Speed of light

The speed of light in vacuum, often called simply the speed of light and commonly denoted c, is a special number that never changes. It is exactly equal to 299792458 m⋅s⁻¹. This means a metre is the distance light travels in vacuum in a very small part of a second. This speed is about 1 billion kilometres per hour or 700 million miles per hour.

All kinds of electromagnetic radiation, including visible light, move in vacuum at speed c. This speed looks the same to everyone, no matter how they are moving. It is also the quickest speed for information, matter, or energy to travel through space. Particles with weight can get very close to this speed but can never reach it.

The speed of light helps us learn about the universe. The starlight we see on Earth often comes from long ago. When we send messages to faraway space probes, it can take hours for them to get there. The speed of light also helps scientists measure big distances very well.

Long ago, Ole Rømer proved that light does not travel right away by watching Jupiter’s moon Io. Later, James Clerk Maxwell thought that light was a kind of electromagnetic wave that moves at speed c. Albert Einstein used this idea in his theory of relativity, showing how the speed of light links space and time and appears in the famous equation E = mc².

Notation

The speed of light in a vacuum is shown with the letter c. We do not know why this letter was chosen. Some think it might stand for "constant" or come from a Latin word, celeritas, which means "swiftness." Famous scientists like Leonhard Euler and Isaac Asimov wrote about this letter being used for speed.

In the past, other letters were used. For example, James Clerk Maxwell used the letter V in 1865. Later, Max Abraham began using c for the speed of light, and this became the standard. Even Einstein used V at first but switched to c later.

Sometimes c is used for the speed of waves in any material, and c₀ for the speed of light in a vacuum. This helps keep things clear. In this article, c always means the speed of light in a vacuum.

In unit systems

Further information: Metre § Speed of light definition

Since 1983, scientists have known the speed of light in a vacuum to be exactly 299,792,458 meters per second. This number helps us define what a meter means — it is the distance light travels in a tiny fraction of a second.

Different countries and scientists sometimes use different ways to talk about distances, like miles instead of meters. In those cases, the speed of light looks a little different but it is still almost the same. Some areas even use special math tricks where the speed of light is counted as "1" to make their equations easier!

Fundamental role in physics

See also: Special relativity

The speed of light in a vacuum never changes, no matter how the light source or the observer moves. This idea came from Einstein in 1905, based on theories about electricity and magnetism. People could not find proof of something called the "luminiferous aether." Experiments show that this idea matches what we see in the real world.

Einstein's special theory of relativity looks at what happens when we assume the speed of light stays the same for everyone, no matter how they move. One result is that the speed of light is the fastest that anything without weight, like light, can travel in a vacuum.

Special relativity has many surprising results that have been proven true. These include that things can seem to weigh more (mass and energy), get shorter (length contraction), and time can seem to go slower (time dilation) when things move very fast. These effects are small at everyday speeds but become very important when things move close to the speed of light.

Space and time can be thought of together as "spacetime," and the speed of light helps connect these two. This idea is important in modern physics, appearing in theories about very small particles and gravity. Most scientists believe the speed of light is the same everywhere and always, but some theories suggest it might have been different in the past. So far, no proof of this has been found.

The speed of light is the fastest that anything with weight can go. It would take an endless amount of energy to make something with weight go as fast as light. We also know that nothing can send information or energy faster than light.

Main article: One-way speed of light

We can only measure the speed of light when it goes to a mirror and back, because we need a way to match clocks at two places. By using a special way to match clocks, the speed of light going one way is the same as when it goes to the mirror and back.

Faster-than-light observations and experiments

See also: Faster-than-light and Superluminal motion

Sometimes things can look like they are moving faster than the speed of light, but they are not. For example, when a laser light moves quickly across a faraway object, the spot of light can seem to move faster than light. But the light itself is still moving at the speed of light.

In space, some objects like jets from distant galaxies can appear to move faster than light. This happens because we see the light from when the jet was farther away later. It makes it look like it moved faster, but the jet is not actually going faster than light.

Some experiments and ideas in science have suggested things might move faster than light, but these do not let us send information faster than light.

Propagation of light

In classical physics, light is a type of electromagnetic wave. Maxwell's equations show that light moves at a fixed speed in empty space. This speed depends on two special numbers about electricity and magnetism.

In modern quantum physics, light is described as tiny packets called photons. These photons have no weight and always move at the same top speed in empty space.

When light moves through materials like water or glass, it usually slows down. Different types of light can move at different speeds in these materials. The speed at which the peaks and valleys of a light wave move is called the phase velocity. The speed at which a whole group of waves moves is called the group velocity. And the speed at which the very front edge of a light pulse moves is called the front velocity.

The phase velocity helps us understand how light moves through different materials. It is linked to something called the refractive index. A higher refractive index means light travels slower in that material. For example, the refractive index of air is about 1.0003, while water, glass, and diamond have higher values, making light move slower in them.

In very special conditions, like super cold materials called Bose–Einstein condensates, light can slow down to just a few meters per second. Scientists have made light seem to stop for a while by storing it in atoms and then releasing it later. However, this doesn’t mean light actually stopped moving during that time.

Even when light seems to slow down or speed up in materials, it never lets us send information faster than the speed of light in empty space. And when certain particles move through materials faster than the light’s phase velocity, they create a special kind of light glow called Cherenkov radiation.

Practical effects of finiteness

The speed of light is important for sending information, whether it is over short distances or across the universe. In computers, the speed of light limits how fast data can travel between parts. For example, a signal can only go about 30 centimetres in the time it takes a processor to complete one operation. This means parts like memory chips need to be placed close together to work well.

When we send information across the Earth or into space, there is always a delay. For instance, it takes about 67 milliseconds for a signal to travel halfway around the world. In space, delays are even longer. When astronauts flew to the Moon, there was a delay of at least three seconds for messages to travel between the Moon and Earth. Communications with Mars can take between five and twenty minutes, depending on where the planets are in their orbits. This means if a robot on Mars faces a problem, we on Earth won’t know about it for several minutes, and it will take the same amount of time for our commands to reach Mars.

We also use the speed of light to measure distances. For example, radar systems and GPS use the time it takes for signals to travel to and from objects to figure out how far away they are. Light from distant stars and galaxies also takes a very long time to reach us, which is why we see these objects as they were in the past.

Determination

There are many ways to find the speed of light. One way is to measure how fast light travels through space or on Earth. Scientists can also use special numbers called electromagnetic constants to help them.

In 1983, people decided that a metre is the distance light travels in a very small piece of time. This made the speed of light exactly 299,792,458 metres per second.

Astronomical measurements

Space is a great place to measure light because it is mostly empty and very big. One famous scientist, Ole Rømer, used the moons of Jupiter to guess how fast light travels. He noticed that the time it took for Jupiter’s moon Io to orbit changed a little depending on how close Earth was to Jupiter. This helped him figure out that light takes about 22 minutes to travel across the distance of Earth’s orbit around the Sun.

Another way to measure light’s speed uses how stars appear to shift position because of Earth’s movement around the Sun. This method was used by James Bradley, who found that light travels about 10,066 times faster than Earth moves in its orbit.

Astronomical unit

Main article: Astronomical unit

Historically, the speed of light helped scientists find the distance from the Earth to the Sun, called the astronomical unit. In 2012, this distance was set exactly to 149,597,870,700 metres, which also fixes the speed of light in space.

Time of flight techniques

One simple way to measure the speed of light is to shine a beam of light at a mirror far away and time how long it takes for the light to come back. This is how scientists like Hippolyte Fizeau and Léon Foucault did their experiments.

Fizeau used a spinning wheel with gaps to let light pass through. By knowing how fast the wheel spun and how far the mirror was, he could calculate the speed of light.

Foucault used a spinning mirror instead. Because the mirror moved while the light travelled to the far mirror and back, the light reflected at a different angle. From this angle change, the speed of light could be found.

Today, scientists use very fast timers to measure how long it takes a pulse of light to travel to a mirror and back. This is often done in school labs.

Electromagnetic constants

Another way to find the speed of light is to use special numbers from electricity and magnetism. These numbers, called vacuum permittivity and vacuum permeability, are linked to the speed of light by a simple rule. Scientists can measure these numbers in lab experiments to find the speed of light.

Cavity resonance

Scientists can also measure the speed of light by finding the exact frequency and wavelength of a wave inside a metal box, called a cavity resonator. By knowing the size of the box and the frequency of the wave inside, they can calculate the speed of light.

A fun way to see this at home is with a microwave oven. If you remove the turntable and heat something like marshmallows, it will melt most where the microwave waves are strongest. By measuring the distance between these spots and knowing the frequency of the microwave (usually shown on the oven), you can calculate the speed of light.

Interferometry

Interferometry is another way to find the speed of light. A beam of light, like from a laser, is split into two paths and then recombined. By changing the path lengths and watching how the light waves fit together, scientists can find the wavelength of the light. Using the wavelength and the known frequency, they can then calculate the speed of light.

Before lasers, scientists used radio waves for these experiments, but the waves were too long to measure very precisely. With lasers, they can use much shorter wavelengths and very accurate frequency measurements to find the speed of light with amazing precision.

History

Until the early modern period, people did not know if light traveled instantly or at a very fast speed. Ancient thinkers in ancient Greece were the first to discuss this. Later, Einstein's theory of special relativity said that the speed of light stays the same no matter where you are or how you move. Since then, scientists have measured it more accurately.

Early history

Empedocles was the first to say that light moves and must take time to travel. Aristotle disagreed, saying light just appears because something is there. Euclid and Ptolemy thought light came from our eyes to see things. Based on this, Heron of Alexandria believed light must be infinite.

Early Islamic philosophers at first agreed with Aristotle's view. In 1021, Alhazen wrote about how light really moves from objects into our eyes, not from our eyes out. He thought light must travel at a speed. Also in the 1100s, Abū Rayhān al-Bīrūnī agreed that light has a speed.

In the 1200s, Roger Bacon argued that light in air does not move forever. In the 1270s, Witelo thought light might move forever in empty space.

In the 1600s, Johannes Kepler believed light moved forever. René Descartes said if light had a speed, the Sun, Earth, and Moon would not line up right during a lunar eclipse. Later, Pierre de Fermat thought light moved slower in denser materials.

First measurement attempts

In 1629, Isaac Beeckman suggested an experiment to measure light's speed. In 1638, Galileo Galilei tried to measure light's speed but could not tell if it was instant or very fast. In 1667, scientists in Florence tried the same thing but still could not see any delay.

The first quantitative estimate of the speed of light was made in 1676 by Ole Rømer. By watching Jupiter's moon Io, he saw that light takes time to travel. Christiaan Huygens used this to estimate the speed of light.

In his book Opticks in 1704, Isaac Newton shared Rømer's idea. In 1729, James Bradley discovered how stars seem to move a little, and used this to figure that light is faster than Earth moves in its orbit.

Connections with electromagnetism

See also: History of electromagnetic theory and History of special relativity

In the 1800s Hippolyte Fizeau found a way to measure the speed of light. Léon Foucault improved this method and in 1862 got a closer number. In 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch measured something related to electricity and found a number very close to the speed of light. The next year Gustav Kirchhoff showed that electric signals move at this speed in a wire.

In the early 1860s, Maxwell showed that his ideas about electromagnetism meant that these waves move at the same speed as light, and he thought light was one kind of electromagnetic wave.

"Luminiferous aether"

Main article: Luminiferous aether

Light acts like a wave, and in the 1800s, scientists thought it moved through something called aether. After Maxwell linked light and electric and magnetic waves, many thought both moved through the same aether.

Some scientists tried to measure Earth's movement through it. The most famous experiment was done by Albert A. Michelson and Edward W. Morley in 1887. They could not find any movement, which was surprising.

Special relativity

In 1905 Einstein said that the speed of light in empty space is the same no matter how you move or where the light comes from. He used this idea to create the special theory of relativity. In this theory, the speed of light is a basic constant.

Increased accuracy of c and redefinition of the metre and second

See also: History of the metre

In the middle of the 1900s, scientists got much better at measuring the speed of light. In 1950, Louis Essen measured the speed. In 1960, the metre was redefined using light from krypton-86, and in 1967, the second was redefined using a special kind of light from caesium-133.

In 1972, scientists measured the speed of light to be c = 299,792,456.2±1.1 m/s. In 1983, scientists decided to define the metre as "the length of the path traveled by light in vacuum during a time interval of 1/299792458 of a second." This made the speed of light exactly 299,792,458 m/s.