The Dirac Sea is a pre-QFT concept. It is not a part of QFT. It was a temporary working hypothesis in the pre-QFT era. It was an attempt to describe the relativistic world of elementary particles with the idea of particles taken from the non-relativistic Quantum Mechanics (QM). It did not work, The QM particles had to be replaced with quantum fields.

The relation of the Dirac Sea picture to QFT is like the Bohr's model of atom for QM. The Dirac Sea fails to explain even some of the most basic facts about the subatomic world. That's why it had to be abandoned and replaced with QFT.

Therefore, it seems to me that discussions based on the Dirac Sea idea are a blind alley here.

Good question! I'm certainly no expert, but I understand that, while the issue has not been definitively resolved, the consensus of physicists is that mass is mass. Please _especially_ see the thorough discussion in http://en.wikipedia.org/wiki/Gravitational_interaction_of_antimatter

and also http://einstein.stanford.edu/content/relativity/q296.html

Since, as I understand, the vast majority of nucleonic mass is the result of not quark rest mass but the confinement of quark kinetic energy via the strong force, for anti-nucleons to have negative mass-energy would seem to require that negative rest mass quarks' vibrations produce negative momentum... Well, it is an interesting question! Also see http://en.wikipedia.org/wiki/Negative_mass#Gravitational_interaction_of_antimatter

"... particle–antiparticle pairs are observed to electrically attract one another, often as the prelude to annihilation."

It also seems unlikely that particle pairs with unlike mass-energies would annihilate - rather, it seems that their energies would simply cancel out...

The short answer is NO. The so-called anti-matter is just matter with of the opposite C-charge to that of matter (C like C in CPT theorem in QFT). The gravitational field couples to the conserved current(s) T^{\mu\nu} known as the stress-energy-momentum tensor which is C-neutral. In other words the `anti-matter' and matter particles gravitate in the same way. So, everything falls universally in the gravitational field. This statement is just another way to phrase the Einsteinian Equivalence Principle adopted to this particular case of matter vs `anti-matter'.

I was told that it took Richard Feynman to explain to experimentalists

from the MIT (in the late 50s ?) that anti-kaons or anti-protons will also fall (universally) in the gravitational field of the Earth. These were the times when most physicists were completely ignorant about general relativity and so they had an excuse. It is rather strange that this issue seems to reappear time after time in each new (scientific) generation. It would be therefore very useful for every physicist to read the Feynman Lectures on Physics.

Thanks for the answers so far. But if you read e.g. the Wikipedia article about positrons http://en.wikipedia.org/wiki/Positron then one could certainly get away from it with the idea that positrons possess negative energy and would thus gravitationally repel ordinary matter, no? (On the other hand, they might still fall in Earth's gravitational field, if one considers F=m*a where in the mass is negative, but since the direction of force is inverted, the acceleration would still be "downwards".)

Ralph,

I can see how one might get that idea, but the "Theory" section also states that:

"Robert Oppenheimer argued strongly against the proton being the negative-energy electron solution to Dirac's equation. He asserted that if it were, the hydrogen atom would rapidly self-destruct.[4] Persuaded by Oppenheimer's argument, Dirac published a paper in 1931 that predicted the existence of an as-yet unobserved particle that he called an "anti-electron" that would have the same mass as an electron and that would mutually annihilate upon contact with an electron.[5]"

More directly, the "Experimental clues and discovery" section states:

"Carl D. Anderson discovered the positron on August 2, 1932[...] The ion trail left by each positron appeared on the photographic plate with a curvature matching the mass-to-charge ratio of an electron, but in a direction that showed its charge was positive."

If the positron had positive charge and negative mass, wouldn't the curvature of its path be distinct from an electron's?

James: Oppenheimer rightly pointed out that positrons (what Dirac predicted) are not protons. - Regarding the ion trail: one could think of a positron as being an electron moving backwards in time. In that case, the curvature of the trajectory due to the magnetic field would be the opposite direction as that for a negatively charged particle (electron) traveling forward in time.

Ralph,

Based on Oppenheimer's argument, "Dirac published a paper in 1931 that predicted the [...] "anti-electron" that would have the same mass as an electron and that would mutually annihilate upon contact with an electron.[5]"

If I understand this correctly, Dirac finally predicted in 1931 that the positron would have positive charge and identical mass to the electron, discarding his earlier negative energy argument.

I'm certainly no particle physicist, but as the Wikipedia entry states:

"The backwards in time point of view is nowadays accepted as completely equivalent to other pictures, but it does not have anything to do with the macroscopic terms "cause" and "effect", which do not appear in a microscopic physical description."

I think that indicates that the macroscopic ion trail cannot be seen to be produced 'backwards in time'. In that case I think that cloud chamber observations do not support the interpretation that positrons have negative mass. I could be wrong...

There's two 'types' of mass, the mass that's measured as a resistance to being accelerated (inertial mass) and the mass measured in response to gravity (gravitational mass). For matter these are the same, and their ratio is equal to 1. However, if antimatter 'follows suit' with the rest of how it interacts with the universe, it could have a ratio of -1.

CERN's Alpha experiment locked 'antihydrogen' atoms (an antiproton orbited by a positron) inside a magnetic field, and then watched where these 'anti-atoms' went when they turned the field off. They were specifically looking for anti-atoms that took the longest time to leave the field (about 20- to 30-thousandths of a second after it was turned off), since they would have the lowest energy, and thus would be affected by gravity more than higher energy anti-atoms.

"Late-escaping particles have very low energy, so gravity's influence is more apparent on them," said Berkeley Lab's Jonathan Wurtele, in a press release. "But there were very few late escaping anti-atoms; only 23 of the 434 escaped after the field had been turned off for 20-thousandths of a second."

With only that many, the question about whether antimatter falls upwards or downwards is still up in the air it seems, but they were at least able to rule out the most extreme cases.

Their results showed that the ratio of gravitational mass to inertial mass for these antihydrogen atoms was somewhere between 110 and -65 (remember that they're looking for it to be somewhere around 1 or -1).

Basically, what that mean is, if antihydrogen falls downward, its gravitational mass is less than 110 times stronger than its inertial mass. If it falls upward, its gravitational mass is less than 65 times stronger than its inertial mass. That's a pretty wide range, but models of the experiment apparently set the limit of the ratio at between 200 and -200, so while their results aren't mind-blowing, they have narrowed it down.

So, we're not exactly at 'flying car' results, but this is really just the first step. The Alpha experiment is due for an upgrade soon, to Alpha-2, which will cool the anti-atoms with a laser before they're released from the magnetic field. That will give them more low-energy atoms to get results from.

According to Joel Fajans of Berkeley Lab in California, "in the unlikely event that antimatter falls upwards, we’d have to fundamentally revise our view of physics and rethink how the universe works."

"Is there such a thing as antigravity? Based on free-fall tests so far, we can’t say yes or no," says Fajans. "This is the first word, however, not the last."

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Up or down: is antimatter the key to anti-gravity?

Geekquinox Wed, 1 May, 2013

Issam Sinjab,

Thanks for the report. I found the ALPHA Collaboration at http://alpha.web.cern.ch/ - the recent research report is currently freely available at http://www.nature.com/ncomms/journal/v4/n4/pdf/ncomms2787.pdf

There is a very thorough news report of the research at http://physicsworld.com/cws/article/news/2013/apr/30/alpha-weighs-in-on-antimatter

Another excellent report - http://spectrum.ieee.org/tech-talk/aerospace/astrophysics/does-antimatter-fall-up - notes that there are two competing experiments within CERN: http://aegis.web.cern.ch/aegis/ and http://gbar.in2p3.fr/ that will proceed later on.

If one (like me) were to prematurely jump to conclusions, the somewhat tighter bounds on an indicated negative gravitational mass (producing apparent antigravity) might suggest that it does not exist. Please see Fig. 2 in the research report. More prudent evaluation should await further tests...

BTW, if antimatter has negative mass, would it be gravitationally 'attractive' to itself? Since mass produces the curvature of spacetime, what effect would aggregated negative mass have on it? It would seem to only be able to aggregate if it also produced an identical curvature...

I also find that there is an observed Positronium - an unstable "exotic atom" composed solely of an electron and positron orbiting around their common center of mass. That this configuration can occur seems to be definitive evidence that electrons and positrons have identical mass.

Please see http://en.wikipedia.org/wiki/Positronium

"Positronium (Ps) is a system consisting of an electron and its anti-particle, a positron, bound together into an "exotic atom". The system is unstable: the two particles annihilate each other to produce two gamma ray photons after an average lifetime of 125 picoseconds or three gamma ray photons after 142 nanoseconds in vacuum, depending on the relative spin states of the positron and electron..."

Please also see http://en.wikipedia.org/wiki/Muonium

"Muonium is an exotic atom made up of an antimuon and an electron...

Due to the mass difference between the antimuon and the electron, muonium (μ+e−) is more similar to atomic hydrogen (p+e−) than positronium (e+e−). Its Bohr radius and ionization energy are within 0.5% of hydrogen, deuterium, and tritium.[4]"

Additionally, the muonium configuration, with its Bohr radius and ionization energy within 0.5% of hydrogen & its variants, seems to strongly indicate that its electron is orbiting the ostensively much more massive antimuon very much like electrons orbit protons in hydrogen atoms. This also seem to preclude antimuons from having negative mass...

The question if I understand it is that would anti matter be affected differently by gravity differently than matter. The evidence suggests otherwise. I.e. there are positrons, but I have never heard of an electron-Positron collision being altered by being in a gravitational field. I am prepared to be wrong though.

Many thanks james for the references.

Except for people who want funding to do hard experiments, (and even then) the overwhelming majority of expert opinion is that matter and antimatter respond identically to the gravitational field. It has been shown very precisely that various matter falls at the same rate toward the earth. As all matter contains some antimatter, these experiments are precise enough to show that antimatter must also "fall down", not up. Moreover, antimatter falling up would require changing the principle of equivalence, which (in turn) allowed the derivation of General Relativity, which has (since) been very well confirmed. Finally, there was lots of antimatter in the early universe and if it responded differently to gravity, there would be lots of changes in big bang cosmology, which (again) is reasonably well confirmed.

Probably, we should not deny funding to experiments that try to establish that the principle of equivalence does not apply to antimatter. Equally, however, we should expect that they will confirm the principle of equivalence rather than call it into question.

In general terms the idea of negative mass are studied many years ago with some experiments that tryed to give a picture about that condition, I read something obout that but in my point of view the experiment presented didn't give a definitive conlusion, that in this idea. In the case of the presence of antimatter around the earth, in principle it's confirmed with a detection of antiprotons in the Kuiper's belt. This detection gave some ideas about the possibility that the antiprotons can be produced by the sun.

the other point I read here, is the consideration of the effect of the gravitational field of antimatter. The gravitational field of course affect the antimatter with the same kind of interactions like normal matter, remember the condition that the matter and antimatter in first aproximation only chance in the carge, the other properties are maintained for both cases

Rolfe Petschek,

"As all matter contains some antimatter..."

I think this assertion is false. Any antimatter contained within a material object would quickly interact with its material counterpart and annihilate. I think this invalidates the remainder of your argument...

Alexis Chechelev,

As I understand, most antiparticles near the Earth are thought to be the product of cosmic ray collisions with particles in the Earth's atmosphere. Please see http://en.wikipedia.org/wiki/Van_Allen_Belt#Antimatter_confinement

"In 2011, a study has confirmed earlier speculation that the Van Allen belt could confine antiparticles. The PAMELA experiment detected orders of magnitude higher levels of antiprotons than are expected from normal particle decays while passing through the SAA. This suggests the Van Allen belts confine a significant flux of antiprotons produced by the interaction of the Earth's upper atmosphere with cosmic rays."

Also see http://arxiv.org/abs/1107.4882v1

James: I agreed with that but, if we put our sight on the nuclear processes on stars we can see that can produce some antiparticles (maybe the flux not necessarily is big, but maybe gives some contribution on it), in which some of them can be antiprotons. The idea of the cosmic rays is obviouly the most suitable theory. thanks for the link of the article i'd lost it

James: the concept about the interaction between both kind of matter not necessarily is incorrect. Some Ideas has been proposed about that, in particular the possibility of existence of domains in which can interact both kind of matter like a Leydenfrost effect ...

Antimatter has a positive mass so it has a behaviour under a gravitational field which is proportional to this mass, regardless of it's 'anti' status. The possible existence of dark energy or a quintessence field which provides a negative pressure accounting for the cosmological constant begets the question of a related form of matter which would have the behaviour under gravity that you describe.

Thanks for all the answers and comments. I want to remark that, as indeed Rolfe pointed out already above, the equivalence principle would require that even negative mass falls "down" (towards Earth). - Simply speaking, one could see that from F (the gravitational force) being the opposite direction for negative masses (pointing "away" from Earth), but then due to a=F/m, the acceleration would be again pointing "towards" Earth, thus causing negative masses to fall down as well. ... But in terms of Coulomb interactions, positron and electron clearly attract each other, so here the negative mass concept does not fit in, so the picture of a hole in a sea of negatively charged electrons seems to give the wrong idea.

Hi, I would like to add a very short comment. The Weak Equivalence Principle can be seen as the statement that all matter falls along geodesics ("Paths") independenlty on its internal composition. But, as said, it is a principle and as such it needs experimental validation. Until now all experiments (see C. Will review on living reviews in relativity, it should be free otherwise search for it on arxiv.org) have ruled out any violation of such principle. However the possibility to have anti-hydrogen could represent a new way to test this principle as in fact having the same mass as the normal hydrogen any violation of the WEP will be due only to a composition dependence.

So if (are we?) we will ever be able to produce anti-hydrogen and keep it stable for long enough time it will surely represent a valuable tests of our gravitational principle.

Dario Bettoni,

I agree - the Weak Equivalence Principle applies to conditions that do not include any negative mass. If negative mass was experimentally found to be in violation, the principle would simply require revision.

As I described previously, I think there is a separate line of evidence that antimatter cannot have negative mass in the even transient configurations of compound Lepton exotic atoms of bound matter and antimatter. Again, please see http://en.wikipedia.org/wiki/Positronium and http://en.wikipedia.org/wiki/Muonium

Moreover, another experiment pointed out to me indicates that electrons and positrons in positronium atoms annihilate faster than predicted by quantum electrodynamics theory. Please see http://www.nytimes.com/1987/04/07/science/science-watch-flaw-in-physics-theory.html?src=pm

“The group reported in Physical Review Letters that atoms of a bizarre, short-lived substance called positronium annihilate themselves significantly faster than the theory of quantum electrodynamics predicts, and hence, there may be something seriously wrong with the theory. According to Dr. Arthur Rich, a member of the group, 'even a difference half as small would be cause for alarm.'”

This result could be explained if the electrons and positrons within the positronium atoms were were also interacting gravitationally, in addition to electrdynamically.

The more direct measurements of antimatter hydrogen atoms' interaction with gravitational fields should confirm expectations. Finding negative mass, however, would require revision of several fundamental tenants of established theory...

The issue with Positronium annihilation is solved, and it agrees with QED calculations very well. There is PRL paper (cca 2009) saying: long-standing discrepancy with Positronium lifetime has been finally resolved. Regarding the anti-Matter reaction to gravitational fields, 95% of physicists say it will be attracted as ordinary matter is, and there are arguments from general theory of relativity supporting this opinion. But we do not know for sure, and that is the reason for AEGIS experiment at CERN, verifying the behavior of anti-Hydrogen subject to gravity. Positronium is formed as a mid-step in AEGIS setup, and when mating with anti-protons the antiHydrogen beam is formed, which then propagates in the beam pipe subjected to gravity of Earth.

So let's wait for the results form CERN !

Peter Filip,

Thanks, but I couldn't find any PRL 2009 paper stating "long-standing discrepancy with Positronium lifetime has been finally resolved." A link would be helpful to me.

At any rate, that would not address the fundamental inertial interaction between electrons and positrons in positronium atoms. I presume that if positrons' invariant rest mass were negative, that they could exhibit neither positive inertial mass (allowing their inertial interaction with electrons in positronium) nor positive gravitational mass. As a result, invariant particle mass, inertial mass and gravitational mass should be at least either all positive or all negative. In this case, the existence of positronium seems to provide evidence that antimatter mass must be positive.

There certainly seems to be a great deal of interest in continuing with the ALPHA experiment - perhaps they can eventually produce significant results, which they have not done to date. Even if they can eventually produce definitive results indicating that antimatter responds to gravitational fields identically to other matter, it might be useful to have some independent confirmational evidence supporting their results!

I don't understand why there should be so much opposition to considering the evidence of antimatter mass provided by positronium and muonium - unless it's considered to be a threat to the continued funding of the related CERN experiments. IMO, the planned experiments should be transparently continued in order to determine whether they can produce reliable results that agree with the evidence provided by the very existence of positronium and muonium atoms.

Hi James,

here is the link: http://prl.aps.org/abstract/PRL/v90/i20/e203402 ,

it was in 2003 when the ortho-Positronium puzzle was finally resolved.

Regarding the gravitational interaction of anti-Matter, there are many arguments, but at the end, these are only the arguments... You need the experiment at the end, because, I think that just arguments would not convince You to put Your head under the Hammer, which is triggered by anti-Matter attraction/repulsion to the Earth. Try to think in this way regarding the final resolution of anti-Matter interaction with Gravity and regarding the statements like "I presume...". Would You put your head under the Hammer ? I would not.

My feeling is that AEGIS experiment is a justified one, as well as was/is ALPHA.

Hi Peter,

Thanks for the link - I'll read it.

I think that the existence of bound particles of matter and antimatter offer observational evidence - more than a theoretical argument. Why should this evidence be dismissed?

I wouldn't expect to have any effect whatsoever on the AEGIS/ALPHA collaboration continuing their experiments. However, based on their assessment, success cannot be assured. It's be a shame to have direct evidence of positive antiparticle inertial mass be ignored just in case its gravitational mass cannot be definitively determined.

If it is found that particles with positive invariant mass can exhibit negative gravitational mass - I think some really interesting revisions to physical theory would be necessary - more so than if! antiparticles had been found to have negative invariant mass!

Peter,

Thanks again for the link. As often happens some have disputed those results: see http://arxiv.org/pdf/quant-ph/0604171v1.pdf. As a casual reader, I see that the Michigan measurements formed the positronium imbeded within s pourus film (to eliminate non-electrodynamic perturbances). I'd have to wonder if this film suspension might interfere with any gravitational influence on decay rates. Again, my suggestion was that the anomalous decay rates conflicted with the prediction of quantum electrodynamic theory because gravitational influences were not considered (were considered to be anomalies)...

Hi James.

There are many interesting aspects of Positronium, including supersymmetry and Mirror universe hypotheses. But the inertial (mass) properties of anti-matter particles were tested many times on accelerators with beams of positrons and anti-Protons, e.g. at CERN and Fermilab. There is no need to change our equations for the accelerator physics with anti-matter beams. The gravitational interaction with Earth is not experimentally verified. I think this should be done, with AEGIS having a chance to do it using neutral antiHydrogen atoms. I remember there was an attempt to verify gravitational interaction of positrons on Earth comparing free fall of positrons and electrons in the vacuum in a special Copper tubes, and it did not work well (too many electromagnetic effects, eddy mirror currents etc.).

Hi Peter,

Thanks for mentioning that the inertial mass of antimatter particles had been established in collider experiments - that has not been mentioned in any report or discussion of ALPHA/AEGIS testing that I've seen. Again, I am not objecting to tests of antimatter's interaction with gravitation - although there seems to be great difficulties that must be overcome to produce reliable results.

Meanwhile, if antiparticles with positive invariant and inertial mass do produce negative gravitational mass effects, wouldn't that necessitate that there is an electrical charge component of gravitation? If so, is there any theoretical basis for this possibility?

Never. See an interesting discussion in

Relativity and

Gravitational waves. first chaptere

Hi all,

I would like to add a couple of points to this interesting discussion. First, in the formalism of the quantum field theory (QFT) particles and their anti-particles are just two different demonstrations of the same quantum field. They are two possible states in which the field can be found. Secondly, the mass is a characteristic of the field itself. As such, it stands above the notions of particles and anti-particles. The mass of the given field is there and exhibits observable consequences even if the given field is in its ground state, i.e. vacuum, with no particles/anti-particles of the given sort flying around in this universe

I like the following analogy: a quantum field is like a coin; the mass is a characteristic of the coin as a whole. Particles and anti-particles are like two sides of the coin. By definition, they have to be associated with the same mass.

Of course, the picture above can be used as long as the QFT is valid. Thus, checking on the equivalence of the mass of particles and anti-particles we are asking about validity of this formalism, I think. The problems with the application of this formalism to the gravity, which in turn is closely related to the notion of the mass, could be a sign that the QFT has limited validity.

On the other hand, the formalism of the QFT has proven to be very successful in describing the remaining three interactions. Therefore, I would not expect the QFT to be thrown away completely one day. It is rather a low energy limit of some more general formalism. Because of that, I would not expect a large discrepancy between the mass of particles and anti-particles to be found, either, if there is any at all.

Now, let us consider the compound objects rather than the elementary particles. The mass of the objects is often mostly the result of the interactions holding the body together rather than the sum of the masses of the constituent particles. In particular, about 90% of the mass of baryonic bodies results from the strong interactions. Should there be a particle/anti-particle discrepancy between the interactions responsible for the masses of compound objects we would observe differences between the masses of ordinary objects and their anti-matter counterparts.

Now the question is can the particle/anti-particle interaction discrepancy occur within the QFT formalism? I might be wrong but I think that the QFT interactions that distinguish particles and anti-particles are those that violate the CP symmetry.

This is a possible QFT scenario. There are even a few processes in which the CP violation have been observed.

Hi Mikulas,

Thanks for your very enlightening comment!

Considering the mass of compound objects, wouldn't their additional binding mass be derived from their fundamental particle's inherent, invariable mass? For example, if I understand correctly, the binding mass of nucleons is the product of their quarks' kinetic (propagation) energy and their invariant mass - bound by the exchange of the strong interaction via gluons. In this case, mustn't total nucleon mass be either positive or negative depending on the state if its component particles' invariant mass'?

Also, in the bound state of nucleons, isn't their total of component particles' invariant mass and their binding mass then considered to be the nucleons' invariant rest mass?

Separately, is there any possible theoretical basis for the concept of 'negative mass', even in QFT, since that also seems to require the existence of negative energy, velocity, momentum, etc.? It would seem to violate many established fundamental laws of physics, especially since the (positive?) inertial mass of antiparticles has already been established in particle collider experiments and, if I understand correctly, both it and gravitational mass are derived from the invariant rest mass and energy of a system.

I think all CP violating phenomena observed so far are related to hadrons (mesons or baryons) containing s,c,b quarks. So if only d,u quarks and d',u' antiquarks are considered, there is no difference between the interaction of matter and anti-matter, which could otherwise be originating from CP-violating phase in (CKM matrix) Standard model.

I believe AEGIS can be a successful experiment in determining gravitational interaction of anti-matter, because they want to measure interference pattern, which is influenced by gravitational phase-shift. It is not just another attempt to measure falling anti-protons or positrons, it is and interference shift measurement...

See here: http://www.mi.infn.it/~trezzi/about.htm

In the simplest of terms, as I understand the Dirac picture of a positron, it is a hole in a (negative-energy) Sea of electrons, each electron with rest mass m. In a vacuum the negative-energy Sea is full, and the positive energy states are empty. The rest energy of an electron is mc^2 so that if a single one is missing from the Sea this gives an energy --mc^2 for the hole, which is the antiparticle. Here it looks like the "rest mass" of the positron might be interpreted to be --m. The hole in a sea of negative charges interacts with another (positive-energy) electron as though it were a positive charge -- this effect being viewable to say that the (positive-energy) electron repels the other negatively charged (negative-energy) electrons in the Sea, so that the electrons of the Sea moving away from the positive-energy electron engender the hole moving towards the positive-energy electron. The dynamics of the hole then are expected to be like that of a positively charged particle with positive inertial mass. This is so far accurately consistent with expts, say on positronium. Next eletrostatic forces are so incredibly much stronger than gravitational forces, that to detect any gravitational force effect it seems almost a prerequisite that one deal with neutral antimatter -- anti-helium would be even better than anti-hydrogen, as the polarizability and Van der Waals forces would then be a little smaller (and the mass a little greater in magnitude). For neutral anti-matter, being a hole in a Dirac Sea of parent particles, one might imagine a gravitational interaction analogous to a Coulomb interaction reversing the direction of the forces associated with the parent particles. That is, the one might imagine that the positive-energy matter gravitationally attracts the negative-energy parent particles and thence (gravitationally) repels the hole. Thence the hole would act as though it has negative gravitational mass (and a positive inertial mass). I feel certain that there is no good direct macroscopic experimental evidence so far that the gravitational mass of anti-matter is positive -- there is so little of it around (in any positively identified context), that macroscopic measurements have no degree of accuracy remotely able to discern its gravitational interactions. Finally the simple Dirac-Sea picture surely must entail lots of renormalization effects -- and QFT and general relativistic equivalence principles are well accepted. But nailing down especially qualititative things (like the conciebable possibility of negative gravitational masses) seems to me a worthy end -- if they can end up making accurate enough measurements.

Douglas,

Wouldn't a negative charge * a positive mass produce negative EM energy, while a positive charge * an identical positive mass produce positive EM energy?

James,

It seems to me that you are asking about my comment on the energy of a hole in the Dirac Sea having an energy of --mc^2. The point here is that out of the Dirac equation, for a single Fermion particle, here taken to be an electron, there comes a conventional continuum of unbound states above the rest energy +mc^2, and also a continuum of unbound states downward in energy below --mc^2. Dirac imagines that for a vacuum the negative-energy (1-electron) states are completely full of ordinary electrons, spin up & down in each level. But one of these "conventional" electrons may be excited from a "low-speed" energy state near --mc^2 up to one near +mc^2, thereby giving a single free electron and a single hole. That is we have pair creation -- such as might be accomplished by a couple of very energetic photons. The electron of course has positive mass (and always had, even before excitation), and rest energy +mc^2. But energy is conserved, and there is a hole in the Sea of states starting at --mc^2 and down, so that this hole has energy --mc^2. So far as I know this is not contraversial -- well except that a problem arises with a single electron problem being suddenly converted to a many-electron problem -- indeed something like an infinity of electrons if the negative-energy levels are to be filled all the way down -- and thence some sort of renormalization problems might arise. These comments ignore the (ordinarily very much smaller) electromagnetic energy of interaction between electron & positron, and its associated mass shift Delta(m) = Delta(E)/c^2. The bound states between a positron & electron are observed for positronium, but are displaced in energy slightly above --mc^2 (for the positron) and below +mc^2 (for the electron).

The Dirac Sea is a pre-QFT concept. It is not a part of QFT. It was a temporary working hypothesis in the pre-QFT era. It was an attempt to describe the relativistic world of elementary particles with the idea of particles taken from the non-relativistic Quantum Mechanics (QM). It did not work, The QM particles had to be replaced with quantum fields.

The relation of the Dirac Sea picture to QFT is like the Bohr's model of atom for QM. The Dirac Sea fails to explain even some of the most basic facts about the subatomic world. That's why it had to be abandoned and replaced with QFT.

Therefore, it seems to me that discussions based on the Dirac Sea idea are a blind alley here.

... and let me add a comment to my first comment which would relate it more closely to the original question we are discussing here.

The mass I was talking there about is the inertial mass. A priori, it has nothing to do with the gravitational force/interaction. It takes the equivalence principle to relate this mass to the gravitational interaction. The equivalence principle has been well tested in the macro-world. How the gravity works in the sub-atomic world is a big question of today's physics.

There exists QED formulation in curved space-time, and Maxwell equations in curved space-time metric are available. However considerations of space-time curvature in the close vicinity (e.g. 10^-12m) of tau-lepton and possible influence of Kerr-Newman metric on elementary QED processes with tau leptons is still missing, I guess. This is however another topic, different from the original discussion here, I think.

No: The CPT theorem implies that particles have the same mass as antiparticles and General Relativity implies that gravitation is always attractive (the graviton has spin 2).

Dear Ralph,

Antimatter, regardless if it is a positron, anti-proton, or more complicated atomic structure, has a positive amount of mass, thus an antimatter would react with gravity very similarly to (regular) matter.

The most common and easily lab-produced reaction is (electron-positron pair annihilation). In this reaction, the amount of end point energy is 1.022 MeV coming from the sum of two 0.511 MeV rest mass of the electron and positron particles. This is plus their kinetic energy (K.E) prior to annihilation, but the (e-e+) reaction cross-section rapidly decreases as the K.E. increases, such that e-e+ annihilation is most preferred at thermal K.E. The production of this amount of energy was experimentally verified to a high precision.This amount of energy (1.022 MeV) clearly shows that the mass of e+ is (+ve 0.511 MeV, or ~ +9.11x10^-31 kg), which will react with gravitational field like an electron does.

However, there is some arguments going that, antimatter might react with gravity somewhat differently than matter (as in free falling-down acceleration), but it is non-proven argument.

Please note that, an (Antimatter) is called by this name for historic reasons only. A more precise nomenclature is a (matter of antiparticles). Antiparticles differ than particles in their intrinsic charge only, they have an opposite charge than their twin particles (not an opposite mass, nor matter).

Also, a natural system produced prior to positron-electron annihilation is the (Positronium Atom, Ps); which might exist in two states: the ortho Ps (o-Ps) when both spins of particles being orthogonal (both up or both down), leading to a long system's lifetime (in vacuum it is ~140 ns); and the para-Ps (p-Ps) when spins are parallel (up-down) with free-space lifetime ~ (125 ps).

These modes, beside the free positron annihilation mode in matter (with ~ 0.5 ns), are the preferred annihilation modes for positron. More complicated systems, as (e-e+e-) occur with very small probability in nature; and those as (e+p-, the anti-hydrogen atom) with even less probability.

Regards

Ahmed, sure for an electron with rest energy mc^2 the rest energy of the positron is mc^2 (and not --mc^2), but the point is that there is a question whether this m is the inertial mass or the gravitational mass. Yes, the reason for the difference in lifetimes for the two positronium levels is because one is a singlet state (with antisymmetric anti-parallel spins) and the other is a triplet level (with 3 states spin-symmetric under spin exchange). The triplet state (for the 2 Fermions) being symmetric in spin space is antisymmetric in coordinate space, so that there is a Fermi hole, meaning that the electron & positron do not get quite as close together, so that in turn triplet positronium has a longer half life than the singlet state which allows contact between the electron & positron, and can then undergo pair annihilation..

Miklaus, indeed the Dirac-Sea picture has severe problems -- and requires at the very least much renormalization. The point is that very useful predictions have been made based on the Dirac-Sea picture -- and still are so taught -- and a further suspicion (if not prediction) which arises from this picture is that the gravitational mass is --m. The equivalence principle from general relativity strikes me as a more reliable indicator that the gravitational mass is + , even though it has not been tested at this scale on antimatter, so far as I know. I have been unsure whether QFT predicts or assumes that the gravitational mass is +m -- I guess that you are saying that QFT predicts this.

To the extent that evidence of positive positronium inertial mass implies that positrons and indeed all fundamental antiparticles in have positive rest mass, how could a bound configuration of antiparticles (such as antihydrogen) produce negative gravitational mass?

Dear Douglas,

Thanks for the clarification. Due to Equivalence Principe, both types of mass act similarly with a gravitational field. Please refer to any of the following illustrations

http://arxiv.org/pdf/hep-ph/9909392.pdf

http://www.as.utexas.edu/astronomy/education/spring06/komatsu/secure/lecture11.pdf

The original question mixes up the idea of Dirac Sea with classical experience. "Falling into a hole in Dirac Sea" is explained like a ball falling into the (water) sea; an explanation that misses the point of positron creation/annihilation, or any particle-hole creation process, entirely. Such an idea exists not only with positron, but with electron layers in a conductive material, and in nuclear reactions as well (the Exciton Model).

In all cases, a (hole) is predefiend as an entity that holds the same mass, but an opposite (something) - charge, potential energy level, or velocity.

The first paper mentioned above suggests creation of gravity events during positron annihilation, which is pointed partially in the main question, hence the confusion with different gravity behavior, I think.

Regards,

Ahmed

Douglas, I believe that

1/ the Dirac Sea concept is not a part of the QFT formalism;

The DS is not compatible with QFT. For example, how to include bosons in this picture? There is a lot of reasons why the DS is not compatible with QFT much simpler ones than renormalization.

2/ there is no such a thing as the gravitational mass within QFT;

simply, because we do not have QFT of gravity. Thus QFT neither assumes nor predicts anything about the gravitational mass. When we relate the gravitational mass to the inertial mass we work outside QFT. All claims about the gravitational mass of elementary particles are just extrapolations of our big world theories and experience.

I can even speculate that successful microscopic theory behind gravity will not contain the notion of the gravitational mass. Recall that while the temperature and the pressure are important and well defined quantities of the thermodynamics it is meaningless to attribute these quantities to an individual molecule of a gas.

Very interesting question, in my view the mass is always positive and anti matter will fall as matter does.

The trapping in 2011 of anti hydrogen for 1000 seconds opened the possibility of cooling these to temperatures where gravitational effects will become apparent. We'll have to wait for new experiments.

The Alpha experiment at LHC aims to test the equivalence principle on antimatter. Of course at moment we have no theoretical reasons to believe that "antimatter" falls any differently from "matter". Nevertheless, the equivalence principle has been so far tested only on "matter", so it is an interesting experiment the possibility of extending the same test to "antimatter" and in case nature has decided to couple extra gravitational degree of freedom (such a scalar field) to antimatter objects than this experiment can put constraints on the amplitude of their couplings. Now to come to your question, if such extra-couplings are there and sufficiently large to be detectable with ALPHA, then they will alter the free fall of antimatter compared to matter, i.e. the Newton constant of antimatter will have a different value than that of matter. Antimatter will fly upward only if these couplings are of opposite sign compared to the tensor coupling and if they are larger such as to reverse the sign of the effective Newtonian constant. Again theoretically there is no reason why this could be so. Nevertheless performing the experiment will be a nice piece of work anyway.

Good observation, Pier. And I argue that until ALPHA is performed that we do not know about the extra gravitational degrees of freedom as you named it. I predict that the tensor couplings are the same "direction" as the couplings which will be measured by ALPHA, which will mean that matter and anti matter behave the same way in a gravitational field.

Actually, there are some particles, notably light / photons, which are their own anti-particles. While the accuracy is not great, it is known that light falls as predicted by general relativity, within experimental error. As we often think of photons as not merely their own anti-particle but also as a mixture of the electromagnetic field and positron-electron pairs, this would seem a confirmation that matter and antimatter behave similarly in gravitational fields.

Moreover, "matter" and "antimatter" are not really terribly fixed concepts. The vast majority of the mass-energy of a nucleus comes from what we might chose to call "matter" quarks. However, at least some of it comes from anti-matter quarks: these are needed (for example) to make pions, which are the primary particles exchanged in the strong nuclear forces. While, for any given nucleus we might imagine defining matter as what we find in that particular nucleus, this can not be done consistently for all nuclei as they contain different numbers of pions. These pions, of course, form and disappear dynamically so that they do not annihilate other matter: only themselves. Very accurate experiments on materials made of quite different nuclei, containing different number of anti-quarks, together with the fact that light behaves as predicted, make it very hard to imagine that anti-matter (specifically an anti proton, anti electron or anti hydrogen) can "fall up".

As others have remarked, it is possible for antihydrogen to fall at a different rate than hydrogen. Theories suggesting this tend not to be about general relativity but about other forces. That is: matter can attract matter differently from antimatter, on large distance scales.

very nice view Prof. Rolfe

To answer the original question "what are your expectations for the outcome of the anti-hydrogen experiment?" I would like to say: I expect them to find that the gravitational acceleration of antimatter on earth is the exact opposite of that of ordinary matter.

I have identified a consistent set of fundamental principles that would make such a repulsion possible, and that also in principle solves the photon/antiphoton problem.

But there is still work ahead as the principles are rather abstract, and of course the whole construct has to be rejected if it is established that gravitation is attraction only.

Dear all

Here I am posting five great mysteries of anti-matter. But I am very much surprised that if antimatter fully existed, so why not one can claim 100% in about the dark energy. As I know in my best knowledge no one claim with full evidences for dark energy. Actually this dark energy is anti-matter as I know.

http://www.newscientist.com/special/antimatter-mysteries

Rolfe,

Interesting discussion points, but how does any of it relate to a gravitational field's effect on antimatter? As you state, there are some reasons to expect that hydrogen and antihydrogen might fall at different rates - but not as a result of gravitation.

As for pions, I have no expertise here, but I understood that gluons were the mediator of the strong nuclear interaction. As I understand, pions do illustrate the effects of strong force interactions...

Moreover, as I've explained previously, the evidence that an electron orbits an antimuon in muonium demonstrates that antimuons' mass is greater than electron mass - if they had negative mass, muons should orbit electrons. Since, as far as is known, the effects of gravitation vary in proportion to particle mass, if antiparticles have positive mass they should respond to gravitational effects just as particles.

Dear Nevzat Guler,

If a gravitational repulsion would be detected then not only the definition of antimatter has to be reconsidered: in my honest opinion, the entire current idea of what matter and antimatter are -- in particular the notion of the 'quantum' -- is then wrong. In that case, notions like for example quarks and virtual pairs are terms in a mathematical model that gives good predictions in its area of application, but their real existence wil then be challenged.

Let us add one more twist to this question: ordinary anti-matter may well be confirmed to be attracted by gravity of Earth, in the AEgIS experiment at CERN. Ordinary here means: antiproton = anti-u and anti-d quarks and positron. But still, there can be a possibility, that s-quarks and s-anti-quarks could be differently interacting with gravitational field of Earth. At least, some time ago, this idea has been proposed in attempts to explain CP violation in neutral Kaon decays...

Peter,

Interesting but, since I understand S (strange) quarks decay into up quarks, it's difficult to understand what distinct property of strange antiquarks would produce an anti-gravitational interaction...

Once more: matter and anti-matter have the *same* mass. So antimatter in a fixed gravitational field, reacts exactly as matter does. Only the charges of internal symmetries ``change sign'' (assuming they're additive, technically they're conjugate); the mass and spin, charges of the Poincaré group, remain the same for matter and antimatter.

The purpose of these experiments, indeed, is to calibrate the apparatus. To search for *new* phenomena, one has to be sure the apparatus can detect *expected* phenomena. So it's necessary to test the stability of the fields that realize the trap by monitoring how antiprotons and positrons move, as well as protons and electrons. In this way, having ``background'' under control, it is possible to speak of a ``signal'', of a new effect.

James, just have a look into original papers... One of them states: "We reexamine the possibility that CP violation observed in the neutral kaon system may be explained by different acceleration of matter and antimatter in a gravitational field. We criticize the impossibility arguments which led, to the rejection of idea..."

Also... It is important to keep in mind, that CPT theorem has not been proved for curved space-time, and it applies to stable particles only. Since s-quarks are unstable, new possibilities become open, e.g. mass of anti-s quark may differ from the mass of s-quark by tiny amount, which may be related to CP violation effects....

Proving that stable matter behaves exactly in the same way as stable anti-matter (e.g. by studying anti-hydrogen in AEgIS experiment at CERN) might not be the whole physics story.

It's interesting that people, that discuss new explanations for some effect don't seem to realize that, if they ocurred in that context, they could have appeared, much more strongly, in other processes.

Antimatter flying upward in the Earth's gravitational field would mean that mass changes sign from matter to antimatter. If this were true, this would mean that pair production of antimatter, e.g. electron-positron pairs, would be very easy, since the energy required would be much less (even zero!) than that required to create a single particle. Chemistry and biology would, hence, be completely different.

It would, also imply that the cosmic ray photo that identified the positron (or many other (anti)particles) couldn't be correct, since the ratio of charge to mass would be the same as for the electron-so it would curve the same way in a magnetic field.

These are just some of the more immediate consequences that rule out that the statement could be correct-the Particle Data Group booklet is a detailed compilation of other reasons that rule it out.

If one wants to claim that ``smaller'' effects could be due to such violations of Lorentz invariance (since this is what a difference of mass between matter and antimatter would entail), for instance, one has to take into account measurements from the KLOE collaboration that tested the consequences of CPT in kaon decays:

http://indico.cern.ch/getFile.py/access?contribId=19&sessionId=2&resId=0&materialId=paper&confId=164376

So a new explanation must confront such constraints.

Anyway, with unstable particles = e.g. s-quarks and anti-s, the question of their interaction with gravity becomes more subtle. There is one known Fermilab measurement of CP-violating parameter "eta+-" in neutral Kaon system, which deviates from the world average data by 9 standard deviations. This was the experiment, where the beam was not exacly horizontal, so speculations exist, that gravitational effects might be involved...

Systematics of beam alignment would overwhelm general relativistic effects of the Earth's field. 9 sigma in this case simply expresses just these systematics.

Thanks for the excellent discussion! As an casual bystander I must refer to http://en.wikipedia.org/wiki/Positonium, which states:

"Positronium (Ps) is a system consisting of an electron and its anti-particle, a positron, bound together into an "exotic atom". The system is unstable: the two particles annihilate each other to produce two gamma ray photons after an average lifetime of 125 picoseconds or three gamma ray photons after 142 nanoseconds in vacuum, depending on the relative spin states of the positron and electron. The orbit of the two particles and the set of energy levels is similar to that of the hydrogen atom (electron and proton). However, because of the reduced mass, the frequencies associated with the spectral lines are less than half of those of the corresponding hydrogen lines."

It continues, in the section "States":

"Positronium in the 2S state is metastable having a lifetime of 1.1 µs against annihilation.[citation needed] If the positronium is created in such an excited state then it will quickly cascade down to the ground state where annihilation will occur more quickly. Measurements of these lifetimes, as well as of the positronium energy levels, have been used in precision tests of quantum electrodynamics.[1][4]

"Annihilation can proceed via a number of channels each producing one or more gamma rays. The gamma rays are produced with a total energy of 1,022 keV (since each of the annihilating particles have mass of 511 keV/c2), the most probable annihilation channels produce two or three photons, depending on the relative spin configuration of the electron and positron. A single photon decay is only possible if another body (e.g. an electron) is in the vicinity of the annihilating positronium to which some of the energy from the annihilation event may be transferred. Up to five annihilation gamma rays have been observed in laboratory experiments,[5] confirming the predictions of quantum electrodynamics to very high order."

Positronium molecules have also been produced - see http://phys.org/news108822085.html.

Wouldn't the respective masses of annihilating electrons and positrons be indicated in the energy levels of the gamma ray photons produced?

Of course and positronium has been extensively studied-it's a standard textbook exercise.

Thanks for responding, of course, but can annihilated electron and positron masses be determined from residual gamma ray photon energies?

Of course: energy-momentum conservation (which includes angular distribution of the photons), along with the knowledge of how they interact with the electromagnetic field.

Yes, observing 2gamma annihilation energy gives sum of the electron and positron mass, with limited precision - due to detector effects. In medical PET scanners, gammas originating from e+e- annihilation are routinely observed to have 511 keV (in 2-gamma channel). Since electron and positron are stable particles, inequality of their rest masses is not considered to be seriously possible (CPT theorem). Mass of the electron is determined via precise atomic spectroscopy http://prl.aps.org/abstract/PRL/v88/i1/e011603.

Particle instability is a red herring-the masses of unstable particles are also constrained and the issues are rather different:

Cf. L. Maiani and M. Testa, http://arxiv.org/abs/hep-th/9709110

for instance, where, precisely, a spacetime treatment for unstable particles is explicitly presented.

A more focused paper is C.~Bernardini, L.~Maiani and M.~Testa,

``Short time behavior of unstable systems in field theory and proton decay,''

Phys.\ Rev.\ Lett.\ {\bf 71} (1993) 2687.

Quarkonium studies have been extensively used to calibrate for other effects, e.g. https://indico.in2p3.fr/getFile.py/access?contribId=25&resId=0&materialId=slides&confId=4422

Once more: if exotic effects are claimed in one context, it must be shown why they don't appear elsewhere. There have been studies in neutron-antineutron interferometry, http://www.int.washington.edu/talks/WorkShops/int_07_1/People/Snow_M/Snow.pdf

that could have been sensitive to such effects.

Thanks for your very helpful response, Peter.

In the context of the question, "Would anti-matter fly upwards in Earth's gravitational field? ", positronium orbital characteristics and its indicated annihilation mass, along with muonium orbital characteristics, should be sufficient to strongly suggest that antimatter mass is positive. Moreover, it would seem that, at most, small variations in unstable quark mass would produce some variation in response to gravitation, but would not allow for any sustained anti-gravitational effect, in ambient conditions at least.

Hopefully the ALPHA antihydrogen experiments in 2014 will provide robust results, but IMO any expectations that significant anti-gravitational effects will be detected should be tempered by existing evidence.

This really is an important news for me, because I have proposed a gravitational repulsive force between fermions and anti-fermions in my cosmological model. The experiment result will determine the fate of my thesis.

As far as I remember, in the Dirac sea, an electron under the surface-level indeed has negative energy, hence negative mass. However, a positron is not such an electron; instead, it is the absence of such electron (it is the hole). The absence of an object with negative mass counts as an object with positive mass.

Furthermore, if you do consider an object with negative mass, it wil fall downwards in a gravity field exactly like if it had positive mass. The gravitational force will indeed be upwards, but an upwards force divided by a negative mass makes a downwards acceleration. This is just another example of the fact that in a gravity field, acceleration is independent of mass.

David, you have to distinguish between gravitational mass and inertial mass. If both would be negative for antimatter, then indeed you would get the behavior that you sketch. But for a matter-antimatter gravitational repulsion one considers the case that the inertial mass of antimatter is positive, and the gravitational mass is negative. Then the force is upwards, and the acceleration also.

However, if the rest mass of fundamental anti-particles is positive, for example, and both inertial and gravitational mass are derived from particles rest mass, how could either be in opposition to anti-particle rest mass?

Please see my preceding comment regarding positronium & muonium, etc.

@James: we know e.g. from the observed stability of antihydrogen that the inertial mass of antimatter is positive; rest mass is the inertial mass of a particle in rest (i.e. a particle with velocity 0 in the inertial reference frame of the observer). So indeed, IF the gravitational mass of antimatter derives from its inertial mass (as in the equivalence principle, which simply says that these are identical), THEN it is positive. But the point is: the antecedent of this implication is not a certainty. It has not been tested with antimatter.

Agreed with Marcoen. We need the experimental test of the gravitational interaction of anti-matter (positive or negative) subject to Earth gravity. Inertial mass of anti-matter (is positive) has been verified many times in accelerators (e.g. antiproton beams).

Marcoen,

So, as we await experimental verification, what mechanism could possibly convert the positive rest mass of anti-particles to negative gravitational mass? Disregarding the equivalence principle, what mechanism of gravitation could dynamically _invert_ positive rest mass to produce negative gravitational mass?

Given the evidence supporting the expectation that antimatter gravitational mass should be positive, it seems some effort should be expended to justify the experiment. IMO, with no working hypothesis for how antimatter gravitational mass could possibly be negative, we seem to be merely testing wishful thinking...

Similar situation, for example, was with the charge of Top-quark (expected Q=+2/3e).

Experimental study = verification of the top-quark charge has been done in 2013 by ATLAS collaboration and 2011 by CDF/Fermilab. Exotic models predicting anomalous anti-matter interaction with gravitational field can be found in Wiki Refs 16-23: http://en.wikipedia.org/wiki/Gravitational_interaction_of_antimatter

James, I have developed and published a theory consistent with positive rest mass and negative gravitational mass for antimatter. See my papers in Annalen der Physik, you can access them through my personal page. It describes which principles underlie such properties.

Marcoen,Peter,

Thanks very much - exactly what I was looking for! Marcoen, I have read though the accessible introduction to your EPT paper and found it very interesting. I can't evaluate but what was troubling me was exactly what you address - that repulsive antimatter gravitation would conflict with many fundamental principles. You've addressed those concerns very directly, and I think very thoroughly!

James,

indeed, both General Relativity and the Standard Model are incompatible with repulsive gravity. These are established theories, so for the majority of physicists this is enough reason to dismiss the idea of repulsive gravity as not interesting. I on the other hand do believe that it is possible, but of course all theoretical results depending on that assumption are speculative at the moment.

So far nobody mentioned a usually negligible but existing fact. In the case antimatter would respect the WEP,  it would posess the same gravitational field before the annihilation as matter. Where would this very tiny localized gravitational field go right after annihilation??? Distributed in the photons ?? In gravitational waves?? The tiny curvature of space-time would change suddenly from something local to something else presumably moving at  light speed?