The general theory developed thus far (Sachs, 1971b, c, d) is applied to two-particle systems. An exact bound state solution of the nonlinear field equations of this theory for a particle-antiparticle pair is demonstrated. From the Lagrangian formalism, this solution is shown to predict all of the experimental facts that are conventionally interpreted in terms of ‘pair annihilation’: (1) the energy-momentum four-vector (and each of the four components, separately) are zero, compared with the energy, 2mc 2, of the state when the particle and antiparticle are (asymptotically) free and (2) the dynamical properties of this state of positronium make it appear in experimentation as two distinguishable currents, correlated with a 90° phase difference and polarised in a plane that is perpendicular to the direction of propagation of interaction with other charged matter. The latter features are conventionally interpreted as the two photons which are produced in the annihilation event — however, there are no photons in this theory. The spectral distribution of blackbody radiation is then derived from the properties of an ideal gas of such pairs, in their ground states of null energy-momentum, as observed in a finite cavity.
The properties of theclosed electron-proton system are considered and the entire hydrogen spectrum is derived — including the Lamb splitting. The correct lifetimes of the excited hydrogenic states are then derived by considering the radiating hydrogen gas to be immersed in the ideal gas of pairs, that explained blackbody radiation.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Bethe, H. A. and Salpeter, E. E. (1957).Quantum Mechanics of One- and Two-Electron Atoms. Academic Press.
Bogoliubov, N. N. and Shirkov, D. V. (1959).Introduction to the Theory of Quantized Fields. Interscience Publishers.
Davies, P. C. W. (1970).Proceedings of the Cambridge Philosophical Society,68, 751.
Dirac, P. A. M. (1947).Quantum Mechanics, 3rd ed., Ch. XI. Oxford University Press.
Einstein, A. and Mayer, W. (1932).Sitzungsberichte der Akademie der Wissenschaften in Wien,8, 522.
Eisenhart, L. P. (1933).Continuous Groups of Transformations. Princeton University Press.
Halberstam, H. and Ingram, R. E. (1967).The Mathematical Papers of Sir William Rowan Hamilton, Volume III: Algebra. Cambridge University Press.
Heitler, W. (1944).The Quantum Theory of Radiation, 2nd ed., Sec. 16. Oxford University Press.
Hylleraas, E. A. (1929).Zeitschrift für Physik,54, 347.
Lamb, W. E., Jr., and Sanders, T. M., Jr. (1956).Physical Review,103, 313.
Lanczos, C. (1966).The Variational Principles of Mechanics, 3rd ed., Appendix II. University of Toronto Press.
Laporte, O. and Uhlenbeck, G. E. (1931).Physical Review,37, 1380.
Layzer, A. J. (1961).Journal of Mathematics and Physics,2, 308.
Lewis, G. N. (1926).Proceedings of the National Academy of Sciences of the United States of America,12, 22, 439.
Pekeris, C. L. (1958).Physical Review,112, 1649.
Pekeris, C. L. (1959).Physical Review,115, 1216.
Petermann, A. (1958).Fortschritte der Physik,6, 505.
Sachs, M. and Schwebel, S. L. (1961).Nuovo cimento (Suppl.),21, 197.
Sachs, M. and Schwebel, S. L. (1962).Journal of Mathematics and Physics,3, 843.
Sachs, M. (1963).Nuovo cimento,27, 1138.
Sachs, M. (1964a).Nuovo cimento,31, 98.
Sachs, M. (1964b).British Journal for the Philosophy of Science,15, 213.
Sachs, M. (1965).Nuovo cimento,37, 977.
Sachs, M. (1967a).Synthese,17, 29.
Sachs, M. (1967b).Nuovo cimento,47, 759.
Sachs, M. (1968a).Nuovo cimento,53B, 398.
Sachs, M. (1968b).Nuovo cimento,55B, 199.
Sachs, M. (1968c).International Journal of Theoretical Physics, Vol. 1, No. 4, p. 387.
Sachs, M. (1969a).Physics Today,22, 51.
Sachs, M. (1969b).Lettere al Nuovo cimento,1, 741.
Sachs, M. (1970a).Philosophy and Phenomenological Research,30, 403.
Sachs, M. (1970b).Nature, London,226, 138.
Sachs, M. (1970c).Nuovo cimento,66B, 137.
Sachs, M. (1970d).British Journal for the Philosophy of Science,21, 359.
Sachs, M. (1971a).International Journal of Theoretical Physics, Vol. 4, p. 145.
Sachs, M. (1971b, c, d, e).International Journal of Theoretical Physics (Parts I, II, III and IV of this series).
Schiff, L. I. (1949)Quantum Mechanics. McGraw-Hill Book Co.
Schilpp, P. A. (1949).Albert Einstein: Philosopher-Scientist. Lib. Liv. Phil.
Tetrode, H. (1922).Zeitschrift für Physik,10, 317.
Triebwasser, S., Dayhoff, E. S. and Lamb, W. E., Jr. (1953).Physical Review,89, 98.
Watson, G. N. (1945).Theory of Bessel Functions. Macmillan, New York.
Wheeler, J. A. and Feynman, R. P. (1945).Review of Modern Physics,17, 157.
Wu, C. S. and Shaknov, I. (1950).Physical Review,77, 136.
About this article
Cite this article
Sachs, M. A new theory of elementary matter Part IV: Two-particle systems: The particle-antiparticle pair and hydrogen. Int J Theor Phys 5, 161–197 (1972). https://doi.org/10.1007/BF00670510
- Blackbody Radiation
- Elementary Matter
- Charged Matter
- Hydrogenic State
- Bound State Solution