An apple accelerates downward at about 9.8 m/s², and Mercury’s orbit precesses by roughly 43 arcseconds per century. Both numbers are famous, but they belong to different kinds of knowledge: regularities we call scientific laws and deeper explanations we call scientific theories. Confusing the two leads to bad arguments from “evolution is just a theory” to “quantum mechanics breaks Newton’s laws.”
This article clarifies scientific law vs theory, shows how they interact with concrete examples and numbers, and offers decision rules for judging claims. The short version: laws describe patterns; theories explain why those patterns hold and where they should break.
What Laws And Theories Are and Are Not
A scientific law is a compact statement often mathematical of a recurring pattern in nature. Kepler’s third law says orbital periods scale as the 3/2 power of the semi-major axis (T² ∝ a³). Ohm’s law states that current is proportional to voltage (I = V/R) in certain materials. These are descriptive, not explanatory. They summarize “what happens” under specified conditions with useful precision.
A scientific theory is a coherent explanatory framework that accounts for multiple laws and observations and makes new testable predictions. Newton’s theory of gravitation explains Kepler’s laws and predicts novel effects (e.g., tides). The kinetic theory of gases explains Boyle’s and Charles’s laws by modeling molecules as particles with statistical motion. Theories answer “why” and “in what domain.”
Critically, a theory does not “graduate” into a law. They serve different purposes. A law can be accurate yet shallow without mechanisms; a theory can be powerful yet only approximately right in certain regimes. Both are tested, refined, and sometimes replaced when data demand it.
How They Interact: Case Studies With Numbers
Orbit prediction shows the division of labor well. Kepler’s laws were empirical fits to Tycho Brahe’s data. Newton’s theory explained them via an inverse-square gravitational force. Later, general relativity refined Newton with small corrections: Mercury’s perihelion advances about 43 arcseconds per century beyond Newtonian predictions, a difference that is tiny for Earth satellites but decisive for precision astronomy. The law captured the pattern; the theory explained it and predicted where it would deviate.
Gas behavior offers another layered view. Boyle’s law (P ∝ 1/V at fixed temperature) and the ideal gas law (PV = nRT) hold within roughly 1% for nitrogen or oxygen near 1 atm and room temperature, but break down near liquefaction or at high pressure. The compressibility factor Z often strays to 0.9–1.1 at 10–50 atm. Kinetic theory explains the law: at 300 K, air molecules move around 500 m/s on average, and their momentum-changing collisions with container walls generate pressure following PV = nRT when interactions are negligible.
Electric conduction illustrates domain limits. Ohm’s law works well for metals at constant temperature and moderate currents. But run a copper wire hard enough that its temperature rises by 10°C and resistance increases about 4% (temperature coefficient α ≈ 0.004/°C). At very high current densities, heating and electromigration cause strong deviations. Semiconductors can be decisively non-ohmic: a diode’s current scales roughly exponentially with voltage. Band theory explains these departures and defines when the ohmic law is a good local approximation.
Testing, Prediction, And Uncertainty
Both laws and theories must be testable, but they differ in the precision and kinds of predictions they offer. Laws often yield high-precision quantitative predictions within defined regimes. For example, the gravitational constant G is measured as 6.67430 × 10⁻¹¹ m³⋅kg⁻¹⋅s⁻² with a relative uncertainty of about 22 parts per million. Many biological and social theories make probabilistic predictions effect sizes and risk ratios because the underlying systems are heterogeneous and noisy, yet the predictions remain testable with statistics.
Cross-domain predictions are a strength of well-supported theories. Planck’s theory of blackbody radiation predicts a specific spectral shape; the cosmic microwave background (CMB) matches a 2.725 K blackbody with deviations measured by COBE FIRAS at less than about 50 parts per million. That is not just curve-fitting; it is a theory specifying how radiation should look across wavelengths and being confirmed to an exacting standard.
The right test often hinges on scale. Near Earth’s surface, Newtonian gravity and general relativity give almost identical results for falling objects; corrections are far below typical experimental noise. But for GPS, relativity is essential: clocks on satellites tick faster by roughly 38 microseconds per day due to gravitational and velocity effects. Without applying the theory’s corrections, positioning errors would accumulate by kilometers per day.
Practical Implications And Misconceptions
When headlines proclaim “a law was overturned,” check the regime. The OPERA collaboration’s 2011 faster-than-light neutrino result would have violated the bedrock laws of relativity; it was later traced to a faulty fiber-optic cable and clock synchronization. Most “law-breaking” stories collapse into instrumentation errors or discoveries that the experiment pushed outside the law’s valid range where a more complete theory already predicts deviations.
Engineering practice codifies domains of validity with safety margins. Hooke’s law (stress proportional to strain) governs materials in their elastic range. For structural steel with yield strengths around 250–500 MPa, building codes select working stresses well below yield and apply factors of safety typically between 1.5 and 3. Where cracks are possible, fracture mechanics provides thresholds like K_IC (fracture toughness), often 30–100 MPa·√m for structural alloys, to decide if growth is likely. Laws enable quick calculations; theories justify limits and failure modes.
In public health, mechanisms and patterns complement each other. The empirical regularity that measles vaccination collapses cases is explained by epidemiological theory: the effective reproduction number Re = R0 × (1 − coverage × efficacy). With measles R0 ≈ 12–18, the herd immunity threshold is 1 − 1/R0, about 92–95% coverage if efficacy is near 100%. Laws do not “prove” specific policies; theories connect interventions to outcomes, quantify thresholds, and show where uncertainty (e.g., heterogeneous contact networks) may alter results.
Conclusion
Use this decision rule: reach for a scientific law when you need a reliable pattern within a known regime; reach for a scientific theory when you need an explanation, a boundary for the law, or predictions in new conditions. Ask three questions of any claim: what domain is assumed, what error bars or uncertainties are attached, and what mechanisms justify extending the pattern? Clear answers separate descriptive regularities from the deeper scaffolding that makes science cumulative rather than merely cataloged.
