*** Phillip Helbig Wrote ***
[Moderator's note: . . . Science depends on testable, quantitative
predictions (but, if done properly, retrodictions are almost as good).
Jay has provided those. I think further discussion of this very
technical but "important if true" matter should address the numbers. If
the numbers don't follow from the theory, then this should be pointed
out. If the numbers agree, then something is interesting. I think it
is clear that the agreement is too good to be a coincidence. The
interesting question is whether they follow unambiguously from
unquestionable principles. Further discussion on this topic is OK, but,
in order to move on, needs to be quantitative. -P.H.]
*** Jay now writes ***
Phil, I appreciate your turning the discussion back to where it belongs. I
have not thus far had anybody actually comment on the merits of my
retrodictions (a better word to characterize what I have done than
predictions), which takes some work beyond looking at dates or looking at
journal names or where the preprints are posted or looking at other extraneous
indicators that dodge doing a serious review.
To help people get a better handle on my research, I will try to talk about
this within the framework you lay out above. I especially want to discuss how
to approach my paper at
http://vixra.org/pdf/1212.0165v4.pdf, because out of
all four papers I have written, that is likely to become the single most
important one.
The Galilean scientific method links together theory and observation in an
unbreakable, complementary, Yin and Yang. Sometime one starts with a theory
and predicts observed data. Other times one starts with observed data and
fashions a theory to explain the data, which is retrodiction. And at other
times still, one simply takes data and systematically characterizes that data,
leaving it for the future to build a theory around the characterization of the
data. And in reality, scientific method often mixes all of these without
clear bright lines. Let me give some historical examples, then let me put my
work into that historical methodological context.
First example: Keppler observed the movement of the planets and characterized
what he observed via the "equal areas in equal times" law. One could call
that a "theory" of planetary movement, but I prefer to thinks of this as a
systematic "characterization." When Newton came along and realized that
Keppler's characterization could be explained by an inverse-square "force"
which had the same meaning as the force F=ma that Newton had developed for
terrestrial events, we had for first time a "theory" that retrodicted the
planetary motions that Keppler had characterized, and tied them to phenomena
beyond their original origin. Then Einstein did Newton one better by making
Newton's theory a consequence of geometric curvature induced by gravitational
= inertial mass. From the theory which Einstein now had, other predictions
became possible, including perihelion precession, and gravitational light
deflection, and black holes, and cosmic expansion and the like. These were
true *pre*dictions (though the perihelion, if I recall correctly, was a
retrodiction).
Second example: Planck in 1901 had in front of him a blackbody radiation
curve from empirical data. Like Keppler, Planck characterized that curve, and
found that the means for doing so was an energy E=nhf which was quantized.
This was analogous to Keppler's area law. Then Einstein comes along four
years later and uses this to explain photoelectric effect and theorizes that
light and energy comes in discrete quantum packets. Now we had a "theory"
rather than a "characterization," and the 20th century quantum revolution was
off to the races.
Final example: before 1905 Lorentz already had a "Lorentz transformation"
between space and time which characterized what had been observed, but again,
it was Einstein who turned it into a theory of measurement and kicked off the
relativistic (and really the invariance and symmetry) revolution that also
runs through the 20th century alongside of the quantum revolution.
Now let me turn to my own work, and how various aspects fit onto this sort of
framework connecting theory to characterization to empiricism, and prediction
with retrodiction.
In my first paper at
http://jayryablon.files.wordpress.com/2013/03/hadronic-journal-volume-35-number-4-399-467-20121.pdf,
I start totally with theory: that the non-vanishing magnetic monopoles which
come about in Yang-Mills (non-Abelian gauge) theory are baryons, which means
that protons and neutrons are particular, and the most pervasive types of,
non-Abelian magnetic monopoles. If you do not want to wade through all 67
pages of this first paper, then please read the introduction of my second
paper at
http://vixra.org/pdf/1212.0165v4.pdf. That introduction summarizes
in 2.5 pages, the entire 67 pages of the first paper, and does so at level
that should be understandable and easy to assimilate. Now, let me boil that
down even further.
My underlying theory is based entirely on four ingredients: 1) Maxwell's
classical equations, 2) Yang Mill gauge theory, 3) Dirac's theory of fermions,
and 4) Fermi-Dirac-Pauli exclusion -- that each fermion in a system must be in
a distinct quantum state with a unique quantum number. I am very conservative
here. Each of these four ingredients is solidly-grounded and
universally-accepted. In Phil's terminology, they are "unquestionable
principles." As a patent attorney, I often tell my clients that most patents
entail "novel combinations of known elements." My theory is entirely a novel
combination of the known elements, and I do not think there is anyone who will
argue against Maxwell, Dirac, Yang-Mills and fermion exclusion as
exceptionally solid and very conservative and well-tested foundations.
So in paper 1 I take Maxwell's electric charge equation, invert it, combine
that with Dirac, and insert that into the Maxwell's magnetic monopole equation
for a Yang-Mills gauge field which makes the monopoles non-vanishing. This
combination reveals that the monopole is a system of exactly three fermions.
So I require exclusion, I use SU(3) to enforce the exclusion, I name the
eigenstates R, G, B as in QCD, and am then able to *derive* QCD as a
consequence. These monopoles contain three colored quarks and have all the
symmetry characteristics of baryons. Whatever they emit and absorb, in turn,
have all the required symmetry characteristics of mesons. Following further
development to show that these monopoles are stable, I derive the special
cases of monopoles which have the required quantum numbers for a proton and
for a neutron. Then I do an analytical calculation of the energies of the
proton and neutron monopoles to see if the resulting energies bear any
resemblance to energies that one associates with the protons and neutrons
observed in the laboratory. So that concludes step 1 of the theoretical /
observational Yin-Yang.
Now that this point, which brings me to sections 11 and 12 of the first paper,
I truly have no idea what energy numbers I am going to derive for these
magnetic monopoles. As I do these energy calculations, I am at risk that the
eight-plus years I have spent working on the thesis that baryons are magnetic
monopoles (I first made the conceptual discovery in December 2004 after a few
drinks at a friend's 50 birthday party) will be a big bust, because I will
obtain energies that make no sense. But I know that I am ignoring the Fermi
vacuum and turning off perturbations so what I am expecting to get are the
very bare energies of the proton and neutron and not their observed energies,
and I have no a priori idea what these bare energies numbers will be. I am at
the mercy of the mathematical calculation.
So I do the calculation and I find out that 1) using the mean up and down
quark masses form PDG, the difference between the bare neutron mass and the
bare proton mass is equal to the observed electron rest mass to within 3%.
That seems to make very good sense that if you stripped out all the vacuum and
interaction effects, the neutron and proton masses should differ by the
electron mass. So, having dodged the bust, I feel somewhat encouraged to
explore further. So next I find out that 2) the neutron and the proton each
have an predicted energy that is less than 20% of the sum of their quark
masses. At first I am perplexed. So, I then calculate these mass
deficiencies, and find that the mass deficiency is about 7.64 MeV for the
proton and about 9.81 MeV for the neutron. Which means if I have a system
with an equal number of protons and neutrons, the average mass deficiency is
about 8.73 MeV per nucleon.
At this point I am playing Keppler or Newton or Planck, putting myself at the
mercy of the data, and working from there to develop a theory about the data
wherever I can, and to simply characterize the data wherever I can't theorize.
The first thing I do is go look at the per-nucleon binding charts, which you
can find by the dozens at
http://www.google.com/search?q=nuclear+binding&hl=en&qscrl=1&rlz=1T4TSNF_enUS453US454&tbm=isch&tbo=u&source=univ&sa=X&ei=lhxzUfOCPPKx0QGD3ICoCQ&ved=0CEwQsAQ&biw=1600&bih=714.
And I see that my 8.73 MeV per nucleon prediction is a perfect retrodiction to
nuclear binding energies at are observed. So while I did not know a priori
what energies I would derive for the proton and neutron magnetic monopoles,
now I conclude based on this very close concurrence, that the energies I have
derived are related in some way to nuclear binding energies. But not every
nuclide has an 8.73 MeV per nucleon binding energy, rather, this represents a
maximum that is most closely approached by ^56Fe. Doing the calculation, I
see that ^56Fe gets 99.84% of the way toward using *all* of this energy for
binding. And I see that all other nuclides get up to less than this 99.84%.
So the other thing I realize is that this plays hand in hand with quark
confinement: this is a *latent* binding energy that is *available* for nuclear
binding, but depending on the nuclide, some or most of this energy may also be
retained to confine the quarks within each nucleon, with the balance released
as fusion energy to bind the nucleons into nuclides. The confinement energy
is on a "see saw" with the nuclear binding energy. Again, here I am driven by
the data. If the energy deficiency had been 2 MeV, or 35 MeV per nucleon, I
would not be talking or thinking about binding energies. But when the energy
number predicted turned out to be 8.73 per nucleon, it became clear that I
needed to be studying and thinking about binding energies.
So the next question of course is how to understand the binding energies of
*particular* nuclides. Because ^2H is the simplest, being just a proton plus
a neutron, I start there. I already knew from PDG data that the current mass
of the up quark is 2.3 +.7 / -.5 MeV. And now that I am on the hunt for
binding energies, I also find out that the deuteron binding energy is 2.224566
MeV, which is within the experimental errors for the up quark mass. So now I
am at a crossroads. I ask myself whether the up current mass and the deuteron
binding energy might be the same, or at least very, very close to the same,
energies. Again, I am playing Keppler or Planck -- just the data, please.
But I also know I need to play a bit of Newton and have a theory for this. So
I think about Bohr and the early quantized electron orbital models and fitting
harmonics into a cavity and surmise that perhaps the masses of the quarks
inside a proton or a neutron are the driving factors that determine the
energies at which they bind, and that the nucleons and nuclides are best
thought of as "resonant cavities." This is now a hypothesis that I have
developed about the numeric data I am seeing, and now the goal is to see if
this hypothesis can be confirmed by enough other empirical data to be promoted
to a real theory. If so, then my original theory that baryons including
protons and neutrons are Yang-Mills magnetic monopoles has a new aspect,
namely, that the protons and neutrons are resonant cavities that emit and
absorb binding energies based on the current masses of the quarks they
contain. And that, in a nutshell, is where I find myself living at the end of
my first paper.
So my second paper at
http://vixra.org/pdf/1212.0165v4.pdf is where I seek to
develop and confirm this resonant cavity aspect of the theory, and I do so by
seeing if this same idea can be used to get the ^3H, ^3He and ^4He binding
energies. If I can do so, then I would have good confirmation that protons
and neutrons are particular types of Yang-Mills magnetic monopoles which do
indeed emit and absorb energies which are based on the current masses of their
quarks. What makes this paper most important is that it is designed to use
empirical data to confirm the theory beyond reasonable doubt. Let me see if I
can boil this down as well.
Basically, there are three main mass numbers which are ingredients of the 8.73
MeV per nucleon binding energies found in the first paper: m_u, m_d, and
sqrt(m_u * m_d). The up mass, the down mass, and the square root of their
product which is also a mass number. (Newton first taught that m_1 * m_2 is
an important number and of course its square root is also a mass of interest.)
And, what I realize is that these mass numbers originate in a pair of 3x3
diagonal matrices which I will call K, one for the proton P with udd, and one
for the neutron N with duu, which are (my fourth paper at
http://vixra.org/pdf/1302.0046v4.pdf develops these as Koide matrices, and
uses these to retrodict the observed neutron and proton masses, fully as
observed):
diag (K_P) = (sqrt(m_d), sqrt(m_u), sqrt(m_u)) (1)
diag (K_P) = (sqrt(m_u), sqrt(m_d), sqrt(m_d)) (2)
as well as taking inner and outer product of these matrices, as well as a
factor of (2pi)^1.5 which came from my first paper due to Gaussian integration
in three spacetime dimensions. So I simply set out to match up all of the
^3H, ^3He and ^4He binding energies, but I restrict myself to using *only* the
three mass numbers m_u, m_d, and sqrt(m_u * m_d), low-integer (e.g., 2, 3, 4)
multiples of these, these with a suitable (2pi)^1.5 divisor, and the electron
mass, all within the context of the matrices (1), (2).
Then, I do find a way to indeed construct each of the the ^3H, ^3He and ^4He
binding energies from only these ingredients, and I also obtain the neutron
minus proton mass difference in the same way, and in all cases, my accuracy is
to about parts per million. (For the neutron minus proton mass difference I
end up at parts per ten million).
So now, let me return to Phil's points, and comment very specifically:
"If the numbers don't follow from the theory, then this should be pointed
out."
I agree. But believe me, you will find that the numbers do follow from the
theory. ***I will bet you the farm on that.***
"If the numbers agree, then something is interesting. I think it is clear
that the agreement is too good to be a coincidence."
I am course advocate that the agreement is too good to be a coincidence, and
that consequently, this is something interesting.
"The interesting question is whether they follow unambiguously from
unquestionable principles."
Excellent question, let's go to it. The principles are unquestionable: 1)
Maxwell's classical equations, 2) Yang Mill gauge theory, 3) Dirac's theory of
fermions, and 4) Fermi-Dirac-Paul exclusion.
The point of discussion I will now explore is about following "unambiguously."
The energy number of 8.73 MeV per nucleon follows unambiguously. The matrices
(1), (2) follow unambiguously. So too do the three mass numbers m_u, m_d, and
sqrt(m_u * m_d).
Going from here to a discussion of nuclear binding is based on it making sense
that an 8.73 MeV per nucleon deficiency looks like a binding energy based on a
Kepplerian or Planckian analysis of this numeric result, because that is what
the empirical binding data shows, and as Phil says, "science depends on
testable, quantitative predictions." Again, if the energy deficiency had been
2 MeV, or 35 MeV per nucleon, I would not be talking or thinking about binding
energies. But a calculated, predicted number of 8.73 MeV per nucleon, which
shows up as an *energy deficiency*, in magnetic monopoles that have all the
theoretical properties of protons and neutrons, lends itself with a very high
degree of credibility to being a binding energy in some way.
Now, from here, I am really playing pure Keppler as to the ^3H, ^3He and ^4He
binding energies and the neutron minus proton mass difference (also an energy
number). The *only* thing I will claim is that I have successfully
retrodicted all of these numbers restricting while myself *only* to m_u, m_d,
and sqrt(m_u * m_d) as outlined above. What I find within parts per million
are the following binding energies:
^2H: m_u
^3H: 4m_u -2 sqrt(m_u*m_d)/(2 pi)^1.5
^3He: 2m_u + sqrt(m_u*m_d)
^4He: latent binding energy for ^4He, minus 2 sqrt(m_u*m_d)
m_n - m_p: m_u -(3m_d +2 sqrt(m_u*m_d) -3m_u)/(2 pi)^1.5
Each of these binding numbers can be represented as the components of a
3x3x3x3 Yang-Mills outer product matrix. This leads me to believe that trying
to see how various binding energies fit into this matrix is a very useful and
interesting exercise that has high relevance to empirical data. As to whether
this is "unambiguous," the sole ambiguity is as follows: I cannot, today,
tell you why the first term in ^3H is 4m_u rather than 2m_u. Or why ^3H has
the (2 pi)^1.5 factor. Like Keppler and the area law, I am merely
*characterizing* this data. As we come to understand a wider part of the
binding data -- go to Li, Be, B, C, N, O, F, Ne and so on -- we may start to
see wider patterns which make us say "aha, now I see why those binding
energies are what they are." Maybe I will have that aha. Maybe someone else
will. That is how science progresses. That is the next step of Newton saying
"aha, there is an inverse square force, and that is the same as the force in
my F=ma."
So what I will claim in the second paper at
http://vixra.org/pdf/1212.0165v4.pdf is to have successfully retrodicted the
2^h, ^3H, ^3He and ^4He binding energies and the neutron minus proton mass
difference each to parts per million generally, based on the unquestionable
principles of 1) Maxwell's classical equations, 2) Yang Mill gauge theory, 3)
Dirac's theory of fermions, and 4) Fermi-Dirac-Paul exclusion, based on the
eminently sensible conclusion that a 8.73 MeV per nucleon energy deficiency
sure looks like a binding energy based on empirical data, and based thereafter
on a purely Kepplerian approach of characterizing observed binding data based
on the limited number of masses m_u, m_d, and sqrt(m_u * m_d) which my theory
makes available for me to use to do so.
Jay