# Speed of light

The speed of light, in any medium, which is usually denoted by ${\displaystyle c}$, is a physical constant important in many areas of physics. It is denoted by 'c^0' especially in vacuum medium, although the symbol 'c' can be used to refer to that in any medium. It is exactly 299,792,458 metres per second (983,571,056 feet per second) by definition.[1][2] A photon (particle of light) travels at this speed in a vacuum.

According to special relativity, ${\displaystyle c}$ is the maximum speed at which all energy, matter, and physical information in the universe can travel. It is the speed of all massless particles such as photons, and associated fields—including electromagnetic radiation such as light—in a vacuum.

It is predicted by the current theory to be the speed of gravity (that is, gravitational waves). Such particles and waves travel at ${\displaystyle c}$ regardless of the motion of the source or the inertial frame of reference of the observer. In the theory of relativity, ${\displaystyle c}$ interrelates space and time, and appears in the famous equation of mass–energy equivalence E = mc2.[3]

The special theory of relativity is based on the prediction, so far upheld by observations, that the measured speed of light in a vacuum is the same whether or not the source of the light and the person doing the measuring are moving relative to each other. This is sometimes expressed as "the speed of light is independent of the reference frame."

## Example explaining how speed does not depend on reference frame

This behavior is different from our common ideas about motion as shown by this example:

George is standing on the ground next to some train tracks (railroad). There is a train rushing by at 30 mph (48 km/h). George throws a baseball at 90 mph (140 km/h) in the direction the train is moving. Tom, a passenger on the train, has a device (like a radar gun) to measure throwing speeds. Because he is on the train, Tom is already moving at 30 mph (48 km/h) in the direction of the throw, so Tom measures the speed of the ball as only 60 mph (97 km/h).

In other words, the speed of the baseball, as measured by Tom on the train, depends on the speed of the train.

In the example above, the train was moving at 1/3 the speed of the ball, and the speed of the ball as measured on the train was 2/3 of the throwing speed as measured on the ground.

Now, repeat the experiment with light instead of a baseball; that is, George has a flashlight instead of throwing a baseball. George and Tom both have devices that are the same to measure the speed of light (instead of the radar gun in the baseball example).

George is standing on the ground next to some train tracks. There is a train rushing by at 1/3 the speed of light. George flashes a light beam in the direction the train is moving. George measures the speed of light as 186,282 miles per second (299,792 kilometres per second). Tom, a passenger on the train, measures the speed of the light beam. What speed does Tom measure?

Intuitively, one may think that the speed of the light from the flashlight as measured on the train should be 2/3 the speed measured on the ground, just like the speed of the baseball was 2/3. But in fact, the speed measured on the train is the full value, 186,282 miles per second (299,792 kilometres per second), not 124,188 miles per second (199,861 kilometres per second).

It sounds impossible, but that is what one measures.

A consequence of this fact, that the speed of light is the same for all (inertial) observers, is that no matter how much energy is used, nothing with mass can be accelerated to reach or go faster than the speed of light. Other key consequences of the constancy of the speed of light, that the lengths of two identical objects, and the rate at which two identical clocks tick, also depend on the reference frame of the observer. These ideas were discovered in the early 1900s by Albert Einstein in his theory of Special Relativity which completely changed our understanding of space and time.

## Relation to fundamental electric and magnetic properties of space

Maxwell's equations predicted the speed of light and confirmed Michael Faraday's idea that light was an electromagnetic wave (a way that energy moves). From these equations, we find that the speed of light is related to the inverse of the square root of the permittivity of free space, ε0, and the permeability of free space, μ0:

${\displaystyle c={\frac {1}{\sqrt {\varepsilon _{0}\mu _{0}}}}\ .}$

The index of refraction of a clear material is the ratio between the speed of light in a vacuum and the speed of light in that material.

## Measurement

### Rømer

Ole Christensen Rømer used an astronomical measurement to make the first quantitative estimate of the speed of light.[4][5] When measured from Earth, the periods of moons orbiting a distant planet are shorter when the Earth is approaching the planet than when the Earth is receding from it. The distance travelled by light from the planet (or its moon) to Earth is shorter when the Earth is at the point in its orbit that is closest to its planet than when the Earth is at the farthest point in its orbit, the difference in distance being the diameter of the Earth's orbit around the Sun. The observed change in the moon's orbital period is actually the difference in the time it takes light to traverse the shorter or longer distance. Rømer observed this effect for Jupiter's innermost moon Io, and he deduced that light takes 22 minutes to cross the diameter of the Earth's orbit.

Another method is to use the aberration of light, discovered and explained by James Bradley in the 18th century.[6] This effect results from the vector addition of the velocity of light arriving from a distant source (such as a star) and the velocity of its observer (see diagram on the right). A moving observer thus sees the light coming from a slightly different direction and consequently sees the source at a position shifted from its original position. Since the direction of the Earth's velocity changes continuously as the Earth orbits the Sun, this effect causes the apparent position of stars to move around. From the angular difference in the position of stars,[7] it is possible to express the speed of light in terms of the Earth's velocity around the Sun. This, with the known length of a year, can be easily converted to the time needed to travel from the Sun to the Earth. In 1729, Bradley used this method to derive that light travelled 10,210 times faster than the Earth in its orbit (the modern figure is 10,066 times faster) or, equivalently, that it would take light 8 minutes 12 seconds to travel from the Sun to the Earth.[6]

### Modern

Nowadays, the "light time for unit distance"—the inverse of c (1/c), expressed in seconds per astronomical unit—is measured by comparing the time for radio signals to reach different spacecraft in the Solar System. The position of spacecraft is calculated from the gravitational effects of the Sun and various planets. By combining many such measurements, a best fit value for the light time per unit distance is obtained. As of 2009, the best estimate, as approved by the International Astronomical Union (IAU), is:[8][9]

light time for unit distance: 499.004783836(10) s
c = 0.00200398880410(4) AU/s
c = 173.144632674(3) AU/day.

The relative uncertainty in these measurements is 0.02 parts per billion (2×1011), as equivalent to the uncertainty in Earth-based measurements of length by interferometry.[10] Since the metre is defined to be the length travelled by light in a certain time interval, the measurement of the light time for unit distance can also be interpreted as measuring the length of an AU in metres. The metre is considered to be a unit of proper length, whereas the AU is often used as a unit of observed length in a given frame of reference.

## Practical effects

The finite speed of light is a major constraint on long-distance space travel. Supposing a journey to the other side of the Milky Way, the total time for a message and its reply would be about 200,000 years. Even more seriously, no spacecraft could travel faster than light, so all galactic-scale transport would be effectively one-way, and would take much longer than than any modern civilisation has existed.

The speed of light can also be of concern over very short distances. In supercomputers, the speed of light imposes a limit on how quickly data can be sent between processors.[11] If a processor operates at 1 gigahertz, a signal can only travel a maximum of about 30 centimetres (1 ft) in a single cycle. Processors must therefore be placed close to each other to minimize communication latencies; this can cause difficulty with cooling. If clock frequencies continue to increase, the speed of light will eventually become a limiting factor for the internal design of single chips.[11]

## References

1. SI Brochure: The International System of Units (SI) (PDF) (9 ed.), BIPM, 2019, p. 128, retrieved 2020-01-12
2. Cox, Brian; Forshaw, Jeff (2010). Why does E=mc2?: (and why should we care?). Da Capo. p. 2. ISBN 978-0-306-81911-7.
3. Uzan, J-P; Leclercq, B (2008). The natural laws of the universe: understanding fundamental constants. Springer. pp. 43–4. ISBN 978-0387734545.
4. Cohen, IB (1940). "Roemya and the first determination of the velocity of light (1676)". Isis. 31 (2): 327–79. doi:10.1086/347594. hdl:2027/uc1.b4375710. S2CID 145428377.
5. "Touchant le mouvement de la lumiere trouvé par M. Rŏmer de l'Académie Royale des Sciences" (PDF). Journal des sçavans (in French): 233–36. 1676.
Translated in "On the motion of light by M. Romer". Philosophical Transactions of the Royal Society. 12 (136): 893–95. 1677. doi:10.1098/rstl.1677.0024. S2CID 186210345. (As reproduced in Hutton, C; Shaw, G (1809). "On the Motion of Light by M. Romer". In Pearson, R (ed.). The Philosophical Transactions of the Royal Society of London, from Their Commencement in 1665, in the Year 1800: Abridged. Vol. 2. London: C. & R. Baldwin. pp. 397–98.)
The account published in Journal des sçavans was based on a report that Rømer read to the French Academy of Sciences in November 1676 (Cohen, 1940, p. 346).
6. Bradley, J (1729). "Account of a new discoved Motion of the Fix'd Stars". Philosophical Transactions. 35: 637–660.
7. at most 20.5 arcseconds Duffett-Smith, P (1988). Practical astronomy with your calculator. Cambridge University Press. p. 62. ISBN 0521356997.
8. Pitjeva, EV; Standish, EM (2009). "Proposals for the masses of the three largest asteroids, the Moon-Earth mass ratio and the Astronomical Unit". Celestial Mechanics and Dynamical Astronomy. 103 (4): 365–372. Bibcode:2009CeMDA.103..365P. doi:10.1007/s10569-009-9203-8. S2CID 121374703.
9. IAU Working Group on Numerical Standards for Fundamental Astronomy. "IAU WG on NSFA Current Best Estimates". US Naval Observatory. Archived from the original on 2009-12-08. Retrieved 2009-09-25.
10. "NPL's Beginner's Guide to Length". UK National Physical Laboratory. Archived from the original on 2010-08-31. Retrieved 2009-10-28.
11. Parhami, B (1999). Introduction to parallel processing: algorithms and architectures. Plenum Press. p. 5. ISBN 9780306459702. and Imbs, D; Raynal, Michel (2009). "Software transactional memories: an approach for multicore programming". In Malyshkin, V (ed.). Parallel Computing Technologies. 10th International Conference, PaCT 2009, Novosibirsk, Russia, August 31-September 4, 2009. Springer. p. 26. ISBN 9783642032745.