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  • Post #8

Frank,

I agree of course that Newton was unaware of many of the more modern concepts of electromagnetic radiation. However, utilizing his theory of gravity (with its single potential) results in a displacement of stars at the Sun's limb of 2GM/rc2 radians compared to Einstein's prediction of 4GM/rc2 (based on ten potentials). You can find a nice description of this in: "The physical foundations of General Relativity" by D.W. Sciama (Doubleday & Company, Inc., Garden City, New York, 1969) p. 67-73.

I have not had a chance yet to read Georgina Parry's essay yet, but I will.

Steven,

Thanks very much for the helpful explanation - and sorry for being slow. I also must belatedly commend you on your very clearly written essay - I tend to obsess on the sticking points...

I also agree that the planned experiment will be most enlightening.

In regards to anti-gravity, I've had difficulty comprehending how a gravitational mechanism (I hold on to the idea that there must be some undescribed physical process or mechanism that produces the very well described effects of gravitation) could distinguish between particles and anti-particles of identical mass - which is fundamentally addressed in your essay.

However, it occurs to me that the baryon number/color charge 'properties' are merely an abstract index of quark combinatorial behavior. IMO, theses properties are most likely proxies for some physical attribute of various types of quarks, such as structural geometry or topology, or a combination thereof, that produce the observed combinatorial behavior.

As such, I strongly suspect that color charge or baryon number has nothing to do with gravitation, and that the gravitational effect will be confirmed to be proportional to the physical property of mass alone. After all, that understanding of gravity is the reason why most physicists would expect that the AEGIS experiment's anti-hydrogen beam will curve towards the Earth.

I certainly hope that AEGIS is carried out. Moreover, I hope that it is also conducted using a beam of hydrogen particles to confirm its predicted behavior in the specific conditions imposed by the experimental apparatus, regardless of any anti-hydrogen results...

Thanks very much for your fine essay!

Steven,

There are two ways in which antimatter could antigravitate. The first way is that it has a negative mass. The Dirac theory has particles in the lower portion of the momentum-energy light cone as negative in mass. These pack in to form the Dirac sea. The positive portion of the cone contains positive mass particles. The standard idea is that by giving a particle in the bottom portion of the cone sufficient energy that it assume a positive mass, but with opposite values of the other quantum numbers. If we assume however that anti-particles have anti-mass, -m, or negative mass, then gravitational interaction with ordinary mass M is

Ma1 = -GM(-m)/r^2

-ma2 = -GM(-m)/r^2

so the accelerations of mass and antimass are

a1 = Gm/r^2

a2 = -GM/r^2

so the mass is repelled by anti-mass, but anti-mass is attracted to mass.

There is a problem with this that connects to Dirac theory. An electron e plus e^= gives photons with positive energy. However if the positron has negative mass then the m(e) m(e^) = 0, which would produce nothing.

Another way is that we would have a parity change with m_i = m_g. We might suppose that that while antimatter mass is positive, that Gm is negative. Then m_i = m_g for matter, but m_g = m_i for antimatter The gravitational constant is somehow sensitive to the matter or antimatter state of a particle. The gravitation equation would be

Ma1 = -GM(-m)/r^2

ma2 = -GM(-m)/r^2

so the accelerations of mass and antimass are

a1 = Gm/r^2

a2 = GM/r^2

In this case matter and antimatter repel each other.

This runs into some funny issues with black holes. Hawking radiation from a Schwarzschild black hole produces an equal number of particles and antiparticles due to the "no hair" theorem. A neutral black hole will produce an equal number of particles and antiparticles. The black hole is then a reservoir of possible particle-antiparticle pairs, but yet it has gravitation or a horizon at r = GM/c^2. Suppose we place a Gaussian sphere around the black hole to contain particles and radiation emitted. This would mean that while there are e-e^ pairs not annihilated that the gravity measured across the Gaussian surface would change. That would be a bit odd.

This experiment or one like it would be worth doing. However, I suspect it will largely confirm what we already know.

Cheers LC

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    • Post #11

    Hi Hyoyoung,

    As I noted in a reply to James Dwyer: "Experiments clearly show that antimatter, like matter, has positive inertial mass. There is no experimental evidence for negative inertial mass, nor do I believe in its existence. A gravitational repulsion between bulk matter and antimatter does not mean that antimatter has negative inertial mass." So I don't think I would add anything constructive to your work but I will read your essay. Years ago, Isaac Asimov wrote some amazing speculations on negative energy in his book "Science, Numbers, And I" Good Luck.

    Dear Steven Dinowitz,

    I am sorry. I apologize for my poor English.

    I agree that "Experiments clearly show that antimatter, like matter, has positive inertial mass." And I do not consider that antimatter is a negative mass.

    In my article,

    =========

    ~

    However, we determined that total energy could not exist at a negative state and abandoned the solution(of relativistic total energy) of negative energy. Only the great physicist, Dirac was able to connect a solution of negative energy to antimatter.

    But, despite how Dirac reached his discovery on antimatter, antimatter still has positive energy. In other words, it is less likely that antimatter is the true owner of a negative energy solution.

    ==========

    For the observation or evidence of negative mass(energy)

    In 1998, an observation by both the HSS team and SCP team obtained a negative mass density from inspected field equations over 70years.(Field eq. has a Lamda=0)

    SCP(Supernova Cosmology Project) team : If Lamda=0, Omega_M= - 0.4(±0.1)

    http://arxiv.org/abs/astro-ph/9805201 refer to 7P

    HSS(The High-z Supernova Search) team : If Lamda=0, Omega_M = - 0.38(±0.22)

    http://arxiv.org/abs/astro-ph/9805201 refer to 14P

    However, the two teams which judged that negative mass and negative energy level could not exist in our universe based on "the problem of the transition of the energy level of minus infinity" and they instead revised the field equation by inserting the cosmological constant.

    Moreover, we considered vacuum energy as the source of cosmological constant Lamda, but the current result of calculation shows 10120, which is unprecedented even in the history of Physics.

    However, if "the problem of the transition of the energy level of minus infinity" does not occur, and thus negative and positive mass can coexist, what would happen?

    It is well known that a cosmological constant can respond to the negative mass density.

    peff = -Lamda/4piG

    Lamda is positive, so peff is negative.

    Please view to my article and simulation video

    Computer Simulation on negative mass

    Again, I'm sorry. Have a nice day!

    --- Hyoyoung, Choi

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    • Post #13

    Lawrence,

    If you are suggesting that those are the only two ways that matter may gravitationally repel antimatter, I simply disagree - See New Rules in my essay if you haven't already. The first way you suggest is, as I'm sure you are aware, a nonstarter since we already know by experiment that antimatter has positive energy and positive inertial mass. The second way you mention is to simply say that antimatter has negative gravitational mass. This indeed has yet to be tested experimentally - and is part of what the AEGIS experiment is about. Until the experiment is actually conducted we are both free to suspect what we wish. At least we agree that such an experiment is worth doing. In 2012 we know the mating habits of shrimp in low Earth orbit, but we don't know if antimatter falls up or down!

    • [deleted]

    • Post #14

    That is of course the state of affairs. The difficulty of course is that gravity is such a weak force and acquiring antimatter is technically difficult. I would say that if you had antimatter in orbit around the Earth, say observed on the International Space Station, that if it is repelled it moves to a larger radius. Ordinarily gravitation determines orbital velocity and frequency by

    mω^2r = GMm/r^2

    leading to ω = sqrt{GM/r}. If you have Gm negative for antimatter, but m is positive, then

    mω^2r = -GMm/r^2

    then ω = sqrt{-GM/r} = i sqrt{GM/r}. This means frequency is not defined and the particle is on an escape trajectory. With regards to energy

    E = 1/2mv^2 - GMm/r

    We assume E is constant and then

    v = sqrt{2E/m - 2GM/r}

    where the sign of 2GM/r is due to the negative sign of Gm. The velocity increases as r -- > ∞ and eventually E_∞ = 1/2mv_∞. This would then suggest the energy involved with preparing antimatter and matter is different. Matter has a negative potential energy while antimatter would be negative

    It would certainly be an odd development. I agree it would be worth testing to make sure nature is not quite as odd, if not pathological, as this.

    Cheers LC

    Dear Steven,

    It seems that the idea of Antimatter Antigravity is not compatible with the Theory of Infinite Hierarchical Nesting of Matter which is considered in my essay. In the theory the substance of all the particles is the same similar to substance for planets and stars. Antiparticles have opposite charge only. And quarks are not real particles but quasiparticles.

    Sergey Fedosin

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    • Post #16

    Dear Sergey,

    Well needless to say I find the Infinite Hierarchical approach to the nature of reality rather matter-centric. Though I agree that we may not be at the limit with quarks, leptons, etc., I do believe there is a limit. Also, I think the experimental evidence for the existence of quarks is substantial. I think Gell-mann's initial quark theory (early 1960's), and Greenberg's notion of color charge (early 1970's) were notions of shear genius. Also, I wonder how the approach you take would handle dark matter and dark energy. These two 'substances' are very different than the substances of planets and stars. I guess if you don't recognize the existence of quarks, you would surely deny the existence of these as well - and at this stage of our ignorance you could probably still make the argument. However, even the argument that both dark matter and dark energy are previously unsuspected properties of gravity itself conflicts with the Hierarchical approach as these theories inevitably introduce new properties of gravity tied to some specific, or even multiple, distance parameter(s).

    As to antimatter antigravity, I don't want to spend another 50 years debating it. You have a theory which is not compatible with antimatter antigravity, and I have one that is. Experiments to determine the gravitational acceleration of antimatter are long overdue.

      In a private communication, I have been asked if the presence of gluons within the proton and antiproton would affect the gravitational force between them under the hypothesis I put forth in the essay (See 'New Rules' in the essay). A very good question.

      Quarks can change color through the exchange of gluons. So, for example, a quark with a blue color charge can become a quark with a red color charge by emitting a blue/anti-red gluon which can then be absorbed by a neighboring quark with a red color charge changing it to a quark with a blue color charge. Thus the two quarks have exchanged color charge. Gluons, like photons, are believed to be spin 1 particles with zero rest mass. Gluons have a baryon number of zero and do not themselves consist of quarks and so under the hypothesis set forth in the essay have a gravitational mass denoted by 'w' just as does every other fundamental particle with zero baryon number.

      This being the case, the presence of gluons within both the proton and antiproton would have to be taken into account when calculating the gravitational force between them. Thus the gravitational force between a proton and antiproton is:

      F = -G/r2(-mcmc-bar + mwmc + mwmc-bar +mwmw)

      where mc is colored gravitational mass of the proton, mc-bar is the anti-colored mass of the antiproton, and mw is the gravitational mass due to gluons.

      Since mw = m - mc = m - mc-bar where m is the mass of the proton we find if mc = m/sqrt2 then F = 0. So if the quarks within the proton contribute over 71% the total mass of the proton the there will be a net gravitational repulsion between proton and antiproton. Indeed, if AEGIS finds antiprotons fall up at a value between 0g and 1g we can take that value and easily calculate the gluonic component of the proton mass.

      Dear Steven

      I think that quarks are quasiparticles. The model of quark quasiparticles is described in §12 of the book: The physical theories and infinite nesting of matter. Perm: S.G. Fedosin, 2009-2012, 858 p. ISBN 978-5-9901951-1-0. And dark matter is explained in the paper: Fedosin S.G. Cosmic Red Shift, Microwave Background, and New Particles. Galilean Electrodynamics, Spring 2012, Vol. 23, Special Issues No. 1, P. 3 - 13.

      Sergey Fedosin

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      • Post #19

      Hello Steven,

      In your essay you write that the main reason why the coupling of antimatter with the gravitational field of "ordinary" matter hasn't been established so far, is that physicists think they already "know" the outcome.

      While I agree with you that group pressure is a factor - it certainly explains why the AEGIS project is a smaller enterprise than the Higgs project - I think, however, that the main reason the experiment hasn´t been done is technological. For example, on paper it sounds very simple that you only have to inject slow antiprotons horizontally into a Faraday cage to measure their gravitational acceleration. But in reality, the process is simply not feasible technically - e.g. no ideal Faraday cage exists. Therefore they know try the experiments with neutral antimatter, and these are at the forefront of technology.

      Your proposal of the sign of your six possible gravitational interactions raises some philosophical questions. For example, on page 8 you imply with (3) that protons and positrons interact attractive, while you imply with (6) that protons and antiprotons interact repulsive. So positrons must have a property that antiprotons do not have. Thus, there is no general symmetry between matter particles and their antimatter counterparts, such as the C-inversion of the current Standard Model (which is, thus, false in your model). Then you get to ontological questions as what mass and energy actually are. Have you thought about this?

      Best regards, Marcoen

        Hi Marcoen,

        As I noted in the essay, back in 1967 Fairbank and Witteborn managed to isolate electrons from external forces without undue difficulty. The problem they faced was the then puzzling absence of much larger forces which had been detected in other experiments. (Later they found that those larger forces are temperature dependent, which explained their absence in the low temperature environment of the original experiment). It was ultimately the failure to obtain funding for a decent positron source that prevented conducting the experiment with positrons. (I actually have an e-mail from Dr. Witteborn that confirms this). Same goes for the planned experiment utilizing antiprotons from LEAR at CERN in the late 1980's; it was not any technological barrier - only funding that failed.

        There is a lot of misinformation out there. In fact many people, and even a good number of physicists, believe experiments to determine the gravitational acceleration of antimatter have already been done. Perhaps it's the fact that these experiments were planned and discussed extensively but never carried out as intended. Also there are articles like "The Light Stuff" in the 11/20/04 issue of New Scientist where physicist Paul Wesson wrote: "In a recent series of experiments, most notably at the Stanford Linear Accelerator in California, researchers looked to see if positrons, the antimatter partners of electrons, fell upwards in the Earth's gravitational field. But like balls, people, and all the other that we know about, they fall towards the center of the Earth." No such experiment was ever performed. Articles like this, in magazines and on the internet feed on themselves as people take information from them and write additional articles without investigating the validity of the original source.

        My proposal is that there are three types of gravitational mass linked to baryon number which is in turn linked to color charge. Quarks (baryon number +1/3 and color charge; red, green, or blue) have a gravitational mass type 'c' (for color). Antiquarks (baryon number -1/3 and color charge; anti-red, anti-green, or anti-blue) have gravitational mass type 'c-bar' (for anti-color). Everything else (zero baryon number) has gravitational mass type 'w' (for color neutral or white). Our 'world' (leaving out antimatter, dark matter and dark energy), the world of protons, neutrons, electrons, photons, neutrinos, etc. is a world of type c and w gravitational mass with the gravitational interactions:

        c c = attractive, c w = attractive, and w w = attractive

        I wanted complete symmetry in the 'antiworld', the world of antiprotons, antineutrons, positrons, photons, and antineutrinos such that one could exchange the matter world for the antimatter world with no observable change taking place. Thus the 'antiworld' is a world of type c-bar and w gravitational mass with the gravitational interactions:

        c-bar c-bar = attractive, c-bar w = attractive, and w w = attractive

        That left c c-bar = repulsive to insure the long range separation of bulk matter and antimatter in a universe where baryon number is strictly conserved. Thus there is a beautiful symmetry in the universe. (Somewhere in a very distant antigalaxy on a small blue planet orbiting a G2 antistar, someone is wondering what happened to all the matter in the universe as physicists search in vain for antiproton decay).

        Yes, by (3) under 'New Rules' in my essay, the gravitational interaction between protons and positrons is attractive. As I noted in the essay, under the hypothesis I proposed, positrons would fall just as electrons do in the Earth's gravitational field. So even if the Fairbank/Witteborn experiment had been performed using positrons they would behave as expected under standard gravitational theory. Yes, by (6) under 'New Rules' in my essay, the gravitational interaction between protons and antiprotons is likely to be mostly repulsive. (See my post just above yours, where I address the effect that the presence of gluons within the proton and antiproton has on the gravitational interaction between them). Yes, antiprotons and positrons have different properties. Antiprotons are composite particles made up of three antiquarks, each with a bayon number of -1/3 and an anticolor charge. Positrons, as far as we know, are fundamental particles with a baryon number of zero, and are color neutral (white).

        As far as I know the notion of three types of gravitational mass linked to baryon number (and thus to quark color charge) and the resulting six distinct gravitational interactions is unique. Until now I have not seen it discussed or in print anywhere. FQXi wanted something original and I think I have delivered. However, that doesn't mean it is right. Only experiment can determine that.

        Best Regards,

        Steve

        Dear Steven,

        I appreciate this timely essay. It's astonishing that the physics community has been so careless about this issue. I was aware that the gravitational behavior of antimatter had not been experimentally determined, but I thought this was principally because of technical issues involving difficulty of production of large quantities of antimatter and the weakness of the gravitational interaction. It's heartening to read that a potentially definitive experiment is just around the corner. Take care,

        Ben Dribus

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        • Post #22

        Steven:

        Thank you for such an insightful and well written essay. Considering the number of gedanken experiments regarding baryon number conservation violation at high-energies in the standard model, it is refreshing to ponder the hypothesis you present as an alternative to matter anti-matter separation in the early universe. Very thought provoking..

        Regards

        Dear Reader,

        I came across a very interesting paper entitled: "Testing CP Conservation at KLOE" (arXiv:hep-ex/0007004v1) in which the authors attempt to retrieve CP conservation by introducing the 'heterodox' assumption that neutral kaons (consisting of a d-quark and an anti-s-quark) and neutral antikaons (consisting of an s-quark and an anti-d-quark) are acted on in opposite ways by the Earth's gravitational field. Using the best available data they calculated that kaons and antikaons experienced gravitational acceleration (in opposite directions) of 8.9 m/s2 (plus/minus 2.7 m/s2).

        Suppose we take that value as valid. Let's suppose the neutral kaons fall up at 8.9 m/s2 = -.91g and the neutral antikaons fall down at .91g. Let's start with the neutral antikaon. Under the hypothesis I proposed in my essay, to get an acceleration of .91g the s-quark would need to contribute .955 the gravitational mass of the neutral antikaon and the anti-d-quark would contibute the other -.045 the neutral antikaons gravitational mass. Thus, under my proposal, the gravitational mass of the neutral antikaon is .955 - .045 = .91 of the neutral antikaons inertial mass. Just the opposite would be true for the neutral kaon; its gravitational mass would be -.91 of its inertial mass. Simple enough.

        But here is where things really get interesting. If this is true then the ratio of the mass of the s quark to the mass of the d quark should be .955/.045 = 21.2. Is it? See for yourself...

        May I direct the reader to the Particle Data Group, 2012 Particle Listings, Quarks, Note on Quark Masses, p.18 see Figure: s/d mass ratio.

        Regards

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          • Post #24

          Steven,

          I have to admit your essay has really got me thinking. Until now, I have dismissed antimatter antigravity theories from the start because they have been unable to explain certain experimental facts. First, the photon, as its own antiparticle, should not be affected by gravity. But we know it is. Second, both neutrinos and antineutrinos from Supernova 1987A arrived at earth at the same time and could only do so if gravity affected them in the same manner. Third, despite your claim to the contrary, I'm pretty sure physicists have done gravity tests on positrons and found that they fall like everything else. Regardless, your idea naturally fits these facts. That's impressive.

          But what really blows me away is your post of 9/19 where you calculate the ratio of the mass of the strange quark to the mass of the down quark. The math is so simple and seems so obvious - after the fact. Yet it's magical! How did you come up with that? I suppose it could be a coincidence, but if so it is one hell of a coincidence.

          Honestly, until now I thought this AEGIS experiment was basically a waste of time and money. Now I'm not at all sure...

          Best,

          Daniel

            Daniel,

            I'm glad to hear my essay really got you thinking and I appreciate your kind words regarding my post of 9/19/12. More about that post later. While you are correct that the hypothesis I put forth in 'New Rules' in my essay naturally explains 1) the deflection of light in the Sun's gravitational field, 2) the simultaneous arrival of neutrinos and antineutrinos from Super Nova 1987A, and 3) the fall of positrons, I don't think these three examples make for a 'case closed' against the more 'traditional' antimatter antigravity theories. Let me explain...

            Light doesn't need to be attracted by a gravitational field in order for it to be deflected by one. Nor is falling into a gravitational field the only way that light may increase its frequency. It is possible that the gravitational field has an index of refraction. Picture a light source surrounded by a solid glass sphere that increases in density as you approach its center. A light beam shot through the glass will be seen to curve about the light source at the center as though it were attracted by the light source. So too, light moving toward the light source will experience an increase in its frequency not because it is gaining kinetic energy as it falls towards the central source, but simply because it's moving through a medium of increasing density. Indeed, if the gravitational field is assigned an index of refraction n = 1+2GM/rc2 it will exactly mimic the effects that gravity has on light as predicted by General Relativity. Thus light does not have to be attracted by gravity in order to be affected by a gravitational field.

            Your example involving neutrinos and antineutrinos from Super Nova 1987A is more weighty (excuse the pun) but still not decisive. The current view of neutrinos has evolved rapidly over the last 20 years. From what I understand there are three different mass eigenstates (v1,v2,v3), and each eigenstate contains varying degrees of the three known neutrino 'flavors' (electron, muon, tau) that change depending on environment and distance of travel. At this point in time we do not know the values of the three mass eigenstates and the only requirement is that they have different values. Thus it is possible that the smallest one is zero. So it is possible that the neutrinos and antineutrinos detected from SN 1987A all had, like the photon, zero rest mass and were affected equally by gravity. I will grant you that most physicists today believe that all the neutrino mass eigenstates are greater than zero. However, experimentally, the only established fact is that the sum of all three neutrino masses is less than .3eV.

            Unfortunately you are not alone in your belief that the gravitational acceleration of the positron has been measured. Over the years I would guess that one in three (maybe more) people who are interested in the subject are under the impression that the experiment has been done, the results were as expected, and this is settled science. I'm not sure why people have this impression. It may have to do with the fact that the original Fairbank/Witteborn experiment was planned, designed, built and actually conducted - though only using electrons. Perhaps people just assume that it must have also been conducted using positrons with the expected results. I have even heard more than one person tell me that of course the experiment was repeated with positrons and the results were so stunning that they have been kept Top Secret!

            Then there is the fact that there are many more papers out there that put forth theoretical arguments as to why positrons should fall down as opposed to just a handful that speculate otherwise. For example, in a very recent paper entitled:"Why We Already Know that Antihydrogen is Almost Certainly NOT Going to Fall Up" author Scott Menary notes that the deflection of light by the Sun...

            "shows experimentally that antimatter is attracted to matter. Recall from QED that the photon isn't really a point particle but is more like a cloud of e+e- pairs. This really illustrates the point that it is equal amounts particle and antiparticle. So there is no other conclusion that can be reached - matter and antimatter attract gravitationally."

            Never mind whether this argument is valid (I don't believe it is), it is papers like this, and there are many, that could easily be interpreted as: "Scientists have shown experimentally that positrons fall down." (By the way, I sent Dr. Menary an e-mail inviting him to comment on my essay, but I have not yet received a response).

            Then there are simple misstatements of the facts. For example, in an article on gravity entitled: "The Light Stuff" in the 11/20/04 issue of New Scientist magazine physicist Paul Wesson wrote:

            "In a recent series of experiments, most notably at the Stanford Linear Accelerator in California, researchers looked to see if positrons, the antimatter partners of electrons, fell upwards in the Earth's gravitational field. But like balls, people, and all the other matter that we know about, they fall towards the center of the Earth."

            This is simply not true. The 'recent' experiment he refers to took place 37 years prior to his article and never tested positrons! Articles like this, in magazines and on the internet feed on themselves as people take information from them and write additional articles without investigating the validity of the original source.

            Thank you for your kind words in regard to my post of 9/19/12. I agree, it is almost magical. You ask how I came up with it. Well I knew any meson is a quark/antiquark pair and by the hypothesis I put forth in the essay I would expect that all mesons would fall at less than 1g in the Earth's gravitational field. Then I remembered that the authors of the paper on neutral kaons had calculated that they fell at .91 g. That value seemed reasonable, so I decided to take it seriously. Under the hypothesis I put forth in the essay I knew that ms/m = 1/2(1 mg/m) where ms is the mass of the s-quark, m is the mass of the neutral kaon and mg is the gravitational mass of the neutral kaon. Thus ms/m = 1/2(1.91) = .955 which left md/m = 1 - .955 = .045 for the ratio of the mass of the d-quark to the mass of the neutral kaon. It naturally followed that if this is true the ratio of the mass of the s-quark to the mass of the d-quark, s/d = .955/.045 = 21.2.

            I had no idea that the value I calculated would match reality. When it did I was in shock and beside myself with joy. It was truly one of those rare 'eureka' moments. And I'm still in shock. Now of course, I smack myself in the head for not thinking of it sooner. It's so simple, how did we all miss it? (And we did miss it - I cannot find such a calculation anywhere).

            And of course we can work it the other way; we can start off with the mass ratio of the quark and antiquark in any meson and calculate its gravitational acceleration. For example, in the Particle Data Group, 2012 Particle Listings, Quarks, Note on Quark Masses, p.7 the mass ratio of the u-quark to the mass ratio of the d-quark, u/d = .56. A pion+ consists of a u-quark and an anti-d-quark. Using the hypothesis I set forth in 'New Rules' in my essay, we find that the ratio of the u-quark mass to the mass of the pion is mu/m = (u/d)/(1 + (u/d)) = .56/1.56 = .36. That means that the ratio of the mass of the anti-d-quark to the mass of the pion = 1 - .36 = .64. Thus the gravitational acceleration of the pion+ is = g(.36 - .64) = -.28g. Thus a pion+ will fall up in the Earth's gravitational field at .28g. A pion- will fall down in the Earth's gravitational field at .28g. You heard it here first!

            I see that you have posted this exact wording for just about every essay I looked at - regardless of topic. If the intent was to get me to view your essay you were successful. However, I will not comment on your essay, neither will I, other than this, reply to your post.

            The equation in the third paragraph up from the bottom, 7th line should read: ms/m = 1/2(1 mg/m)