Speed of light

The speed of light in vacuum, often called simply the speed of light and commonly denoted c, is a universal physical constant exactly equal to 299792458 m⋅s⁻¹. This means a metre is defined as the length of the path travelled by light in vacuum during a time interval of 1⁄299792458 second. This speed is about 1 billion kilometres per hour or 700 million miles per hour.

All forms of electromagnetic radiation, including visible light, travel in vacuum at speed c. This speed is the same for all observers, no matter how they are moving. It is also the fastest speed at which information, matter, or energy can travel through space. Particles with mass can get very close to this speed but can never reach it.

The finite speed of light helps us study the universe. The starlight we see on Earth often comes from the distant past. When we talk to faraway space probes, it can take hours for messages to arrive. The speed of light also helps scientists measure large distances very accurately.

Long ago, Ole Rømer showed that light does not travel instantly by watching Jupiter’s moon Io. Later, James Clerk Maxwell suggested that light was an electromagnetic wave that travels at speed c. Albert Einstein used this idea in his theory of relativity, showing how the speed of light connects space and time and appears in the famous equation E = mc².

Notation

The speed of light in a vacuum is usually shown with the letter c. We aren't exactly sure 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, but not always for light specifically.

In the past, other letters were also used. For example, James Clerk Maxwell used the letter V in 1865. Later, in 1903, Max Abraham began using c to mean the speed of light, and this became the standard. Even Einstein used V at first in 1905 but switched to c by 1907.

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, just like other letters are used for related ideas in physics, such as μ₀ for vacuum permeability and ε₀ for vacuum permittivity. 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 special number helps us define what a meter really means — it is the distance light travels in just 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 does not change, no matter how the light source or the observer is moving. This idea was suggested by Einstein in 1905, based on theories about electricity and magnetism and because no one could find proof of something called the "luminiferous aether." Experiments have shown that this idea matches what we see in the real world.

Einstein's special theory of relativity looks at what happens when we assume that the speed of light stays the same for everyone, no matter how they are moving. 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 because it would mean effects could happen before their causes, leading to impossible situations.

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 it looks like things 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 is because we see the light from when the jet was farther away later, making 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. The rules for these waves are explained by Maxwell's equations, which show that light travels at a fixed speed in empty space. This speed depends on two special numbers related to 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 travel 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 even 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 matters for sending information, whether 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 other physics rules that include the speed of light, like measuring special numbers called electromagnetic constants.

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. For a long time, many debated the idea until Rømer made the first calculation of the speed of light. 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 and 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 because faraway stars look like they appear right away when we open our eyes.

Early Islamic philosophers at first agreed with Aristotle's view that light did not travel at a speed. 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, and that it slows down in denser materials. Also in the 1100s, Abū Rayhān al-Bīrūnī agreed that light has a speed, and noticed it is much faster than sound.

In the 1200s, Roger Bacon argued that light in air does not move forever, using ideas from Alhazen and Aristotle. In the 1270s, Witelo thought light might move forever in empty space but slow down in denser materials.

In the 1600s, Johannes Kepler believed light moved forever because empty space has no obstacles. René Descartes said if light had a speed, the Sun, Earth, and Moon would not line up right during a lunar eclipse. Since they did line up, he thought light moved forever. 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 using a mirror far away. In 1638, Galileo Galilei tried to measure light's speed by watching a lantern from far away, 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, and guessed it takes 22 minutes for light to cross Earth's orbit. Christiaan Huygens used this to estimate the speed of light at 220,000 km/s, which is a bit less than the real value.

In his book Opticks in 1704, Isaac Newton shared Rømer's idea and said it takes "seven or eight minutes" for light to travel from the Sun to Earth (the real time is 8 minutes and 19 seconds). In 1729, James Bradley discovered how stars seem to move a little, and used this to figure that light is 10,210 times faster than Earth moves in its orbit (the real number is 10,066 times faster).

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 using time and distance, and got 315,000 km/s. Léon Foucault improved this method and in 1862 got 298,000 km/s. 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. He tested this idea in 1868.

"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 thought the aether was a special reference point and 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. Modern tests show the speed of light is the same in every direction.

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 along with the idea that the laws of physics are the same for everyone to create the special theory of relativity. In this theory, the speed of light is a basic constant that shows up in many places, even when we are not talking about light.

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, first using special cavities and later using lasers. They also changed how we define the metre and the second. In 1950, Louis Essen measured the speed as 299,792.5±3.0 km/s. 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 in the US National Bureau of Standards in Boulder, Colorado 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.