Quantum Measurement Problem: Schrödinger's Cat and Many‑Worlds

The measurement problem in quantum mechanics is a fundamental and ongoing debate concerning how measurement works within the quantum realm. This problem has been a source of controversy since the inception of quantum theory and continues to be discussed today.

Schrödinger's Cat and the Measurement Problem

To illustrate the measurement problem, the thought experiment of Schrödinger's Cat is often used:

1. Setup: A cat is sealed in a box with a radioactive atom, a hammer, and a vial of poison.
2. Quantum Superposition: If the atom decays, it triggers the hammer, smashes the poison vial, and kills the cat. If it doesn't decay, the cat lives. According to quantum mechanics, the radioactive atom can exist in a quantum superposition of having decayed and not decayed simultaneously.
3. Entanglement: This superposition then spreads through entanglement:
   • The hammer enters a superposition of having triggered and not triggered.
   • The poison vial enters a superposition of being smashed and not smashed.
   • Finally, the cat enters a superposition of being both dead and alive.

The controversial part arises when an observer opens the box. In everyday life, we don't observe objects in superposition. The question is: what does the observer actually see?

• Many-Worlds Theory: Some argue that the observer also becomes entangled with the system, leading to a superposition of the observer seeing a dead cat and another version of the observer seeing an alive cat. This leads to the "many-worlds theory," where different versions of reality (or "worlds") branch off.
• Collapse Theories: Others propose that somewhere along the chain of entanglement, an irreversible collapse into a single state occurred. This means the cat was either dead or alive at some point before the observer looked.

The Measurement Postulate and Its Limitations

Standard quantum mechanics includes a "measurement postulate," which states that a measurement causes the system being measured to collapse into a single state. However, this postulate does not explain how this collapse happens. When an observer opens the box and "measures" the cat, the postulate dictates a collapse into either a dead or alive state, but the underlying physical mechanism remains unexplained. This unresolved question of what physically causes the cat to become a single state during measurement is at the core of the measurement problem.

Interpretations of Quantum Mechanics: Collapse vs. No-Collapse Theories

The different "interpretations" of quantum mechanics are, in essence, different scientific theories attempting to explain the measurement problem. They are broadly categorized into:

Collapse Theories

These theories propose that measurement causes an irreversible collapse into a single state through some mechanism.

• Copenhagen Interpretation: This is the most famous and often considered the default interpretation. It states that observing a system in superposition causes it to irreversibly collapse into a single state. It essentially re-states the measurement postulate as a fundamental aspect of physics without explaining the mechanism of collapse.

No-Collapse Theories

These theories treat the measurement device and the observer as quantum systems themselves, continuing to apply quantum theory beyond the initial system.

• Many-Worlds Interpretation: In this view, when the observer looks into the box, they become entangled with the system, just as the atom entangled with the hammer, poison, and cat. This means the observer enters a large entangled superposition. One version of the observer sees a dead cat, and another sees an alive cat. Both versions of the observer, with their respective experiences, are considered to exist, leading to the idea of multiple parallel worlds. The observation does not cause an irreversible collapse but rather an entanglement that leads to branching realities.

Wigner's Friend Thought Experiment

This thought experiment highlights the disagreement between collapse and no-collapse theories and helps bring these ideas into sharp focus.

1. Setup: An observer, Wigner, has a friend (another observer) who is inside a lab and performs a measurement on a quantum system in superposition (e.g., a system that can be in state 0 or 1).
2. Friend's Perspective: The friend measures the system and sees a definite outcome (e.g., 0 or 1). From the friend's perspective, the system collapsed into a single state the moment they measured it.
3. Wigner's Perspective: Wigner, outside the lab, asks the friend for the measurement result. From Wigner's perspective, everything inside the lab (including the friend and the measured system) was in a superposition until Wigner learned the outcome. Therefore, Wigner would say the collapse happened when he asked the friend.

This creates a disagreement: when did the collapse occur?

• Collapse Resolution: If one adheres to collapse theories, one must define a condition for what constitutes a "measurement." If the friend's measurement satisfies this condition, then the collapse happened when the friend measured, and Wigner simply learned an already collapsed outcome.
• Many-Worlds Resolution: If one follows the many-worlds view, both interactions are entanglements. The friend became entangled with the system, and then Wigner became entangled with the friend. There is no collapse; instead, the universe branches.

The original Wigner's Friend experiment, while illuminating, doesn't allow for experimental distinction between these two explanations because both Wigner and the friend would ultimately observe a single outcome.

Extended Wigner's Friend Experiment and Quantum Computing

An extension of Wigner's Friend, proposed by David Deutsch, allows for a potential experimental distinction between collapse and no-collapse theories. This experiment also laid the groundwork for the idea of quantum computing.

The core idea is to determine whether the friend's measurement of the system causes an irreversible collapse or if the measurement is reversible, allowing the superposition to be restored.

• Irreversible Collapse: If the collapse is irreversible, Wigner's friend measures a random outcome, and this state cannot be undone.
• Reversible Measurement: If the measurement is reversible (as suggested by no-collapse theories like Many-Worlds), Wigner can perform an operation that "reverses" the friend's measurement, restoring the original superposition. If this is possible, Wigner would consistently measure the same outcome every time the experiment is repeated.

This reversibility implies that if the Many-Worlds interpretation is correct, when the friend made the measurement, two versions of the friend existed (one seeing 0, one seeing 1). When the measurement is reversed, these versions "remerge." The friend might remember seeing a single outcome but not which outcome (0 or 1) after being reversed, potentially retaining a note confirming "I saw a single outcome."

Connection to Quantum Computing

David Deutsch conceived of this extended experiment and realized that performing it on a human observer would be incredibly difficult. He proposed a more "realistic" way: simulating the friend on a computer and having quantum control over that simulation. For this to work, the computer's hardware would need to sustain superpositions. This thought experiment, and a subsequent paper, explicitly introduced the idea of a quantum computer. Deutsch even suggested superconductors as a physical implementation, which is a popular approach in quantum computing today.

Inter-Branch Communication in the Quantum Multiverse

A common question regarding the quantum multiverse (many-worlds) is whether an observer in one branch could communicate with an observer in another. Standard quantum mechanics typically suggests this is impossible, as branches are difficult to reconnect once they've split.

However, the Wigner's Friend experiments, which involve re-interfering (reconnecting) these branches, suggest a potential mechanism for inter-branch communication. Maria Vularis has been exploring a proposal based on this:

1. Setup: An observer (the "friend") is in a superposition, and an outside observer wants to send a message from one branch of the friend to another.
2. Challenge: The outside observer cannot simply apply a quantum operation to transport the message if they don't know its content.
3. Proposed Solution: Instead of sending the message, the outside observer, who knows the friend's superposition state, could swap everything else between the two branches, leaving the message in its original location. This effectively moves the "context" around the message.

This idea comes with caveats, such as the friend needing to create the message without leaving any trace in their branch. However, it presents a "fun way to hack the laws of quantum physics" to enable a form of inter-branch communication. Furthermore, if such an experiment were possible and an observer found a message "popping up from nowhere" from their "other self," it would provide strong evidence for the existence of these other selves and, by extension, the many-worlds theory over single-world theories.