Measurement of the speed of light
Early attempts
Isaac Beeckman proposed an experiment (1629) in which a person would observe the flash of a cannon reflecting off a mirror about one mile away. Galileo proposed an experiment (1638), with an apparent claim to having performed it some years earlier, to measure the speed of light by observing the delay between uncovering a lantern and its perception some distance away. This experiment was carried out by the Accademia del Cimento of Florence in 1667, with the lanterns separated by about one mile. No delay was observed. Robert Hooke explained the negative results as Galileo had by pointing out that such observations did not establish the infinite speed of light, but only that the speed must be very great.
Rømer's observations of the occultations of Io from Earth.
Astronomical techniques
The first quantitative estimate of the speed of light was made in 1676 by Ole Christensen Rømer, who was studying the motions of Jupiter's moon, Io, with a telescope. It is possible to time the orbital revolution of Io because it enters and exits Jupiter's shadow at regular intervals (at C or D). Rømer observed that Io revolved around Jupiter once every 42.5 hours when Earth was closest to Jupiter (at H). He also observed that, as Earth and Jupiter moved apart (as from L to K), Io's exit from the shadow would begin progressively later than predicted. It was clear that these exit "signals" took longer to reach Earth, as Earth and Jupiter moved further apart. This was as a result of the extra time it took for light to cross the extra distance between the planets, time which had accumulated in the interval between one signal and the next. The opposite is the case when they are approaching (as from F to G). On the basis of his observations, Rømer estimated that it would take light 22 minutes to cross the diameter of the orbit of the Earth (that is, twice the astronomical unit); the modern estimate is about 16 minutes and 40 seconds.
Around the same time, the astronomical unit was estimated to be about 140 million kilometres. The astronomical unit and Rømer's time estimate were combined by Christiaan Huygens, who estimated the speed of light to be 1,000 Earth diameters per minute. This is about 220,000 kilometres per second (136,000 miles per second), 26% lower than the currently accepted value, but still very much faster than any physical phenomenon then known.
Isaac Newton also accepted the finite speed. In his 1704 book Opticks he reports the value of 16.6 Earth diameters per second (210,000 kilometres per second, 30% less than the actual value), which it seems he inferred for himself (whether from Rømer's data, or otherwise, is not known). The same effect was subsequently observed by Rømer for a "spot" rotating with the surface of Jupiter. And later observations also showed the effect with the three other Galilean moons, where it was more difficult to observe, thus laying to rest some further objections that had been raised.
Even if, by these observations, the finite speed of light may not have been established to everyone's satisfaction (notably Jean-Dominique Cassini's), after the observations of James Bradley (1728), the hypothesis of infinite speed was considered discredited. Bradley deduced that starlight falling on the Earth should appear to come from a slight angle, which could be calculated by comparing the speed of the Earth in its orbit to the speed of light. This "aberration of light", as it is called, was observed to be about 1/200 of a degree. Bradley calculated the speed of light as about 298,000 kilometres per second (185,000 miles per second). This is only slightly less than the currently accepted value. The aberration effect has been studied extensively over the succeeding centuries, notably by Friedrich Georg Wilhelm Struve and de:Magnus Nyrén.
Diagram of the Fizeau-Foucault apparatus.
Earth-bound techniques
The first successful measurement of the speed of light using an earthbound apparatus was carried out by Hippolyte Fizeau in 1849. (This measures the speed of light in air, which is slower than the speed of light in vacuum by a factor of the refractive index of air, about 1.0003.) Fizeau's experiment was conceptually similar to those proposed by Beeckman and Galileo. A beam of light was directed at a mirror several thousand metres away. On the way from the source to the mirror, the beam passed through a rotating cog wheel. At a certain rate of rotation, the beam could pass through one gap on the way out and another on the way back. But at slightly higher or lower rates, the beam would strike a tooth and not pass through the wheel. Knowing the distance to the mirror, the number of teeth on the wheel, and the rate of rotation, the speed of light could be calculated. Fizeau reported the speed of light as 313,000 kilometres per second. Fizeau's method was later refined by Marie Alfred Cornu (1872) and Joseph Perrotin (1900).
Leon Foucault improved on Fizeau's method by replacing the cogwheel with a rotating mirror. Foucault's estimate, published in 1862, was 298,000 kilometres per second. Foucault's method was also used by Simon Newcomb and Albert A. Michelson. Michelson began his lengthy career by replicating and improving on Foucault's method.
In 1926, Michelson used a rotating prism to measure the time it took light to make a round trip from Mount Wilson to Mount San Antonio in California, a distance of about 22 miles (36km). The precise measurements yielded a speed of 186,285 miles per second (299,796 kilometres per second).
Laboratory-based methods
During World War II, the development of the cavity resonance wavemeter for use in radar, together with precision timing methods, opened the way to laboratory-based measurements of the speed of light. In 1946, Louis Essen in collaboration with A.C. Gordon-Smith used a microwave cavity of precisely known dimensions to establish the frequency for a variety of normal modes of microwaves—which, in common with all electromagnetic radiation, travels at the speed of light in vacuum. As the wavelength of the modes was known from the geometry of the cavity and from electromagnetic theory, knowledge of the associated frequencies enabled a calculation of the speed of light. Their result, 299,792±3km/s, was substantially greater than those found by optical techniques, and prompted much controversy. However, by 1950 repeated measurements by Essen established a result of 299,792.5±1km/s; this became the value adopted by the 12th General Assembly of the Radio-Scientific Union in 1957. Most subsequent measurements have been consistent with this value.
Speed of light set by definition
In 1983, the 17th Conférence Générale des Poids et Mesures defined the meter in terms of the distance traveled by light in a given amount of time, which amounts to adopting a standard value for the speed of light in vacuum:
The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.
Here, the term vacuum is meant in the technical sense of free space. This definition of the metre relies on the definition of the second, which is:
The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.
The consequence of this definition is that further refinements in the current experimental value of the speed of light would only refine the definition of a metre. This point is made explicit by nondimensionalization in the article on Maxwell's equations. The value of c, or c0, namely:
combined with the definition of magnetic constant μ0, also defines the electric constant ε0 in SI units. The magnetic constant μ0 is not dependent on c and as a result of the definition of the ampere, has a standard value in SI units of:
.
The electric constant has then the exact value
These constants appear in Maxwell's equations.
Special relativity
After the work of James Clerk Maxwell, it was believed that light travelled at a constant speed relative to the "luminiferous aether", the medium that was then thought to be necessary for the transmission of light. This speed was determined by the ( permittivity and permeability) of the aether.
A schematic representation of a Michelson interferometer, as used for the Michelson-Morley experiment.
In 1887, the physicists Albert Michelson and Edward Morley performed the influential Michelson-Morley experiment to measure the speed of light relative to the motion of the earth, the goal being to measure the velocity of the Earth through the aether. As shown in the diagram of a Michelson interferometer, a half-silvered mirror was used to split a beam of monochromatic light into two beams traveling at right angles to one another. After leaving the splitter, each beam was reflected back and forth between mirrors several times (the same number for each beam to give a long but equal path length; the actual Michelson-Morley experiment used more mirrors than shown) then recombined to produce a pattern of constructive and destructive interference. Any slight change in speed of light along each arm of the interferometer (because the apparatus was moving with the Earth through the proposed "aether") would change the amount of time that the beam spent in transit, which would then be observed as a change in the pattern of interference. In the event, the experiment gave a null result.
Ernst Mach was among the first physicists to suggest that the experiment amounted to a disproof of the aether theory. Developments in theoretical physics had already begun to provide an alternative theory, Fitzgerald-Lorentz contraction, which explained the null result of the experiment.
It is uncertain whether Albert Einstein knew the results of the Michelson-Morley experiment, but the null result of the experiment greatly assisted the acceptance of his theory of relativity. The constant speed of light is one of the fundamental Postulates (together with causality and the equivalence of inertial frames) of special relativity.
Measuring the speed of light
Since the speed of light is so great, it is very difficult to measure.
Note that the terms speed of light and velocity of light are used. Either one is acceptable, but you must remember that speed means how fast something is going, while velocity means how fast it is going in a given direction.
Echo method not practical
It was thought that the velocity of light could be measured that same way as for the velocity of sound. A common method to measure the velocity of sound is to calculate the time it takes for an echo to return and then divide that by the distance the sound travels there and back. Since distance equals velocity times time:
c = d/t
where
- c is the speed of light (light's speed is always denoted as c)
- d is the distance traveled
- t is the time it takes to go that distance
- d/t is d divided by t
But the velocity of light is so large at 186,000 miles/sec (300,000 km/sec), that in 1/1000 of a second, the light would travel from Milwaukee to Chicago and back (or from Los Angeles to San Diego and back). That is over 90 miles (150 km) one way.
If you used a timer or shutter that could measure in 1/100,000 of a second, it might be be more practical.
Spinning pinhole
One clever method that was one of the first to measure the speed of light was to shine a light through pinhole on a spinning disk. The light was then reflected off a mirror that was some distance away.
Since light travels so fast, it would normally be reflected back through the pinhole (provided everything was lined up properly). By adjusting the speed of the spinning disk and/or the distance, the pinhole could be made to move enough that the light would not pass through it. Then, by calculating the size of the pinhole, the speed of the disk, and the distance to the mirror, the speed of light could be calculated.
Modern methods
With modern electronics, the speed of light can now be measured in a physics lab.
One example to measure the speed of red light is to use equipment that includes a LED (light-emitting diode) that emits a regular series of pulses of red light that are only 20 nanoseconds in duration.
(A nanosecond is one-billionth of a second or 1/1,000,000,000 second. It is also written as 10-9 seconds, 10^-9 or 1e-9, where the -9 indicates the number of zeros in the denominator.)
That means the pulse of light blinks on for 20 billionths of a second or 20/1,000,000,000 second and blinks 40,000 times per second. Having such a short pulse allows the scientist to measure the difference in time it takes to travel two different paths. If the duration was longer, the distance traveled would have to be longer.
By splitting the light beam with a half-silvered mirror, one beam travels to a mirror 10 meters away and then back to a photodiode detector. The other beam is reflected off a mirror only a few centimeters away. The time difference for the two beams is about 67 nanoseconds, which can be displayed on a regular dual beam oscilloscope.
The total distance the light travels is 20 meters, which equals 0.02 kilometer (20/1000).
The speed of light is then:
c = 0.02 kilometers/67*10-9 seconds = 298,500 kilometers per second
This is a fairly accurate reading and pretty close to the actual speed of 299,792 km/s.
Speed through matter
The speed of electromagnetic waves passing through transparent matter is slower than it is in a vacuum. Glass is transparent to visible light, radio waves will easily pass through non-metals, and x-rays pass through most materials except lead.
Most measurements of the speed of light are made in the atmosphere. Since the effect on the speed when passing through air is so very small, the speed of light in air is almost the same as it is in a vacuum. The difference is negligible.
The reason electromagnetic waves travel slower though transparent materials is the effect that the electrons have on the waves. They act somewhat like a "friction" on the waves.
Light through glass
The fact that light moves slower through matter can be seen when visible light passes through glass. If you shine a light at an angle through a piece of glass, the light beam will be bent or refracted.
(See Refraction of Light for more information.)
The ratio of the speed of light in vacuum divided by the speed of light in the material is called the index of refraction for the material. The index of refraction of glass or other material indicates how much slower the light travels through the material than in a vacuum.
Typically, the index of refraction of glass is from 1.2 to 1.5. That means the speed in a material of index 1.5 is 66% of the speed in vacuum.
Extreme slowing
Although the speed of an electromagnetic wave through matter is can be up to 50% less than the speed through a vacuum, scientists were able to greatly reduce the speed through matter in special situations. This was first done in 1999.
Danish physicists performed an experiment where they slowed light down to only 38 miles per hour or about 57 kilometers per hour. They did this by sending a beam through a material made of sodium atoms cooled to near absolute zero (-273°C or -460°F). They achieved this low temperature by using lasers to slow down the atoms, through a special method used in quantum mechanics called the Bose-Einstein condensate. (Explanation of this goes away beyond the scope of this course).
Speed is the maximum
The speed of light is supposed to be the maximum speed at which matter can travel.
Matter changes
In fact, according to Einstein's Theory of Relativity, strange things happen to matter as it approaches the speed of light. Matter becomes compressed as it gets within 90% of the speed of light, such that a ruler would appear shortened. Also, the mass of the matter starts to increase.
Time changes
Another interesting phenomenon happens when matter approaches the speed of light, and that is that time for the matter slows down. In other words, if you were traveling through space near the speed of light, you would age more slowly than a person on Earth. A year year trip might seem like 10 minutes to you, while it would seem like a full year to everyone else.
Time travel or going at "warp speed" as is seen in such TV shows as Star Trek is not physically possible, as far as we know.
Summary
The speed of light is approximately 186,000 miles per second or 300,000 kilometers per second in a vacuum. All electromagnetic waves, including visible light, travel at that speed. Modern electronics allow the measurement of the speed of light in a physics lab. Light and other electromagnetic waves slow down when they pass through matter. According to the Theory of Relativity, the speed of light is the fastest at which anything can travel. The speed of light is the maximum speed for matter.