To explore quantum phenomena, one must enter the abstract realm of Hilbert space. At the heart of quantum mechanics lie rules for predicting possible futures rather than tracking present objects. The theory uses vectors in an alien domain to represent quantum states.
These vectors are not pointing at locations but directions in a possibility space. John von Neumann recognized that the math capturing atomic conduct had left the real world behind, defining the quantum world as Hilbert space. This insight unified Werner Heisenberg's matrix mechanics and Erwin Schr"{o}dinger's wave mechanics, showing they are reflections of the same entity.
Before observation, a quantum object does not have fixed properties like position. Instead, it exists in quantum superposition, a combination of all possible outcomes. The theory's central object, the quantum state, predicts how properties change.
Von Neumann's commandments emerged from unifying two 1920s quantum mechanics forms. David Hilbert sought a mathematical structure to unite these forms. The early quantum pioneers did not initially realize the arcane math capturing atomic conduct had left the real world behind.
Von Neumann showed that Heisenberg's towers and Schr"{o}dinger's waves represented the quantum state. A superposition combines all possible places a particle might end up being.
Source: Hacker News · Summarized by HeadlinesBriefing