For a composite system consists space-like separated subsystems, the assumption of super observer must be abandoned and the relational formulation of quantum measurement becomes necessary. Traditional quantum mechanics assumes a super observer who can instantaneously know the measurement results from any location.

However, description of a quantum measurement must be explicitly relative. We show that for a given quantum system, it is possible to describe its time evolution without explicitly calling out a reference system. More importantly, the formulation results in significant conceptual consequences. By studying how the relational probability amplitude matrix is transformed and how mutual information is exchanged during measurement, we derive the formulation that is mathematically equivalent to the traditional quantum measurement theory. Quantum measurement and quantum operation theory is developed here by taking the relational properties among quantum systems, instead of the independent properties of a quantum system, as the most fundamental elements. It is also argued that the destruction of information as the present and past become identical should release heat by Landauer's principle, and this might make this proposal testable. Consequently, the present and past become indistinguishable because when we measure an observable in the system its value is the same as if the two particle were still together or very close. Here we present a simple resolution to this paradox in which the uncertainty in the energy of the two particle system is reduced by its lack of interaction during the journey so that the uncertainty in time becomes greater than the time they have been separating. Explanations from quantum mechanics remain commonplace today, but they fail to explain the EPR paradox totally in a way that be accepted by the whole community. The resolution of the paradox depends on one's interpretation of quantum mechanics. The EPR paradox appears when measurement results of some properties of two distantly-entangled particles are correlated in a way that cannot be explained classically, and apparently violate locality.

Uncertainty principle