Posted by Uncle Al on May 29, 2003 at 11:52
(68.5.243.16)
Re: Noether theorem vs. Runge_Lenz (cont'd) (Pasti)
A fully discretized Noether theorem is quite a pickle indeed! This monstrous gap has not prevented mainstream physics from including parity and charge conjugation as symmetry-coupled conserved physical properties. CPT conservation is *the* fundamental underpinning of all quantum field theories without exception. We've both got to be missing something.
If a qualified Eotvos balance gives reproducible net output, the Equivalence Principle is empirically counterdemonstrated and falsified. There are no footnotes, there is no waffling, there is no escape. This is an irrefutable fact. The conclusion remains unchanged whether test mass composition or geometry is contrasted.
An Eotvos balance fulfills all the requirements of locality. That is one reason why the rotor has such a small diameter vs. torque advantages of long moment arm. Its test masses are also small. The Indian TATA Institute has a comparitively huge rotor of different design holding physically large and massive samples. Their sensitivity is less than Adelberger's.
The Equivalence Principle has never been tested against calculated parity pair test masses of identical composition and maximally opposite geometric parity. This is a fact. To have examined the problem for 400+ years in every conceivable way to achieve 100% null results, then to reject one additional very different quantititative test mass variable as "too risky" vs. failure is insanity.
We have the numbers for alpha-quartz. Rigorous QCM gave uniform COR=1 to 1131 atoms for spheres of increasing radii to 15 A in the alpha-quartz lattice independent of submitted atom labeling and connectivity. COR=1 is the boundary condition for running FastCHI. CHI vs. radius for alpha-quartz ground out 100,000 A radius in 61.65 CPU-hours on a 2 GHz Athlon running Linux. This is the linear least squares fitted result:
Start radius: 3.6 A, 14 atoms
End radius: 100,000 A, 3.3357x10^14 atoms
Number of points: 585
log(1-CHI) vs log(radius)
===========================================
Theoretical slope: -2
Least squares slope: -1.999101 (99.955%)
Hypothesized intercept: 0.523599 [pi/6]
Least squares intercept: 0.523167 (99.918%)
Standard deviation: 0.996796
I'll have the graph of log(1-CHI) vs. log(radius) on the Web tomorrow. Quartz has 2.7 times as many atoms/volume as tellurium. The overall goodness of fit is astounding given the standard deviation is 11.24% of log(1-CHI) range.
Quartz reduces the cost of 3-cm diameter test masses from that of two airport bomb scanners (tellurium) to that of two quality propane barbecues. For both tellurium and quartz, calculated test mass CHI = 1 - ~10^(-15). That is adequately close to theoretically perfect CHI=1.
I don't care if it is wildly different from 400 years of expert opinion. I don't care who doesn't like the taste of it. I have published ab initio math that gives an extremal solution to a new test mass variable. Existing qualified apparatus can run inexpensive parity pair test masses. The proper test of theoretical spacetime geometry is calculated test mass geometry.
The worst the parity Eotvos experiment can do is fail. That puts it squarely on the curve of the best researcher's best efforts. Because it is radically different it might succeed. Somebody should look.
The only academic mathematician I know who can make a definitive call on Noether is weirder than a snake's suspenders, having quietly turned down a MacArthur Fellowship. I'm working on it.
--
Uncle Al
http://www.mazepath.com/uncleal/eotvos.htm
(Do something naughty to physics)
Re: Noether theorem vs. Runge_Lenz (cont'd) Uncle Al 30/5 12:19
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