The Duality of Time Theory

The ensemble interpretation of Quantum Mechanics considers the quantum state description to apply only to an ensemble of similarly prepared systems, rather than supposing that it exhaustively represents an individual physical system. In 1926, Max Born used the German words “Haufen gleicher”, translated as “ensemble”, because the atoms in his assembly were uncoupled, meaning that the ensemble was an imaginary set of independent atoms that defines its observable statistical properties. The members of the ensemble are said to be in the same state, which is mathematically denoted as a statistical operator that maps from a certain corresponding Hilbert space to itself, and may be written as a density matrix.

The state function is not taken to be physically real, or any literal summation of states. Rather, the wave-function is taken to be an abstract statistical function, only applicable to the statistics of repeated preparation procedures. The ket does not directly apply to a single particle detection, but only the statistical results of many. This is why this interpretation does not refer to bras, and mentions only kets.

The advocates of the ensemble interpretation of Quantum Mechanics claim that it is minimalist; making the fewest physical assumptions about the meaning of the standard mathematical formalism. It proposes to take to the fullest extent the statistical interpretation of Max Born, for which he won the Nobel Prize in 1954.