The Spacetime Metric

Level 2 · Secondary physics teaching kit · Grades 10–12

Quantum physics: states, amplitudes, and measurement

Use the learner record during the live investigation, then use the instructor guide to facilitate comparison, address misconceptions, and assess evidence-bounded reasoning.

Learner lab record

Wave-packet width and uncertainty record

How does narrowing a wave packet in position change its momentum spread and later evolution?

Setup

Use the wave-packet laboratory. Compare broad and narrow packets while keeping the central momentum fixed, then follow their modeled spreading over time.

Predict first

  1. 1. Predict which initial packet has the larger momentum spread.
  2. 2. Predict which packet spreads more rapidly in the free-particle model.
Variables
VariableRoleUnit
Initial position widthindependentmodel length
Central momentumcontrolledmodel momentum
Momentum spreaddependentmodel momentum
Packet width over timedependentmodel length

Observation columns

initial widthcentral momentummomentum spreadtimelater widthuncertainty product

Analyze

  1. 1. Which comparison isolates initial width?
  2. 2. Does uncertainty describe instrument carelessness or the modeled state?
  3. 3. What does the probability distribution predict?
  4. 4. Which model assumptions limit the result?

Conclusion frame

Narrowing the initial packet from ___ to ___ changed momentum spread from ___ to ___ and later spreading by ___ because ___.

Instructor guide · 45–60 minutes

Teach the investigation, not the interface

Learning target: Learners connect localization with momentum spread without treating a wavefunction as a literal material wave or hidden classical path.

Prepare

  • Review probability distributions and standard deviation.
  • Distinguish central value from spread.
  • Prepare repeated-measurement language before opening the model.

Facilitation moves

  • Ask what an ensemble of trials would show.
  • Keep packet width separate from particle size.
  • Require learners to name the free-particle idealization.

Accessibility and participation

  • Pair every graph with a numeric center-and-spread table.
  • Describe widening verbally and avoid animation-only evidence.
  • Permit spreadsheet calculations for standard deviations.

Evidence of learning

  • A controlled width comparison
  • Correct center-versus-spread language
  • One stated model limitation

Misconception checks

Uncertainty is only poor measurement technique.

The modeled quantum state itself can have irreducible spreads even with ideal measurement.

The wave packet is a tiny classical cloud with a hidden exact trajectory.

It encodes amplitudes for possible outcomes; interpretations add different ontologies beyond the shared predictions.

Extension

Compare free spreading with a confined packet and identify which Hamiltonian term changes the evolution.