Interpretation Of Quantum Mechanics, Slides of Physics

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Various Interpretations Of Quantum

Mechanics

Prashant Bisht

TIFR-Hyderabad

24 April 2025

The Blind Men and the Elephant

What is Quantum Mechanics?

Quantum mechanics is a theory: The standard model for matter and energy at small scales (photons, atoms, nuclei, quarks, gluons, leptons,... ). Like all theories: Mathematical formalism + interpretation. Unlike other theories: Formalism accepted for 80 years, but interpretation debated. Rival QM interpretations exist, like the 6 blind men’s views.

The Role of an Interpretation

An interpretation of a formalism should: An interpretation of quantum mechanics is a statement which attempts to explain how QM informs our understanding of nature. Link mathematical symbols to the physical world. Neutralize all paradoxes. Provide tools for visualization or speculation/extension. Not have its own sub-formalism. Not make testable predictions (but may be falsifiable if inconsistent with formalism and experiment).

Paradox (Wave vs. Particle): Wheeler’s Delayed Choice

Experiment : Source emits one photon; wave function passes slits 1 and 2, making interference. Observer’s Choice (after photon passes slits): (a) Measure interference at plane σ 1 (photon travels both slits). (b) Measure at plane σ 2 which slit (photon passes slit 2 only). Paradox : Photon decides wave/particle after passing slits (particle: one slit; wave: both slits). Key Issue : Measurement choice retroactively determines wave/particle nature!

Paradox (Non-Locality): EPR Experiment Malus and

Furry

EPR Experiment : Measures correlated polarizations of entangled photons, obeying Malus’ Law: P ( θ rel) = cos^2 θ rel. Result : Same as if photons were in the same state. Furry’s Proposal : Photons in the same random polarization state—gives a weaker correlation. Paradox : Measurement on one photon causes the other’s state to change, even light years apart. FTL Issue : EPR “influence across space-time”—no FTL signaling possible.

The Copenhagen Interpretation

Heisenberg’s Uncertainty : Wave-particle duality, conjugate variables (e.g., x and p , E and t ); impossible to measure simultaneously. Born’s Statistical Interpretation : Wave function ψ as probability: P = ψψ ∗; QM predicts only averages. Bohr’s Complementarity : System and apparatus as a whole; wave-particle duality: particle or wave. Heisenberg’s “Knowledge” Interpretation : ψ reflects observer’s knowledge; collapse is non-local knowledge change. Heisenberg’s Positivism : “Don’t-ask/Don’t-tell” on meaning/reality; focus on observables and measurements.

Everything Is Quantum: Everett’s Many-Worlds

Interpretation

Key Principles There is no “classical realm.” Everything is quantum, including you, the observer. Wave functions never “collapse.” Only smooth, deterministic evolution. Apparent collapse due to entanglement/decoherence. Unobserved possibilities – other “worlds” – still exist.

Schrödinger’s Cat: Textbook (Copenhagen) Version

The cat is in a superposition of |awake⟩ and |asleep⟩, then observed. (Hilbert space = all such superpositions.)

Initial State |cat⟩|observer⟩ = (|awake⟩ + |asleep⟩) |observer⟩

observation/collapse

Final State |cat⟩|observer⟩ = |awake⟩|observer sees awake⟩

|cat⟩|observer⟩ = |asleep⟩|observer sees asleep⟩

Schrödinger’s Cat: Many World(Everet) Version

Now the cat and the observer are both quantum.Consider environment also. Initial State |cat⟩|observer⟩|env.⟩ = (|awake⟩ + |asleep⟩) |observer⟩|env⟩

Measurement

Decoherence

The world structure in the MWI and a single-world

universe.

Everettian QM: Overview, Objections, Questions

Bottom Line: Everettian QM Everettian QM: Wave functions evolve smoothly. No collapse, no measurement, fully deterministic. Entanglement with a messy environment means outcomes never interfere, don’t affect each other—like separate worlds.

Misguided Objections (^1) Too many universes? Hilbert space size is fixed; all QM includes many worlds—you just let them happen. (^2) Untestable? EQM follows Schrödinger; falsifiable via collapse or extra variables (e.g., dynamical collapse, hidden variables).

Open Questions 1 Why probabilities from | ψ |^2? Why probabilities at all in a deterministic theory? 2 Classical world emergence? Why quasiclassical branching? Why spacetime?

Entanglement in Composite Systems

Key Idea Subsystems S 1 and S 2 do not have definite states independently due to entanglement in the composite system. There does not exist a single state for one subsystem:

ψS^ ̸= ψS^1 ⊗ ψS^2 (in general)

One can only ask the state relative to a given state of the remainder:

State of S 1 is relative to S 2 , and vice versa

The Concept of Relative States

Definition For a chosen state ξk of S 1 , the relative state of S 2 is:

ψ ( S 2 ; rel ξk, S 1 ) = Nk

∑

j

ak,j ηS j^2

where Nk is a normalization constant. The total state can be represented as:

ψS^ =

∑

i

Ni ξi ⊗ ψ ( S 2 ; rel ξi, S 1 )

This relative state uniquely describes S 2 ’s state given S 1 = ξi.