Searching for Common Principles of Relativity & Quantum Mechanics

The article reviews and introduces an approach or way of exploration for the unification of the most important theories in physics and finding a common framework to reconcile them. Step by step, the exploration encompasses two postulates that it puts forward as the principles which underlie as well as underpin both relativity and quantum mechanics: (I) deflection occurs between any two coordinates with motion relative to one another; (II) the space-time area (product of length and time) is invariant under deflection. Based on these postulates, the paper interprets the conception of Einstein’s theory for length contraction and time dilation in a simple manner; it presents a cause for stochastic phenomena in the quantum world and derives Schrödinger’s equation from a complex function in which the deflection of space reduces to an amplitude probability distribution. In the last part, a new precession formula for the planets is presented and the results calculated using the new equation are detailed in a table.

These postulates, as principle (I) and (II), can explain both relativity and quantum mechanics mathematically and conceptually without contradiction or paradox, and are already verified by light aberration, an astronomical phenomenon discovered for almost 300 years, and length contraction and time dilation in experiments without any falsification.

Furthermore, the peculiar quantum phenomena, such as entanglement, particle-wave duality, double slit interference and Schrödinger's cat, as well as unification of gravitation with other interactions will be discussed and interpreted by taking into account the postulates as new principles and concepts.

Both real part and imaginary part of the complex function in the article originate from the postulates as principle (I) and (II). It may be incomplete to derive the Schrödinger equation without discussing the role of imaginary part in quantum theory. We have wondered for many decades what is hidden behind the Schrödinger equation. Considering the imaginary part of the complex function, we can make new discoveries and interpretations of the phenomena such as consciousness, life, dark matter & energy, elementary particles and origin & evolution of universe. The advance of physics is the work of the entire science community.