The ‘Annus Mirabilis’ papers, coming from the Latin meaning ‘extraordinary year’, refer to the four papers of Albert Einstein published in 1905. Each of these papers was to have a substantial influence on the development of physics in the 20th century.
- Photoelectric effect
- Brownian motion
- Special relativity
- Matter and energy equivalence
While the latter 3 papers were to fundamentally change our perception of space, time and matter; the first was potentially even more far reaching in that it was another step in the transition from classical to quantum physics.
The photoelectric effect describes how electrons are emitted from matter as a consequence of absorbing energy from electromagnetic radiation of a very short wavelength, such as visible or ultraviolet light.
Einstein’s photoelectric paper was entitled "On a Heuristic Viewpoint Concerning the Production and Transformation of Light " and was published 9 June 1905. In this paper, Einstein outlines the idea of energy quanta, which would later become known as the photon, by extending the idea of quantized energy as initially introduced by Max Planck, in 1900, in the context of black body radiation. In the opening introduction of his paper, Einstein states:
“It seems to me that the observation associated with black body radiation, fluorescence, the photoelectric effect, and other related phenomena associated with the emission or transformation of light are more readily understood if one assumes that the energy of light is discontinuously distributed in space. In accordance with the assumption to be considered here, the energy of a light ray spreading out from a point is not continuously distributed over an increasing space, but consists of a finite number of energy quanta which are localized at points in space, which move without dividing, and which can only be produced and absorbed as complete units.”
In the main body of the paper, Einstein highlights that the photoelectric effect depends on the wavelength, and therefore the frequency, of the light. At low frequencies, even intense light will not produce electrons, but at a certain frequency, even low intensity light will produce electrons. In these statements, Einstein recognised the link to Planck's hypothesis, which suggested that light could only be emitted in discrete packets, or quanta, of energy as defined by the equation [E=hf]. He then goes on to postulate that light also propagates as quanta, although not necessarily explaining how. The photon energy depends on the frequency and therefore only light above a certain frequency would have enough energy to liberate an electron from its position within the structure of the material. However, even after empirical experiments had confirmed that Einstein's equations for the photoelectric effect were accurate, his explanation was not universally accepted, even by those who would go on to pioneer quantum theory.
In 1887, Heinrich Hertz observed the photoelectric effect, while carrying out experiments to confirm Maxwell's theory of electromagnetism. However, Hertz noticed that when he shone ultraviolet light onto the metal electrodes, the voltage needed to make sparks hop between the electrodes was lowered. From this effect, he concluded that the light must be having some electrical effect, but came to no specific conclusion as to the cause.
Later, in 1899, J.J. Thomson suggested that the ultraviolet light falling onto a metal surface might be triggering the emission of electrons. At this time, Thompson had only just demonstrated that electrons were tiny charged particles, which he believed were a material component of atoms. Therefore, the conjecture was that the photoelectric effect was linked to the electrons inside the atoms, of a given metal, being made to vibrate by the oscillating electric field associated with the light waves falling on the metal. As a consequence, some electrons might be shaken so hard that they could be ejected from the metal’s surface.
The next step was taken by Philipp Lenard, in 1902, who obtained the first quantitative measurements of the photoelectric effect. Lenard used a carbon arc light to study how the energy of the emitted electrons varied with the intensity and frequency of the light. In the course of his experiments he noted that by increasing the frequency of light caused the electrons emitted to have more associated energy. However, it was also noted that that simply increasing the intensity of the light had no effect at all on the average energy associated with each ejected electron. This was an unexpected result as physicists, at this time, believed that the photoelectric effect resulted from an interaction between electrons and electromagnetic waves, such that a light with more intensity should result in electrons being ejected with more energy.
Then, in 1905, Einstein put together Lenard's observations of the photoelectric effect and Planck's idea about energy quanta associated with blackbody radiation. His insight was to recognise that light is also subject to an energy quantization in which light propagates in the form of a discrete energy quanta defined by Planck’s equation [E=hf], where [f] is the frequency associated with the light source. As a consequence, Einstein speculated that an incoming light quantum, i.e. a photon, was colliding with an electron on the surface of the metal and transferring its energy to the electron.
Einstein then went on to describe how a certain amount of energy, called the work function, would be needed to overcome the force of attraction binding the electron within the metallic lattice before the electron could be ejected. This helped to explain why there was no photoelectric effect until a certain threshold was reached, after which any ‘surplus’ energy would be converted into the kinetic energy linked to the ejected electron. Within this model, simply increasing the intensity of radiation, i.e. the number of light quanta per unit area, would have no effect as the process required the individual photon quantum, which collided with an electron, to exceed a specific energy threshold. Accepting the energy-frequency relationship implied in Planck’s equation [E=hf], then explained why increasing the frequency of the light source would result electrons being ejected with ever greater energy.
However, as indicated above, the idea of light quanta was not immediately accepted by the scientific establishment of the day. In fact, it would take another 16 years before the idea received formal recognition, when Einstein was awarded the Nobel Prize, in 1921, for his paper on the photoelectric effect. Possibly one of the greatest problems associated with this work, when initially published, was that it raised the old ‘chestnut’ about the true nature of light:
Is light wave-like or particle-like?
It had taken nearly 200 years, i.e. 1670-1864, to overcome the view that light was particle-like. This particle-like position was initially established on the basis of Newton’s work, and reputation, and although it had been seriously challenged by many, especially by Thomas Young in the early 19th century, it was only the publication of Maxwell’s equations, in 1864, which finally shifted the establishment towards the general acceptance of the wave-like nature of light. The implication that the wave conclusion could be reversed, in less than 40 years, was possibly too much for the scientific establishment, in 1905, to accept on the basis of a speculative hypothesis submitted by a ‘patent clerk’ working in Bern.
Thomas Young is now famously associated with what is called the double-slit experiment. There is a certain irony in that Young’s experiment that would shift the balance of opinion about the nature of light being particle-like to wave-like at the beginning of the 19th century, while Einstein’s work on the photoelectric effect would shift opinion back towards a particle-like nature at the beginning of the 20th century. The irony is not in these events, but rather that Young’s double-slit would later be used to highlight a profound paradox that is now discussed in terms of the wave-particle duality of light and matter.
Einstein's photoelectric theory was eventually tested and verified in the laboratory, albeit a decade after its initial publication, by Robert Millikan. However, Millikan had originally undertaken the task to prove Einstein wrong and uphold the position that light was wave-like in nature. So, at this point, while we might see that the seeds of the ‘quantum revolution’ had been sown, although it was not yet time to harvest this idea.