# 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