Level 5 · Graduate study teaching kit · Master’s and early doctoral level
Zero-point-field inertia programs
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
ZPF spectral-response and null-test bound
How does a declared vacuum-response spectrum map to an inertial coefficient, and what experimental null result constrains it?
Setup
Use the ZPF-response workspace. Declare the Gaussian response center, width, amplitude, cutoff, and effective volume; integrate the modeled coefficient, then compare a composition modulation with an experimental uncertainty bound.
Predict first
- 1. Predict how shifting response toward higher frequency changes a quartic-weighted integral.
- 2. Predict when a null experiment excludes rather than merely fails to resolve the model.
| Variable | Role | Unit |
|---|---|---|
| Response center, width, and amplitude | model inputs | frequency and dimensionless |
| Spectral cutoff and effective volume | regularization/geometry inputs | frequency and volume |
| Response-derived mass coefficient | dependent model output | kg |
| Composition contrast and experimental bound | test diagnostics | dimensionless |
Observation columns
Analyze
- 1. Which assumption regularizes the spectral integral?
- 2. How sensitive is the coefficient to cutoff and response shape?
- 3. Does the model include QCD and binding contributions to observed mass?
- 4. Which systematic could imitate composition-dependent inertia?
Conclusion frame
The declared response produced mass coefficient ___ and contrast ___; compared with bound ___, this parameter point is ___ under assumptions ___.
Instructor guide · 70–90 minutes
Teach the investigation, not the interface
Learning target: Learners reproduce a response-based inertia coefficient, expose its spectral assumptions, and convert a calibrated null result into a model bound.
Prepare
- • Review vacuum spectral density and response integrals.
- • Declare normalization and cutoff conventions.
- • Prepare one composition-dependent precision bound.
Facilitation moves
- • Vary cutoff and resonance separately.
- • Compare inferred mass with a reference mass budget.
- • Demand a unique predicted modulation before discussing anomalies.
Accessibility and participation
- • Plot the response and cumulative integral together.
- • Translate frequency decades into contribution factors.
- • Provide an assumption-to-bound dependency map.
Evidence of learning
- • A reproducible spectral integral
- • A sensitivity analysis
- • A quantitative excluded/allowed decision
Misconception checks
A coefficient proportional to acceleration proves all inertia is vacuum drag.
The model must reproduce relativistic covariance, composition, QCD/binding mass, gravity, and decisive experiments.
A null result cannot teach anything.
With calibrated sensitivity, it excludes a defined parameter region and improves the theory.
Extension
Replace the Gaussian response with two resonances and test whether existing composition bounds permit either component.