Grounding the randomness of quantum measurement

Area of Science:

• Quantum mechanics
• Mathematical physics

Background:

• Julian Schwinger developed a mathematical framework for quantum mechanics based on measurement sequences.
• This framework utilizes an algebra of symbols representing discrete quantum measurements and their outcomes.

Purpose of the Study:

• To evaluate Schwinger's assumption of random phase parameters in quantum mechanics.
• To ground the objective probabilities in quantum mechanics by relating phase randomness to the principle of plenitude.

Main Methods:

• Examining Schwinger's algebraic reconstruction of quantum mechanics.
• Analyzing recent critiques of randomness.
• Connecting the principle of plenitude with the randomness of phase parameters.

Main Results:

• Schwinger's assumption of random phase parameters is evaluated against contemporary understandings of randomness.
• A link is established between the "principle of plenitude" and the randomness of phase parameters.
• This provides a foundational basis for quantum mechanical probabilities.

Conclusions:

• The study provides a fundamental grounding for the objective, irreducible probabilities in quantum mechanics.
• It reconciles Schwinger's model with modern critiques of randomness.
• The principle of plenitude offers a basis for the definite measured values observed in quantum mechanics.