Relativistic Paths: A Feynman Problem

Wei Wen, Yan-Kui Bai

Quantum measurement problem has existed many years and inspired a large of literature in both physics and philosophy, but there is still no conclusion and consensus on it. We show it can be subsumed into the quantum theory if we extend the Feynman path integral by considering the relativistic effect of Feynman paths. According to this extended theory, we deduce not only the Klein-Gordon equation, but also the wave-function-collapse equation. It is shown that the stochastic and instantaneous collapse of the quantum measurement is due to the “potential noise" of the apparatus or environment and “inner correlation" of wave function respectively. Therefore, the definite-status of the macroscopic matter is due to itself and this does not disobey the quantum mechanics. This work will give a new recognition for the measurement problem.

Stephen J. Gustafson, Israel Michael Sigal

Nandita Rudra

The path integral approach to quatum mechanics was developed by Feynman when he was a graduate student at Princeton University. The method provides a deep insight into quantum dynamics. Due to computational complexity the path integral formalism is not convenient to deal problems in non-relativistic quantum mechanics. It, however, provides an excellent method for quantizing quantum fields and has become a powerful tool in quantum field theory, statistical physics and numerical computation.

R. Shankar

Stephen P. Martin

Wei Wen

Quantum measurement problem is still unconsensus since it has existed many years and inspired a large of literature in physics and philosophy. We show it can be subsumed into the quantum theory if we extend the Feynman path integral by considering the relativistic effect of Feynman paths. According to this extended theory, we deduce not only the Klein-Gordon equation, but also the wave-function-collapse equation. It is showing that the stochastic and instantaneous collapse of the quantum measurement is due to the "potential noise" of the apparatus or environment and "inner correlation" of wave function respectively. Therefore, the definite-status of the macroscopic matter is due to itself and this does not disobey the quantum mechanics. This work will give a new recognition for the measurement problem.