Hugh Everett’s dissertation, “The Theory of the Universal Wavefunction,” presents the foundations of what later became known as the Many-Worlds Interpretation (MWI) of quantum mechanics. Here are the key points from his dissertation:

  1. Quantum State and Processes:
    • A physical system is described by a state function πœ“ in a Hilbert space, providing probabilities for different observations.
    • There are two types of changes to the state function:
      • Process 1: Discontinuous change due to measurement, collapsing the state πœ“ to an eigenstate πœ™π‘— with probability ∣(πœ“,πœ™π‘—)∣2.
      • Process 2: Continuous, deterministic change according to the wave equation π‘‘πœ“π‘‘π‘‘=π‘ˆπœ“, where π‘ˆ is a linear operator.
  2. Measurement and Observer Paradox:
    • Everett discusses the paradoxes that arise when considering an observer and a system being measured as a single composite system. If another observer (B) considers the first observer (A) and the system (S) together, B’s description using only Process 2 conflicts with A’s experience of probabilistic outcomes from Process 1.
  3. Many-Worlds Interpretation (MWI):
    • Everett proposes that instead of having a special process (Process 1) for measurement, we should treat the entire universe, including observers and measuring devices, using only the continuous and deterministic Process 2.
    • This approach avoids the need for wavefunction collapse and suggests that all possible outcomes of a quantum measurement actually occur, each in a different “branch” of the universe.
  4. Universal Wavefunction:
    • The state function of the entire universe, which Everett calls the “universal wavefunction,” evolves deterministically and encompasses all possible configurations of every system.
    • Observers are part of this universal wavefunction, and their observations correspond to different branches or worlds within this larger structure.
  5. Relative State Formulation:
    • After a measurement, the combined system of the observer and the measured system exists in a superposition of different states, each corresponding to a different measurement outcome.
    • Each branch or world has a version of the observer who perceives one of these outcomes, making the probabilistic nature of quantum mechanics a subjective experience rather than an objective reality.
  6. Implications and Advantages:
    • The MWI offers a logically consistent and complete description of quantum mechanics without the need for additional postulates about wavefunction collapse.
    • It maintains the principle of psycho-physical parallelism, meaning that observers are treated as physical systems like any other.
    • The theory suggests that while the formalism is continuous and deterministic, subjective experiences appear discontinuous and probabilistic due to the branching of the universal wavefunction.
  7. Quantitative Definitions:
    • Everett develops quantitative definitions for concepts like the “sharpness” or “definiteness” of an operator and the “degree of correlation” between subsystems, using concepts from Information Theory.
    • These definitions help describe the probabilistic appearances and correlations that arise in the many-worlds framework.

Everett’s dissertation laid the groundwork for the Many-Worlds Interpretation, fundamentally challenging the traditional Copenhagen interpretation and offering a new perspective on the nature of reality and quantum mechanics​​.