Protocols for validating physical plausibility of computational results - dimensional analysis, limiting cases, order-of-magnitude estimates, and analytical cross-checks. Use when checking if results make physical sense.
Protocols for ensuring computational results are physically plausible.
Every physical quantity has dimensions. Units must balance in any equation.
Base dimensions (SI):
For any equation A = B:
def check_dimensions(left_dims, right_dims):
"""Verify dimensional consistency."""
if left_dims != right_dims:
raise ValueError(f"Dimensional mismatch: {left_dims} vs {right_dims}")
return True
| Quantity | Dimensions | SI Units |
|---|---|---|
| Velocity | [L][T]^-1 | m/s |
| Acceleration | [L][T]^-2 | m/s^2 |
| Force | [M][L][T]^-2 | N |
| Energy | [M][L]^2[T]^-2 | J |
| Power | [M][L]^2[T]^-3 | W |
| Entropy | [M][L]^2[T]^-2[K]^-1 | J/K |
| Information | dimensionless | bits/nats |
Watch for:
Before trusting a general result, check that it reduces correctly in limits:
## Limiting Case Analysis: {quantity}
### Case 1: {limit description}
When {parameter} -> {limit value}:
- Expected: {physical expectation}
- Observed: {what the model gives}
- Match: {yes/no, explanation}
### Case 2: {next limit}
...
Get the rough answer first. If detailed calculation differs by orders of magnitude, something is wrong.
## Order of Magnitude: {quantity}
Relevant scales:
- Length: {characteristic length} ~ {value}
- Time: {characteristic time} ~ {value}
- Energy: {characteristic energy} ~ {value}
Dimensional estimate: {quantity} ~ {scale combination}
Expected magnitude: ~ {power of 10}
Detailed result: {actual value}
Agreement: {within order of magnitude? If not, why?}
| Law | What is Conserved | How to Check |
|---|---|---|
| Energy | Total energy | Sum before = sum after |
| Momentum | Total momentum | Vector sum conserved |
| Probability | Total probability = 1 | Integral/sum = 1 |
| Information (closed) | von Neumann entropy | Check for spurious changes |
Before accepting any result:
Watch for these warning signs:
| Red Flag | Possible Issue |
|---|---|
| Negative probability | Normalization error |
| Energy from nothing | Conservation violation |
| Faster-than-light | Causality violation |
| Infinite values | Missing regularization |
| Non-smooth where smooth expected | Numerical instability |
| Wrong limiting behavior | Formula error |
## Physics Validation: {result description}
### Dimensional Analysis
- Claimed dimensions: {X}
- Verified: {yes/no}
### Limiting Cases
1. {case 1}: {pass/fail}
2. {case 2}: {pass/fail}
### Order of Magnitude
- Estimate: {value}
- Result: {value}
- Agreement: {within factor of X}
### Conservation Laws
- {law 1}: {checked/violated}
- {law 2}: {checked/violated}
### Physical Plausibility
- [ ] All values in physical range
- [ ] No spurious singularities
- [ ] Behavior matches intuition
### Verdict
{VALID / NEEDS INVESTIGATION / INVALID}
{If not valid, what is wrong}