Interpretations

All interpretations agree on the mathematical formalism and experimental predictions. They disagree on what the mathematics means, what kind of reality (if any) the wavefunction represents. This is not merely philosophy. Different interpretations guide intuition differently, suggest different research programs, and have different implications for quantum gravity and cosmology.

Copenhagen Interpretation

The "orthodox" view, developed by Bohr, Heisenberg, and Born in the 1920s. It remains the default teaching framework.

Core Ideas

• The wavefunction is a tool for calculating probabilities, not a description of physical reality
• Measurements produce definite outcomes; asking what happens "before" measurement is meaningless
• Classical concepts (position, momentum) apply only to measurement outcomes
• The quantum/classical divide exists, but its location is pragmatic, not fundamental

The Role of the Observer

Copenhagen is often caricatured as putting consciousness at the center. Bohr was more subtle: the classical description of apparatus and results is necessary because that's how we communicate physics. The "observer" is the classical world, not necessarily a conscious being.

Criticisms

• The quantum/classical boundary is arbitrary and undefined
• "Shut up and calculate": avoids fundamental questions
• Problematic for quantum cosmology (who observes the universe?)

Many-Worlds Interpretation

Proposed by Hugh Everett in 1957. The most parsimonious interpretation in terms of fundamental postulates. It simply removes the collapse postulate.

Core Ideas

• The wavefunction is physically real and never collapses
• The Schrödinger equation always applies, even during measurement
• What looks like collapse is actually the observer becoming entangled with the system
• All measurement outcomes occur, in different "branches" of reality

Branching

When you measure a spin:

$$|\text{ready}\rangle \otimes (|\uparrow\rangle + |\downarrow\rangle) \to |\text{saw up}\rangle|\uparrow\rangle + |\text{saw down}\rangle|\downarrow\rangle$$

Both terms persist. Each branch contains an observer who saw a definite result. From inside a branch, it looks like collapse occurred.

The Probability Problem

If all outcomes happen, why do we see Born rule probabilities? This is the main technical challenge. Various approaches (self-locating uncertainty, decision theory, typicality) attempt to derive the Born rule within Everett.

Pilot Wave Theory (Bohmian Mechanics)

Developed by de Broglie (1927) and Bohm (1952). Particles have definite positions at all times, guided by the wavefunction.

Core Ideas

• Particles have actual trajectories: position is always definite
• The wavefunction is a real "pilot wave" that guides particle motion
• The guidance equation determines velocity from the wavefunction
• Measurement outcomes depend on actual (but unknown) initial positions

The Equations

For a single particle:

$$\frac{dx}{dt} = \frac{\hbar}{m}\text{Im}\left(\frac{\nabla\psi}{\psi}\right) = \frac{j}{|\psi|^2}$$

The particle rides along the flow of probability.

Resolving Measurement

In Bohmian mechanics, particles always have positions. When we "measure," we're simply revealing the pre-existing position. The Born rule follows from the "quantum equilibrium" distribution of initial conditions.

Nonlocality

The guidance equation for entangled particles involves the positions of all particles, explicitly nonlocal. This was seen as a defect, but after Bell's theorem, we know some form of nonlocality is unavoidable.

Objective Collapse Theories

These modify quantum mechanics by adding a physical collapse mechanism. The most developed is GRW (Ghirardi-Rimini-Weber, 1986).

GRW Mechanism

• Each particle has a tiny probability (~10⁻¹⁶ per second) of spontaneous "localization"
• Localization multiplies the wavefunction by a narrow Gaussian
• For single particles, this is negligible
• For macroscopic objects (10²³ particles), localizations happen ~10⁷ times per second
• This rapidly collapses any macroscopic superposition

Gravity-Induced Collapse

Penrose and Diósi proposed that gravity triggers collapse. A superposition of different mass distributions creates a superposition of different spacetimes, which is unstable. The larger the gravitational self-energy difference, the faster the collapse.

QBism and Epistemic Views

QBism (Quantum Bayesianism) treats quantum states as expressions of an agent's beliefs, not descriptions of external reality.

Core Ideas

• Probabilities are personal: degrees of belief, not frequencies
• The wavefunction represents an agent's information and expectations
• Measurement is an action that creates an experience for the agent
• There's no "collapse" because there's nothing objective collapsing
• Different agents can assign different quantum states to the same system

Avoiding the Measurement Problem

If the wavefunction is epistemic (about knowledge), not ontic (about reality), then collapse is just Bayesian updating, learning new information. The "problem" dissolves.

Comparing Interpretations

Feature	Copenhagen	Many-Worlds	Bohm	GRW	QBism
ψ is real?	No	Yes	Yes	Yes	No
Collapse?	Pragmatic	Never	Never	Physical	Updating
Deterministic?	No	Yes	Yes	No	No
Hidden variables?	No	No	Yes	No	No
Extra ontology	None	Branches	Positions	Collapse field	None
Testable diff?	No	No*	No	Yes	No

*Many-Worlds could differ if branching structure has observable effects

What Does This Mean for Learning Physics?

For practical calculations, interpretation doesn't matter. All agree on the formalism. But for understanding:

• Many-Worlds provides a clear picture of superposition persisting everywhere
• Bohm gives intuitive particle trajectories (useful for visualizing interference)
• Copenhagen reminds us to focus on observable predictions
• QBism warns against over-interpreting the formalism

Most working physicists are pragmatic pluralists, using whichever picture helps for the problem at hand.