sources from past data and experience.

Steady sources said to be “fairly bright for all the week” are encouraging to see, because gravity at a given relative location and time period is normally a steady field.  Most sources above 100 MeV are indeed steady, and let us be reminded that even the closest celestial body to the earth, the moon, is “an object with an absolutely known gamma-ray output” [3], and a stunning image [4].

[1] http://fermi.gsfc.nasa.gov/

[2] http://fermisky.blogspot.com/

[3] https://www.fruechtetheory.com/blog/2007/11/14/glast-calibration/

[4] http://apod.nasa.gov/apod/ap970210.html

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/k_m) = 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.

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

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:

http://www.nasa.gov/images/content/498886main_DF4_bubbles_graphs.jpg

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.

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

It seems I suggested to the GLAST people at one point, when the Fermi Gamma Ray Space Telescope was still in a pre-launch test phase, that they try pointing the telescope straight up into the sky and turn the instrument on to see what they could read.  As long as the anti-coincidence shield did not activate, there would be a gamma ray fog from the earth’s atmosphere, considerably stronger than the diffuse background that is found with the telescope now in space and pointing away from the earth.  With a planned schedule already at the time, they probably did not try it.

As far as new equipment goes, another way to test whether or not our atmosphere emits gamma rays is to send a gamma ray telescope up as the payload of a high altitude balloon.  The instrument would point at an acute angle to the vertical so as to keep the balloon itself out of the picture.  As the balloon ascends to high altitude there should be a gradually decreasing flux density of gamma rays.  The energies to look for are centered on 312.76 MeV.

The suggestion would otherwise be to place the instrument looking out an opening of a high altitude engine propelled aircraft as it ascends, except that vibrations may at times affect the readability.

It is always refreshing when instances are found where the physics world is honest, and shows that they really have some integrity and responsibility, because going way back things can get out of hand once in a while before they come back to reality.  At Fermilab, the CERN LHC, and other labs, with all the particles smashing together almost anything can be found with some imagination and maybe a matrix made to match.

Here is one instance where responsibility recently prevailed: http://www.physorg.com/news/2010-12-large-hadron-collider-signatures-microscopic.html

The link seems to have generated a lot of interesting comments as well.

In one of the FGT YouTube videos of February 2008 it was mentioned that unlike a tug of war where the tension in the rope is the same throughout when the rope is stationary, gravity is one mass acting independently on another.  In the case of two masses of spherical shape the force is known to be F₁₂ = Gm₁m₂/r₁₂², which we can equate to m₁a or m₂a, depending on whether we want to calculate the acceleration of m₁ or m₂, and where r₁₂ is the distance between the centers of the two masses.  With planetary masses that are close to spherical, and the objects they pull, this formula has been used most reliably, while it has been known for a long time by learned mathematical and scientific people that shape matters, and using center of mass with the standard physics book formula can cause increased error in some instances.

As an analysis that has already been done, let us use Kline Chapter 16, Sections 5, 6, and 7.  Starting with Section 5, “Gravitational Attraction of Rods”, the example given is that of a “rod 6 feet long and of mass 18 pounds which is uniformly distributed” and “so thin that we think of it as extending in one dimension only.  Three feet from one end of the rod and along the line of the rod is a small object of mass 2 pounds which we shall regard as located at one point.”   Kline first calculates the force that the rod exerts on the 2-pound mass as though the entire mass of the rod were concentrated at its center, according to the standard F₁₂ = Gm₁m₂/r₁₂² formula, which comes out as equaling G poundals.  Then he does the calculation properly using an integration over the rod, showing that the force that the rod exerts on the 2-pound mass is actually (4/3) G poundals.  In Section 6, “Gravitational Attraction of Disks” [1], again a difference from the standard formula is shown which for comparison includes Exercise 1 from that section.  Finally, in Section 7 it is shown that the standard physics book formula can be used with spheres.

Since the title of the referenced book includes “An Intuitive and Physical Approach”, intuition may tell us that, since the rod was integrated along its length to obtain a correct answer, every piece of a nearly one dimensional rod in the limit of a Riemann sum exerts a gravitational force independently on a separate point mass.

With General Relativity, unproven to date, a mass produces surface curvature in space, which may contact a series of points on other surfaces, due to another mass, through a tensor product [2] that reduces to a force vector.  This may be interpreted as space-time surface interaction, and not necessarily complete independent action.  At least two multi-million dollar projects are built and running ([3], [4]) and at least one is being developed [5] in attempts to prove General Relativity.

Special Relativity, on the other hand, E = mc², has long been proven correct, and the gravitational theory presented on this web site would not work without it.  Some physicists in their writings seem to make a transition from Special to General Relativity as though the two are somehow linked, and in reality they bear no relationship to each other.

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

[2] Rainich, George Yuri, Mathematics of Relativity, John Wiley and Sons, Inc., 1950, Chapter 4

[3] http://www.ligo.caltech.edu/

[4] http://www.nasa.gov/mission_pages/gpb/index.html

[5] http://lisa.nasa.gov/