Archive for the 'General Relativity' Category

Feb 11 2016

Ripples in Space-Time

Published by under General Relativity

Many of you have read the news by now about LIGO reading ripples in space-time caused by a violent black hole merger, which were likely giant phononic pulses. The Coulomb force is transmitted faster than the speed of light by phonons transmitting through a gravitational field. Similarly, what LIGO read would have been phononic pulses of immense dimensions.

An interesting aspect of this black hole event is that it probably happened much more recently than scientists think it did. Phonons can travel much faster than the speed of light in a vacuum.

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Feb 22 2011

LHC Motto

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

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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 14 2010

Independent Action

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/

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Apr 29 2007

Some Logical Conclusions

Questions that may be answered by this theory include why the particles in the solar wind are not pulled back toward the Sun by its gravity within the first few thousand miles, but rather travel on through the solar system, and why the Van Allen belts do not warp, keeping their shape in the magnetic bottles formed by the Earth’s magnetic field lines.
Other things that can be explained better are neutron stars, and maybe even black holes.  By rough calculation an electron in an atomic orbital can give off only 61 gravitons before it collapses into the nucleus of the atom if no gravitons are absorbed by the electron in that time.  In areas where the gravitational field is not strong enough, hydrogen atoms in stars will indeed gradually collapse in sequence, and if the resulting neutrons have their magnetic dipole moments aligned in a lattice such as to stabilize the resulting energy, and not decay in just over 15 minutes, a neutron star may result.
Unfortunately, there are also established outcomes of theoretical physics that may no longer be needed, those presumably being the concepts of the quark, the positron, general relativity, dark energy, and string theory.

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