Hadron Mass Spectrum From First Principles
Robert L. Oldershaw
Kerr relation between M, J and G:
J = aGM2/c.
If you solve for M and treat "a" as a quantized parameter
[= ...2, 1, 1/2, 1/3/ 1/4,...], and if you set the proton mass
as the n=1 mass, then you can predict the masses of Pion,
K, eta, Xi, Omega, D , D(s), Lambda(c) at the 85% to 95% level.
Fits are at the 95% level for M > proton mass.
Given that the Kerr formula is a very rough approximation
which neglects the effects of EM, these results seem promising.
If anyone thinks this is worth pursuing, I will be happy to
provide a more detailed derivation of the hadron masses.
Maybe something new for a new decade and a new century?
Robert L. Oldershaw
wrote:
>
The problem set up yesterday has been taken
one step further and has a much improved set
of solutions.
We propose that the masses of subatomic particles
can be retrodicted approximatey [1st approx.] using
a Kerr solution of GR.
Basic equation is: J = aGm^2/c
Rearrange, assume a = 1/n, assume unit J = 1/2 hbar.
You get M(n) = [n]^1/2 [constant]. Think it through.
The [constant] = the corrected Planck mass [= 674 Mev],
which I have showed you how to calculate several times.
Or see: http://arxiv.org/ftp/astro-ph/papers/0701/0701006.pdf
Then:
Planck mass: n=1
proton : n=2
Xi: n=4
Omega(-): n=6
D: n=8
D(s): n=10
Lambda(c); n=12
KAON: n=1/2
PION: n=1/25
I think we are now uniformly at the 90-95% level
after two 45 minute efforts.
Is nature not the most magnificent perfection!
Big fun for any scientist who wants to join in,
RLO
www.amherst.edu/~rloldershaw
Robert L. Oldershaw
wrote:
>
Add the muon to the list: n=1/36 [yes, I know it's a lepton].
Agreement at 93% level, I think.
------------------------------------------------------------------------------
BTW, CDMS laid a real "DM" stink bomb today.
2 "WIMPS" at the 75% level?????
2 background false positives at 99.9999% is more likely.
RLO
www.amherst.edu/~rloldershaw
Robert L. Oldershaw
wrote:
>
I did a more careful comparison of the theoretically
"predicted" masses and the empirically measured
mass values for 11 of the most well-known particles.
The retrodictive agreement ranges from 94% to 99.9%,
with an average agreement of 97.1%
For a 1st approximation test with the Kerr solution
that is probably as good as it gets. When the full
Kerr-Newman solution is tested in this way I expect
even more remarkable results.
I also expect to get almost no encouragement from
the physics community. To be realistic, I can predict
substantial hostility. This will not stop me, or the
coming of the new paradigm.
RLO
www.amherst.edu/~rloldershaw
Robert L. Oldershaw
wrote:
>
Here's the predicted response from a pseudo-physicist.
--------------------------------------------------------------------------
RLO: Look, I really do not mean to discourage you.
But before you waste more of your time you might
want to think about what I said. It is not much of a
surprise that, if you take all the particles in the particle
data booklet, elementary or not elementary, you can
find some "almost-regular" series for some of them,
that "reproduces" some of the masses to some accuracy.
That's a numerical game, not science. To make it science
you'll have to reproduce ALL particle masses. And that still
wouldn't be a prediction, but a postdiction. And if you do so,
please go an publish it in Nature and not on this blog.
Sabine Hossenfelder, fud
---------------------------------------------------------------------------
Here is my response:
Dr. H, [here I use the term very loosely]
Look, the General Relativity-based model I am working
with already does better than QCD. In less than two hours
one person is retrodicting particle masses with one simple
formula.
QCD has had decades to perfect its Ptolemaic model,
and 1000s of grunts "adjusting" it into conformity, and
it still takes multiple supercomputers working for days to
gets results that I can do in an afternoon with paper
and pencil.
You got that straight? Or do I need to spell it out more
clearly for you?
Obviously there are precious few open-minded thinkers at your
self-admiration society, so I will not waste my time further there.
Enjoy your pseudoscience. You richly deserve it.
Sincerely,
RLO
www.amherst.edu/~rloldershaw
Robert L. Oldershaw
wrote:
>
If you don't mind I'll get back to the science of this thread.
Kerr solution: J = aGM^2/c
m(n) = [n]^1/2 [constant], i.e., sqrt[n] [constant]
where: a = 1/n and
constant = corrected Planck mass = 674 Mev
-n----n]^1/2[constant]----Empirical mass---Agreement
1/36------112.3------muon 105.7------------94.0 %
1/25------134.8------pion 134.98-----------99.9 %
1/2--------476.6-----kaon 497.7-------------95.8 %
3/4--------583.7-----eta 547.8--------------93.4%
1----------674---------Planck mass-------- -----
2----------953.2-------proton 938-------------98.3 %
2----------953.2-------neutron939.2?--------98.5%
2----------953.2-------eta' 958--------------99.5 %
3--------1167.4-------Lambda 1115.7------95.4 %
3--------1167.4-------Sigma 1192----------97.9 %
4--------1348.0-------Xi 1314.8------------97.5 %
5--------1507.1-------N ~ 1450------------96.1 %
6--------1651---------Omega 1672.5-------98.7 %
7--------1783---------TAU 1784.1---------99.95%
8--------1906.3-------D 1864.-------------97.8 %
10------2131.4-------D(s) 2112.2-----------99.1 %
12------2334.8-------Lam(c)2284.9---------97.8%
Well, that is the 16 most common and stable of the
particles observed, with the exception of the electron
which has n = 1/(1319)^2 and I want to study that a
bit more. Maybe only a full K-N solution will suffice here.
My argument is that this high degree of ordering
demands an explanation. The fact that it was achieved
with the admittedly very approximate Kerr solution
makes things even more interesting. The fact that
Discrete Scale Relativity is definitively required to
determine the crucial value of the corrected Planck
mass should be fully appreciated.
Barking dogs may now start barking.
Scientists will undoubtedly start thinking.
Happy Winter Solstice [33rd anniversary of DSR]
Robert L. Oldershaw
www.amherst.edu/~rloldershaw
Sjouke Burry
> On Dec 18, 11:39 pm, "Robert L. Oldershaw" <rlolders...@amherst.edu>
> wrote:
> If you don't mind I'll get back to the science of this thread.
>
> Scientists will undoubtedly start thinking.
About fractals?? This thread sounds like a couple of trolls
abusing a fractal news site.
Robert L. Oldershaw
wrote:
>
> About fractals?? This thread sounds like a couple of trolls
> abusing a fractal news site.
Mr Burry,
The 12/21/09 analysis showing good agreement between 16 subatomic
particle masses and the expectations based a Kerr solution are:
(1) Based on a discrete fractal paradigm for nature, and
(2) Require the fractal scaling of the paradigm for any degree of
success.
What is not fractal enough for you? Would you prefer mediocre graphics
that mostly advertise the dubious artistic taste and limited
creativity of their makers?
Robert L. Oldershaw
wrote:
On the morning of 12/21 I was playing around with the basic
Kerr relation between M, J and G:
Kerr solution: J = aGM^2/c
One can rearrange terms and get this simple equation.
m(n) = [n]^1/2 [constant], i.e., sqrt[n] [constant]
where: a = 1/n and
constant = corrected Planck mass = 674 Mev
The [constant] = the corrected Planck mass [= 674 Mev],
See: http://arxiv.org/ftp/astro-ph/papers/0701/0701006.pdf
for a derivation of this constant.
--------------------------------------------------------------------
Retrodictive Test
So we can perhaps understand Regge trajectories and
the particle mass spectrum using only 4-d GR + classical EM
+ DSR. No need of extra dimensions, strings, or other epicycles.
Happy Winter Solstice [33rd anniversary of DSR]
Robert L. Oldershaw -
www.amherst.edu/~rloldershaw
Robert L. Oldershaw
wrote:
> On Dec 21, 1:01 pm, "Robert L. Oldershaw" <rlolders...@amherst.edu>
> wrote:
>
> On the morning of 12/21 I was playing around with the basic
> Kerr relation between M, J and G:
>
That's Schwarzschild radius, dear editor
[of Advanced Physics Forums], not "Swartzchild".
And yes I understand the Schwarzschild radius
quite well, thank you.
There is no scientific proof that the value of G
in the subatomic realm is the same as the macroscopic
Newtonian value. Rather it has always been ASSUMED
that they are the same. If G in the subatomic realm is
different from the Newtonian value then the Planck mass
is changed since the Planck is defined as the
sqrt of [h-bar times c divided by G].
We have been through this before. If you want to take
the conventional Planck mass as absolute received wisdom,
feel free to do so. But be aware that this has not
been scientifically tested.
What I have done is to show that if G scales in a
discrete self-similar manner, then theoretical physics
becomes orders of magnitude more simple. Not to
mention the fact that you can retrodict the subatomic
mass spectrum, resolve the vacuum energy density crisis,
explain the meaning of the fine structure constant for the
first time in history, ... .
For science to progress, theoretical physicists
must be willing to question their ASSUMPTIONS.
Yours in science
Robert L. Oldershaw
www.amherst.edu/~rloldershaw
Robert L. Oldershaw
<rlolders...@amherst.edu> wrote:
> > On Dec 21, 1:01 pm, "Robert L. Oldershaw" <rlolders...@amherst.edu>
> > wrote:
>
of the retrodiction of subatomic particle masses [100 - 6400 Mev].
Now about 20 particles.
RETRODICTING THE SUBATOMIC PARTICLE MASS SPECTRUM
FROM FIRST PRINCIPLES
Basic relationship for J [angular momentum.],
M [mass] and a [dimensionless spin parameter]
of a Kerr black hole (McClintock et al, 2007):
J = aGM^2/c
Rearrange:
M = (Jc/aG)^1/2
Note: For a = 1, the above equation resembles
the definition of the Planck mass.
Assume that a = 1/n, where n = 1, 2, 3, … and
that the unit J = ћ.
Then:
M(n) = (nћc/G)^1/2 = (n)^1/2 (ћc/G)^1/2 =
(n)^1/2 (Planck mass).
A crucial next step is to determine the correct value
of (ћc/G(−1))^1/2, the Planck mass.
This requires Discrete Scale Relativity:
[ http://arxiv.org/ftp/physics/papers/0701/0701132.pdf ]
which can be used to determine that the G(−1) that applies
in the case of Atomic Scale systems is 2.18 x 10^31 cgs.
Putting G(−1) into the Planck mass formula:
M = (ћc/G(−1))^1/2 = 674 Mev.
With this revised Planck mass based on
Discrete Scale Relativity we may now calculate
a first approximation of the subatomic particle
mass spectrum based on the assumption that
the particles are Atomic Scale Kerr ultracompacts.
Of course, it is expected that a more exact [2nd order]
retrodiction of the subatomic particle mass spectrum
will require the full Kerr-Newman solution of the
Einstein-Maxwell equations.
Based on the 1st approximation Kerr solution results
presented below, we may predict that the actual
subatomic particle masses are eigenvalues of the
Kerr-Newman solution of the Einstein-Maxwell equations.
n————[n]^1/2—-[n]^1/2 [674 Mev]—-Particle/mass—-Agreement
1/36—−0.1666——–112.3—————−105.66————94%
1/25—−0.2000——– 134.8—————−134.98————99.87%
1/2—–0.7071——– 476.59—————497.65————95.77%
3/4—–0.8660——– 583.70—————547.75————93.44%
1——−1.0000——– 674.00————M/ 674————— —
2——−1.4142——– 953.18———–p+/ 938—————98.34%
2——−1.4142——– 953.18————n/ 939.27————98.50%
2——−1.4142——– 953.18————n’/ 958—————99.5%
3——−1.7320——–1167.40———–/ 1115.68————95.36%
3——−1.7320——– 1167.40———–/ <1192>————97.90%
4——−2.0000——– 1348.00———–/ 1314.83————97.48%
5——−2.2360——– 1507.11———–N(1440)/<1450>——~ 96.06%
6——−2.4495——– 1650.96———–/ 1672.45————98.72%
7——−2.6458——– 1783————–/ 1784.1————−99.95%
8——−2.8284——– 1906.34———–D0/ 1864.6———–97.76%
10——3.1623——– 2131.39———–Dsi/ 2112.1———–99.09%
12——3.4641——– 2334.80———–/ 2284.9————–97.82%
14——3.7417——– 2521.91———–/ <2522.75———-~ 99.97%
16——4.0000——– 2696.00———–/ 2697.5—————99.94%
64——8.0000——– 5392.00———–Bji/ <5313.25>——-~ 98.52%
90——9.4868——– 6394.13———–Bci/ <6400>———-~ 99.91%
Note: particle symbols would not translate correctly.
Full file as a pdf available upon request.