Lecture 3: Quantum Particles
“We do not know how to predict what would happen in a given circumstance, and we believe now that it is impossible — that the only thing that can be predicted is the probability of different events.”
— Richard P. Feynman, 1965 Nobel Laureate
Learning Goals
- Understand that quantum particles only remember the last thing that was measured about them
- Be able to predict the results of repeated measurements on quantum particles
- Analyze experiments with analyzer loops (quantum erasers)
- Understand how quantum measurements can be erased
Prerequisites: Understanding how Stern-Gerlach analyzers work, especially in multiple-measurement configurations.
What We’ve Learned So Far
- Quantum mechanics is stochastic. We cannot determine precisely what will happen — only the probability of different events.
- These results are real and hold for all quantum systems.
- Quantum mechanics allows extreme precision in certain measurements (light color, clock ticking) — verified more accurately than any other theory in science.
- Amidst uncertainty, there is remarkable certainty in other quantities.
”Atoms Are Stupid” — And What Comes Next
The atom is schizophrenic — it has more than one identity. The core theme: the atom only remembers the last axis it had its projection measured on.
Preview of This Module
- Analyzer loops — extending the SG experiment to explore quantum interference
- Two-slit analog — introducing the quantum mystery via Stern-Gerlach devices
- John Wheeler’s delayed-choice experiment — deciding about interference after the particle has passed
- Einstein-Podolsky-Rosen (EPR) — “spooky action at a distance”
- Bell inequalities — proving hidden variable theories incorrect
- Real-world applications — NMR (nuclear magnetic resonance) and MRI
The Stern-Gerlach analyzer loop
What Is It?
A new apparatus that erases the measurement made by a Stern-Gerlach analyzer. It consists of two parts:
- Front end: Conventional Stern-Gerlach analyzer — separates atoms into two paths
- Back end (quantum eraser): Undoes what the analyzer did — brings the two paths back together in such a way that we cannot tell which path the atom traveled
Key property: Because the two branches are constructed to be absolutely identical, there is no way to determine which path an atom took. The analyzer loop appears to do nothing — an atom enters with an unknown state and emerges with that same unknown state.
(Video demonstration:
sge_exp_1-08_al_intro.html)
Why “Doing Nothing” Is Profound
- The analyzer creates a correlation between the atom’s state and its position
- The eraser destroys that correlation
- The measurement of the projection is erased, and the atom proceeds as if the analyzer loop wasn’t there
Gates and Controlled Measurements
We can add gates on each branch to control which path atoms can take. This gives four configurations:
Gate Configurations
| + Branch Gate | − Branch Gate | Result |
|---|---|---|
| Open | Closed | Acts like a regular analyzer (100% to D1) |
| Closed | Open | Acts like an upside-down analyzer (100% to D2) |
| Closed | Closed | All atoms blocked — no detection |
| Open | Open | Analyzer loop appears to do nothing (~50% each) |
When both branches are open, the atoms emerge as if they were never measured at all — the analyzer loop is completely transparent. This is because we have no which-path information.
Known-State Atom Source
To simplify further experiments, we construct a source that always emits atoms in a known state.
How It Works
Chain together:
- A random-source atom gun
- A Stern-Gerlach analyzer
- A half-open gate (blocking one output)
The source is marked with an arrow pointing in the direction corresponding to the + state. Atoms from this source always measure as + when passed through an analyzer oriented in the same direction.
If the source is flipped upside-down, all atoms emerge in the − state instead.
Experiments with Analyzer Loops and Known States
Setup: Analyzer Loop at 90° to Source
- Source: Atoms in known +z state
- Analyzer loop: Oriented along x (rotated 90° from z)
- Final analyzer (B): Oriented along z
With One Branch Blocked
When only the +x branch is open (gate on −x closed):
- All atoms reaching analyzer B must have passed through the +x branch
- The analyzer loop acts like a regular analyzer at 90°
- Results: ~50% D1, ~50% D2 — exactly as if we had a single perpendicular analyzer
When only the −x branch is open (gate on +x closed):
- Same results — 50/50 split
(Video demonstration:
sge_exp_1-09_al_known_states.html)
With Both Branches Open — The Surprise
When both gates are open, something dramatically different happens:
- 100% of atoms go to D1, 0% to D2
This cannot be explained by classical probability reasoning. The classical expectation (adding probabilities from each branch) would predict 50/50. This discrepancy is the topic of Lecture 4 — the two-slit analog.
Key Takeaways
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Quantum particles are “dumb”: They only remember the last measurement — the most recent axis their projection was measured on.
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The Stern-Gerlach analyzer loop erases measurements: By bringing two paths together in an indistinguishable way, the which-path information is destroyed and the atom’s state reverts to what it was before the analyzer.
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What the atom “knows” depends on whether we can know its path: When both branches are open and indistinguishable, the analyzer loop is completely transparent. When gates force one path, it behaves like a regular analyzer.
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Classical probability breaks down: The analyzer loop with both branches open (and a known-state source) produces results that cannot be predicted by adding probabilities classically — foreshadowing quantum interference.
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Quantum mechanics bridges randomness and precision: While individual events are random, quantum theory enables extraordinary predictive accuracy for measurable quantities (energy levels, frequencies, times).