Il Nuovo Cimento B (1965-1970)

, Volume 63, Issue 1, pp 132–142 | Cite as

Gravitational coupling of negative matter

  • A. Inomata
  • D. Peak


The relevance of the sign of mass in general relativity is examined by analysing a simple model universe in which Dirac matter distributes uniformly. Mass reversal, converting a source of positive matter into one of negative matter, gives rise to a concomitant change in sign of the gravitational coupling. The principle of equivalence is invoked in order to generalize the result to all negative-matter sources. The admissibility of a Dirac source in general relativity implies that the sign of mass is irrelevant in gravitational interactions.


Inertial Mass Gravitational Mass Normal Matter Negative Mass Dirac Matter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Гравитационная константа свяэи для отрицательного вешества


Исследуется уместность энака массы в обшей теории относительности, посредством аналиэа простой модельной Вселенной, в которой вешество Дирака распределено неоднородно. Иэменение энака массы, путем преобраэования источника положительного вешества в источник отрицательного вешества, приводит к сопутствуюшему иэменению энака гравитационной константы свяэи. Испольэуется принцип зквивалентности для того, чтобы обобшить реэультат для всех отрицательных источников вешества. Приемлемость дираковского источника в обшей теории относительности оэначает, что энак массы является неуместным в гравитационных вэаимодействиях.


Si esamina l’importanza del segno della massa in relatività generale analizzando un semplice modello di universo in cui la materia di Dirac si distribuisce uniformemente. L’inversione di massa, convertendo una sorgente di materia positiva in una di materia negativa, dà origine ad una variazione concomitante del segno dell’accoppiamento gravitazionale. Si invoca il principio di equivalenza per generalizzare il risultato a tutte le sorgenti di materia negativa. L’ammissibilità di una sorgente di Dirac nella relatività generale implica che il segno della massa è irrilevante nelle interazioni gravitazionali.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. (1).
    H. Bondi:Rev. Mod. Phys.,29, 423 (1957).ADSMathSciNetCrossRefGoogle Scholar
  2. (2).
    A. Föppl:Sitzber. Math. Phys. Kl. Kongl. Bayrisch. Akad. Wiss. München,27, 97 (1890). WhileFöppl developed a logically consistent theory of positive and negative masses, the possibility of stars composed of negative mass was considered byK. Pearson:Am. Journ. Math.,13, 309 (1891). For a historical account on negative mass, seeM. Jammer:Concepts of Mass in Classical and Modern Physics, Ch. 10 (New York, 1964).Google Scholar
  3. (3).
    A. Schüster:Nature,58, 367, 618 (1898). Although our attention is focused on the coupling of negative matter, it is important to clarify the relationship between negative matter and antimatter. An interesting discussion on the gravitational properties of antimatter has been given byL. I. Schiff:Proc. Natl. Acad. Sci. U.S.,45, 69 (1959); see alsoS. Weinberg:Phys. Rev.,135, B 1049 (1964);K. Hiida andY. Yamaguchi:Progr. Theor. Phys. Suppl., Extra Number, 261 (1965).ADSCrossRefGoogle Scholar
  4. (4).
    B. Hoffmann: article inPerspective in Geometry and Relativity (Indiana, 1966), p. 176. See alsoY. P. Terletsky: article inQuasi-Steller Sources and Gravitational Collapse (Chicago, 1965), p. 466; andParadoksy Teorii Otnositel’nosti, Chap. 6 (Moscow, 1966).Google Scholar
  5. (5).
    This experimental indeterminacy may imply more generally the irrelevance of the phase of mass, and the corresponding automorphism is the chiral gauge transformation. SeeA. Inomata:Progr. Theor. Phys.,28, 569 (1962).ADSMathSciNetCrossRefGoogle Scholar
  6. (6).
    J. Tiomno:Nuovo Cimento,1, 226 (1955);S. Hori andA. Wakasa:Nuovo Cimento,6, 304 (1957);J. J. Sakurai:Nuovo Cimento,7, 649 (1958).MathSciNetCrossRefGoogle Scholar
  7. (7).
    A. Inomata:Nuovo Cimento,46 B, 132 (1966).ADSCrossRefGoogle Scholar
  8. (8).
    The theoretical assumptions determining the sign of the gravitational force have been extensively studied byS. Deser andF. A. E. Pirani:Ann. of Phys.,43, 436 (1967). It is reported that in general relativity the sign of the coupling is arbitrary unless the gravitational field energy is ensured to be positive-definite. An exceptional case is the interaction between gravitational geons, in that the sign is completely determined. The present model may be considered as belonging to the latter case since it can be looked upon as a geometrization of the massive Dirac field in Rainich-Misner-Wheeler’s sense. For geometrization of the massless Dirac field, seeA. Inomata andW. A. Mckinley:Phys. Rev.,140, B 1467 (1965).ADSCrossRefGoogle Scholar
  9. (9).
    We ignore the cosmological term from the Machian aspect; seeA. Inomata:Progr. Theor. Phys.,39, 1071 (1968).CrossRefGoogle Scholar
  10. (10).
    In the view that the Einstein equation (1) is derivable from the Lorentz-invariant field theory, the Dirac source is quite natural;S. Gupta:Rev. Mod. Phys.,29, 334 (1957);W. E. Thirring:Ann. of Phys.,16, 96 (1961);V. I. Ogievetsky andI. V. Polubarinov:Ann. of Phys.,25, 358 (1963);S. Weinberg:Phys. Rev.,138, B 990 (1965).ADSMathSciNetCrossRefGoogle Scholar
  11. (11).
    SeeJ. A. Wheeler:Geometrodynamics (New York, 1962), in which the problems associated with geometrization of the Dirac field are extensively discussed.Google Scholar
  12. (12).
    R. H. Dicke:Experimental Relativity (New York, 1964), p. 4.Google Scholar
  13. (14).
    V. G. Soloviev:Nucl. Phys.,6, 618 (1958);S. Ozaki:Progr. Theor. Phys.,23, 221 (1960).CrossRefGoogle Scholar
  14. (15).
    The center of a wave packet formed of negative-energy solutions describes a uniform motion of velocity in the opposite direction to its momentum and behaves like a negative-mass particle; seeA. Messiah:Quantum Mechanics, vol.2 (Amsterdam, 1962), p. 952.ADSGoogle Scholar
  15. (16).
    See,e.g.,J. L. Anderson:Principles of Relativity Physics (New York, 1967), p. 360.Google Scholar

Copyright information

© Società Italiana di Fisica 1969

Authors and Affiliations

  • A. Inomata
    • 1
  • D. Peak
    • 1
  1. 1.Department of PhysicsState University of New YorkAlbany

Personalised recommendations