Functional differential equations. 6: Quantum Mechanics

C. K. Raju

Centre for Studies in Civilizations in New Delhi

Reformulating classical physics using functional differential equations (FDEs) is of significant value in itself. But does it lead to quantum mechanics? Formally, the use of mixed-type FDEs leads to a structure of time, and thence to a quantum logic, and the postulates of quantum mechanics. Here, we give a simple and intuitive account of the structured time interpretation of quantum mechanics (STIQM), that quantum mechanics may be due to advanced interactions. We solve the modified Maxwell’s equations in a linear approximation, for both retarded and advanced cases. The solutions show that a free electron oscillates under its own self-action. The oscillations are sustained because both damping and anti-damping are present even in the fully retarded case. Quantitative agreement with the de Broglie wavelength is possible with a simple extra hypothesis, though we do not examine it further here. A structure of time corresponds to many logical worlds, which we explain using the close analogy to parallel computing. With STIQM wave-particle duality does not present any conceptual difficulty. If quantum mechanics is indeed due to advanced interactions then a scalable quantum computer must necessarily be an android.