The Quantum Universe_ Everything That Can Happen Does Happen - Brian Cox [31]
We know the date and time of Planck’s revelation so well because he and his family had spent the afternoon of Sunday 7 October 1900 with his colleague Heinrich Rubens. Over lunch, they discussed the failure of the theoretical models of the day to explain the details of black body radiation. By the evening, Planck had scribbled a formula on to a postcard and sent it to Rubens. It turned out to be the correct formula, but it was very strange indeed. Planck later described it as ‘an act of desperation’, having tried everything else he could think of. It is genuinely unclear how Planck came up with his formula. In his superb biography of Albert Einstein, Subtle is the Lord …, Abraham Pais writes: ‘His reasoning was mad, but his madness has that divine quality that only the greatest transitional figures can bring to science.’ Planck’s proposal was both inexplicable and revolutionary. He found that he could explain the black body spectrum, but only if he assumed that the energy of the emitted light was made up of a large number of smaller ‘packets’ of energy. In other words the total energy is quantized in units of a new fundamental constant of Nature, which Planck called ‘the quantum of action’. Today, we call it Planck’s constant.
What Planck’s formula actually implies, although he didn’t appreciate it at the time, is that light is always emitted and absorbed in packets, or quanta. In modern notation, those packets have energy E = hc/λ, where λ is the wavelength of the light (pronounced ‘lambda’), c is the speed of light and h is Planck’s constant. The role of Planck’s constant in this equation is as the conversion factor between the wavelength of light and the energy of its associated quantum. The realization that the quantization of the energy of emitted light, as identified by Planck, arises because the light itself is made up of particles was proposed, tentatively at first, by Albert Einstein. He made the proposition during his great burst of creativity in 1905 – the annus mirabilis which also produced the Special Theory of Relativity and the most famous equation in scientific history, E = mc2. Einstein received the 1921 Nobel Prize for physics (which due to a rather arcane piece of Nobelian bureaucracy he received in 1922) for this work on the photoelectric effect, and not for his better-known theories of relativity. Einstein proposed that light can be regarded as a stream of particles (he did not at that time use the word ‘photons’) and he correctly recognized that the energy of each photon is inversely proportional to its wavelength. This conjecture by Einstein is the origin of one of the most famous paradoxes in quantum theory – that particles behave as waves, and vice versa.
Planck removed the first bricks from the foundations of Maxwell’s picture of light by showing that the energy of the light emitted from a hot object can only be described if it is emitted in quanta. It was Einstein who pulled out the bricks that brought down the whole edifice of classical physics. His interpretation of the photoelectric effect demanded not only that light is emitted in little packets, but that it also interacts with matter in the form of localized packets. In other words, light really does behave as a stream of particles.
The idea that light is made from particles – that is to say that ‘the electromagnetic field is quantized’ – was deeply controversial and not accepted for decades after Einstein first proposed it. The reluctance of Einstein’s peers to embrace the idea of the photon can be seen in the proposal, co-written by Planck himself, for Einstein’s membership of the prestigious Prussian Academy in 1913, a full eight years after Einstein’s introduction of the photon:
In sum, one can say that there is hardly one