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Reply to “Comment to a paper of M. Villata on antigravity”

M. Villata

INAF, Osservatorio Astronomico di Torino, Via Osservatorio 20, I-10025 Pino Torinese (TO), Italy

villata@oato.inaf.it

ABSTRACT

In this short paper we reply to the Comment by M. J. T. F. Cabbolet on Villata’s theoryof antigravity. The criticisms of methodological and ontological kind presented by that authorcome from a misinterpretation of some concepts, perhaps due to some lack of clarity or omissionof details in Villata’s original article. In order to clarify these points, here we provide additionalexplanations regarding the assumptions and results of the theory.

Subject headings: Gravitation of antimatter in general relativity — Charge conjugation, parity, and time

reversal — Cosmology

In his Comment (Cabbolet 2011), the authorcriticizes Villata’s theory of antigravity from themethodological and ontological points of view.But, some concepts are misinterpreted by him,and, consequently, also his ontological discussionis not appropriate.

In his paper, Villata (2011) starts from the well-established general theory of relativity, and ex-tends it in the most natural way to incorporateantimatter. This is done in agreement with theFeynman-Stueckelberg interpretation for antimat-ter as matter that travels backwards in time.

Indeed, there are two possible interpretationsfor the existence of antimatter. The more conven-tional one is that antiparticles really exist as en-tities distinct from their matter counterparts, andthat they travel forward in time (FIT), as all or-dinary particles. The other interpretation is thatantiparticles do not really exist as distinct parti-cles, but that they are nothing else than the cor-responding particles that are traveling backwardsin time (BIT). There are several reasons why thelatter appears more convincing.

In the BIT interpretation the number of ex-isting particle species is halved and time is sym-metrized. It may appear as a matter of taste, butthe need of doubling particle species with quasi-identical (but marginally existing) ones looks likean artifact. Even more strange is the unusual ten-

dency of particles and antiparticles to destroy eachother (or to be created in pairs). More interestingand elegant is the view of a particle changing itstime direction by emitting or absorbing photons.But the most convincing argument in favor of theBIT interpretation is just the CPT symmetry ofphysical laws, since it offers a physical explanationto the need of coupling C with T (and P) for de-scribing the behavior of antimatter: if antimatterwere not traveling back in time, why should we ap-ply the time inversion? In other words, accordingto the BIT interpretation, CPT is the operationthat transforms events, particles and fields fromone time direction to the other: the role of T isobvious, since it inverts time intervals, P is neededto get a proper Lorentz transformation (T and Palone are improper), and C provides the neededcharge reversals to see time-reversed matter as an-timatter.

In any case, FIT or BIT interpretation, CPTsymmetry is universal and assured by the CPTtheorem, while the C-only symmetry usuallyadopted to transform matter into antimatter isnot guaranteed (and indeed it is violated in weakinteractions), and may be seen as a deceptive ef-fect of theories that are C, P and T invariant alsoseparately.

These are the reasons why the CPT transfor-mation has to be considered as the correct opera-

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tion to convert matter into antimatter in a givenphysical system governed by CPT-invariant laws,instead of the more conservative C-only prescrip-tion.

The first flaw in Cabbolet’s Comment is his crit-icism, in the Introduction, that CPT symmetry,coming from another theory, should not be takenas an assumption in general relativity. However,as it is well known, the CPT theorem is well es-tablished in flat space-time, and, even if it is notproven in curved space-time, nobody expects thatgeneral relativity violates it (apart from the caseof very peculiar topologies). Thus it is not sur-prising that Villata first assumes CPT invarianceand then checks it in the relevant gravitationalequations: as expected, since the C operation isineffective there, the well-known PT invariance isverified.

Moreover, Cabbolet uses some incorrect expres-sions, such as “a new equation is constructed” and“This is then interpreted as the equation that. . . ”.Actually, eq. (9) is not a new equation that is firstconstructed and then interpreted, but it is the di-rect transformation of the equation of motion ofgeneral relativity extended to consider the gravi-tational interaction between objects belonging tothe two opposite space-time reference frames, i.e.between matter and antimatter.

In Sect. 2 of Cabbolet (2011), the authorspeaks of “cart before the horse” and “inadmissi-ble method”, and here he is partly right, in thesense that in his paper Villata is more concernedwith scientific results and to give an intuitive andunderstandable view of the theory rather than tofollow a rigorous and unassailable (but less effec-tive) methodology. Now we hope that what hasbeen explained above can clarify the matter andfill that gap.

Regarding the discussion on the ontology ofgeneral relativity and the thought experiment pro-posed by Cabbolet, there is a bit of confusion.

Unlike what is affirmed in Cabbolet (2011), thegravitational field is not the metric of space-time,but some combination of derivatives of the metrictensor, and, while the metric tensor is a rank-2tensor and hence is (C)PT-even, the gravitationalfield is (C)PT-odd and so it is “seen” invertedfrom the reversed space-time of the antineutron,or, from the “point of view” of the gravitational

field space-time, the antineutron is “seen” withan inverted gravitational charge. The confusionin the discussion by Cabbolet is perhaps due tothe fact that we speak of “opposite space-times”,but everything is observed and measured froma single space-time, the observer one, while theother is treated like any other reference frame, andthe (C)PT transformation is what translates whathappens in the other frame into what is observed.Thus, Villata’s theory is merely the extension ofgeneral relativity to consider the opposite space-time, which is observed through a simple Lorentztransformation, PT, so that it is not in conflictwith the ontological presuppositions of general rel-ativity. It would be different if we wanted to con-struct a theory that “wander” from one space-timeto the other, e.g. following the neutron along itsworld line in the BIT interpretation, which, in thecase of the neutron-antineutron pair production,would arrive from our future, would reverse itstime direction, and would return (with us) towardsthe future: then yes that a single space-time wouldno longer be the set for all events.

Consequently, the discussion and conclusionsin Sect. 3 in Cabbolet (2011) are not appropriate.While Santilli’s and Cabbolet’s theories requirenew mathematical and ontological approaches,Villata’s theory is the mere and immediate ex-tension of the well-established general theory ofrelativity to the already existing interpretationthat antimatter is matter that goes backwards intime, without any other new assumption or con-struction of new formalism. In other words, anti-gravity comes out as a result of already existingtheories.

Even though Villata’s theory is not concernedwith the unification of general relativity withquantum mechanics, Cabbolet’s statement that“it will thus not bring a solution to this main prob-lem of contemporary physics any closer” should bedemonstrated. Indeed, merely the fact that anti-gravity is predicted is in the right direction to findthe interface between the two theories.

Finally, the author quotes the famous argumentagainst antigravity: “a photon is identical to itsantiparticle, yet it sees the same metric as ordinarymatter”.

The explanation is simple. In general relativity,the electric charge and other quantum propertiesthat distinguish particles from their antiparticles

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do not affect gravity. In other words, C is ineffec-tive anyway, no matter whether particle and an-tiparticle are identical or different from each other.What works is PT, which converts retarded pho-tons into advanced photons, i.e. those going backin time (as expected for photons emitted by an-timatter). And these advanced photons would berepelled by a matter gravitational field. Indeed,the equation of motion for photons is formallyidentical to that for material particles:

d2xλ

dσ2= −Γλ

µν

dxµ

dσ

dxν

dσ, (1)

where σ is a parameter describing the trajectory,which for photons can not be equal to the propertime τ , since dτ = 0, and its elements have thesame (C)PT properties as in the equation for mas-sive particles.

But advanced photons can not be observed (atleast not at the astrophysical-cosmological leveland with the usual detectors), since from our op-posite time direction the roles of emitter and ab-sorber are interchanged, and then they are des-tined to “return” to their source: if we could de-tect them, i.e. intercept them along this path, theywould never have been emitted, i.e. they could notexist, even though this may sound like a contra-diction.

Similarly, visible photons, i.e. retarded ones, arerepelled by an antimatter gravitational field, thusproviding a test for the theory: even if antimattercan not be detected directly by its advanced pho-tons, it could be revealed by its gravitational effecton the retarded radiation coming from the back-ground, giving rise to an antigravitational lens-ing, i.e. a diverging lens type effect, which bringsthe images of the background sources closer to thelensing object.

It could thus seem that matter emits only re-tarded radiation and antimatter only advanced ra-diation, and this would provide an immediate ex-planation for the invisibility of antimatter in theUniverse, in particular regarding its presence incosmic voids suggested in Villata (2011). But thishypothesis is not necessarily true. If possible an-timatter stars and galaxies emit also retarded ra-diation (advanced from their point of view), thenthey could be well visible. In this case, the in-visibility of antimatter in cosmic voids must haveanother explanation: either it is in a state that

does not emit at all, or the emission is weak orstrongly absorbed somewhere. But a more thor-ough discussion on this topic is beyond the aim ofthis paper.

Some of the arguments discussed in this paperalso provide answers to the objections raised byCross (2011) in his Response to “CPT symmetryand antimatter gravity in general relativity”.

REFERENCES

Cabbolet, M. J. T. F. 2011, Ap&SS, submitted

Cross, D. J. 2011, arXiv:1108.5117v1 [gr-qc]

Villata, M. 2011, EPL (Europhysics Letters), 94,20001

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