Classical Mechanics: Knowing position and velocity allows predictions using Newton's second law.
Quantum Mechanics: Knowing a particle's wave function allows predictions using the Schrodinger equation.
The wave function evolves smoothly, but measurement results in detecting a particle at a single point.
Wave Function and Measurement
The measurement is considered more real than the wave function by early quantum theorists.
Max Born's Contribution: Proposed that the square of the wave function's amplitude gives the probability of finding a particle.
This interpretation introduced probability into quantum mechanics, moving away from determinism.
Wave Function Collapse
Two sets of rules:
Without Measurement: Wave function evolves according to the Schrodinger equation.
With Measurement: Wave function collapses, and probabilities are determined by the amplitude squared.
Schrodinger's cat thought experiment:
Cat in a box with a radioactive atom, a detector, and cyanide gas.
The cat's fate is tied to the decayed state of the atom.
The atom can exist in a superposition of decayed and not decayed states.
Superposition and Entanglement
Superposition: Quantum objects can exist in multiple states simultaneously.
Double Slit Experiment: Evidence of superposition as electrons create an interference pattern.
Entanglement: Particles that interact become entangled; one particle's state instantly affects the other's.
They are described by a single wave function after interaction.
Re-evaluating Measurement
Measurement is just an interaction of quantum systems.
Suggestion to discard distinct measurement rules:
Opening the cat box does not collapse the wave function; it entangles with the observer.
Observers see different outcomes (alive or dead cat) in separate realities.
Many Worlds Interpretation
Hugh Everett's Many Worlds Theory: Branching of the wave function creates multiple realities.
Every outcome from a quantum event exists in its own universe.
Environmental decoherence causes branching into slightly different realities.
Measurement doesn't collapse wave function; it results in entanglement with the environment.
Philosophical Implications
The universe is deterministic; all outcomes occur with 100% certainty in the many-worlds framework.
Experience of reality is limited to a tiny fraction of the multiverse.
Expert Insights (Sean Carroll)
Energy conservation in many worlds is clear in the mathematics; the total wave function energy is conserved.
The number of worlds is large, branching happens frequently due to quantum interactions.
Many-worlds does not imply everything possible happens, but follows the Schrodinger equation's predictions.
Branches: They are a convenient human description; their nature is not fundamental to reality.
Conclusion
The many-worlds interpretation provides a cleaner, more coherent understanding of quantum mechanics, while the traditional view complicates reality with the concept of wave function collapse.