Speed of light

The speed of light in a vacuum (observed to be the same for all inertial observers, a fact which gave rise to the Special Theory of Relativity) is 299,792,458 meters per second (approximately 186,282.3 miles per second). This is the speed by definition. It is used to give the SI definition of the meter, in terms of the SI definition of the second, which is derived from the Cesium clock.

In physics, it is often represented in equations by the letter .

Where

is the wavelength of an electromagntic wave in vacuum

is the frequency of the wave

is the speed of light

The speed of light is about one foot per nanosecond. The late computer pioneer Admiral Grace Hopper was fond of keeping foot-long lengths of wire in her purse; she used them as props for her talks, referring to them as "nanoseconds," and using them to explain how the speed of light set limitations on computing systems: no signal could possibly propagate in any wire faster than the speed of light.

The speed of light is slower in any medium which is not a vacuum, and varies from medium to medium. This variation gives rise (as a result of Fermat's principle of least time) to the phenomenon of refraction. When a charged particle exceeds the speed of light in the medium in which it is travelling, it emits Cherenkov Radiation.

Since the speed of light in a vacuum is observed to be constant, it can be used to define distances as well. The distance that light travels in one year is known as a light-year, which is about 6 million million (6x10¹²) miles.

The speed of light raises questions regarding the age of the universe, which are usually summed up under the term "starlight problem".

History

In 1676, the Danish astronomer Ole Rømer became the first person who attempted to quantitatively estimate the speed of light. His method was based on observation of the orbit of the satellites of Jupiter such as Io and evaluating their eclipse data as seen from the Earth. The Dutch scientist Christiaan Huygens was first who applied the arithmetic onto Rømer's estimate for the maximum time delay between periodical observations of Io's eclipse by Jupiter at the Earth's nearest and farthest position with respect to Jupiter. In 1849, the French physicist Fizeau developed method which enabled to measure the speed of light between two points at the Earth by means of using the light source, rotating strobe disc (spinning toothed wheel), and the mirror. He shone a light ray between the teeth of a rapidly rotating toothed wheel. A mirror reflected the beam back through the same gap between the teeth of the wheel over the round-trip distance of 17 km. By varying the speed of the wheel, it was possible to determine at what speed the wheel was spinning too fast for the light to pass through the gap between the teeth, to the remote mirror, and then back through the same gap, and the rotational speed at which the light returned through the next gap. The experiment showed that the light traveled over the known distance in 1/18000 second. The resulting speed of light through air was obtained by dividing the known distance by time. The more precise methods, involving a rapidly rotating mirror, have been used by Americans Michelson and Newcomb.

Does light travel at the "speed of light"?

Surprisingly, the answer seems to be no. It appears to travel at about 1 part in 300 million slower than the speed that physicists denote c.

Much of modern theoretical physics, including all of relativity, involves a fundamental "speed of light", denoted c. Relativity has its origins in the behavior of light in various experiments, notably the Michelson-Morley experiment. So the behavior of light is used as the definition of c in various formulas, such as E=mc², E^2=(mc^2)^2+(pc)^2, and Maxwell's Equations. This also fits in perfectly with the notion that a photon, being massless, must have speed c in all frames of reference. And it fits in with the notion that particles of exceedingly small rest mass, but reasonable energy, will travel at nearly the speed of light.

The electron neutrino is believed to have a mass of 0.25 Ev, or .44x10⁻³⁶ kg, and hence travel at very nearly the speed of light for reasonable energies. An announcement from the OPERA/Gran Sasso experiment in 2011 seemed to indicate that neutrinos were observed traveling faster than light. (This finding was later found to be flawed). Assuming the neutrinos had energy of about .27x10⁻⁸ joules, their speed would have been slower than c by a factor of 1 in 10²², which would come out to .25x10⁻²⁴ seconds over the 730 kilometer test. That time difference would be many orders of magnitude too small to observe.

But 20^th century theories of Quantum Electrodynamics indicate that photons interact with the "vacuum polarization" of the vacuum through which they are traveling. Photons can spontaneously split into electron-positron pairs, which interact with each other gravitationally before recombining. This causes light to travel about 1 part in 300 million slower than c. Since neutrinos don't interact with the electromagnetic force, they are not subject to the vacuum polarization effect, and travel only 1 part in 10²² slower than c, which is faster than photons.

In order to observe this effect, an extremely long travel path for neutrinos and photons is needed. The supernova SN1987A provided such a path—it is 186,000 light years from Earth. (So the supernova actually occurred 186,000 years ago.) There are theoretical reasons to believe that the flash of light would have been delayed about 3 hours from the neutrino burst, since the photons had to pass through the exploding star, interacting with it, whereas the neutrinos had no such interaction. But the observation of the light flash was 7.7 hours later than the neutrino burst, indicating that it took 4.7 hours longer to travel to Earth. This is consistent with the predicted slowing of photons due to vacuum polarization.

Has the speed of light changed through the history of the universe?

Briefly, no. There is no credible evidence for this. There is a simple logical argument. There are photons that have been traveling since near the beginning of the universe. They obey the formula

where E and p are the energy and momentum, respectively. If the speed of light had changed while a photon was in flight, either its energy or its momentum, or both, would have had to change. Exact conservation of energy and momentum are cornerstones of physics. If they weren't valid, the way the universe works would be radically altered.

Now there have been a few careful investigations of whether the fine structure constant, α, could have changed slightly. These involve examination of spectra from very distant stars, and examination of the isotopic mix of the fission products from the Oklo event. But these results are speculative and far from convincing.

Some Fundamentalists and Creationists posit a serious decline in the speed of light over the eons, but these are typically in the context of a view of the universe that is radically different from the accepted view. For example, some suggest that the Earth was in some kind of "time dilation field", sometimes gravitationally caused, for some period of time. These theories are rarely found outside of Fundamentalist web sites.

Theories of serious decline in the speed of light are often called C decay. One of the proponents of this, Barry Setterfield, suggests the use of different time scales, an "atomic" scale and a "gravitational" one, to get the effect. He published graphs showing the consequent C decay, with the curves conveniently converging to the modern value, always just in time to stay within the ever-increasing precision of measurements, and then extrapolated backward over many orders of magnitude. Interestingly, his redefinition of the time scale meant abandoning the "Young Earth" theory and accepting an age of the universe close to the scientifically accepted value of about 13 billion years.