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!