Abstract
Based on complex quantum Hamilton-Jacobi theory and its natural complex spacetime configuration, we realized new states for both positive and negative values of energy and momentum, and we discuss this complex configuration in a relativistic entangled "space-time" state and the resultant 12 extra wave functions than the four solutions of Dirac equation for a free particle. Accordingly, we calculate the quantum forces between particles and antiparticles in a relativistic entangled "space-time" state.
Highlights
The origin of complex spacetime stems from complex time, as first proposed by El Naschie [1], according to a special case of E∞ theory [2,3,4] and applied by C
The complex spacetime proposed by Yang is: xμ = xμR + ixμI, x μ R
; xμ = mentioning that the boundary between classical and quantum mechanics could be broken, since the quantum operators are derived from Hamilton equation of motion [5, 6]
Summary
The origin of complex spacetime stems from complex time, as first proposed by El Naschie [1], according to a special case of E∞ theory [2,3,4] and applied by C. It was mentioned that the entangled state, causing the faster-than-light links, is a consequence of an entangled energy, plus a quantum potential, i.e. E2 + 2m0c2Q , resulting in a constant quantity. This quantity if used in the relativistic H-J equations, may describe quantum multiple trajectories. The basis of our work here is on a paper of Yang [13] in which after characterizing the complex time t involved in an entangled energy state and writing the general form of energy considering quantum potential, two sets of positive and negative energies could be realized. We will calculate the quantum forces between particles and antiparticles in a relativistic entangled "spacetime" state
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