The Speed of Light: A Universal Cosmic Constant

The Speed of Light Is a Constant

The speed of light in a vacuum is exactly 299,792,458 m/s, a universal constant independent of reference frame. It took 400 years of experiments, from Galileo to Fizeau, to measure this value that appears in Einstein's equation E=mc2 and limits the maximum speed of information transmission in the universe.

The speed of light is one of the most important constants in physics. Its value appears, for example, in Einstein's famous equation

which allows us to calculate how much energy is released when a given mass is converted into pure energy.

All waves of the electromagnetic spectrum travel at the speed of light: a cardinal principle of Einstein's relativity and a physical limitation on the transmission of information. Consider, for example, the applications in a space mission far from Earth, such as to Mars. The crew on Mars would receive communications from Earth in a time ranging between 3 and 21 minutes regardless of the medium used to communicate (the difference is due to the elliptical orbits of the planets, which, as they rotate, can be at different distances).

Thanks to Einstein, we now know that c is constant in a vacuum, independent of the reference frame from which it is measured, and equals 299,792,458 m/s. But how did we manage to measure such a large number that seems beyond human comprehension? The idea of catching a ray of light without the aid of some instrumentation is unthinkable; if we watch fireworks, the light reaches us instantly, while we hear the bang with a delay since the speed of sound is 343 m/s. The extreme magnitude of the speed of light does not allow us to determine whether it propagates instantaneously or possesses a determined and finite speed using our eyes alone. The study of the speed of light took 400 years to complete and arrive at a definitive answer about its finiteness.

A Galilean Conquest

The Greek philosopher Aristotle was convinced that light had infinite speed, and this claim survived until the Middle Ages. During the Renaissance, there were still conflicting opinions and sometimes doubts about the finiteness of the speed of light; for example, the philosopher and essayist Francis Bacon wrote in Novum Organum:

"...it suggests a curious doubt to me, namely whether we see the vault of a starry sky at the actual instant in which it exists, and not a little later; and whether there is not, for celestial bodies, a real time and an apparent time, just as there is an apparent place and a real place which astronomers account for when they correct for parallax. It is hard to believe that the image or rays of celestial bodies could reach our sight instantaneously through such an immense space..."

The thinking changed radically in 1638 with the publication of "Discourses and Mathematical Demonstrations Relating to Two New Sciences" by Galileo Galilei, in which the Italian scientist imagined a dialogue where his literary counterpart "Salviati" described an experiment aimed at settling once and for all the finiteness of the speed of light.

The experiment proposed by Galileo was very simple and has gone down in history as the "hilltop experiment". Galileo imagined going to a hill with a covered lantern, with another experimenter in the same conditions on a distant and visible hill. He thought of measuring the speed of light this way: when one of the two experimenters uncovers their lantern, the other must do the same. If the speed of light were infinite, the two lanterns would be uncovered at roughly the same instant. It is unclear whether Galileo actually carried out this experiment on the Tuscan hills, but what we do know is that it would have been useless in determining the speed anyway.

Its magnitude is too great and is not compatible with the reaction times with which the experimenters could uncover their lanterns. Suppose the two experimenters equipped with lanterns were placed at a distance of 1 kilometre. Since the speed of light is approximately 300,000 km/s, the delay would be only 0.000003 seconds. Galileo himself clearly stated that the proposed thought experiment could not lead to unambiguous conclusions, but it was not a complete failure, since it inspired Fizeau's experiment 200 years later.

The Moons of Jupiter

The Tuscan scientist was a volcano of revolutionary ideas in the scientific field, and despite the miss of the hilltop experiment, we indirectly owe to him the first calculation of the speed of light. Using the telescope, he discovered the moons of Jupiter, which have a very precise period. In 1676, the two astronomers Cassini and Romer noticed that the satellite showed a certain irregularity in its orbital period. The latter measured a difference in the orbital period of approximately 10 minutes. If the speed of light were infinite, electromagnetic waves should propagate through space instantaneously and the measurement of the orbital period of Jupiter's moons should not vary. This observation was the first clear evidence of the finiteness of c, which caused the period to vary depending on Jupiter's distance from Earth.

Romer estimated that light travelled from the Sun to Earth in 11 minutes, while fellow astronomer Christiaan Huygens, based on his data, deduced a speed of approximately 200,000 km/s -- not far from the value accepted today.

Recent Experiments

The first accurate measurement of the speed of light came only in 1849 thanks to Fizeau's experiment. Fizeau's experimental apparatus consisted of a beam of light concentrated by a lens, which was bounced off a mirror while passing through a rotating toothed wheel at a certain speed -- controllable by the experimenter. The light could bounce off the mirror placed several kilometres away only at a specific wheel speed, and by knowing the distance to the mirror (i.e., the path travelled by the light), the speed of the wheel and the distance between the teeth, a speed very close to the real value of 315,000 km/s could be measured.

Further confirmation of the existence of c as a constant value came in the 1860s through studies on electromagnetism carried out by, among others, Maxwell and Kirchhoff, who measured a speed for electromagnetic waves equal to c and in this way demonstrated that light is nothing more than a type of electromagnetic wave that we can perceive through sight.

A DIY Measurement

It may seem bizarre, but it is possible to measure the speed of light at home with a do-it-yourself experiment! Let's look at the ingredients:

• A microwave oven
• The frequency value of the specific model you own
• A water-rich food that can be easily heated, such as cheese or a chocolate bar
• A ruler

We know that speed in physics can be calculated by dividing the distance travelled by the time taken to travel it; in the case of waves, this equation translates to the ratio between lambda (the wavelength) and the period (the time needed for the wave to repeat itself). Alternatively, we can measure the speed of a wave by multiplying the wavelength by the frequency f, which is the reciprocal of the period and represents the number of "repetitions" per second.

Today we know that not only does the speed of light equal c, but all electromagnetic waves propagate in a vacuum at the same speed. This occurs because light is just one type of electromagnetic wave -- the one our eyes perceive as the colours that allow us to admire the environment around us.

Almost everyone at home owns a microwave oven, a specific appliance improperly called an oven since it does not use infrared like a traditional oven, but microwaves to vibrate the water molecules present in food and heat them through friction. Inside the microwave, a standing wave develops with a specific frequency that oscillates in place, producing zones where heating is maximum (the antinodes of the standing wave) and zones where heating is minimum (the nodes).

It is very simple to use the appliance to approximately measure the value of c at home. We must begin the experiment by checking on the box or on the label generally placed inside the oven compartment for the specific frequency of our model and noting it down.

Choose a water-rich food that the microwave heats easily, such as grated cheese, and place it on a microwave-safe plate, covering it entirely with a thin layer of cling film. It is important to emphasise that we must prevent the microwave from performing the classic rotation it uses to heat evenly, because we need to prevent the maximum heating zones from shifting during cooking. Modern microwaves have a button that allows you to lock the turntable. Put the cheese in to heat for the time needed to partially melt it. In the cooking compartment, the microwaves will heat and melt the cheese only at certain points, corresponding to the maximum heating areas.

Remove the partially melted cheese from the oven and measure with a ruler the distance between the two points where the cheese melted, and multiply it by two since we are interested in the wavelength, which is defined as the distance between two crests. Multiply the result obtained (in metres) by the frequency previously read from the oven's specifications -- and you're done! You'll be surprised by the accuracy of the result!

FAQ

What is the exact value of the speed of light?

The speed of light in a vacuum is exactly 299,792,458 metres per second (approximately 300,000 km/s). This value is a universal constant, independent of the reference frame from which it is measured, and is denoted by the letter "c" in physics equations.

Why is the speed of light a universal limit?

According to Einstein's theory of relativity, no information or matter can travel faster than light. This is a fundamental principle of physics: even space communications between Earth and Mars take 3 to 21 minutes because signals travel at the speed of light.

How can you measure the speed of light at home?

You can use a microwave oven with grated cheese. By locking the turntable, you get melting points corresponding to the standing wave antinodes. Measuring the distance between points and multiplying by two (wavelength), then by the oven frequency, yields a value very close to c.

Who first measured the speed of light?

The first calculation was made in 1676 by Cassini and Romer observing irregularities in the orbital period of Jupiter's moons. The first accurate measurement was by Fizeau in 1849 with a rotating toothed wheel. Maxwell and Kirchhoff in the 1860s confirmed that light is an electromagnetic wave.