# Physics in a Nutshell: A Brief History of the Speed of Light

We have estimates for the speed of light. But in truth, it is conceivable that further refinements will be made.

What is the speed of light? It's such an easy question to answer in the age of the internet. But have you ever wondered how we reached our current estimate of 299,792,458 m/s?

Could you even imagine how would you go about measuring it? Many great minds attempted to tackle this very question throughout history.

[Image Source: LucasVB via Wikimedia Commons]

Early attempts at actual "physical" measurements got off to a good start with Galileo. In one particular instance, he and his assistant stood on opposing hilltops with a known distance between them. Galileo would open the shutter of his lamp. The plan was then for the assistant to open the shutter of the other lamp as soon as he saw the light from Galileo's. However, his experiments resulted in "inconclusive" results, as the light was far too fast to measure.

Groundbreaking work from the likes of Romer and Einstein seem to have finally put that to bed. However, this is only the most recent individuals to work on this issue. Research into it actually began far, far earlier.

## Early ideas

Some of the earliest discussions appear to be from Aristotle. He famously quotes Empedocles, who suggested that the light from the Sun must take some time to get to Earth. True to form, Aristotle disagreed with this assumption. Aristotle seemed to suggest that light traveled instantaneously.

"light is due to the presence of something, but it is not a movement" - Aristotle

Euclid and Ptolemy built upon Empedocles's ideas and speculated that light was emitted from the eye which enabled sight. Later, Heron of Alexandria argued that the speed of light is probably infinite since distant objects, stars etc, appear immediately when you open your eyes. Addittionally, Heron ultimately formulated the principle of the shortest path of light. It states that, if light has to travel from point A to point B, it will always take the shortest route possible.

Jumping forward to the 17th century, Johannes Kepler came to the conclusion that, if the speed of light was finite, the Sun, Earth, and Moon should be out of alignment during lunar eclipses. As this did not seem to occur, Descartes reached the same conclusion as Aristotle. Descartes went on to postulate that the speed of light is infinite or instantaneous and that it even sped up through denser mediums.

## How to measure the "infinitely" fast

One of the first serious attempts to measure the speed of light came from Dutch Scientist Isaac Beeckman. In 1629, using gunpowder, he placed mirrors at various distances from an explosions. He asked observers whether they could see any difference in when the explosion flash was reflected from each mirror with their eyes. As you can imagine, the results were somewhat inconclusive.

Later, in 1638, the great Galileo, in his work Two New Sciences, summed up the Aristotelian position pretty neatly. "Everyday experience shows that the propagation of light is instantaneous; for when we see a piece of artillery fired at great distance, the flash reaches our eyes without lapse of time; but the sound reaches the ear only after a noticeable interval," he wrote

Galileo went on to deduce that nothing about its speed can, in fact, be gleaned from simply observing light. Later in the piece, Galileo goes on to suggest a means of potentially measuring the speed of light.

## Galileo's Light Speedometer

Galileo's idea to measure the speed of light was surprisingly simplistic. He suggested having two people at a known distance from one another with covered lanterns. The plan was a remarkably simple one. First, one of the lantern bearers uncovers their lantern. Then the other one observing the first lantern's light immediately uncovers their own. This process should be repeated several times so that the participants become well practiced to improve reaction times to as small as possible.

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Once they become accustomed to the process, they were to repeat the process over ever greater distances until finally needing telescopes to view one another's lantern lights. This was to enable the experiment to discover whether there is, in fact, a perceptible time interval and the speed of light. Galileo claims to have run this experiment, but as you can guess, to no avail.

He couldn't detect a perceptible time lag, as we would expect today given light's speed. He concluded that light "if not instantaneous, it is extraordinarily rapid". It is believed he used a water clock to measure the time lag for the experiment. He did, however, manage to deduce that light must travel at least ten times faster than sound.

## Measuring gets serious

Danish Astronomer Ole Romer began to make the first real measurements of the speed of light about 50 years after Galileo. Working at his Paris Observatory in 1676, he began to make a systematic study of I0, one of Jupiter's moons. This moon is eclipsed by Jupiter pretty regularly as it orbited the giant planet. This motion is predictable and handy for this kind of experiment. As he continued his observations, he found that over several months the eclipses seemed to lag more and more behind what might otherwise be expected. Then they began to pick up again. Weird!

In September of the same year, he correctly predicted the one eclipse on November the 9th should be about ten minutes "late". Much to his joy, perhaps relief, this was indeed the case allowing him to gloat in front of his skeptical colleagues at the Observatory.

Romer explained that this lag is probably because the Earth and Jupiter moved in different orbits and as they did so the distance between them was changing. The light reflected from Io must, therefore, take some time to reach Earth with the greatest "delay" occurring when Earth and Jupiter were at their maximal separation. The eclipse "delays" were also a consequence of this variance in distance between us and Io/Jupiter.

His observations further enabled Romer to conclude that light takes around twenty-two minutes to reach Earth.

[Image Source: NASA/JPL/University of Arizona]

## Building on Romer's work

Romer's brave estimate was a good start but a tad of an overestimate. Later Sir Isaac Newton would write in Principia (Book I, section XIV):

"For it is now certain from the phenomena of Jupiter’s satellites, confirmed by the observations of different astronomers, that light is propagated in succession (note: I think this means at finite speed) and requires about seven or eight minutes to travel from the sun to the earth.”

Newton adjusted for the distance between the Earth and Sun to calculate that it would take around seven or eight minutes to travel between them. In both Romer's and Newtons estimations the figure they derived was that far off.

We now know this to be a much better estimate, but "kudos" to Romer. To measure the "speed" of anything, you tend to need to know the distance between two points. Let's take the distance of the Sun from the Earth, for instance.

During the 1670s, various attempts were made to measure the parallax of Mars. The parallax is a measurement of how far Mars has shifted against a background of distant stars. To do this, observations need to be made simultaneously from different places on Earth. This would show a very subtle shift which can be used to measure the distance of Mars from the Earth. With this measurement in hand, astronomers could then estimate Earths relative distance from the Sun.

The relative distances of celestial bodies in our solar system had already been established at this point through observations and geometrical analysis.

## Experiments get ever more precise

In Modern Theories of the Universe, by Michael J.Crowe, these observations concluded that this distance is around 40 to 90 million miles. These measurements finally agreed on a value of 93 million miles (149.6 million kilometers), which is more or less correct as we know today. This agreement between astronomers came from Romer's, or use of his data by Huygens, correct value for the distance.

Christiaan Huygens used Romer's estimate and combined it with an estimate of the Earth's diameter to derive a new speed of light. Huygens's work resulted in the speed of light to be around 201,168 (to nearest whole number) kilometers per second. This is about three-quarters of the real value of 299,793 (to nearest whole number) kilometers per second.

Why the error? We'll it can be explained by taking into account the time taken for the light to cross the Earth's orbit to be around twenty-two minutes rather than the correct value of sixteen minutes.

Further improvements were made to the estimate of the speed of light in 1728 by English Astronomer James Bradley. He noted whilst on a sailing trip down the Thames that the little pennant on the ship's mast changed positions each time the boat "put about". He likened this event to the Earth in orbit with starlight akin to the wind playing with the boat's sails and pennant. Bradley further reasoned that the starlight "wind" could be thought of us either blowing behind or into the oncoming "Earth boat".

## It never rains, it pours!

Another analogy would be starlight akin to a downpour of rain on a windless day. With Earth being a person walking in a circle at a space pace through it. The incoming direction of rain would not be vertical but rather at an angle. Let's say the rain is falling at around 10 km/h and you are walking at around 5 km/h, the rain will have a vertical and horizontal speed that matches these figures. James Bradley thought that light could be thought of us acting in a similar fashion.

He reasoned that given the Earth's speed of about 18 miles per second he knew that Romer's work has estimated light to be about 10,000 times more. From this Bradley mused that the angular variation in incoming light was about the magnitude of the small angle of a right-angled triangle. The triangle will have one side that is 10,000 times longer than the other and about two-hundredths of a degree.

The advent of the telescope and improvement to engineering that time allows this small angle to be accurately measured. From his thought experiment and observations, Bradley concluded that the speed of light is around 297,729 kilometers per second. This only about 1 % of the mark!! Pretty incredible.

## What's with all the indirect measurements?

Ok, so let's take stock here. We've gone from arguments about whether light travels instantly to some actual figures. Not bad. Sadly most of these are not actual direct measurements. Rather, they are indirect assertions. Granted, with very good precision, but there is still a lack of "direct" observation.

Galileo's punt at it with lanterns would have worked well, given we would have had an actually known distance to work with. So far the speed had been inferred from indirect deductions based on slight changes in positions of celestial bodies. As we know today, relatively small distances like those needed by Galileo are far too small to make an appreciable measurement.

This was resolved, in part, by two bitter French rivals in 1850. Fizeau and Foucault used slightly differing techniques to reach a similar conclusion. Fizeau used a piece of apparatus that shone a beam of light between the teeth of a rapidly rotating toothed wheel. This meant that the light source was constantly being covered and uncovered. He also used a mirror to reflect the light back where it passed through the toothed wheel a second time.

This innovation clearly eliminated the need for two lanterns, as in Galileo's experiment, as well as provided a more predictable pattern rather than relying on human reactions.

The idea was that the reflected light could bounce back through the toothed wheel at certain times. For instance, the same one if "slow" enough, or a further tooth hole if fast enough or of course blocked by the "wedges" in between. The beauty of the design was that you could easily make wheels with hundreds of teeth and rotate them very fast enabling measurements of a fraction of a second. This method worked very well indeed.

## Foucault strikes back

His rival, Foucault's method was based on a similar principle except it incorporated a rotating mirror rather than a toothed wheel. At one point in the rotation, the reflected beam of light would fall onto another distant mirror which was reflected back again to the rotating one. The rotating mirror had clearly rotated a little distance over the time it takes for the light to re-reflect back to it.

This method provided a means of measuring the new position of the light beam and hence provide a speed. He was able to figure out how far the mirror had turned during the time it had taken the light to make its round trip.

Both these ingenious techniques provided a speed of 298,000 kilometers per second. That's a mere 0.6% "off" the modern estimate.

## Albert Michelson steps up to the plate

Mr Michelson was born in Strzelno, Poland. His parents migrated to the U.S. when Albert was 4 years old to escape the escalating anti-Semitism in the region. Albert later went on to spend some time with the U.S. Navy before becoming an instructor in Physics and Chemistry in 1875.

His time at sea, and his musing's about how everything looks the same in a closed room moving at a steady speed as it does at rest, were reminiscent of Galileo's earlier findings.

When he began lecturing, Michelson decided to try out Foucault's method. He soon realized, however, when setting up the apparatus that he could perhaps redesign it to provide greater accuracy. He decided to up the ante and increase the distance between the mirrors and lenses.

Instead of Foucault's 18 meters, he decided to extend the distance to 610 meters. He also managed to raise funds to use very high-quality mirrors to focus the light beams. So good were his findings that he recorded the speed of light as 298,299,96 kilometers per second only 48.28 kilometers per second of the today's value.

His experiment's accuracy was so good it became the standard and most accurate measurement for the next 40 years.

## The 20th century looms

Light and electromagnetism were known to be interwoven towards the end of the 19th century. This would allow for further refinement over the next few decades. Physicists worked tirelessly measuring electromagnetic and electrostatic charges to gain a numerical value very close to those measured by Fizeau.

Building on this, German Physicist Willhelm Eduard Weber suggested that light was, in fact, an electromagnetic wave. Enter stage left, Albert Einstein with his groundbreaking work in 1905. "On the Electrodynamics of Moving Bodies" showed to the world that the speed of light in a vacuum is the same in all "inertial" frames of reference. Not only that but it was completely independent of the motion of the source or observer.

Einstein's calculations further allowed him to develop his Theory of Special Relativity providing the scientific world with the value c, now a fundamental constant. Prior to Einstein, scientists were in deeply entrenched in their quest for something called the  "luminiferous aether". Such a seemingly strange concept was employed to describe how light actually propagated. The aether was once thought to be for "moving" light along throughout the universe.

## The universal speed limit

Einstein's work advanced the principle that the speed of light is constant in a vacuum and that strange thing occurs the nearer to its speed you reach. Including effects such as time dilation or the slowing of time the faster you travel. The speed of light seems to be the fastest a body with mass can travel. Perhaps future developments in physics will overturn this notion too. Only time will tell.

Relativity also succeeded in reconciling Maxwell's equations for electricity and magnetism with the laws of mechanics. They also simplified mathematical calculations by making superfluous explanations redundant. Modern techniques, including interferometers and cavity resonance techniques, have been employed to give us our modern value. These have further refined our estimate for the Universe's so-called speed limit. Our currently recognized value of 299,792,458 m/s was derived in 1972 by the U.S. National Bureau of Standards in Boulder, Colorado.

## The final word

Well, that is quite a journey. We have traveled from the great Aristotle to no other than Albert Einstein. Other great minds including Isaac Newton, French and Polish scientists have all "had a go" at tackling this seemingly simple question. It has truly been a labor of love across time and a Universal "tag team" event. We've gone from pure thought to a couple of blokes with lanterns to finally the cutting edge of scientific experimentation to provide the answer. Yes ok, there were some further refinements and ingenious methods in between.

Mankind's constantly annoying habit of asking awkward questions can sometimes result in long waits for seemingly simple questions. Perhaps the speed of light is the greatest example of this. It is a fine testament to our ancestors that we would not stop in our quest to answer this question. Although we do have a current estimate, it is conceivable that further refinements will be made over the coming centuries. Whatever the future has in store, we hope you'll never take it for granted from this point on.

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