The Law of Conservation of Baryon Number, Antimatter Anitigravity, and the Experiment That Never Gets Done by Steven Dinowitz

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

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)

Peter,

Thanks for your kind words.

Before I discuss what use we might make of antimatter antigravity, we need to do the experiment. We need to drop some antihydrogen and see how it falls. If the AEGIS experiment is completed (2015?) and we find that antihydrogen falls up we will have the makings of a Scientific Revolution on our hands the likes of which we have not seen since the creation of Relativity and Quantum Theory in the early 20th century. Relativity will not survive it. Antimatter antigravity is a direct violation of the Principle of Equivalence - the very foundation of General Relativity. Physicists will have to come up with an entirely new theory of gravity that explains everything that General Relativity has explained over the last century as well as antimatter antigravity. A task truly worthy of the next Einstein. Who knows what doors such a theory would open...

Also, if we find that antihydrogen falls up we would have to do additional experiments to see what else does. Do positrons fall up or down? The 'traditional' antimatter antigravity theories predict that positrons would also fall up, but the hypothesis I put forth in my essay predicts that positrons, like electrons and in fact all leptons, will fall down at 1g in the Earth's gravitational field. So too will all hadrons with a Baryon Number of +1 (which includes the proton and neutron).

However, all hadrons with a Baryon Number of -1 (which includes the antiproton and antineutron) will exhibit antigravity and fall up in the Earth's gravitational field.

Hadrons with a net Baryon number of zero - the mesons - composed of a quark and antiquark, such as the pion and the kaon are, in a way, the most interesting. Based on the hypothesis set forth in my essay and my posts of 9/19/12 and 9/25/12 we can take the mass ratio of the quark and antiquark that make up a given meson and calculate the acceleration of the meson in the Earth's gravitational field. Thus it is predicted that:

Pion+ (u, anti-d) will fall up at .28g

Pion- (anti-u, d) will fall down at .28g

Neutral Pion (u, anti-u or d, anti-d) will be weightless at 0g.

Kaon+ (u, anti-s) will fall up at .95g

Kaon- (anti-u, s) will fall down at.95g

Neutral Kaon (d, anti-s) will fall up at .91g

Neutral AntiKaon (anti-d, s) will fall down at .91g

What about photons? The hypothesis I put forth in my essay predicts that photons will all fall as expected in the Eath's gravitational field. So I don't have to resort to the additional assumption of a gravitational index of refraction. I only brought up the notion of the gravitational field having an index of refraction n = 1 + 2GM/rc2 to show that even the 'traditional' antimatter antigravity theories that predict that gravity does not attract photons, are in fact not ruled out by the observed behavior of photons in a gravitational field. Regardless, I will certainly read your essay.

You ask if we will be able to make anything durable from antiprotons to make use of antigravity? Well not us, and certainly not now. However consider where our technology may be in a million years - or consider where an alien technology with a million years on us may be now. (A million years is but a drop in the bucket in a universe 14 billion years old). Aliens may have established trade with their counterparts in a distant sector of the universe consisting of antimatter. One of the materials traded may be antineutronium (material from an antineutron star). A mere speck (say a mm in radius) might weigh a million metric tons. The antineutronium speck consists of antiquarks, each with a -1/3 Baryon Number and has, according to 'New Rules' in my essay, negative gravitational mass. A negative gravitational mass of a million metric tons. But why antineutronium?

We are used to thinking of antimatter as the most dangerous substance conceivable. Any contact between matter and antimatter results in total conversion of mass into energy. But what if the antimatter is in a form so dense, its antigravity field so intense at small distances, that contact between matter and antimatter is impossible. As all matter around it at short distance would be intensely repelled the antineutronium speck would be surrounded by a pure vacuum far better than anything man has achieved. It would be a self-isolating system. In this form, the most dangerous substance conceivable, may be safe to handle. We could place antiprotons on the outer surface of the antineutronium speck giving it a nice electric charge and thus make it possible to hold in place using a powerful electric field.

If the antineutronium speck has an antigravitational mass of a million metric tons it could lift a million metric tons of normal matter. That's more than enough to levitate an aircraft carrier! And if you used less than a million tons of normal matter, say only 100,000 tons, the antineutronium speck would propel the whole thing away from the Earth, and ultimately away from the Sun - giving you a 'star drive' propulsion system. How's that for starters?

But let's come back down to Earth. Mankind presently, and for the foreseeable future, has the ability to generate only the tiniest quantities of antimatter (less than a millionth of a trillionth of a kilogram) and certainly not at anything remotely approaching neutron star densities. But you asked, so I just wanted to touch on what might be possible in a million years (provided we don't nuke ourselves back to the stone age).

I appreciate your kind words with regard to my essay. I naturally agree that it should have a higher ranking than it does. However to be fair to the FQXi community, there are hundreds of essays (I have only had a chance to read a handful myself) and I got mine in just under the wire (though I was amazed to see how many came in after mine). I know time is short, but I am still hopeful that I will rise in the ranking.

Regards,

Steve

Lawrence,

Even stranger, under the hypothesis I put forth in the essay, what the observer on the Gaussian surface experiences gravitationally as the situation within the surface to begin with depends upon the compositional nature of the observer itself. For example, if the observer were a photon, or an electron it would not experience the internal situation you set up as M - m, but as M m. Such an observer would record no change in the gravitational force throughout the process of pair annihilation and photon reflection. Yet an observer made up of quarks (or antiquarks) would. But as I noted, this may only illustrate the fact that the gravitational force depends on the compositional nature of the observer.

I am still taken with the notion that by making use of the assumption that antiquarks exhibit antigravity a simple relationship between the mass ratio of the quark and antiquark in any given meson and the gravitational acceleration that the meson experiences can be derived that may (I repeat, may) reflect reality.

Regards,

Steve

Sergey,

I was simply going to ignore your first post with regard to rating, but after the monstrosity you just left me, may I respectfully ask you not to post me a third time on this matter. Look, it's just an essay contest, it's not the noble prize. At the same time I don't want to give you the impression that I'm beyond it all, I'm not - I would like to win as much as the next person. However, I did not enter thinking that I would win. I was happy to have simply entered before the deadline. Also I had the very good fortune of possibly making an actual discovery (see my post of 9/19/12) that I'm still in shock over. I would much rather discuss that than FQXi ranking procedures!

Regards,

Steve

Dear Concerned Public,

Yes I know. My essay plummeted from the top third in ranking to the bottom third in ranking (~90 positions) after I received Sergey's post. Why Sergey felt obliged to let people know that it was he who dragged down their ranking is any ones guess! Ego? It reminded me of one of Khan's lines from 'Star Trek II: The Wrath of Khan' - "I have deprived your ship of power, and when I swing around, I mean to deprive you of your life. But I wanted you to know who it was who had beaten you."

Drama aside, Sergey was operating within the established FQXi rules. A FQXi member might make the argument that if an essay already had a high number of good ratings, then a single very low rating would do little damage. True, but forget about Sergey for a minute.

FQXi members should ask if there are actions essay writers might take to increase the likelihood that their essay garner a high number of ratings in the first place? It's not rocket science - First, rather than focus on a single topic, write an essay that has a little something for everyone. By so doing the essay will have a wider general appeal (and, as an added bonus, it is much easier to say a little something about several topics than something meaningful about just one). Second, once your general multi-topic essay has been accepted, just read the abstract of another authors essay, maybe view a couple of the other comments and create a short complimentary, ego-boosting paragraph to post to their essay - a nice little harmless powder-puff of a paragraph. Do so for as many essays as you can (the more the better) and lo and behold you are likely to find yourself ranked in the top 35. How so? When people get around to rating essays, the first group they are likely to choose are those who responded in a positive way to their own essay. It's just human nature. (Of course after making it into the top 35 your essay is on it's own...but at least you can say that you made it into the top 35). And no, I'm not saying that all top ranked essays used this approach, but I do think some did.

The real problem, I think, is allowing the authors to rate the essays and have those ratings count for anything. Do FQXi members believe this system works to encourage any real discussion of the essays and the ideas they raise? Prior to October 6, how many people, for fear of a rating retribution, say what they really think? So Concerned Public, even as you go off on Sergey, realize he is a rank amateur (literally), the symptom, not the disease - and there are people out there who, unlike Sergey, are so good at gaming the system that you don't even know they are doing it!

Hi Julian,

I don't have an answer as to why no one has previously applied antigravity to antiquarks and then looked at the potential consequences. I do know that the fact that no one did left me with some open unexplored territory. Still, when I wrote the essay I had no idea that I might discover a simple relationship between the mass ratio of the quarks within a given meson and the gravitational acceleration it experiences. It now (as of mid-September) seems obvious, and if true the following should be the case:

Pion (u, anti-d) will fall up at .28g

Pion- (anti-u, d) will fall down at .28g

Neutral Pion (u, anti-u or d, anti-d) will be weightless at 0g

Kaon (u, anti-s) will fall up at .95g

Kaon- (anti-u, s) will fall down at .95g

Neutral Kaon (d, anti-s) will fall up at .91g

Neutral AntiKaon (anti-d, s) will fall down at .91g

By the way, this also implies that the gravitational effect of gluons within baryons and mesons (see my 9/11/12 post) is, despite current theory, negligible. If the numbers above are valid the implication is that the gravitational mass of a baryon or meson is simply due to the energy of the quarks that make them up. This further implies that antiprotons will simply fall up at 1g at the Earth's surface. If the AEGIS experiment is ever carried out we will learn if this is the case in reality.

I like your concept of gravitroscopic analysis. However, even if AEGIS finds that antihydrogen falls up, and eventual improvements in precision (from 1% to say .01%) are able to determine the gravitational acceleration of the positronic component as well, it will be many more decades before we have direct data on the gravitational acceleration of mesons. They are all unstable and have lifetimes on the order of 10-8s. (The neutral pion sticks around for only 10-16s!)

Also, I want to make it clear that the whole thing could be coincidence, as the only mesons we have 'data' on (such as it is) is the neutral kaon and antikaon. Nonetheless, the fact that the relationship between the mass ratio of the s/d quarks within neutral kaon and antikaon and the gravitational acceleration they experience actually seems to work is very intriguing.

I have actually solicited the comments of a few appropriate fellow essay writers, as well as a few appropriate people outside FQXi the with regard to my 9/19/12 post. So far, no one I solicited has responded to the 9/19 post. Just crickets and tumbleweed... So I truly thank you for your kind words and especially for recognizing that something new and possibly noteworthy is going on here.

Regards,

Steve

By the way, if you want to calculate the mass ratio of the s-quark to d-quark directly it is simply: s/d = (1 mg/m)/(1 - mg/m) = (1 .91)/(1 - .91) = 1.91/.09 = 21.2

Recall that the value of 8.9 m/s2 ~ .91g for the gravitational acceleration of the neutral kaon and antikaon was experimentally determined in the paper: "Testing CP Conservation at KLOE" by G. Mambriani and L. Trentadue (arXiv:hep-ex/0007004v1, 3 Jul 2000) and that the s/d mass ratio is given in the Particle Data Group under Particle Listings, Quarks, Note on the Quark Masses, s/d mass ratio p. 18.

Also, the value of 8.9 ± 2.7 m/s2 given as the gravitational acceleration of the neutral kaon or neutral antikaon in "Testing CP Conservation at KLOE" by G. Mambriani and L. Trentadue means that the gravitational acceleration could be as low as 6.2 m/s2 or as high as 11.6 m/s2. This still permits one to speculate, as those with 'traditional' antimatter antigravity views do, that the neutral kaon will fall at 1g = 9.81 m/s2 and the neutral antikaon will rise at 1g = 9.81 m/s2.

However, using the hypothesis in my essay (which is that antiquarks have negative gravitational mass) we can do better. First, since the neutral kaon consists of a d-quark and an anti-s-quark and since the anti-s-quark is far more massive, we know that it is the neutral kaon that will rise and the neutral antikaon (anti-d, s) that will fall. Second, the Particle Data Group; 2012 Particle Listings; Quarks; Note on the Quark Masses; Chart for s/d mass ratio (p.18) gives a range for the s/d mass ratio from 17 to 22. Using the hypothesis in my essay we find that for neutral kaons and neutral antikaons:

|mg/m| = (ms/md -1)/(ms/md +1) where mg/m is the ratio of the gravitational mass of the neutral kaon (or neutal antikaon) to its inertial mass and ms/md is the ratio of the mass of the s-quark to the d-quark.

Using ms/md = 17 we find mg/m = 16/18 = .888g = 8.72 m/s2

Using ms/md = 22 we find mg/m = 21/23 = .913g = 8.96 m/s2

which gives us a value of 8.84 ± 0.12 m/s2 - a tolerance 22.5 times smaller than the tolerance obtained by Mambriani and Trentadue in their paper and one that does not permit a gravitational acceleration of 1g.