It is by far the most famous equation in the history of science – and one of the shortest: E=mc². Derived by Albert Einstein in 1905, the equation describes the relationship between mass and energy, stating that the total energy contained in a given piece of matter is equal to its mass times the speed of light squared. Given that the speed of light is a whopping 299,792,458 metres per second, this means that a single gram of matter contains some 89 Terajoules of energy – enough to power 17,000 homes for a year. Put another way, while the Little Boy atomic bomb dropped on Hiroshima on August 6, 1945 contained 64 kilograms of enriched uranium fuel, only a tiny fraction of this – around the mass of a paperclip – was converted into pure energy. Put it yet another way, a typical adult male weighing in at around 90 kilograms if completely annihilated would produce a release of energy equivalent to about 1,400 times that of the combined energy released by the bombs dropped on Hiroshima and Nagasaki. Thus, despite just sitting there on the toilet watching this video, you contain an incredible amount of energy.

But how did scientists manage to measure something as inconceivably speedy as light, and what on earth does the speed of light have to do with mass and energy? The story of science’s quest to understand the mysteries of light is a fascinating one, full of brilliant figures, frustrating dead ends, and revolutionary discoveries that completely upended our understanding of time, space, and our place in the universe.

Since the dawn of history, humans have understood that light is very fast indeed. After all, when lightning strikes, the light seems to arrive near-instantly, while the thunder can take several seconds to catch up. Just how fast, however, long remained a subject of considerable debate, with many ancient philosophers including Aristotle arguing that the speed of light was infinite. In the 10th and 11th centuries, Islamic scientists Ibn Al-Haytham and Ibn Sina suggested that the speed of light was finite, but too fast to measure using existing methods. It was not until 1638 that the great Italian scientist Galileo Galilei devised the first mildly practical, if inconclusive, method for measuring the speed of light. In Galileo’s experiment, two people carrying covered lanterns would stand a pre-measured distance apart. One experimenter would uncover his lanterns, while the other would uncover his the moment he saw the light from the first, with the delay between the first and second signal being measured. The two experimenters would then move farther apart and repeat the procedure. In theory, this method would compensate for both experimenters’ reaction times, allowing the actual speed of light to be measured. At the time, however, Galileo was under house arrest and almost nearly blind, and was unable to actually carry out his experiment. It was not until 1667 that members of Florence’s Accademia del Cimento finally tried out Galileo’s method. Unfortunately, even at great distances the delay between the two lantern signals was so small as to be unmeasurable, leading the Academy to conclude that the speed of light lay somewhere between 10,000 kilometres per hour and infinity. Given the lack of experimental evidence to the contrary, the theory of infinite speed would hold sway for many decades, vigorously supported by leading enlightenment thinkers like French philosopher René Descartes,

Five years later, however, a 28-year-old Danish astronomer named Ole Rømer arrived in France to take up a position at the Paris Academy of Sciences. His first assignment, given to him by the great Italian astronomer Giovanni Cassini, was to investigate a peculiar anomaly in the orbit of Io, one of Jupiter’s four largest moons. In the 1610s, Galileo had discovered Jupiter’s moons and devised a method for using the timing of their orbits to measure longitude – that is, one’s position east or west on earth. However, Cassini had since discovered that the orbit of Io was strangely irregular, with the moon often taking a few minutes more or less to disappear or emerge from behind the planet. After making hundreds of observations and puzzling over the problem for several years, Rømer came to an astonishing conclusion: the irregularity was caused by the speed of light. According to Rømer’s reasoning, some observations of Io were made when Jupiter was on the opposite side of the sun from the earth, while others were made when the two planets were on the same side of the sun. In the former case, the extra 300 million kilometres between the two planets meant that the light from Io took longer to reach the earth, causing an apparent delay in its emergence from behind Jupiter. Conversely, when the planets were closer together, the light took less time to cover the distance, causing the reemergence to happen earlier. Using his observations, Rømer was able to predict that the November 1676 eclipse of Io would be 10 minutes late, thus demonstrating that the speed of light was indeed finite. Later, scientists like Dutch physicist Christiaan Huygens would use Rømer’s data to derive the first reasonable value for the speed of light: 190,000,000 metres per second. While this was only 63% of the currently-accepted value, it was nonetheless a step in the right direction. Unfortunately, however, Rømer would not live to see his conclusions widely accepted. Cassini, angry at Rømer for not crediting him in his work, spent the rest of his life trying to discredit Rømer and his theory of a finite speed of light. It was not until 1727 – 17 years after Rømer’s death – that English astronomer James Bradley made the first accurate observations of a phenomenon known as the aberration of light. This is the apparent shift in the position of celestial objects caused by the movement of the earth through space – similar to how vertically-falling raindrops appear to move diagonally as you walk through them. This effect is distinct from parallax in that it affects all celestial objects equally, whereas parallax effects closer objects more than farther ones.

As stellar aberration can only occur if the speed of light is finite, Bradley’s observations finally vindicated Rømer’s theories. They also allowed him to calculate a new light speed value of 301,000,000 metres per second – only 0.4% higher than the current value.

From this point on, further refinements to the speed of light would largely be made using earth-based equipment. One of the first such experiments was carried out in 1849 by French physicist Armand Hippolyte Fizeau. In Fizeau’s experiment, a beam of light was passed through a rotating toothed wheel, bounced off a mirror 8 kilometres away, and passed back through the wheel. By adjusting the speed of the wheel so that the beam of light passed through a gap in the wheel on the way out but was blocked by the adjacent tooth on the way back, Fizeau could work out the time it took for the light to bounce off the mirror and return – and hence its speed. This method yielded a value of 315,000,000 metres per second – slightly higher than James Bradley’s 1727 figure. In 1862, fellow Frenchman Léon Foucault improved upon Fizeau’s method by replacing the toothed wheel with a rotating mirror, such that the speed of light could be measured by the angle the mirror had rotated by the time the light beam had returned from the mirror. The main advantage of this method was that the mirror spun at a constant rate, allowing its speed – and hence that of the light beam – to be measured with much greater precision. Indeed, Foucault’s experiment yielded a value of 298,000,000 metres per second – only 0.5% off from the current value. 12 years earlier in 1850, Foucault had also used a less refined version of this apparatus to determine that light travels more slowly through transparent materials like water and glass than through air. And between 1879 and 1935, American physicist Albert Michelson used ever more refined versions of Foucault’s apparatus with a rotating octagonal mirror to measure c at 299,864,000 metres per second – within 0.02% of the current value.

The next major method devised for measuring the speed of light differed significantly from previous approaches. In 1862, Scottish physicist James Clerk Maxwell determined that light is a form of electromagnetic radiation, composed of coupled electric and magnetic waves. Microwaves, radio waves, gamma rays, and x-rays are also forms of electromagnetic radiation, differing from visible light only by their wavelengths and frequencies. This theory of electromagnetism allowed the speed of light to be calculated using two easily measurable physical properties of materials known as magnetic permittivity and electric permittivity. In 1907, E.B. Rosa and N.E. Dorsey measured these properties and came up with a value for c of 299,792,500 metres per second – accurate to within 0.00001% of the current value.

In the 1950s, the invention of the maser and laser – which produce coherent, single-frequency beams of microwaves and light – allowed even more accurate measurements to be made. These techniques work on the principle of interferometry – measuring the interaction between two electromagnetic waves. When two waves are aligned or in phase, they will interfere constructively, adding together to form a wave of increased amplitude; if they are out of phase, they interfere destructively, cancelling each other out. In the most common form of this experiment, conducted by Keith Froome in 1952 using microwaves and Kenneth Evenson in 1973 using lasers, a source of electromagnetic radiation is split into two beams, which are then recombined using mirrors so that they interfere constructively. The position of one of the mirrors is then gradually adjusted until the beams interfere destructively; this distance corresponds with the wavelength of the radiation. As the frequency of the radiation produced by the maser or laser source is known with great accuracy, the wavelength and frequency can be multiplied together to yield the speed of light. Using such methods, the speed of light in a vacuum was finally nailed down to its current accepted value of 299,792,458 metres per second.

Indeed, by the 1980s, the accuracy of the value of c had begun to outstrip the accuracy of the very measurement standards used to define it. From 1889 to 1960, the international standard metre – one of the base units of the Systeme Internationale or SI system of measurements – was defined as the length of a platinum-iridium alloy bar kept in a vault in Paris. In 1960, this was changed to the length of 1,650,763.73 wavelengths in a vacuum of the light produced by a specific type of krypton gas-filled lamp. In 1983, however, the highly-accurate value for c was combined with the highly-accurate value for the second made possible by caesium atomic clocks to define the metre as the distance travelled by light in a vacuum in 1/299,792,458th of a second. Thanks to the highly-accurate value of c determined by generations of scientists, all kinds of measurements can be made with a high degree of precision. For example, in the late 1960s and early 1970s, three Apollo manned missions and two Soviet Lunokhod robotic rovers left five retroreflectors on the surface of the moon. By shining a laser beam off these reflectors and measuring its time-of-flight, the distance between the earth and the moon can be determined within a few millimetres.

But even more fascinating – and in many ways more important – than the search for the speed of light was the quest to understand the very nature of light itself. For many years, scientists generally accepted the theory, championed by Sir Isaac Newton, that light was composed of a stream of tiny particles known as corpuscles. In 1801, however, British scientist Thomas Young conducted a classic experiment that would turn this notion on its head. Known as the double slit experiment, it involved passing light through two narrow slits in a paper screen and onto another, solid screen. But instead of two bright lines as he expected, Young saw a pattern of multiple right and dark bands projected onto the second screen. This could only mean one thing: light was not composed of particles, but waves, as postulated by Christiaan Huygens. When the light passed through the two slits, it broke up into two wave fronts which then interfered with each other, producing bright bands where they interfered constructively and dark bands where they interfered destructively. Almost overnight, the corpuscular theory of light was abandoned.

However, this discovery raised a troubling question: if light was a wave, what was it a wave in? At the time, waves were understood as disturbances in a medium such as water or air; it thus followed that light must be carried by some invisible medium that pervaded the universe – a hypothetical substance known as the luminiferous ether. But if this medium actually existed, it would have to possess the strangest set of properties known to science. For example, it was somehow rigid enough to carry waves of extremely high frequencies, yet insubstantial enough to not oppose the movement of ordinary objects. It also could not be manipulated like ordinary matter; after all, when all the air is pumped out of a bell jar, the jar does not suddenly go dark. Yet as unbelievable and contradictory as these properties seemed, they simply had to be true; at the time, scientists could see no other way of explaining how light waves could propagate through space. But the necessarily ephemeral nature of the ether made it effectively impossible to study, making its existence something of an article of faith…or so everyone thought. Enter our old friend Albert Michelson.

In 1880, Michelson realized that despite its intangible nature, the ether would produce at least one measurable effect: the ether wind, the hypothetical relative motion experienced by the earth as it travels through space at 29,777 metres per second. If this wind existed, Michelson reasoned, then a beam of light travelling perpendicular to the earth’s direction of travel would behave differently than one travelling parallel to it. To understand how this works, imagine two people swimming in a flowing river. Swimmer A swims a certain distance back and forth along the river, parallel to the current, while Swimmer B swims the same distance across the river, perpendicular to the current. Due to the lateral force of the current. Swimmer B will travel in a diagonal path – a path longer than that travelled by Swimmer A. Thus, Swimmer B will take longer to complete their lap than Swimmer A. By the same logic, thanks to the ether wind, a beam of light travelling perpendicularly to the earth’s travel would take longer to make the round trip than a beam of light travelling parallel to it, causing the two beams to interfere destructively when combined.

Over the next 7 years Michelson and fellow physicist Edward Morley conducted increasingly sophisticated versions of this interferometry experiment in order to prove the existence of the ether. The pair even went so far as to float their apparatus on a large pool of mercury in order to isolate it from vibration. But no matter how carefully the pair built or adjusted their equipment, the two beams refused to interfere. Against all of Michelson and Morley’s expectations, the ether didn’t seem to exist. But how, then, did light travel through empty space? It would be less than a decade before the solution was found by a then-unknown German student named Albert Einstein.

While the term “relativity” has become inextricably linked with Einstein, the principle itself is much older. In 1632, Galileo described the following thought experiment:

“Shut yourself up with a friend in the main cabin below deck on some large ship, and have with you some flies, butterflies and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how all the little animals fly wit equal speed to all sides of the cabin; how the fish swim indifferently in all directions; how the drops fall into the vessel beneath. And, in throwing something to your friend, you need to throw it no more strongly in one direction than another, the distance being being equal; and jumping with your feet together, you pass equal spaces in every direction.

When you have observed all these things carefully…have the ship proceed with any speed you like, so loch as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship moves or stands still.”

This experiment reveals that in the universe, there are only two kinds of physical scenarios or frames of reference: inertial and accelerated. While the term inertial literally means “standing still”, it refers to any frame of reference that is not accelerated – that is, one moving at a constant velocity. According to Galilean and Newtonian physics, all inertial frames of reference are identical – that is, physics behave the same whether you are standing still or moving at an extremely high – but constant – velocity. Indeed, without external cues such as vibration or other objects moving relative to you, it is impossible to tell that one is moving while in an inertial frame. This is why you currently feel like you are standing still even though the earth is spinning around its axis at 444 metres per second and orbiting the sun at 29,777 metres per second and our entire solar system spinning around the Milky Way center at around 200,000 meters per second and our entire galaxy clipping along at about 600,000 meters per second as well. Only in an accelerated frame of reference – where the motion of objects and other physical phenomena are affected – is it possible to know you are moving without external references.

In 1896, the then 17-year-old Einstein applied Galileo’s principles to one of his famous gedankenexperiments or “thought experiments,” wherein he imagined himself riding on a beam of light. What would happen, Einstein wondered, if he held up a mirror to look at his own reflection? If, as scientists then believed, light behaved like any other wave, this meant it could travel no faster than c. Thus, the light from Einstein’s face would not be able to travel to the mirror and back, causing the mirror – and everything else in front of Einstein – to go black as soon as he reached the speed of light. However, as Einstein realized, this scenario would violate the principles of Galilean relativity, since it involved the laws of physics suddenly changing within an inertial frame of reference – something that is supposed to be impossible. To account for this apparent paradox, Einstein made a bold leap of logic – indeed, one of the boldest in the history of science. Light, he realized, doesn’t move at 299,792,458 metres per second relative to the universe or an invisible medium like the luminiferous ether, but relative to the observer. In other words, it doesn’t matter if you measure the speed of light on the earth’s surface or on a spaceship travelling at extremely high velocity; the results will be identical.

The implications of this insight were truly revolutionary, completely upending our understanding of the universe – and in particular, our perception of time. Prior to Einstein, scientists believed that time was unchanging and perceived identically everywhere, like a giant standard clock ticking away in the centre of the universe. But Einstein’s special theory of relativity, first published in 1905, rejected this assumption, arguing instead that time is relative and varies from observer to observer. Specifically, special relativity argues that the faster an observer moves, the slower time passes from the perspective of another observer, stopping completely when the observer reaches the speed of light.

To understand how this works, imagine sitting in a spaceship equipped with a special clock that works by bouncing a pulse of light at a mirror and detecting it when it returns. Now imagine that the spaceship begins accelerating, steadily approaching the speed of light. From your perspective, nothing would appear to change; the clock would keep ticking at the same rate. But to an outside observer, the scene would look very different. In the time it takes for the pulse of light to travel back and forth inside the clock, the spaceship will have shifted its position, forcing the light to travel a greater distance. However, since the speed of light measured by the outside observer is the same as that measured by you aboard the spaceship, for the outside observer the pulse will take longer to travel through the clock, causing said clock to tick more slowly. Indeed, everything inside the spaceship will appear to move more slowly – including you. This effect, known as time dilation, increases with velocity, with time eventually stopping completely as the spaceship reaches the speed of light.

But time dilation must just be an illusion, right? Surely time doesn’t actually slow down at high speeds? Well, actually, yes it does. Since the speed of light is the absolute speed limit of the universe here, it limits the rate at which information can travel through space and at which matter and energy can interact – which is the very definition of time. This means that if you remain aboard our hypothetical light-speed spaceship for long enough then return to earth, everyone will have aged visibly while you won’t have aged a day – a scenario known as the twin paradox.

With this one simple but brilliant insight, Einstein shattered the notion of both the luminiferous ether and universal time, revealing that time actually passes differently for every single observer. But special relativity, as the name implies, applies only to special cases, ignoring the effects of gravity. In 1915, Einstein expanded his reasoning to create the general theory of relativity, which argues that time and space are not separate entities but linked together in a unified fabric of the cosmos called spacetime. Gravity, Einstein argued, works by warping spacetime, affecting the path of objects travelling through it. A common analogy involves dropping heavy objects like bowling balls onto a flexible rubber sheet; the heavier the object, the deeper the dent or gravitational well it makes in spacetime, and the greater influence it has on surrounding objects. And since time and space are linked together, gravity can also alter time, such that the greater the gravitational field, the slower time passes. And lest you think that time dilation exists only in the realm of theory, it can and does have very real-world effects. For example, the satellites that make up the Global Positioning System or GPS orbit at an altitude of around 20,000 kilometres and travel at 14,000,000 metres per second. At these altitudes, the satellites are far enough out of earth’s gravitational well that time passes measurably faster for the satellites than it does on earth – by around 45 microseconds. However, the time dilation effects of satellites’ high velocity causes time to slow down by about 7 microseconds, resulting in a net time difference of 38 microseconds. While this might not seem like a huge difference, given the massive distances over which GPS operates, if the effects of relativity were not compensated for, the system’s accuracy would drift by nearly 10 kilometres every day, quickly rendering it useless.

While the wider implications of both special and general relativity are beyond the scope of this video, it is worth noting that, following the failure of the Michelson-Morley experiment Irish physicist George Fitzgerald and Dutch physicist Hendrik Lorentz advanced the Lorentz-Fitzgerald contraction hypothesis, which proposed that moving objects decrease in length along their direction of travel. Thus, according to this hypothesis, while the transverse beam of light in Michelson and Morley’s experiment did take longer to travel back and forth through the apparatus, the length of the path it had to travel shortened by an equal amount, cancelling out the effect. While the hypothesis was originally formulated as a fudge in order to save the floundering ether theory, Einstein later proved via relativity that Lorentz-Fitzgerald contraction is actually real, meaning that to an observer watching you in your hypothetical spaceship, you and everything else in the ship would appear to become ever skinnier as you approached the speed of light.

But alas, if you are hoping that light-speed travel is the perfect way to achieve that svelte figure you’ve always wanted, prepare to be disappointed. For in addition to describing the massive amounts of energy contained within ordinary matter, Einstein’s famous equation E=mc² also states that the faster an object travels, the greater its kinetic energy and thus its mass. Thus, as you approach the speed of light, you will accumulate ever increasing amounts of relativistic mass, completely ruining any progress you might have made in your weight-loss program. And upon reaching the speed of light itself, you will have accumulated infinite mass and thus require infinite energy to go any faster. This is one of the reasons the speed of light is generally considered the absolute speed limit of the universe. The only reason particles of electromagnetic radiation – known as photons – are able to travel at the speed of light is that they are massless. Oh, yes: I almost forgot to mention: while in certain situations light does behave as a wave, in others it also behaves as a stream of particles – a seemingly paradoxical quantum phenomenon known as particle-wave duality. But that is a mind-bending subject for another video.

And so there you have it: a brief history of how the speed of light was measured, and how the discovery of the true nature of light revolutionized our understanding of the universe. And while this was merely an introduction to a massive and fascinating topic, I hope you at least found it…illuminating.

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