Alpha Institute for Advanced Studies

omega = d theta / dt = cb m(r) / r squared

The angle change in time t is measured to milliarcseconds, and the distance r is measured by a laser or satellite. By Ockham’s Razor this is the preferred test. Here cb is a constant.

Many thanks again, the experiment is simple – just measure r at two or more points in the orbit with a laser or radio beam, and the time between two positions of the orbiting object. Repeat all around the orbit. Kepler’s second law is true for any orbit, open or closed, or any curve in a plane, i.e.

dA / dt = (1/2) r squared d theta / dt = (1/2) r squared omega = constant m(r)

So measure t and r to find dA / dt for any object, e.g. a star in a whirlpool galaxy or the earth’s moon, or Halley’s comet (epsilon about 0.9). This experiment has never been done before as far as I know. A laser can measure the earth moon distance to great accuracy, and there are also very accurate clocks. In general relativity, dA / dt is not a constant.

a cubed = y m(r) squared tau squared

where y is a constant. This assumes that the orbit is an ellipse of area

A = pi ab = pi a power 3 / 2 alpha power half

Kepler’s law is also modified, so the way in which all orbits are computed via Kepler’s law is also modified. I do not think that these modifications have ever been accounted for. Kepler’s law used to be a an intractable problem using iterative approximation, but with computers that is no longer a problem. In astronomy only a few things can be observed directly, notably tau the time for one orbit. The orbital velocity can be measured directly, but the distance r cannot be measured directly unless a laser is used, or a radio beam. All other facts about an orbit must be deduced from tau and v. At aphelion and perihelion v is perpendicular to r. Marion and Thornton give tables for a and tau but now it is seen that a cubed proportional to tau squared is not correct. The true relation is as given above. Using lasers or radio signals to measure r, the areal velocity dA / dr can be computed, and this gives m(r) directly. So Kepler’s second law is by far the easiest way of obtaining m(r) experimentally. It should be different from unity and should have an r dependence or perhaps an r, theta dependence.

www.wbabin.net/eeuro/vankov.pdf

and was also criticised almost immediately by K. Schwarzschild in a letter dated 22nd Dec., 1915 to Einstein. Vankov cites Stephen Crothers. It is unknown to Vankov who misrepresented and falsified the Schwarzschild metric. I can see that in the second equation of this paper, Einstein uses a symmetric connection, so the rest of the paper is incorrect. He starts with his incorrect field equation of 1915. Vankov also points out serious errors of ordinary mathematics, dubious approximations and so forth. In fact this is typical of Einstein, who strains to get the result he has in mind and sod the mathematics and physics. As one G. ‘t Hooft mentioned infamously, “bad physics”, and ‘t Hooft should know all about bad physics and editorship. Schwarzschild wrote that he was declaring a “friendly war” on Einstein, who ignored him until the former was safely dead (1916 of disease). Einstein again uses the null geodesic heavily criticised by Eckardt and myself in UFT 150 and 155.The original m function of Schwarzschild first appears in this letter, and is

m = 1 – gamma / R

where R = (r cubed + r0 cubed) power 1/3 as pointed out correctly by Stephen Crothers. This does not, repeat not, give a black hole singularity. So claims to observe black holes are false (see UFT 120).

m(r) = 2 – exp(2exp (- r / R))

or generalizations of this. What actually happened is explained in this note, Einstein and contemporaries (whoever they were really) replaced the correct eq. (12) with an effective potential (24) extracted from eq. (12), and used this effective potential in a CLASSICAL (non relativistic) method to claim eq. (28). This is obviously self inconsistent if one begins to think for oneself. They then proceeded to make dubious approximations about the incorrect eq. (28) in order to try to force a precessing ellipse to come out of the calculation. In UFT 190 we give the correct method for the first time, and find the correct m(r) for the first time. This will be written up for J. Found. Phys. Chem.

I think I will write this up as essay 43 and call it “Nobody is Even Close to Being Right in the Standard Model”. I am sure that Horst Eckardt could write a wonderful sequel to “Nobody’s Perfect”.

a190thpapernotes9.pdf