[Paper Review] Quantum mechanics without measurements

Robert B. Griffiths|ArXiv.org|Dec 8, 2006

Quantum Mechanics and Applications25 references3 citations

TL;DR

This paper proposes a reformulation of quantum mechanics that eliminates the foundational role of measurements by introducing consistent probabilities through quantum histories and the Schrödinger equation, enabling a coherent, measurement-free description of quantum dynamics. The key contribution is replacing wave function collapse with conditional probabilities, offering a more intuitive and logically consistent framework for teaching and understanding quantum mechanics.

ABSTRACT

Many of the conceptual problems students have in understanding quantum mechanics arise from the way probabilities are introduced in standard (textbook) quantum theory through the use of measurements. Introducing consistent microscopic probabilities in quantum theory requires setting up appropriate sample spaces taking proper account of quantum incompatibility. When this is done the Schrodinger equation can be used to calculate probabilities independent of whether a system is or is not being measured, and the results usually ascribed to wave function collapse are obtained in a less misleading way through conditional probabilities. Toy models that include measurement apparatus as part of the total quantum system make this approach accessible to students. Some comments are made about teaching this material.

Motivation & Objective

• To address the conceptual confusion students face in quantum mechanics, particularly the reliance on measurements to introduce probabilities.
• To resolve the foundational issues of standard quantum mechanics, such as wave function collapse and the measurement problem, by removing measurement as a fundamental concept.
• To provide a pedagogically accessible framework using toy models that illustrate quantum dynamics without measurement axioms.
• To replace the traditional textbook approach—often described as 'shut up and calculate'—with a logically coherent, probabilistically consistent interpretation of quantum theory.
• To demonstrate that quantum mechanics can be taught and understood without invoking measurement as a primitive concept, using only the Schrödinger equation and consistent histories.

Proposed method

• Uses the consistent histories (or decoherent histories) approach to define quantum probabilities without reference to measurement.
• Applies the Born rule to closed quantum systems described by the Schrödinger equation, assigning probabilities to histories of system evolution.
• Constructs sample spaces of consistent histories that respect quantum incompatibility, ensuring probabilistic consistency.
• Models measurement processes as unitary evolution of a combined system-apparatus quantum state, avoiding wave function collapse.
• Employs conditional probabilities to describe the outcome of a measurement without postulating collapse, showing how pre-measurement properties can be inferred.
• Uses toy models—such as a decaying nucleus and alpha particle detection—to illustrate measurement as a quantum process within the same formalism as non-measurement dynamics.

Experimental results

Research questions

• RQ1 Can quantum probabilities be consistently defined without invoking measurements as a foundational concept?
• RQ2 How can the Schrödinger equation alone be used to calculate probabilities for quantum systems without measurement postulates?
• RQ3 What is the role of conditional probabilities in replacing the concept of wave function collapse?
• RQ4 Can measurement processes be understood as unitary quantum dynamics when the apparatus is included in the system?
• RQ5 Is it possible to teach quantum mechanics meaningfully without relying on the measurement postulate?

Key findings

• Probabilities in quantum mechanics can be consistently assigned to quantum histories using the Born rule, without reference to measurement.
• The Schrödinger equation alone suffices to calculate probabilities for isolated quantum systems, even in the absence of measurement.
• Wave function collapse is not a fundamental process but can be understood as a consequence of conditional probability in a consistent histories framework.
• Measurement outcomes can be explained as the result of unitary evolution of a combined system-apparatus, with no need to postulate a separate measurement process.
• Toy models demonstrate that real measurements—such as alpha decay detection—can be analyzed using standard quantum dynamics without invoking collapse or measurement axioms.
• The approach provides a coherent, logically consistent foundation for quantum mechanics that avoids the conceptual paradoxes of the standard textbook formulation.