Predicting the Proton and Neutron Masses, Based on Baryons which are Yang-Mills Magnetic Monopoles and Koide Mass Triplets

[Jay R. Yablon]

Dear Friends:

At the link http://vixra.org/abs/1302.0046 you may find a new paper I just
wrote titled “Predicting the Proton and Neutron Masses, Based on Baryons which
are Yang-Mills Magnetic Monopoles and Koide Mass Triplets.” In the next day
or two I expect to submit it for journal review and publication.

In this paper I have woven together the Koide relationships with my own thesis
that baryons are Yang-Mills magnetic monopoles, after noticing that my thesis
was spinning out relationships that were identical in form to terms in the
Koide relationships. This paper does four things that I know Koide followers
will be interested in, and one very important thing I have been pursuing for a
very long time:

Insofar as the Koide relations, I have shown 1) how to recast these into a
statistical formulation involving the variance of the Koide terms in each
generation, which 2) yields some new relationships and in particular spins out
Koide relations for the neutrinos, the up quarks, and the down quarks which I
do not believe have been seen before (please correct me if I am mistaken).
Also, 3) I have shown how to recast the Koide relationships into a Lagrangian
/ energy formulation, which addresses the question as to underlying origins of
these relationships, so that they are not just curious coincidences, but
rooted in fundamental, physics principles. Finally, 4) as to the issue of
negative signs for some of the square roots in Koide relations (e.g., for the
csb triplet), I take these negative signs and raise you: to complex
coefficients.

In terms of my interest, the Koide relationships in synergy with my own recent
work provide the tools needed to predict the proton and neutron masses to six
parts in 10,000 as a function of the up and down quark masses and the Fermi
vev, only. Then, I take a naturally emergent phase (which is what gives us
complex Koide coefficients in point 4 above) and show how this phase can be
used to dial out the .06% gap between the predicted and empirical proton and
neutron masses to unlimited precision. For reasons I outline in the paper, I
believe that the phase I have stumbled upon here, is very much related to the
CP violating phase that emerges from weak mixing of three fermion generations.

I think / hope you will enjoy this paper.

Best regards,

Jay
_________________________________________________
Jay R. Yablon
910 Northumberland Drive
Schenectady, New York 12309-2814
Phone / Fax: 518-377-6737
Email: jya...@nycap.rr.com
Co-moderator: sci.physics.foundations
Blog: http://jayryablon.wordpress.com/

[Jay R. Yablon]

To all:

The paper discussed below was just accepted for publication in the Journal of
Modern Physics, Special Issue on High Energy Physics, which will go to press
in April 2013!

Best regards,

Jay

"Jay R. Yablon" wrote in message news:ankhnt...@mid.individual.net...

Dear Friends:

At the link http://vixra.org/abs/1302.0046 you may find a new paper I just
wrote titled

“

Predicting the Proton and Neutron Masses, Based on Baryons which
are Yang-Mills Magnetic Monopoles and Koide Mass Triplets.

â€

[Moderator's note: Please post only 7-bit printable ASCII or, at worst,
8-bit corresponding to ISO-8815-1 or ISO-8815-15. Anything else will be
garbled and look like the above to many readers or won't be visible at
all if the moderator removes it. -P.H.]

[Alfred Einstead]

On Feb 10, 5:47 am, "Jay R. Yablon" <jyab...@nycap.rr.com> wrote:
> At the linkhttp://vixra.org/abs/1302.0046you may find a new paper I just

> wrote titled “Predicting the Proton and Neutron Masses, Based on Baryons which
> are Yang-Mills Magnetic Monopoles and Koide Mass Triplets.” In the next day
> or two I expect to submit it for journal review and publication.

As you're probably aware, AO Barut was well-known for messing around
with relativistic many-body dynamics (which, given the Leutwyler "no
interaction" theorem is saying a lot). One of his directions of
research was to push the idea of an anomalous magnetic moment for the
neutrino and then use it to construct bound leptonic states whose mass/
energy spectra mimicked the hadron spectrum.

The main reason this never picked up is because there is no well-
established formalism for relativistic many-body dynamics! The
Leutwyler Theorem puts severe restrictions on its very existence. So,
to scale this up to a full-fledged formalism; possibly even one that
could reconstruct the weak and strong forces from electromagnetism +
Barut's magnetic moment; requires getting the interaction issue
resolved.

In quantum theory, of course, the problem is worse since the Haag
Theorem (= the quantized version of the Leutwyler Theorem) puts severe
restrictions on the very existence of an interaction picture. So a
particle-based quantized theory that incorporates Barut's ideas (as
well as vacuum polarization!) was never yet forthcoming.

[Jay R. Yablon]

"Alfred Einstead" wrote in message
news:fe97a044-7131-4f25...@q6g2000yqa.googlegroups.com...

On Feb 10, 5:47 am, "Jay R. Yablon" <jyab...@nycap.rr.com> wrote:
> At the linkhttp://vixra.org/abs/1302.0046you may find a new paper I just

> wrote titled ???Predicting the Proton and Neutron Masses, Based on Baryons
> which
> are Yang-Mills Magnetic Monopoles and Koide Mass Triplets.??? In the next

> day
> or two I expect to submit it for journal review and publication.

As you're probably aware, AO Barut was well-known for messing around
with relativistic many-body dynamics (which, given the Leutwyler "no
interaction" theorem is saying a lot). One of his directions of
research was to push the idea of an anomalous magnetic moment for the
neutrino and then use it to construct bound leptonic states whose mass/
energy spectra mimicked the hadron spectrum.

The main reason this never picked up is because there is no well-
established formalism for relativistic many-body dynamics! The
Leutwyler Theorem puts severe restrictions on its very existence. So,
to scale this up to a full-fledged formalism; possibly even one that
could reconstruct the weak and strong forces from electromagnetism +
Barut's magnetic moment; requires getting the interaction issue
resolved.

In quantum theory, of course, the problem is worse since the Haag
Theorem (= the quantized version of the Leutwyler Theorem) puts severe
restrictions on the very existence of an interaction picture. So a
particle-based quantized theory that incorporates Barut's ideas (as
well as vacuum polarization!) was never yet forthcoming.

**** Jay Writes ****

You make some very interesting points. Back in December through February when
I was trying the obtain my eventual predictions specifically about binding
energy and the proton and neutron mass, I got hung up and on thought that I
would have to do an analysis for the nuclides -- and even of each nucleon --
as a many-body system. I poked around in the literature and even starting
drawing up models of how to do that.

Fortunately, I found in the end that the Yang-Mills tensors I had discovered
could be used to get extremely tight parts-per-million predictions of binding
energies even without having to do the many-body problem. Tensors are
remarkable things, in that way.

While I do not know the ultimate answer, I am now starting to think that the
binding energy and proton and neutron mass results I obtained and the tensor
of which they are components might contain some clues that allow us to
"backtrack" into a better way to model these many-body systems.

That is, where I thought at first I would need to solve a many-body system to
find binding energies, I now wonder -- working backwards -- if the binding
energies I already have derived to parts per million accuracy can give use
some clues about how to solve multi-body systems.

Physics is always a work in progress!

Jay

[Jos Bergervoet]

On 4/14/2013 3:11 AM, Jay R. Yablon wrote:
> "Alfred Einstead" wrote in message
>

>> The main reason this never picked up is because there is no well-
>> established formalism for relativistic many-body dynamics! The
>> Leutwyler Theorem puts severe restrictions on its very existence. So,
>> to scale this up to a full-fledged formalism; possibly even one that
>> could reconstruct the weak and strong forces from electromagnetism +
>> Barut's magnetic moment; requires getting the interaction issue
>> resolved.
>>
>> In quantum theory, of course, the problem is worse since the Haag
>> Theorem (= the quantized version of the Leutwyler Theorem) puts severe
>> restrictions on the very existence of an interaction picture. So a
>> particle-based quantized theory that incorporates Barut's ideas (as
>> well as vacuum polarization!) was never yet forthcoming.

...

> Fortunately, I found in the end that the Yang-Mills tensors I had discovered
> could be used to get extremely tight parts-per-million predictions of binding
> energies even without having to do the many-body problem. Tensors are
> remarkable things, in that way.

Can you now disprove Haag's theorem?

> While I do not know the ultimate answer, I am now starting to think that the
> binding energy and proton and neutron mass results I obtained and the tensor
> of which they are components might contain some clues that allow us to
> "backtrack" into a better way to model these many-body systems.
>
> That is, where I thought at first I would need to solve a many-body system to
> find binding energies, I now wonder -- working backwards -- if the binding
> energies I already have derived to parts per million accuracy can give use
> some clues about how to solve multi-body systems.

Can you explain why your results should have anything
to do with the many-body systems discussed here, when
you say you did not solve many-body systems? How can
you be sure that it is more than numerology?

--
Jos

[Jay R. Yablon]

[Moderator's note: Attributions corrected (hopefully correctly). -P.H.]

"Jos Bergervoet" wrote in message
news:516ad696$0$2599$e4fe...@news2.news.xs4all.nl...

> On 4/14/2013 3:11 AM, Jay R. Yablon wrote:
> > "Alfred Einstead" wrote in message
> >
> > > The main reason this never picked up is because there is no well-
> > > established formalism for relativistic many-body dynamics! The
> > > Leutwyler Theorem puts severe restrictions on its very existence. So,
> > > to scale this up to a full-fledged formalism; possibly even one that
> > > could reconstruct the weak and strong forces from electromagnetism +
> > > Barut's magnetic moment; requires getting the interaction issue
> > > resolved.
> > >
> > > In quantum theory, of course, the problem is worse since the Haag
> > > Theorem (= the quantized version of the Leutwyler Theorem) puts severe
> > > restrictions on the very existence of an interaction picture. So a
> > > particle-based quantized theory that incorporates Barut's ideas (as
> > > well as vacuum polarization!) was never yet forthcoming.
> > ...
> > Fortunately, I found in the end that the Yang-Mills tensors I had discovered
> > could be used to get extremely tight parts-per-million predictions of
> > binding
> > energies even without having to do the many-body problem. Tensors are
> > remarkable things, in that way.
>
> Can you now disprove Haag's theorem?

*** Jay writes ***

I do not think that disproving Haag is the question. While I cannot claim
expertise in Haag, I note that in Wiki it is stated that "Among the
assumptions that lead to Haag's theorem is translation invariance of the
system. Consequently, systems that can be set up inside a box with periodic
boundary conditions or that interact with suitable external potentials escape
the conclusions of the theorem." My results are very explicitly based on the
thesis that proton and neutrons are resonant cavities (i.e., boxes with
boundaries) which have their binding energies determined based on the current
masses of the quarks they contain. So I do not have to disprove Haag, rather,
my theory does not fall within the assumptions of Haag.

*** End Jay writes ***

> > While I do not know the ultimate answer, I am now starting to think that the
> > binding energy and proton and neutron mass results I obtained and the tensor
> > of which they are components might contain some clues that allow us to
> > "backtrack" into a better way to model these many-body systems.
> >
> > That is, where I thought at first I would need to solve a many-body system
> > to
> > find binding energies, I now wonder -- working backwards -- if the binding
> > energies I already have derived to parts per million accuracy can give use
> > some clues about how to solve multi-body systems.
>
> Can you explain why your results should have anything
> to do with the many-body systems discussed here, when
> you say you did not solve many-body systems? How can
> you be sure that it is more than numerology?

*** Jay Writes ***

I said that I am not sure what connection is with many body systems. I
raised that as a question to be explored, not an answer.

As to numerology, you should read the details how how I get my results
and especially the Yang-Mills tensors involved. But if you want to
start at the 30,000 foot level of probabilities, I derive five
*independent* energy relationships (four binding energies and the
neutron minus mass difference) all to within parts per million, using
the thesis that protons and neutrons are resonant cavities with binding
energies which are functions of their current quark masses. There are
perhaps different ways to calculate the probability that this is lucky
numerology rather than a physically-meaningful result. I'll try one,
you can tell me yours. Let's say you consider that a prediction to
within 1% starts to maybe be meaningful and not just numerical
coincidence. So a single better than 1 in 100,000 prediction (which is
the accuracy for all five of my results) has odds against numerical
coincidence at 1 in 1000. If you have five such predictions which stem
from a common physical premise but are each numerically *independent* of
one another as are my predictions, then the odds again this being just
numerology are 10^15 to 1. That is a billion-trillion to 1. That is
about as good as it gets when trying to show that an underlying theory
is not contradicted and in fact strongly supported by empirical
evidence.

Jay

[Jay R. Yablon]

PS: In my reply below a few lines from the bottom, I messed up counting
zeros. 10^15 is a million-billion, not a billion-trillion. Jay

[Moderator's note: The original, non-corrected portion is below. -P.H.]

[Alfred Einstead]

"Alfred Einstead" wrote in message

> In quantum theory, of course, the problem is worse since the Haag
> Theorem (= the quantized version of the Leutwyler Theorem) puts severe
> restrictions on the very existence of an interaction picture.

On 4/14/2013 3:11 AM, Jay R. Yablon wrote:
> Fortunately, I found in the end that the Yang-Mills tensors I had discovered
> could be used to get extremely tight parts-per-million predictions of binding
> energies even without having to do the many-body problem. Tensors are
> remarkable things, in that way.

On Apr 14, 12:15 pm, Jos Bergervoet <jos.bergerv...@xs4all.nl> wrote:
> Can you now disprove Haag's theorem?

If I can jump in here, there are a few comments I can add at this
point.

Of course, you can't disprove a theorem -- other than by rendering its
preconditions invalid or irrelevant.

In the case of Haag, there is a significant insight to be drawn from
the (apparent) absence of any non-relativistic version of the theorem.
The first thing you should ask when seeing this discrepancy is:
"What's up with this?! I thought we were supposed to have a
Correspondence Limit property going on here. So how can the limit of
'No' be 'Yes'?"

In reality the key word in the above sentence is "apparent". If you
take the idea of a Correspondence Limit seriously, then there should
indeed be a non-relativistic version of Haag's Theorem! Only, its
conclusion will miss the mark and fail to exclude interactions.

So, now, if you start at the non-relativistic limit and *slowly* turn
on the "relativity parameter" alpha = 1/c^2 from 0 on up, you should
be able to keep the pristine situation you found in non-relativistic
theory at least over some range of alpha over an open set surrounding
0. A result should not draw a sharp distinction between 0 and
everything else -- because that would in principle provide a way to
determine the precise value of a continuous parameter ... which is
absolutely verboten.

However, what you (apparently) find is that the very instant alpha
goes from 0 to anything that's non-zero, Haag's conclusion appears to
go from "No" to "Yes" on the question "is there a non-trivial
interaction?"

What this shows, then, is that the root of the problem is that we lost
something when running the correspondence limit in reverse and that
what we call relativity is actually not the complete account of what
relativity should be. In other words, the theory of relativity has not
yet been completely discovered or developed! In particular, the one
thing that's missing is the very thing we need to render Haag
impotent.

So, what's missing? The answer actually is sitting in clear sight, and
has been hiding in clear sight for a very long time. It is this: in
non-relativistic theory, the symmetry group is NOT the Galilean
transformation group. Rather, it is the Bargmann group, which has one
generator in addition to the Galilei group. This discrepancy shows up
when you place the Galilean transformation
x -> x - vt, t -> t, y -> y, z -> z
for coordinates alongside the BARGMANN TRANSFORM(!)
H -> H - v px + v^2/2 m, px -> px - vm, py -> py, pz -> pz, m -> m
for kinetic energy H, momentum p = (px, py, pz) and mass m.

We can, correspondingly, form 2 invariants out of this rather than
just one:
mu = m -- the linear invariant
rho = px^2 + py^2 + pz^2 - 2 m H -- the quadratic invariant.
So see what the second invariant is and what it means, take the case
of a non-relativistic interacting body with momentum p, and energy
potential U:
H = p^2/2m + U.
For rho we then get:
rho = -2mU.

Now, compare this situation to relativity. The kinetic energy H takes
the form:
H = mc^2/root(1 - v^2/c^2) - mc^2.
To put this in a form that more closely compares to the non-
relativistic form, rewrite it as:
H = mv^2/(1 + root(1 - alpha v^2))
with alpha = 1/c^2 being the relativity parameter.

But now look at what happens when you substitute this into the mass
shell invariant of relativity with the total energy E = H + mc^2:
E^2/c^2 - p^2 = m^2 c^2 --> rho = p^2 - 2mH - alpha H^2 = 0.
Look at what happens to the linear invariant:
mu = E/c^2 - alpha H = m.
This is the relativistic version of rho. When taking the non-
relativistic limit, the result is
mu -> m; rho -> 0.
The potential U is gone.

That's what's missing. So, when you run through Haag's theorem or the
classical version (Leutwyler's Theorem), the result is that you end up
drawing the conclusion that U = 0 ... because that's effectively the
assumption you started with!

To fix the problem requires restoring the Correspondence Limit. But
first, this requires recognizing that the Correspondence Limit should
be with the Bargmann group, not the Galilei group. Since Bargmann has
11 generators, then so must the symmetry group in relativity that
leads to Bargmann. In addition, it includes Poincare' as a subgroup.

The Bargmann group is a non-trivial central extension of the Galilei
group that is obtained by modifying the Lie brackets between the
momentum (= translation generator) P and the moment (= boost
generator) K from
[K_i, P_j] = delta_{ij} (alpha H) (= 0 for Galilei)
(where H is the time translation generator), to the form:
[K_i, P_j] = delta_{ij} (alpha H + mu) (= delta_{ij} m for
Bargmann)
Pooincare' only admits "trivial" central extensions. And here, that
"trivial" central charge is just mu itself. Nonetheless, despite its
triviality, the alpha -> 0 limit of the centrally extended group is a
non-trivial central extension. So, to have a valid Correspondence
requires keeping the additional generator "mu" in the Poincare' group.

Consequently, the creed "Poincare' is the symmetry group for
Relativity" is revoked and replaced by the creed "the central
extension of Poincare' is the symmetry group for Relativity".

So, now we come back to Haag. This is where Haag runs afoul. We want a
vacuum state |0> to be boost-invariant. This means that K |0> = 0. We
want it to be homogeneous, which means P |0> = 0. With the Poincare'
group we draw the conclusion that
H |0> = (1/alpha) [K, P] |0> = 0
and we note that the non-relativistic form is immune since alpha was
0.

But with the centrally extended Poincare' group, the only conclusion
we can draw is that
M |0> = 0
where [K, P] = M = mu + alpha H is no longer the energy or time-
translation generator, but the relativistic mass! In other words, we
draw the same conclude in place of Haag (after replacing Poincare' by
its central extension) that the vacuum has no mass.

But the only conclusion to be drawn for the energy H is
H |0> = (M - mu)/alpha |0> = -mu/alpha |0>.
And noting the expression mu = m - alpha U, we simply find:
H |0> = U |0>.

The interaction potential U survives Haag!

The meanings of the generators subtly shift. This is best seen by
writing a coordinate form of the Bargmann transform and then
converting it to relativistic form. We do this by associating a
coordinate u with the mass mu and writing the canonical 1-form:
theta = px dx + py dy + pz dz - H dt + mu du.
It we take the Bargmann transform on (p, H, mu) and require that theta
be an invariant, then we can conclude the corresponding transform for
the coordinate differentials:
theta = (px - v m) dx' + py dy' + pz dz' - (H - v px + v^2/2 m) dt'
+ mu du'
= px dx + py dy + pz dz - H dt + mu du.
From this, we conclude:
dx' = dx - v dt, dy -> dy, dz -> dz, dt -> dt, but also du -> du +
v dx - v^2/2 dt!

The relativistic form of this would be a generalization of Lorentz to
a "Bargmann Lorentz":
dx' = (dx - v dt)/root(1 - alpha v^2), dy' = dy, dz' = dz, dt' =
(dt - alpha v dx)/root(1 - alpha v^2)
du' = du + v dx/root(1 - alpha v^2) - dt/root(1 - alpha v^2) v^2/(1
+ root(1 - alpha v^2))
In the alpha -> 0 limit, you can clearly see the v^2/2 term emerge
from the du transform.

The relativistic version of the canonical 1-form can be written in
either of two ways:
theta = px dx + py dy + pz dz - H dt + mu du
or
theta = px dx + py dy + pz dz - H ds + M du.
In the second form, the (t,u) coordinates combine to give you s = t +
alpha u. This is an invariant and gives us a vestige of the "absolute
time" of non-relativistic theory.

What was originally the time translation generator in relativity E = M
c^2, is here now just the translation generator for the u coordinate,
where s is kept fixed.

So, after Poincare' is centrally extended, the Haag theorem's
assumptions are no longer that the vacuum is isotropic, boost-
invariabnt, spatially homogeneous AND time-translation invariant; but
only that it is the first three of these four AND u-translation
invariant. "Time-translation" of Poincare' becomes "u-translation" of
the centrally extended Poincare' group. So all the theorem allows you
to conclude is that a u-symmetric, isotropic, boost-invariant,
homogeneous vacuum has 0 relativistic mass, 0 momentum, 0 moment and 0
angular momentum ... but not zero energy!

It is out of the extra energy term U that one can safely tuck away all
sorts of nice goodies, like the energy needed for pair production,
interaction potentials a' la non-relativistic theory and so on.

[Jos Bergervoet]

You wrote that your theory treats the quarks as
if they're in some cavity, which sounds similar
to the MIT bag model or the Anti-de Sitter Bag
Model. Do you have the following parameters:
. cavity size
. 3 quark masses
. some coupling constant (e.g. alpha_QCD)
and are these free to fit?

If so, fitting the 5 experimental quantities,
as you do, would be less impressive (although
still not trivial, I guess, with this precision).

If you do not fit them, then what quark masses
do you use? There is no exact value know with
the precision you claim to obtain in your
model. So if you just took some literature
value it would be strange to get very accurate
predictions at all.

--
Jos

[Jay R. Yablon]

"Jos Bergervoet" wrote in message

news:5176ee91$0$2170$e4fe...@news2.news.xs4all.nl...

*** Jay now writes ***

Jos, Excellent, pertinent questions, please allow me to reply.

The "cavity" is a mnemonic device for thinking about the problem, but does not
come into play explicitly in the process of deriving the numeric results. At
one point in time I thought this would be necessary to do and was drawing up
shapes and sizes, but in the end found out I could derive my concurrence with
data without explicitly doing so. Yes, things like MIT bag especially, were
very influential throughout in terms of how I have thought about the whole
question of "what is a baryon?"

As to:

Do you have the following parameters:

. cavity size NO
. 3 quark masses YES
. some coupling constant (e.g. alpha_QCD) NO
and are these free to fit? THERE IS NO FREEDOM TO FIT. THE QUARK MASSES ARE
THE *ONLY* INPUTS

You then say:

"If so, fitting the 5 experimental quantities, as you do, would be less
impressive (although still not trivial, I guess, with this precision)."

I agree fully, and I thank you for pointing out to me another argument that
strengthens the results in my paper, because there is not any fitting at all.
The two (not three) quark masses for up and down are the ONLY parameters used.
(The sqrt (m_u*m_d) is a third parameter but it is not independent from m_u
and m_d separately, just a convenient mass quantity.

"If you do not fit them, then what quark masses do you use? There is no exact

value know[sic] with the precision you claim to obtain in your model. So if

you just took some literature value it would be strange to get very accurate
predictions at all."

100% on target question, you understand exactly what is going on. The
precision claimed for the up and down masses is not known presently. Correct.
Let me now explain this clearly:

The quark masses I use are masses I derive in cascading fashion as follows:

1. I derive a formula for the electron mass as a function of the difference
between the up and down quark masses. The electron mass is known with extreme
high precision. First high precision experimental input.

2. My first use of the "resonant cavity hypothesis" is to postulate that the
mass of the down quark is equal to the binding energy of the deuteron. This
is well within known experimental errors for the up quark mass. The deuteron
binding energy is also known with extreme high precision. Second high
precision experimental input.

(Later, at the end of my second paper at http://vixra.org/pdf/1212.0165v4.pdf
I modify this postulate so that the deuteron binding energy and the up quark
mass end up differing from one another at the parts-per-ten million level,
because the neutron-minus-proton mass difference, first derived at the
parts-per-ten million level, is what I take to be an exact relationship, so
everything gets recalibrated and the parts-per-ten million discrepancy
shuttles over to the deuteron binding energy retrodiction.)

3. Now I have both the (known) electron and the (postulated) up mass with
high precision, so I use the formula in 1 to derive the down mass with similar
high precision.

That is how I have high precision quark masses which then allow me to derive
all the nuclear binding energies with equivalent high precision.

Another "result" of all this that I have not explicitly highlighted, and
probably should discuss more, is that I walk away from all this with up and
down quark masses specified at about ***8 to 9 orders of magnitude in AMU
better than they are known at present.*** These up and down quark masses now
become known to the same precision as the electron mass, the deuteron binding
energy, and the proton and neutron masses, all of which influence my final
predicted up and down quark masses as well as my retrodicted binding energies.
As measurements of up and down masses get more precise in the future, that
will be a further way to validate (or disqualify) my theory. And ... using
Phil Helbig's "retrodiction" versus "prediction" dichotomy, the up and down
masses are true *pre*dictions amenable to validation, and not retrodictions.

Thank you for you good observations and questions.

Jay

[Jay R. Yablon]

[Moderator's note: This is the correct version of this post; I have
made the change suggested by Jay. No other moderator should post a
similar post as that is probably the incorrect one. -P.H.]

that the mass of the up quark is equal to the binding energy of the