Speed of light

• 1. Introduction

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  The speed of light in vacuum, denoted by the lowercase letter c, equals exactly 299792458 metres per second. That number is not measured. It is decreed. By international agreement, the metre is defined as the distance light travels in vacuum in a tiny fraction of a second, which fixes c forever as an exact value rather than something experiments can refine.

  This is a strange kind of constant. It tells you how fast light moves, but it also sets a cosmic speed limit that nothing carrying matter, energy, or information can ever cross. It links space to time. It appears in equations that have nothing to do with light at all. Why does one number do so much work?

  The answer runs through Jupiter's moon Io, a rotating cogwheel, a microwave oven full of marshmallows, and a galaxy whose light has been travelling for 13 billion years. It runs through ancient Greek philosophers who could not agree whether light moved at all, and through a postulate that rewrote space and time. The story of this number is the story of how humans learned to measure the unmeasurable, and what they found waiting at the edge of speed.

• 2. A Universal Speed Limit

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  Particles with rest mass can be accelerated to approach c, but they can never reach it, in any frame of reference. The reason is brutal arithmetic. An object's kinetic energy grows with the Lorentz factor, and that factor climbs toward infinity as speed approaches c. To actually hit the speed of light, a massive object would need an infinite amount of energy. The door is closed.

  Causality is the deeper reason nothing outruns light. If the distance between two events is greater than the time between them multiplied by c, then some frames of reference see one event first, others see the reverse, and still others see them happen together. Send something faster than c, and in some frame it travels backward in time. An effect could be observed before its cause. Such a violation has never been recorded, and it would open paradoxes like the tachyonic antitelephone.

  The limit reaches into things that do not look like light at all. General relativity predicts that c is also the speed of gravity and of gravitational waves, and observations of gravitational waves have matched that prediction. The constant also threads through quantum electrodynamics, quantum chromodynamics, and the Standard Model of particle physics. Massless particles and field perturbations all obey the same rule, travelling at c regardless of the motion of their source.

  Einstein arrived at all of this from a single postulate in 1905. He assumed the speed of light is constant for any non-accelerating observer, independent of the motion of source or observer. From that one assumption flowed special relativity, with consequences that sound impossible. Moving objects shorten in the direction of travel. Moving clocks run slow. At 86.6 percent of the speed of light, time dilation reaches a factor of two; at 99.5 percent, it climbs further still. These predictions have been confirmed in experiments like the Kennedy-Thorndike and Ives-Stilwell tests.

• 3. Speeds That Only Seem To Cheat

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  Sweep a laser beam quickly across a distant wall, and the spot of light can race across that wall faster than c. No law is broken. The only things actually moving are the laser and the light it emits, and that light still crawls from the laser to each new position at exactly c. A shadow cast on a far object can be made to slide faster than light in the same way. In neither case does any matter, energy, or information cross the limit.

  Quantum entanglement looks like an even cleaner violation. Two entangled particles share a superposition of states until one is measured. Observe one, and the other's state is fixed instantaneously, however far apart they sit. This is the heart of the EPR paradox. Yet you cannot choose which state the first particle takes, so no message can be sent. The Hartman effect raises a similar tease, where a virtual particle's tunnelling time through a barrier stays constant no matter how thick the barrier grows. Again, no information rides along.

  The sky offers its own illusion. The relativistic jets of radio galaxies and quasars show what astronomers call superluminal motion. The jets are not breaking the limit. They move near the speed of light at a small angle toward Earth, and the geometry compresses the timing of what we see into an apparent faster-than-light streak.

  The universe's expansion produces the boldest-looking exception. Distant galaxies drift apart faster the farther they are, and beyond a boundary called the Hubble sphere, their distance from Earth grows faster than the speed of light. These recession rates are increases in proper distance per cosmological time, not velocities in any relativistic sense. They are a coordinate artifact. In 2011, an experiment seemed to clock neutrinos beating light; it turned out to be experimental error.

• 4. Light Inside Matter

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  Drop light into glass, water, or diamond, and it slows down. The ratio between c and the speed at which light moves in a material is that material's refractive index, n. For visible light, glass sits around 1.5, water near 1.3, and diamond around 2.4. Air barely slows light at all, with an index of about 1.0003. Larger indices mean lower speeds.

  A pulse of light does not travel as one simple thing. Its individual crests and troughs move at the phase velocity, the overall envelope moves at the group velocity, and its earliest leading edge moves at the front velocity. These can differ. The phase velocity of X-rays through most glasses routinely exceeds c, but phase velocity does not carry information. When the phase velocity differs across frequencies, a pulse smears out over time, a process called dispersion.

  The extremes are stranger still. In a Bose-Einstein condensate near absolute zero, the effective speed of light can drop to only a few metres per second. Two independent teams of physicists claimed to bring light to a complete standstill by passing it through a condensate of rubidium. The light was not frozen in flight. It was stored in the excited states of atoms and re-emitted later when a second laser pulse triggered it. During that pause, it had ceased to be light at all.

  A charged particle can move through a medium faster than the phase velocity of light there, while staying below c. When it does in a dielectric material, it radiates an electromagnetic shock wave called Cherenkov radiation. Group velocities exceeding c were proposed theoretically in 1993 and achieved experimentally in 2000, and in principle the group velocity can even run backward in time. None of it lets information beat the front velocity, which can be shown to always equal c.

• 5. Where The Delay Bites

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  Inside a computer, a signal in one clock cycle travels only so far. If a processor runs at a high enough frequency, light covers roughly 30 centimetres in a single cycle, and in practice less, because the printed circuit board slows the signal. Processors and memory chips must be crowded close together to keep communication latencies small. As clock frequencies rise, the speed of light may become a limit on the internal design of a single chip.

  Grace Murray Hopper, a naval officer and computer scientist, made this tangible. In the late 1960s she handed colleagues foot-long wires, each the distance light travels in a nanosecond, to show why smaller components mean faster computing.

  The planet itself is small enough to feel the delay. The equatorial circumference of the Earth is about 40075 kilometres, and the shortest theoretical time for information to cross half the globe along the surface is about 67 milliseconds. In optical fibre, with a refractive index around 1.52, the trip takes longer still, slowed by roughly 35 percent. High-frequency traders care intensely about these fractions of a second. Some have switched to microwave links between trading hubs, because radio waves through air run closer to c than fibre-optic signals do.

  Space stretches the wait into something human. When Apollo 8 became the first crewed spacecraft to orbit the Moon, ground control had to wait at least three seconds for the answer to every question. The delay to Mars swings between five and twenty minutes depending on planetary positions. If a robot on the Martian surface hits trouble, its controllers stay ignorant for roughly 4 to 24 minutes, and commands take another 4 to 24 minutes to arrive.

• 6. Looking Into The Past

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  Light from the faraway galaxies in the Hubble Ultra-Deep Field images took 13 billion years to reach Earth. Those photographs, taken today, show the galaxies as they appeared 13 billion years ago, when the universe was less than a billion years old. Because more distant objects appear younger, astronomers can trace the evolution of stars, of galaxies, and of the universe itself simply by looking far away.

  Distances at this scale get measured in light-years, the distance light covers in one Julian year. That is around 9461 billion kilometres, or 5879 billion miles, or 0.3066 parsecs. In round figures, a light-year is nearly 10 trillion kilometres or nearly 6 trillion miles. Proxima Centauri, the closest star to Earth after the Sun, sits about 4.2 light-years away.

  The finite speed of light is also a measuring tool. Radar systems find a target's distance by halving the round-trip travel time of a reflected radio pulse and multiplying by the speed of light. A GPS receiver works out its position by timing how long radio signals take to arrive from each satellite. Since light covers about 300000 kilometres in a second, these timings of small fractions of a second have to be extraordinarily precise. The Lunar Laser Ranging experiment, radar astronomy, and the Deep Space Network measure distances to the Moon, the planets, and spacecraft the same way.

• 7. Catching The Uncatchable

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  Ole Rømer made the first quantitative estimate of the speed of light in 1676, using a moon of Jupiter. He noticed that the periods of Io, Jupiter's innermost major moon, looked shorter when Earth approached Jupiter than when it receded. The cumulative difference over months pointed to a finite speed, and he deduced that light takes 22 minutes to cross the diameter of Earth's orbit. Christiaan Huygens combined that with an estimate of the orbit's diameter to get 220000 kilometres per second, about 27 percent below the true value.

  James Bradley found another route in 1729 through the aberration of light. A moving observer sees light arrive from a slightly shifted direction, and because Earth's velocity changes as it orbits the Sun, the apparent positions of stars trace small circles, up to 20.5 arcseconds across. Bradley concluded that light travels 10210 times faster than Earth in its orbit; the modern figure is 10066 times. In his terms, light would take 8 minutes 12 seconds to reach Earth from the Sun.

  Hippolyte Fizeau brought the measurement down to Earth in the 19th century. He aimed a beam at a mirror 8 kilometres away, sending it through a rotating cogwheel. At the right rotation rate the beam slipped through one gap going out and the next coming back; at other rates a tooth blocked it. From the distance, the tooth count, and the rotation rate, he calculated a value of 315000 kilometres per second. Léon Foucault swapped the cogwheel for a rotating mirror and reached 298000 in 1862, and used the same apparatus, on a suggestion from François Arago, to compare light's speed in air against water.

  The trail stretches back much further than any instrument. Empedocles, who lived around 490 to 430 BCE, was the first to claim light has a finite speed, arguing it was something in motion that must take time to travel. Aristotle disagreed, calling light a presence rather than a movement. In 1021, Alhazen published the Book of Optics, dismissing the idea that vision comes from rays leaving the eye and proposing instead that light moves into the eye at a finite, variable speed. Roger Bacon argued the same in the 13th century, while Kepler and Descartes still insisted, in the 17th, that light was instantaneous.

• 8. Fixing The Number

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  By 1950, Louis Essen had pinned the speed to 299792.5 kilometres per second using cavity resonance, measuring the frequency of microwaves in a cavity of precisely known dimensions. The Essen and Gordon-Smith result of 1946 was already far more precise than optical methods, and the cavity approach has a kitchen version. Remove the turntable from a microwave oven, heat marshmallows or margarine until they melt at the hottest spots, measure the distance between those spots as half a wavelength, and multiply by the oven's frequency, often around 2450 megahertz. The answer comes out, often with less than 5 percent error.

  The decisive leap came in 1972. A group at the US National Bureau of Standards in Boulder, Colorado used laser interferometry and the new definitions of the metre and second to measure c with a fractional uncertainty of about 3.5 parts in a billion. This was 100 times less uncertain than the previously accepted value. The remaining doubt was mostly about the definition of the metre itself, not the speed of light.

  That realization flipped the whole problem around. In 1983, the 17th meeting of the General Conference on Weights and Measures redefined the metre as the length light travels in vacuum in 1/299792458 of a second. The second was already tied to the caesium-133 atom, whose hyperfine transition counts out 9192631770 cycles of radiation. So the speed of light stopped being something to measure and became a defined constant. Today, a better experiment no longer sharpens the value of c. It sharpens the metre. In the 2019 revision of the SI, this same explicit-constant logic was extended across the base units, with each one anchored to an exact value of a fundamental constant.