How does the Copenhagen interpretation explain quantum indeterminacy?

The Copenhagen interpretation explains quantum indeterminacy by asserting that randomness is a fundamental feature of nature rather than a result of incomplete knowledge. Unlike classical physics, where apparent randomness arises from ignorance of initial conditions, the Copenhagen view maintains that quantum systems are inherently probabilistic.12

Key aspects of this explanation include:

• Fundamental Indeterminacy: The theory posits that variables, such as a particle's position and momentum, cannot be simultaneously measured with absolute precision, as defined by the uncertainty principle. This relationship is not due to measurement limitations but is an intrinsic property of the physical world.12
• Rejection of Hidden Variables: The interpretation rejects the existence of "hidden variables"—hypothetical, unknown properties that would restore deterministic causality—arguing that such concepts are unmeasurable and unnecessary.2
• Wave Function Collapse: During measurement, the wave function undergoes an abrupt, discontinuous, and unpredictable change, known as collapse. The Copenhagen interpretation adopts a pragmatic stance, distinguishing between microscopic quantum systems and macroscopic measuring instruments, and accepts this collapse as a fixed outcome without requiring a deeper mechanical explanation.3

By focusing on what can be experimentally observed, this interpretation encourages physicists to accept indeterminacy as a foundational reality.2