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A new theory of elementary matter Part IV: Two-particle systems: The particle-antiparticle pair and hydrogen

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Abstract

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.

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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

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Keywords

  • Blackbody Radiation
  • Elementary Matter
  • Charged Matter
  • Hydrogenic State
  • Bound State Solution