Quantum Mechanics 101 · Unit 5: Entanglement & Reality

Quantum Academy · Chapter 22: Interpretations, Decoherence & Schrödinger's Cat

Same equations, wildly different stories about reality

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Instructions. Work through these questions with the lesson closed, then check yourself against it. For calculations show every step and give answers to the precision of the data, two or three significant figures. Useful relations: visibility after N interactions V = V₀ γ^N; collisional decoherence V = V₀ e^(−p/p₀); GRW mean waiting time t̄ = 1/(Nλ) with λ ≈ 1×10⁻¹⁶ s⁻¹ per nucleon; nucleon mass ≈ 1.66×10⁻²⁷ kg; Born rule P = |amplitude|². One point for each vocabulary match and each question; the challenge is a bonus.

Part A Vocabulary matching

Write the letter of the matching definition in the blank beside each term.

1.Measurement problem
2.Copenhagen interpretation
3.Heisenberg cut
4.Many-worlds interpretation
5.Pilot-wave theory
6.Quantum equilibrium
7.Objective collapse model
8.QBism
9.Relational quantum mechanics
10.Decoherence
11.Pointer state
12.Improper mixture

A.A state, such as a definite position, that survives continual monitoring by the environment and therefore looks classical.
B.The view that quantum states encode an agent's personal degrees of belief, so that collapse is the updating of those beliefs.
C.Rovelli's 1996 interpretation in which states and properties are defined only relative to other physical systems.
D.The de Broglie-Bohm theory, in which particles always have definite positions and move as directed by the wavefunction through a guiding equation.
E.A modified quantum dynamics, such as GRW or Diósi-Penrose, in which wavefunctions collapse spontaneously at rates that grow with size or mass.
F.A state that looks like a classical probability mixture only because part of an entangled whole has been ignored.
G.In pilot-wave theory, the condition that particle positions are distributed as |ψ|², which reproduces the Born rule and forbids signalling.
H.The family of views from Bohr, Heisenberg and colleagues that treats the wavefunction as a predictive tool and measurement as a primitive, classically described event.
I.The suppression of interference between alternatives when a system becomes entangled with an environment that records them.
J.Everett's 1957 proposal that the universal wavefunction never collapses and every measurement outcome occurs in its own branch.
K.The conflict between linear Schrödinger evolution, which produces superpositions of outcomes, and the single definite outcomes we observe.
L.The movable boundary between the system treated quantum mechanically and the apparatus treated classically.

Part B Questions

1.
What was Schrödinger's main purpose in describing the cat in 1935?Circle one
1. ATo show that everyday objects, cats included, routinely sit in superpositions until observed
2. BTo show the absurdity of reading the wavefunction as a literal, complete picture of reality
3. CTo demonstrate that a conscious observer is needed to collapse the wavefunction
4. DTo propose a practical experiment for measuring how quickly decoherence acts
2.
In de Broglie-Bohm pilot-wave theory, each electron in a double-slit experiment passes through both slits.Circle one
TrueFalse
3.
Which of Maudlin's three claims does the GRW collapse model reject?Circle one
1. AThe wavefunction is a complete description of a system
2. BEvery measurement has a single, definite outcome that we can observe
3. CThe wavefunction always evolves by the linear Schrödinger equation
4. DMeasurement probabilities always follow the Born rule
4.
The loss of interference that occurs when a system becomes entangled with an environment that records its state is called .Fill in the blank
5.
In Everett's many-worlds interpretation the wavefunction of the universe never collapses.Circle one
TrueFalse
6.
In QBism, a quantum state represents an agent's personal degrees of about the outcomes of their future actions on the world.Fill in the blank
7.
Why can the nonlocality of Bohmian mechanics never be used to send a faster-than-light message?Circle one
1. ABecause the guiding equation couples each particle only to its nearby neighbours
2. BBecause Bohmian particles never travel faster than light, so no signal can either
3. CBecause positions are distributed as |ψ|², so local statistics never reveal distant choices
4. DBecause the wavefunction collapses as soon as either distant partner is measured
8.
After decoherence, the joint state of cat, atom and environment is no longer a superposition.Circle one
TrueFalse
9.
Using the idea of which-path records, explain why a dust grain in air decoheres far faster than an electron in a well-isolated interferometer.Short answer
10.
What is the essential difference between an objective collapse model and an interpretation such as many-worlds, and how has a collapse model been tested?Short answer
11.
Each environmental photon scattered by a particle in a two-path interferometer has overlap γ = 0.90 between its two possible final states. Starting from 100 percent visibility, what is the fringe visibility after 20 photons?Show your working
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Answer:
12.
In a fullerene interferometer the vacuum visibility is V₀ = 0.40 and the decoherence pressure is p₀ = 0.80×10⁻⁶ mbar. Find the visibility at p = 1.2×10⁻⁶ mbar and the fraction of molecules that cross without any collision.Show your working
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Answer:
13.
A 1.0 μg dust grain (1.0×10⁻⁹ kg) is placed in a superposition of two positions more than 10⁻⁷ m apart. According to GRW, what is the mean time before a spontaneous collapse?Show your working
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Answer:
14.
In a version of the cat box, a single radioactive atom with a half-life of 1.0 hour controls the poison. What probability does every interpretation assign to finding the cat alive after 3.0 hours, and what is the magnitude of the 'alive' amplitude?Show your working
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Answer:

Part C Mad scientist challenge bonus

Decohere a dust grain by degrees. A grain is in the superposition α|L⟩ + β|R⟩ with |α|² = |β|² = 1/2, and each environmental particle that hits it ends in |e_L⟩ or |e_R⟩ with real overlap ⟨e_L|e_R⟩ = cos θ. (a) Show that after N independent hits the off-diagonal element of the grain's reduced density matrix is (1/2)(cos θ)^N. (b) If each hit carries only weak information, θ = 0.10 rad, how many hits reduce the coherence to one millionth of its starting value? (c) In still air at room temperature a grain of radius 5 μm suffers about 9.3×10¹⁷ collisions per second. Even with such weak records, how long does that take? (d) Explain what this calculation has not shown.

Working

Memory aid

Mnemonic The cat's report card: four A's and a D. Picture it pinned to the box. The four A's are the ways out of the measurement problem. Add something: pilot-wave theory adds particle positions. Alter the equation: GRW and Diósi-Penrose collapse change Schrödinger's law. Accept every outcome: many-worlds keeps them all. Adjust what ψ means: Copenhagen, QBism and relational quantum mechanics treat it as a tool, a belief or a relation. The D is Decoherence, which Doesn't Decide: it explains why the cat looks classical, never which cat you get. To use it, take any interpretation and ask which A it earns; and if you are ever tempted to say decoherence solved everything, remember that it only got a D.

In one line Rival stories, same predictions so far: decoherence explains why cats never look smeared, but which story is true remains open.