PreprintArticleVersion 1Preserved in Portico This version is not peer-reviewed
Klein-Gordon, Dirac and Schrodinger Equations, Matter and Wave Function Collapses, Photon Momenta and the Gamma Ray Burst based on the 4-D Euclidean Space
Version 1
: Received: 22 December 2022 / Approved: 23 December 2022 / Online: 23 December 2022 (07:57:12 CET)
How to cite:
Hwang, J. Klein-Gordon, Dirac and Schrodinger Equations, Matter and Wave Function Collapses, Photon Momenta and the Gamma Ray Burst based on the 4-D Euclidean Space. Preprints2022, 2022120450. https://doi.org/10.20944/preprints202212.0450.v1
Hwang, J. Klein-Gordon, Dirac and Schrodinger Equations, Matter and Wave Function Collapses, Photon Momenta and the Gamma Ray Burst based on the 4-D Euclidean Space. Preprints 2022, 2022120450. https://doi.org/10.20944/preprints202212.0450.v1
Hwang, J. Klein-Gordon, Dirac and Schrodinger Equations, Matter and Wave Function Collapses, Photon Momenta and the Gamma Ray Burst based on the 4-D Euclidean Space. Preprints2022, 2022120450. https://doi.org/10.20944/preprints202212.0450.v1
APA Style
Hwang, J. (2022). Klein-Gordon, Dirac and Schrodinger Equations, Matter and Wave Function Collapses, Photon Momenta and the Gamma Ray Burst based on the 4-D Euclidean Space. Preprints. https://doi.org/10.20944/preprints202212.0450.v1
Chicago/Turabian Style
Hwang, J. 2022 "Klein-Gordon, Dirac and Schrodinger Equations, Matter and Wave Function Collapses, Photon Momenta and the Gamma Ray Burst based on the 4-D Euclidean Space" Preprints. https://doi.org/10.20944/preprints202212.0450.v1
Abstract
The negative energy solutions of the Klein-Gordon and Dirac equations have been used to define the antiparticle with the positive energy from the Feynman - Stueckelberg interpretation in the standard model based on the 4-D Minkowski space with the relative time. The negative energy solutions of the Klein-Gordon and Dirac equations are used to define the antiparticles with the negative energy in the present 3-D quantized space model. Note that all the present results are based on the 4-D Euclidean space with the absolute time (t) and relative time (tl). Then the particle with the positive energy and antiparticle with the negative energy have the 4-D P4 = TCP = TcP symmetry. The continuity equations are derived from the Klein-Gordon, Dirac and Schrodinger equations. The Klein-Gordon and Schrodinger equations with the potential barriers are solved. The Klein paradox is explained by using the pair production of the electron with the positive energy and positron with the negative energy under the P4 = TcP symmetry, The effective velocity ( c_eff=√2 " c " ) and effective energy ("Etl =" √2 E ) along the relative time axis (ctl) give the relative time momentum of "ptl"=E_tl/c_eff =(√2 E)/(√2 c)=E/c=p_t=p_x. This indicates that the photons with the energy of E have the constant photon velocity of c and the constant photon momentum of "ptl"=E_tl/c_eff =(√2 E)/(√2 c)=E/c=p_t=p_x. For the negative energy particles, the space momentum directions are opposite to the particle velocity directions because the energy is negative. And the matter collapse to the photons at the very high particle velocity is discussed from the length expansion. It is, for the first time, proposed that the gamma ray burst is originated from the matter collapse to the photons near the black hole. Also, the wave function collapse is explained from the length expansion. The wave function collapse takes place when the measurement makes the particle velocity to be zero. It is concluded that the negative energy solutions of the Klein-Gordon and Dirac equations support the existence of the partner antimatter universe with the negative energy and negative time direction. Our matter universe has the positive energy and the positive time direction.
Keywords
P4 = TcP symmetry; Matter collapse; Wave function collapse; Klein paradox; Continuity equations; Negative energy solutions; Gamma ray burst; Photon momenta
Subject
Physical Sciences, Particle and Field Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
