# Speed of light

 Poetry of realityScience We must know. We will know. A view from theshoulders of giants. v - t - e
 “”Cubert Farnsworth: That's impossible. You can't go faster than the speed of light. Professor Farnsworth: Of course not. That's why scientists increased the speed of light in 2208. —Futurama - 'A Clone of My Own'

The speed of light (more precisely, unstructured light[1] in a perfect vacuum) is a numerical constant in physics usually denoted by the letter c. It is 299,792,458 m/s exactly, since the metre is defined to be the distance light travels through vacuum in 1/299,792,458 of a second.[2][note 1]

The speed of light is considered to be an "ultimate cosmic speed limit". This is because massive ("massive" as in "having mass", not the colloquial "really fuckin' big") particles and objects can attain speeds that approach light speed, but never actually reach it. As the photons which make up light do not have any rest mass, they not only can travel at this speed, but must travel at this speed — hence the name "speed of light" to refer to c. According to special relativity and the experiments that back it up, the speed of light is the same for all inertial observers.

## The modern science

### Definition

In 1983, the Conférence Générale des Poids et Mesures (General Conference of Weights and Measures, or CGPM) defined the metre as the following:[3]

 “”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.

Since the metre is defined in terms of the speed of light, this definition fixes the speed of light at 299,792,458 metres per second (m/s).[4]

Of course, as these people were Europeans, they insisted on spelling the word correctly as 'metre', but we shall cavalierly revert to Noah Webster's 'meter'[note 2] from now on.

### Constancy of the speed of light

A natural question is, "What gives the CGPM the right to define the speed of light and a unit of length in this way?" The answer is that the speed of light in a vacuum is a universal constant; it has the peculiar property that all observers measure the speed of light as c.[note 3] This property makes light very different from, for example, a baseball. Suppose a baseball pitcher is standing on a train moving at 90 miles per hour relative to the ground. The pitcher throws a 90 mile-per-hour fastball towards the back of the train. While the pitcher and anyone else on the train would measure the speed of the baseball as 90 miles per hour, an observer on the ground would measure the baseball's speed as 0 miles per hour — the motion of the ball against the train cancels out as far as the observers on the ground are concerned. That is, the baseball would appear to hang in midair, until the back wall of the train caught up to it. Similarly, if the pitcher threw the ball in the other direction, at the same speed, the people on the ground would see the ball travel at an impressive 180 miles per hour, as the ball would gather momentum from the train and the speeds would combine. However, if the pitcher shines a flashlight toward the back of the train, he would measure the speed of the light as c… and so would the observer on the ground. The same analogy works for cricket bowlers.

This constancy of the speed of any light beam as measured by any observer has enormously important implications, and the resulting physical theory describing this is relativity.

Some of the earliest experimental clues that c must be constant for all observers were derived from Maxwell's equations. These mathematical formulations, uniting electricity and magnetism, predict the existence of electromagnetic waves that travel at a certain speed. That speed can be deduced from the equations by measuring certain physical constants, and unlike classical mechanics and the example of the baseball pitcher described above, the equation says nothing about what this speed is measured relative to. Light can travel in a vacuum, and Maxwell's equations simply say what the speed is, and are perplexingly silent on the "medium" that it is measured relative to — although some did think that this would be the fabled aether. The electromagnetic waves predicted by Maxwell's equations turned out to be light, and those equations are considered to be one of the greatest triumphs of mathematical physics.

Attempts to unravel the mystery contained in Maxwell's equations by making experimental measurements of the speed of light in different directions were negative. The Michelson-Morley experiment was the first confirmation of this. The apparent paradox of a universally constant speed was found to be true.

### An ultimate speed limit

The speed of light is considered to be an ultimate speed limit — massive objects can obtain speeds arbitrarily close to the speed of light, but can never reach it. Relativity predicts that an infinite amount of energy would be required to accelerate an object of any mass to the speed of light — particles without mass, however, can travel at and only at the speed of light.

The existence of some faster-than-light particles, such as tachyons, has been suggested. Tachyons, if they existed, would be confined to the "other side" of the light-speed barrier; they would be restricted to speeds faster than the speed of light[5] and would require an infinite amount of energy to slow them down to the speed of light.

## Light year

A light year is the distance that light travels in one Julian[6] year in a vacuum. By using the fact that the speed of light (${\displaystyle c}$) = 299,792,458 m/s (this is exact, as the meter is defined in terms of the speed of light), a light year can be calculated by dimensional analysis (a fancy term for "solve for x") to equal (299,792,458 m/s × 3600 s/h x 24 h/d × 365.25 d/y) = 9,460 billion kilometers (9.46 × 1015 meters). These fixed units have been officially defined since 1984, based on SI units (seconds for time and ${\displaystyle c}$ for the speed of light) derived from physical constants — general and special relativity show the need for that. Prior to this definition by the International Astronomical Union (IAU), the solar year and a measured speed of light was used, producing a slightly different value.

The light year is commonly used by laypersons, amateur astronomers, and sci-fi authors (who may also refer to a "light minute" or "light second" for comparably shorter distances), while professional astronomers tend to prefer to use the parsec (~3.26 light years), as it is based on the movement of 1 arcsecond of parallax motion, and therefore most easily convertible to observational data.

A nanosecond is occasionally referred to informally as a "light foot", because the distance that light travels in a billionth of a second is approximately 11.8 inches (299,792,458 meters divided by 1,000,000,000 is very nearly 30 centimeters).

## Breaking the speed of light

It's a well-established fact that nothing can travel faster than light, so as a speed limit, it cannot be broken. But this statement needs further refinement; matter, energy, and information cannot travel faster than light. This means that there are cases where the speed of light can be broken, but we can't necessarily do anything about it. These exceptions involve exploiting the properties of waves and are both theoretical and actually observed. To understand how waves allow this apparent break in the laws of physics, imagine an analogy with a tsunami wave going through the ocean. The wave of energy created by a tsunami can travel nearly 600 mph (970 kph) across deep oceans, but the individual water molecules themselves are confined to much lower speeds — it's not a body of water actually moving, it's the motion of an energy wave. A similar thing is observed with electric current, where "electricity" can travel at the speed of light, but the individual electrons can be shown to be a mere walking pace.

To break the speed of light, the properties of such waves can be exploited.[7][8] Imagine a row of LED lights flashing in a sequence from end to end, with each one flashing for a short period of time as an electric current passes it. Much like the tsunami example, the individual lights aren't moving, but a wave of "on" lights is created and traveling along at the speed of the electric current, and this wave is traveling at the speed of light. But imagine now that instead of flashing immediately, each LED flashes with a delay that decreases along the line (imagine millions of them in a row). The first LED has a long delay, and each subsequently decreases until the final one flashes the moment the current hits. If the delays were set so that the first LED came on when the current was half-way, it will take the same length of time for the wave to travel the full circuit as it takes for the current to only travel half of it. The moving wave of "on" lights would then be exceeding the speed of light by a factor of two.[9]

Energy, matter, and information hasn't broken the light barrier in this case (the information about the wave has already been transmitted at sub-light speeds), but the moving wave has travelled faster than light. When anti-relativity cranks attempt to disprove Einstein by saying things have exceeded the speed of light, this is invariably the type of phenomenon they are talking about. Well, up till now, it invariably was, but we will have to see.

Superluminal motion has been observed in the jets expelled by some active galactic nuclei. However these are just projection effects caused by such jets pointing more or less to us. Likewise, distant galaxies are said to be speeding from us faster than light so their light will never reach us but it's the space between us and them what is expanding faster than light, carrying the galaxies with it, as space-time itself is free of the above restrictions –most notably during the Cosmic inflation era.

### Neutrino observations in 2011

According to non-peer reviewed reports by the Oscillation Project with Emulsion-tRacking Apparatus (OPERA) in Italy announced in in 2011, neutrinos might be able to travel just that little bit faster than light. Of course, like all of science, this needed to be first peer reviewed, published in a recognized journal, and then confirmed through reproducible experiments. Until this process has been gone through, there would not seem to be any reason to put too much stock by the reported results, as "publication by press conference" does not really have a good history; consider the cold fusion debacle. Also, proving faster-than-light travel would require evidence that isn't yet available. It probably did not happen.[10]

#### Reactions

From the more scientifically-minded community, the general reaction was that "Time will tell."[11][12][13] Other reactions to this news have ranged from muted skepticism to hilarious overreaction. Brian Cox, as the BBC's resident science-bod, weighed in to urge caution and to teach people how the result would be verified first.[14] Another professor and pop science advocate, Jim Al-Khalili, even went so far as to say the following (see 2:46):

Of course, while everyone would love this to happen, it's unlikely. Cox himself has cited several possibilities that would just mean the neutrinos are taking "shortcuts" through extra dimensions, so they aren't really breaking the light barrier, exactly.

Meanwhile, the woo community embraced it fully. Advocates of homeopathy have used it as an example of how science is "wrong" and therefore why can't homeopathy be true.[15] Naturally, they seem to have ignored the lack of evidence for homeopathy, while we do have tentative evidence for neutrinos going faster than light. This sort of thing seems to happen whenever science is proven "wrong" about anything. And participants on the Islamic Awakening blog all seemed to confuse it with disproving atheism and the Big Bang.[16] Someone claims confirmation.[17] Others have been asking whether or not FTL communication of this sort might be a basis for psychic phenomena,[18] as if our brains' ability to fool us weren't a more plausible explanation.

#### Possibilities

Some neutrinos from the supernova SN 1987A were observed arriving simultaneously with light photons,[19] though if neutrinos travel faster than light, they should have arrived earlier. If other neutrinos arrived earlier, scientists may have overlooked them because scientists did not know about the supernova before photons reached Earth.

Could the scientists overlook something? These things are certainly possible, which is why science submits itself to the scrunity of hundreds of individuals; eventually someone will spot the obvious flaw. They’re from the same organisation that a year ago was telling us the Higgs boson travels backwards through time and acts purposely to sabotage its own discovery. Another simple possibility is a calibration error associated with relativistic corrections required because the Earth is rotating. This is analogous to the corrections applied to GPS satellites, but was overlooked because the detectors were on the ground and not in orbit. The correction would have been far smaller because of this, on the order of nanoseconds rather than milliseconds, but is potentially significant. There have been dozens of papers submitted to arXiv covering the neutrino topic, many of which postulate these simple solutions that the OPERA team overlooked, but the "correct" answer has not yet been fully decided upon.

#### Conclusion?

In February 2012, it emerged that a faulty cable connection may have been responsible for the 60-nanosecond discrepancy between the speed of light and the observed Speed of Neutrino. Further potential timing difficulties were revealed at the same time.[20] Then, in March, a paper appeared (also on arXiv) to the effect that the long-awaited replication attempt from the ICARUS experiment (located just meters away) had come up negative.[21] They discovered that their "result [was] compatible with the simultaneous arrival of all events [both that of light and of the neutrinos] with equal speed, the one of light."

Reactions here too were mixed, with some saying that this was 'case closed'. Others — including Nobel Prize-winning physicist Carlo Rubbia (spokesman for the ICARUS project) — wanted to wait for further confirmation and the discovery of exactly what went awry in the OPERA experiment. The BBC reported that it is very unlikely that neutrinos travel faster than light, and Jim Al-Khalili managed to sleep easy.[22]

## Pre-modern conceptions of the speed of light

### Ancient Greeks

Hypotheses about light and its speed date back to ancient Greece. One of the most famous ideas to come from Greece at the time was the Emission Theory, which stated that vision was created by rays of light being beamed from a person's eyes. Empedocles of Acragas (492-432 BCE) apparently believed that the speed of light was finite; however, Aristotle (384-322 BCE) was not convinced and argued for an infinite speed,[23] because of course he did. Like most Greek thinking at the time, both arguments were only based on pure reason, not empirical science, but Aristotle's position — like his position on nearly everything — became the accepted viewpoint and went unchallenged for nearly 2000 years. Which sucks, because Aristotle was rarely right about important things.

### Measurement attempts

Michelson's illustration of the Foucault experiment: lens L forms an image of slit S at spherical mirror M. If mirror R is stationary, the reflected image of the slit reforms at the original position of slit S, regardless of how R is tilted, as shown in the lower annotated figure. However, if R rotates rapidly, the time delay due to the finite speed of light traveling from R to M and back to R results in the image of the slit S becoming displaced.

In 1626, Galileo attempted to measure the speed of light using two observers with lanterns placed far apart. Unfortunately, the speed of light is too great to measure with this technique, and the best Galileo could conclude was that light traveled at least 10 times faster than sound.

Fifty years later, in 1676, Ole Rømer used astronomical observations of the moons of Jupiter to determine that the speed of light was finite. He calculated a speed of 214,000 km/s, which is about 70 percent of the current accepted value. The discrepancy is due to Rømer's uncertainty in the distance from Earth to the Sun.[24]

Several other measurements were performed using progressively better and more precise methods (see table). A notable measurement was performed by Albert Michelson in 1877, when he measured the speed to be 299,910 ± 50 km/s. This value was the standard for about 40 years.[24] Modern techniques use lasers and precision electronic equipment, but as the speed of light is now defined precisely and it is the measurement of space that is relative to it, so trying to measure the speed of light has become a fairly moot point.

Notable measurements of the speed of light[25]
Date Investigator Method Result (km/s) Uncertainty
1626 Galileo Uncovering lanterns >10 × speed of sound
1676 Ole Rømer Satellites of Jupiter 214,000
1726 James Bradley Stellar aberration 301,000
1849 Armand Fizeau Toothed wheel 315,000
1862 Leon Foucault Rotating mirror 298,000 ± 500
1877 Albert Michelson Rotating mirror 299,910 ± 50
1926 Albert Michelson Rotating mirror 299,796 ± 4
1973 Evanson et al Lasers 299,792.4574 ± 0.001
1983 CGPM Definition[26] 299,792.458 0

## Abuse by fundamentalists, reactionaries, and lunatics

Many modern fundamentalists have a very hard time accepting that the speed of light is so fast, or is constant, and they concoct elaborate theories conjectures to contradict science for the sake of their biblical literalism.

They also have a problem with the fact that we can see light from stars that are billions of light-years away.

### The starlight problem

The "starlight problem" can be stated succinctly as follows: there are visible stars that are known to be more than 6,000 light years away, based on the Cepheid Variable technique.[27] Since the speed of light is constant, light from these stars must have taken over 6,000 years to reach Earth. Ergo, the universe is more than 6,000 years old.

Since one of the main goals of creationism is to spread it as science, this scientific paradox is one that creationism must solve to even flirt with the idea of being "scientific". While creationists make an effort to solve the starlight problem, it is in many ways the "silver bullet" of creationism:[note 4] in attempts to solve the unsolvable starlight problem, creationists often stumble upon and make some of their most blatantly false arguments — even Jason Lisle, the actual real astrophysics expert employed by Answers in Genesis, can't make a decent stab at solving it. By using the starlight problem to push creationists onto the steady, non-controversial grounds of astronomy, some of the most damning underlying flaws in creationism have been made apparent.

Nevertheless, like any crank or denialist,[note 5] a good creationist never admits defeat, even in the face of overwhelming logic to the contrary. Therefore, creationists have come up with some ways to reconcile their cognitive dissonance,[note 6] by trying to solve the starlight problem.[28]

Their efforts are discussed and refuted below:

1. White hole cosmology: God placed the earth in a time-dilation field during the six-day creation, meaning that time slowed for Earth to only six days, while millions of years passed in the outside universe. Therefore, six Earth days passed in billions of universe-years. The idiocy of this argument is obvious: astronomy is not Star Trek. More to the point, this argument is unfalsifiable.
2. c-decay theory: The speed of light was higher in the past. This "theory" is wrong for a couple of reasons:
• Laser rangefinders and digital clocks, in use since the 1960s, are precise enough to detect even small rates of residual decay, but none is observed.
• The major physical constants have not changed in any appreciable manner.[29]
• The speed of light ${\displaystyle c}$ is not simply an isolated value; it is intimately tied up with the very structure of spacetime, and is also a crucial factor in the mass/energy equivalence as given by Einstein's famous equation E = mc2. A higher value of c would lead to a far higher energy yield from nuclear processes (where mass is converted into energy), making existence impossible for the very stars whose light creationists attempt to explain. Since we can actually see those stars, we can also see that the nuclear processes fueling these stars are the same for all stars, regardless of distance.
• The "scientist" behind c-Decay theory, Barry Setterfield, uses poor math and worse scientific methodology.[30]
• Triangulation disproves this.
3. The omphalos hypothesis: God created the starlight already on its way to Earth, to make it look like it had been emitted from stars much farther away. This "hypothesis" is irrefutable precisely because it isn't scientific — it is impossible to devise an experiment that can tell the difference between real starlight and a perfect imitation of starlight. And, like other evidence for an old Earth and an old universe, it doesn't paint a very friendly picture of God.

Hardcore creationists don't seem to dwell too much on the most obvious solution to this: that God created the universe before he created the Earth. This is the view often seen with variants of Old Earth Creationism, but isn't too appealing to the more stubborn fundamentalists, possibly because it would imply that humans are not the most important thing in the entire universe, even though you always build the fish tank before you add the fish.

## Notes

1. Does this seem a little circular? Not really. The important part about our units of measurement, whether it be distance or electric current, is that they have to first be defined against something. The most objective way to do this is to define these measurements against the various physical constants, which are unchanging values associated with the universe.
2. The non-US use of the word 'meter' refers exclusively to measuring devices (e.g. thermometer), however.
3. Well, all uncompromised observers, anyway. As we shall see later in this article, faulty measuring devices that record the speed of particles incorrectly can give off the impression that the speed of light has been broken. This can potentially cause a scientific kerfuffle — and this has already happened at least once, giving cranks and denialists around the world something vaguely resembling ammunition in their ongoing war on science.
4. Or would it be the silver bullet of anti-creationism?
5. Yes, there is a difference between cranks and denialists. These two flavors of idiot or charlatan frequently overlap, but some morons or mountebanks fall into one category and not the other. Essentially, a crank relentlessly pushes some fringe hypothesis or theory as being true or some fringe system or phenomenon (such as homeopathy or psychic powers) as being viable (often because they have some vested interest in people accepting that idea), despite a complete or near-complete lack of empirically-collected data in support of said hypothesis, theory, system, or phenomenon; a denialist asserts that some established hypothesis or theory must be false, some established system cannot work, or some established phenomenon (such as [anthropogenic] climate change) cannot happen or is not happening (often because they have some vested interest in people rejecting that idea), despite the existence of a large amount of empirically-collected data supporting that hypothesis, theory, system, or phenomenon.
6. Well, to resolve their cognitive dissonance without changing their worldview or beliefs. That's the important part. See the "path of least psychological resistance" paragraph in our cognitive dissonance article for more details.

## References

1. Speed of light not so constant after all: Pulse structure can slow photons, even in a vacuum by Andrew Grant (5:00pm, January 17, 2015) Science News.
2. Handbook of Chemistry and Physics 72nd ed. CRC Press: Boca Raton, 1991.
3. For those interested, a 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." From here.
4. [1]
5. Defined as 365.25 days, where 1 day is defined 86,400 SI seconds long.
6. See the Wikipedia article on Phase velocity.
7. See the Wikipedia article on Faster-than-light.
8. Minute Physics — How to break the speed of light
11. http://www.bbc.co.uk/news/science-environment-15017484
12. http://www.waterstechnology.com/sell-side-technology/opinion/2111804/step-closer-messaging-faster-light-speed
13. BBC News — Brian Cox on Cern's baffling light-speed find
14. Gaia-Health.com — Subnuclear Particles May Move Faster Than Light. Who Says Homeopathy Can’t Work?
15. Islamic Awakening — Speed of light 'broken' by scientists
16. Can time be reversed?
17. Faster than Light Neutrinos? Comments
18. http://heritage.stsci.edu/1999/04/sn1987anino.html
19. Timing glitches dog neutrino claim
20. Measurement of the neutrino velocity with the ICARUS detector at the CNGS beam
21. Neutrinos clocked at light-speed in new Icarus test
22. http://njsas.org/projects/speed_of_light/empedocles/index.html
23. http://galileo.phys.virginia.edu/classes/109N/lectures/spedlite.html
24. http://njsas.org/projects/speed_of_light/index.html
25. No, this is not cheating