Wave phenomena can be found everywhere in nature and the waves as described by classical mechanics are part of our daily experience. A wave is a propagating excitation of a medium – for example a mass of air or water – with the property that the medium counteracts the excitation: this counteraction is in fact the very reason for the propagation of waves.
Different types of waves
In a sound wave, the compression of the medium leads to an increase in pressure, which would make the medium expand, therefore restoring it. Likewise, an excitation on the surface of a liquid is restored, either by the weight of the liquid above the surface, or by the increase of surface, such that the surface tension pushes the liquid back. An excitation on a string is pulled back by the tension of the string itself.
Those described so far are mechanical waves. A common trait is that they lead to harmonic solutions, and one can predict the propagation velocity of these waves from the properties of the medium they are propagating through. Commonly, this propagation velocity depends on the ratio between the strength of the restoring force and the inertia of the medium.
This is immediately clear when looking at a piano: the low-pitched strings are thicker than the high-pitched ones, increasing therefore inertia and making the propagation velocity of waves on the string slower, resulting in a lower note. Applying additional tension to the string increases the restoring force, leading to a higher note.
In the nineteenth century scientists were debating the nature of light. If light was a wave, as suggested by the experiments conducted by Thomas Young, it would have remarkable properties: It would be unclear which medium would carry such a wave, and how the properties of this medium would determine the wave propagation velocity. At first sight, it must be either a very strong restoring force or a medium with very low inertia in order to explain the high propagation velocity of light. At the time, this hypothetical medium was referred to as the aether. As more experiments were being performed, however, aether was required to have more and more unrealistic properties.
In classical mechanics, it is always possible to choose a frame of reference that moves at exactly the velocity with which the wave propagates. In this frame, the wave is stationary and its amplitude only depends on the distance from the observer: A nice example would be a surfer on a wave on the ocean, who moves at exactly the wave velocity and relative to whom the wave is stationary.
Would a similar observation be possible with electromagnetic waves, i.e. with light? Assuming classical mechanics to be correct, one would need to choose a frame of reference that moves at the speed of light – which might be technically difficult because the speed of light is quite large. From this frame of reference, an observer would then measure stationary electric and magnetic fields, and moving faster would reverse the propagation velocity.
This was tried out in a famous interferometer experiment by Albert Michelson and Edward Morley at the end of the nineteenth century, who tried to measure the propagation velocity of light in the direction parallel to Earth’s motion around the Sun, relative to the velocity perpendicular to it. They obtained a null result, demonstrating that light always propagates at the same velocity, irrespective of the frame of reference. This would later lead to the formulation of special relativity, although it was already clandestinely contained in Maxwell’s equations. And it was a very clever idea to use the Earth as a moving laboratory to achieve high velocities of a few ten kilometers per second!
The phenomena of electricity and magnetism are described by Maxwell’s equations, which were developed by James Clerk Maxwell in the 1860s. First of all, this set of equations relate the properties and the evolution of electric and magnetic fields to two quantities: the electric charge and the electric currents.
But there is a second phenomenon: If an electric or magnetic field changes in time, it gives rise to the other field. This is known as induction and is used technologically in generators, where time-changing magnetic fields generate electric fields which can be used to separate electric charges.
It is possible now to setup a system similar to the mechanical ones described above: A time-varying electric field gives rise to a magnetic field, which itself changes in time and generates an electric field again. In this way, the electromagnetic wave changes constantly from electrical fields to magnetic fields, and propagates in the process.
The propagation velocity is determined by the processes of electromagnetism. It is independent of a medium for propagation, and is unambiguously determined by a single number, which appears as (the only) parameter in Maxwell’s equation: the speed of light, relating the rate of change in time of the ‘original’ fields to the newly generated fields.
And there is an added bonus: the propagation of light does not depend on the wavelength (at least in a vacuum).
At the beginning of the twentieth century, Albert Einstein discovered that Maxwell, without noticing it, had a new principle in his equations, which unified space and time. Having the speed of light as a parameter made sure that distances and time-intervals could be measured in the same unit.
Only later, with the newly discovered framework of Einstein’s special relativity, it became possible to explain that the speed of light is constant in all frames of reference. At the same time, special relativity forbids an observer to move into a frame of reference relative to which an electromagnetic wave is stationary.
Special relativity was published in 1905. Ten years later, Einstein realised that there was something even more fundamental, namely a common geometry of space and time that could be influenced by the presence of gravity. He presented this in his general theory of relativity in 1915 – exactly a hundred years ago.
And he discovered in theory something mind-blowing: There are, similarly to electromagnetic waves, excitations in the common geometry of space and time which can propagate in a wave-like fashion. According to general relativity, these gravitational waves are also propagating at the speed of light; however, they are still to be detected directly.
The theoretical description of light as electromagnetic waves has had an enormous impact on physics in the past two centuries. It was the first example of unification, i.e. the notion that electric and magnetic phenomena have a common origin. Besides, it led to the discovery of a new relativity principle called special relativity, and it disproved the existence of aether as a medium that was supposed to carry light as an elastic excitation. Perhaps the detection of gravitational wave will further confirm our fundamental ideas of space, time and mass.
Bjoern Malte Schaefer is a theoretical astrophysicist. He works at the Centre for Astronomy in Heidelberg, Germany, studying problems in weak gravitational lensing and the anisotropies in the cosmic microwave background and is involved in the Planck- and Euclid-projects. He teaches courses at Heidelberg University on theoretical physics, theoretical astrophysics and relativity. He writes about science on www.cosmologyquestionoftheweek.blogspot.de.