Physics Validation

Physics Validation Skill

Protocols for ensuring computational results are physically plausible.

Dimensional Analysis

The Fundamental Check

Every physical quantity has dimensions. Units must balance in any equation.

Base dimensions (SI):

• [L] Length (meters)
• [M] Mass (kilograms)
• [T] Time (seconds)
• [I] Current (amperes)
• [K] Temperature (kelvin)
• [N] Amount (moles)
• [J] Luminosity (candela)

Dimensional Consistency

For any equation A = B:

• dim(A) must equal dim(B)
• Addition/subtraction requires matching dimensions
• Exponents must be dimensionless

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

Common Derived Quantities

Dimensional Traps

Watch for:

• Logarithm arguments must be dimensionless
• Exponential arguments must be dimensionless
• Trig function arguments must be dimensionless (radians)
• Dimensionless ratios are often the meaningful quantities

Limiting Cases

The Sanity Check

Before trusting a general result, check that it reduces correctly in limits:

1. Weak coupling limit - Does it reduce to non-interacting case?
2. Strong coupling limit - Does behavior saturate appropriately?
3. Large/small parameter limits - Asymptotic behavior correct?
4. Classical limit - Does quantum reduce to classical?
5. Equilibrium limit - Does dynamics reach expected steady state?

Template

## 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}
...

Order of Magnitude Estimates

Before Detailed Calculation

Get the rough answer first. If detailed calculation differs by orders of magnitude, something is wrong.

Fermi Estimation Approach

1. Identify relevant scales
2. Use dimensional analysis to constrain form
3. Estimate coefficients (often O(1))
4. Compare to detailed result

Example Pattern

## 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?}

Analytical Cross-Checks

When to Use

• Verify numerics against solvable subcases
• Check conservation laws are satisfied
• Validate symmetry properties

Conservation Laws

Symmetry Properties

• Time-reversal: Is dynamics reversible when it should be?
• Spatial symmetry: Does solution respect boundary conditions?
• Exchange symmetry: Bosons/fermions behave correctly?

Physical Plausibility Checklist

Before accepting any result:

• Dimensions are consistent
• Limiting cases work correctly
• Order of magnitude is reasonable
• Conservation laws satisfied
• No physically impossible values (negative probabilities, etc.)
• Behavior is continuous where it should be
• Singularities are physically meaningful

Red Flags

Watch for these warning signs:

Validation Template

## 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}