Speed of Light in Vacuum: Fixing the Metre

Definition and Role in the SI

Since the 17th CGPM (1983), the metre has been defined as the distance travelled by light in vacuum during a time interval of 1/299 792 458 of a second. With the second realized via the cesium-133 hyperfine transition, c inherits exactness and provides a bridge between time and length. Any measurement of distance that relies on propagation of electromagnetic waves can thus achieve traceability to the SI without a physical artefact.

The definition assumes that light propagates in vacuum without dispersion. In practice, laboratories approximate vacuum conditions using evacuated cavities or by correcting for refractive index variations in air. The mise en pratique for the metre details interferometric techniques, such as stabilized lasers locked to atomic or molecular transitions, to realize the definition with uncertainties below nanometre scales.

Because c is constant, derived quantities such as impedance of free space, vacuum permittivity, and vacuum permeability become defined parameters. The ampere and volt, realized through the elementary charge and Planck constant, integrate seamlessly with c via Maxwell’s equations, establishing a consistent electromagnetic framework for calibrations.

Historical Determinations and Experiments

Early estimates of the speed of light date back to Ole Rømer’s 1676 observation of Io’s eclipses, which suggested a finite propagation speed. Subsequent terrestrial experiments by Hippolyte Fizeau (1849) and Léon Foucault (1850) used toothed wheels and rotating mirrors to measure transit times over laboratory baselines. Albert A. Michelson refined interferometric methods, achieving increasingly accurate values in the late 19th and early 20th centuries.

Microwave cavity resonance experiments in the 1950s and 1960s, coupled with precise frequency standards, reduced uncertainty to a few parts in 10⁹. Laser technology then enabled measurements with sub-metre coherence lengths, culminating in the 1972 determination by Evenson and colleagues, who used a laser stabilized to the methane absorption line at 88 THz to measure c with unprecedented precision.

These advances convinced the CGPM that the limiting uncertainty stemmed from the metre artefact, not the speed of light. By fixing c and redefining the metre, metrologists transferred uncertainty budgets from length to time measurements, where technology offered greater stability. The cesium hyperfine article explains how atomic clocks supplied the necessary temporal accuracy based on ΔνCs.

Theoretical Foundations and Consequences

Maxwell’s equations predict that electromagnetic waves propagate through vacuum at a speed determined by the vacuum permittivity ε₀ and permeability μ₀: c = 1/√(μ₀ε₀). Einstein’s theory of special relativity elevates c to a fundamental constant that sets the maximum speed for information and matter, leading to time dilation, length contraction, and mass-energy equivalence E = m·c².

Lorentz invariance ensures that c remains identical in all inertial frames, a principle experimentally confirmed by Michelson-Morley and modern resonator comparisons. General relativity further ties c to spacetime curvature, with gravitational fields affecting path length and travel time. Precision navigation systems account for these relativistic effects when converting between coordinate time and proper time.

In quantum electrodynamics, c enters renormalization calculations and influences the fine-structure constant α = e²/(4π ε₀ ħ c). Fixing c and h in the SI means α’s value depends on the elementary charge, emphasizing the interplay between defining constants. Researchers search for possible variations of α over cosmological timescales by comparing spectral lines in distant quasars to laboratory references, demonstrating how cosmology tests the constancy of c indirectly.

Dimensional Analysis and Derived Units

Many derived units hinge on c. For example, the electric impedance of free space Z₀ equals μ₀c, while the radiance of blackbody radiation involves c in Planck’s law. Radar cross-section, antenna gain, and photon momentum calculations all include c explicitly. Understanding these dependencies ensures consistent unit conversion across engineering disciplines.

Realization Techniques and Best Practice

Laboratories realize the metre by measuring optical frequencies and counting wavelengths over known distances. Stabilized lasers locked to iodine, acetylene, or cesium transitions provide reproducible frequencies. Interferometers convert phase differences into distance measurements, while frequency combs connect optical and microwave domains to compare lasers with atomic clocks.

Free-space time-of-flight measurements employ pulsed lasers and fast photodetectors to measure travel times over baseline distances. Accurate timing requires synchronization using cesium or optical clocks and calibration of detector response. Refractive index corrections rely on Edlén or Ciddor equations, demanding precise monitoring of temperature, pressure, and humidity.

Fibre-optic links disseminate stabilized optical signals over hundreds of kilometres with minimal phase noise, enabling remote interferometry and geodesy. Space missions such as NASA’s Lunar Laser Ranging and ESA’s Sentinel altimetry programs depend on c-calibrated timing to convert round-trip delays into distance with millimetre precision.

Quality Assurance Tips

• Use dual-wavelength interferometry to correct for dispersion in air or optical media.
• Reference all timing electronics to traceable atomic standards to avoid drift.
• Document environmental parameters and apply real-time refractive index corrections.
• Calibrate photodetector linearity and timing jitter for high-speed measurements.
• Validate measurement setups using round-trip tests or comparison against calibrated artefacts.

Applications and Future Outlook

The fixed value of c influences domains ranging from telecommunications to fundamental physics. Optical fibre networks rely on precise knowledge of propagation delay to synchronize data transmission. Astronomy uses c to convert redshifts into cosmic distances and to analyse time-of-flight in pulsar timing arrays searching for gravitational waves.

Geodesy exploits c-based measurements in satellite laser ranging, GNSS, and interferometric synthetic aperture radar. Autonomous vehicles and robotics integrate lidar systems calibrated against c to reconstruct spatial environments. In medicine, optical coherence tomography and time-resolved spectroscopy depend on c to interpret depth information.

Looking forward, quantum communication, deep-space exploration, and gravitational wave observatories will continue to push timing and distance measurement requirements. Maintaining traceability to the exact value of c ensures interoperability between terrestrial laboratories and spaceborne platforms. Explore related guides on the Planck constant and elementary charge to appreciate the unified constant-based SI.