Abstract

We show that the electron-positron annihilation process resulting with the creation of two gamma photons cannot be fully determined without the conservation of the angular momentum which has two elements, namely, the conservation of the spin angular momentum and the conservation of the quantum flux which work as the conservation of the magnetic moments as well. The conservation of the quantum flux has never been considered so far for any collision process. We show that the missing conservation rule in the above process is the conservation of the total quantum flux which is the hidden variable of that process. By using the quantum entanglement together with the conservation of the quantum flux we show that the initial and the final states of this collision are fully determined. We also show that each of the gamma photons created in the end carries a quantum flux of ±Φ=±hc/e with itself along the propagation direction. Here the (+) and (−) signs correspond to the right hand and left circular helicity, respectively.

Highlights

  • We show that the electron-positron annihilation process resulting with the creation of two gamma photons cannot be fully determined without the conservation of the angular momentum which has two elements, namely, the conservation of the spin angular momentum and the conservation of the quantum flux which work as the conservation of the magnetic moments as well

  • We show that the missing conservation rule in the above process is the conservation of the total quantum flux which is the hidden variable of that process

  • By using the quantum entanglement together with the conservation of the quantum flux we show that the initial and the final states of this collision are fully determined

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Summary

Introduction

Electron-positron annihilation process has been known since the year 1930. After the collision we have two gamma photons with the same energy E = m0c2 = ћω but with different helicities. Wan and Saglam [4] calculated quantum mechanically the intrinsic magnetic flux of an electron due to its orbital motion in a non-relativistic hydrogen atom by using the Schödinger equation and extended their result to incorporate the spin angular momentum as well. They showed that the intrinsic magnetic flux quanta coming from the quantum numbers ml and ms are (−mlΦ0) and (−msΦ0) respectively.

The Need for Hidden Variables in the Electron-Positron Annihilation Process
Conclusions
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