# Inter-relational Quantum Mechanics. (arXiv:1706.01317v3 [physics.gen-ph] UPDATED)

Non-relativistic quantum mechanics is reconstructed based on two basic ideas.

1.) The relational properties among quantum systems are more fundamental than

the independent properties of a quantum system. 2.) A physical measurement of a

quantum system is a probe-response bidirectional process. The framework to

calculate the probability of an outcome when measuring a quantum system should

model this inter-relational process. This implies the probability can be

derived from product of two quantities with each quantity associated with a

unidirectional process. Such quantity is defined as relational probability

amplitude. Specifically, the probability of a measurement outcome is

proportional to the summation of probability amplitude product from all

alternative measurement configurations. The properties of the quantum systems,

such as coherency and entanglement, are manifested through the rules to count

the alternatives. As results, Born's rule is recovered, wave function is found

to be a summation of relational probability amplitudes, and Schr\"{o}dinger

Equation is derived when there is no entanglement in the relational probability

amplitude matrix. An explicit calculation of the relational probability

amplitude is shown using path integral method and gives consistent results with

traditional path integral formulation.