Requiem for Relativity

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Joe Keller</i>
<br />...the bismuth nucleus weighs slightly more than 207 protons. A muon weighs almost 207 times as much as an electron. Therefore maybe bismuth-209 is very slightly radioactive. ...<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

I learned today, that in 2002 (see: Nature, April 24, 2003) scientists from the Univ. of Paris, discovered that bismuth-209 is radioactive, with a half-life of 19 quintillion yr. These inequalities hold:

mass of lead-208 nucleus :: mass of proton &lt;
mass of muon :: mass of electron &lt;
mass of bismuth-209 nucleus :: mass of proton

All the nuclei for which the second inequality holds, are radioactive.

Equipartition of Angular Momentum: More Evidence for Barbarossa

The Milky Way, the Solar System (if Barbarossa's parameters are as I think), our gas giants, and Earth (without Luna), all have about the same ratio, L/M^2, where L is their intrinsic angular momentum and M their mass. Here is the arithmetic:

Earth (without Luna)
0.3308*1*6377^2/(24/(2*pi))/1^2 = 3,522,000 km^2/hr/Earthmass

Jupiter
0.254*317.83*71492^2/(9.9259/(2*pi))/317.83^2 = 2,586,000

Saturn
0.210*95.162*60268^2/(10.656/(2*pi))/95.162^2 = 4,726,000

Uranus
0.225*14.536*25559^2/(17.24/(2*pi))/14.536^2 = 3,685,000

Solar system, with Barbarossa system = 3000 Earthmasses at 198 AU
3000*(198*149600000)^2/(198^1.5*365.25*24/(2*pi))/335000^2 * 0.995(c.o.m. corr.) * (1+1/(10*sqrt(40))+1/(30*sqrt(20)))(Jupiter & Saturn corr.) = 6,143,500

Let's approximate our Milky Way galaxy crudely, as a solid thin disk of uniform surface density with our sun on the rim. Let's measure mass in solar masses, distance in A.U., and speed in units of Earth's speed around the sun. Crudely approximating the disk's gravity as though the mass were at the center, I find for our sun's galactic orbit, that V^2*R = M, the mass of the galaxy. For the disk, the average angular momentum per unit mass, is V*R/2. So, L/M^2 = M*V*R/2/(M*V^2*R) = 1/(2*V). For the sun, V = 240km/s / 30km/sec = 8.

In these units, our Solar System would have this same L/M^2, if Earth were replaced by an object of 1/16 solar mass. Alternatively, there could be an object of 1/(16*sqrt(196)) = 1/224 solar mass, at 196 AU. If Barbarossa has 1/100 solar mass, then our galaxy has about half the L/M^2 value of our solar system, but about the same as our rotating planets.

The galaxy and the rotating planets resemble the spin-1/2 electron, with half a quantum of angular momentum. The solar system resembles the hydrogen atom, with a full quantum of angular momentum.

The Gravitational Planck Constant

The "electric to gravity [force] ratio", q^2/(G*m^2), where q & m are the charge & mass of the electron, and G the gravitational constant, is 4.166*10^42. For an electron with spin angular momentum L = hbar/2, the quantity L/m^2, when divided by the electric to gravity ratio, becomes 328,000 km^2/hr/Earthmass.

Let's add Jupiter's rotational angular momentum to that of the Galilean moons, to find L/M^2 for the entire Jovian system:

0.254*317.83*71492^2/(9.9259/(2*pi)) +
0.0149*422000^2/(1.77*24/(2*pi)) +
0.0080*671000^2/(3.55*24/(2*pi)) +
0.0248*1070000^2/(7.16*24/(2*pi)) +
0.0181*1883000^2/(16.69*24/(2*pi)) =
2.6389*10^11; divided by 317.895^2, = 2,611,300 km^2/hr/Earthmass

which is 7.96 times the value for the electron.

This suggests that the L/M^2 observed, for rotating planets, for the Milky Way galaxy, and (if Barbarossa exists) for our solar system, is the gravitational counterpart of either spin, or orbital, electron angular momentum. The analogy involves the electric to gravity ratio, and a factor of 8.

The angular momentum is proportional to the square of the number of particles, because it arises through the interactions of pairs of particles. This further suggests that the electron itself is composed of many subparticles (see: R. L. Mills) so that the same statistical process, applied to electricity and gravity respectively, gives momentum to electrons and to planets.

In the electrical case, there is an acceleration, (q^2/r^2)/m, which when divided by the speed of light, c, gives a "proper frequency", q^2/(r^2*m*c). The significance of the fine structure constant, alpha = q^2/(hbar*c) = 1/137.0359991 (PhysRevLett 100:120801, 2008), seems to be that the effective rotational frequency is the "proper frequency" multiplied by 1/alpha = 137. So, the angular momentum is ((q^2/(r^2*m*c))/alpha)*m*r^2 = hbar.

Let's find the angular momentum of the Earth-Luna system:

Earth rotation
0.3308*1*6377^2 = 1.345 * 10^7 Earthmass-km^2/(day/(2*pi))

Luna-Earth orbit ( + Luna rotation (negligible) )
0.0123*384400^2/27.322 * (1-0.0123/2) (corr. for c.o.m.) * (1+0.4*(1736/384400)^2) (corr. for Luna rotation) * sqr(1-0.0549^2) (corr. for orbital eccentricity) = 6.601 * 10^7

The ratio is 4.91, also close enough to a whole number, to suggest quantization.

Hi Joe, as you know Im looking at ratios for the speed of light and the speed of gravity, and I think the best contender is h = c^2 / b^2 where b is the speed of gravity. So I rearranged the equation for the fine structure constant with
1 - h = 2Gm / r c^2 to get h = e^2 mu / 2a epsilon.
e = electron charge
mu = permeability of free space
epsilon = permittivity of free space.

Now something had to alter and I decided to go with mu. Mu alters and becomes the reciprocal of the speed of light. Now thats rather odd but I had to think that it might be an artefact. This possible speed of gravity keeps throwing up reciprocals. Lots of ones and noughts and some very nearly constant values.

Then I found this in a book called the trouble with physics
"... One example is a version of Yang-Mills theory called n = 4 super-Yang-Mills theory, which has as much supersymmetry as possible... There is good evidence that this theory has a version of S-duality. It works roughly like this. The theory has in it a number of electrically charged particles. It also has some emergent particles that carry magnetic charges. Now, normally there are no magnetic charges , there are only magnetic poles. Every magnet has two, and we refer to them as north and south. But in special situations there may be emergent magnetic poles that move independently of each other - they are known as monopoles. What happens in the maximally super theory is that there is a symmetry within which electrical charges and magnetic monopoles trade places. When this happens, if you change the value of the electrical charge to 1 divided by the original value, you dont change anything in the physics described by the theory."

The more I look at this the more I think that Newton was right, the speed of gravity is instantaneous, gravity takes an exponential form over vast distances. Yet its quantised into h intervals.

What Im now looking at is the Riemann conjecture. Complex harmonics have to play a role in a space which has a negative refractive index. I dont, I hasten to add, expect to solve it!!! Im far too thick. Still, the zeta function does look a lot like the lorentzian, when we write the lorentzian in terms of refractive index. z(x) = 1 / (1 - 1 / p^s)

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Stoat</i>
<br /> "[1] ... One example is a version of Yang-Mills theory called n = 4 super-Yang-Mills theory, which has as much supersymmetry as possible... ...in the maximally super theory is that there is a symmetry within which electrical charges and magnetic monopoles trade places. ..."

[2] ...the zeta function does look a lot like the lorentzian... <hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">


[2] I've seen books about slight generalizations of Riemann's zeta function, called "zeta functions", which arise in quantum mechanics. To my knowledge, you're the first ever to have noted the similarity of the Lorentzian to the zeta function. The solution of the equation

gamma = 1/sqrt(1-beta^2) = zeta(e^e)

is beta = 1/134.89. If e is replaced with e*(1+alpha/(4*pi)), where alpha is the fine structure constant, then the solution is beta = 1/137.15. Zeta(x^x) is such a sensitive function of x, that given beta=alpha, x differs from e by only 1 part in 2000.

[1] The empirical equation, L/M^2 (Jupiter system) = L/M^2 (spinning electron) * 8/(electric to gravity ratio), suggests a mechanism involving all possible subsets of 3 things: 2^3 = 8. This would be a kind of supersymmetry.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Joe Keller</i>
<br />The Gravitational Planck Constant

...This suggests that the L/M^2 observed, for rotating planets, for the Milky Way galaxy, and (if Barbarossa exists) for our solar system, is the gravitational counterpart of either spin, or orbital, electron angular momentum. The analogy involves the electric to gravity ratio, and a factor of 8. ...<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Paul Wesson's 1981 article in Physical Rev. D, has a chart showing the constancy of L/M^2 for astronomical objects, from planets, to galaxy clusters. With Barbarossa, the solar system has no more than twice too much angular momentum, vs. the planets; without Barbarossa, 30 to 60 times too little.