# MAX PLANCK (1856-1947)

1900 – Germany

‘Energy is not a continuous quantity but it is quantised; it flows in discrete packets or quanta. When particles emit energy they do so only in quanta’

According to Quantum theory, the energy (E) of one quantum (photon) is given by E = hf where f is the frequency of radiation and h is Planck’s constant.
Its value is 6.63 x 10-34 joules per second

h is a tiny number, close to zero, but it is has a finite value. This implies energy is released in discrete chunks, a revolutionary notion.

By the late 1800s the science of thermodynamics was developing to the point that people were beginning to understand the nature of energy.
The traditional view was that energy was released in a continuous stream and that any amount of energy could be indefinitely divided into smaller and smaller ‘lumps’. Planck’s work on the laws of thermodynamics and black body radiation led him to abandon this classical notion of the dynamic principles of energy and formulate the quantum theory, which assumes that energy changes take place in distinct packages, or quanta, that cannot be subdivided. This successfully accounted for certain phenomena that Newtonian theory could not explain.

The basic laws of thermodynamics recognised that energy could not be created or destroyed, but was always conserved. The second law was drawn from an understanding that heat would not pass from a colder body to a hotter body.
The study of thermodynamics was based on the assumption that matter was ultimately composed of particles. LUDWIG BOLTZMAN had proposed an explanation of thermodynamics, saying the energy contained in a system is the collective result of the movements of many tiny particles rattling around. He believed the second law was only valid in a statistical sense; it only worked if you added up all the bits of energy in all the little particles.
Among his detractors was Max Karl Ernst Ludwig Planck.

Planck began his work on the second law of thermodynamics and the concept of entropy. He investigated how materials transform between solid, liquid and gaseous states. In doing so he found explanations for the laws governing the differing freezing and boiling points of various substances.
He also looked at the conduction of electricity through liquid solutions (electrolysis).

In the mid 1890s Planck turned his attention to the question of how heated substances radiate energy. Physicists were aware that all bodies radiate heat at all frequencies – although maximum radiation is emitted only at a certain frequency, which depends on the temperature of the body. The hotter the body, the higher the frequency for maximum radiation. (Frequency is the rate per second of a wave of any form of radiation).

Planck had been considering formulae for the radiation released by a body at high temperature. Using ideas developed by ROBERT KIRCHOFF, he knew it should be expressible as a combination of wavelength frequency and temperature. For a theoretical ‘black body’, physicists could not predict expressions that were in line with the behaviour of hot bodies at high frequencies and were in agreement with other equations showing their nature at low frequencies. Thus no law could be found which fitted all frequencies and obeyed the laws of classical physics simultaneously.
Plank resolved to find a theoretical formula that would work mathematically, even if it did not reflect known physical laws. His first attempts were partially successful, but did not take into account any notion of particles or quanta of energy, as he was certain of the continuous nature of energy. In an ‘act of despair’ he renounced classical physics and embraced quanta.

The final straw had been a concept developed by John Rayleigh and James Jeans that became known as the ‘ultraviolet catastrophe’ theory. They had developed a formula that predicted values for radiation distribution and worked at low frequencies, but not at high frequencies. It was at odds with Planck’s formula, which worked for high frequencies but broke down at low frequencies. In June 1900 Rayleigh had pointed out that classical mechanics, when applied to the oscillators of a black-body, leads to an energy distribution that increases in proportion to the square of the frequency. This conflicted with all known data.

Planck’s answer was to introduce what he called ‘energy elements’ or quanta and to express the energy emitted as a straightforward multiplication of frequency by a constant, which became known as ‘Planck’s constant’ (6.6256 x 10-34 Jsec-1). This only works with whole number multiples which means for the formula to have any practical use one must accept the radical theory that energy is only released in distinct, non-divisible chunks, known as ‘quanta’, or for a single chunk of energy, a ‘quantum’. This completely contradicts classical physics, which assumed that energy is emitted in a continuous stream. The individual quanta of energy were so small that when emitted at the everyday large levels observed, it appears that energy could seem to be flowing in a continuous stream.
Thus classical physics was cast into doubt and quantum theory was born.

Planck announced his theory on December 14 1900 in his paper ‘On the Theory of the Law of Energy Distribution in the Continuous Spectrum’. Planck said ‘energy is made up of a completely determinate number of finite equal parts, and for this purpose I use the constant of nature h = 6.55 x 10-27(erg sec)’ When ALBERT EINSTEIN was able to explain the ‘photoelectric’ effect in 1905, suggesting that light is emitted in quanta called ‘photons’, by applying Planck’s theory – and likewise NIELS BOHR in his explanation of atomic theory in 1913 – the abstract idea was shown to explain physical phenomena.

Planck was awarded the Nobel Prize for Physics in 1918. TIMELINE HEAT QUANTUM MECHANICS

# ALBERT EINSTEIN (1879-1955)

1905 – Switzerland

1. ‘the relativity principle: All laws of science are the same in all frames of reference.
2. constancy of the speed of light: The speed of light in a vacuüm is constant and is independent of the speed of the observer’

The laws of physics are identical to different spectators, regardless of their position, as long as they are moving at a constant speed in relation to each other. Above all the speed of light is constant. Classical laws of mechanics seem to be obeyed in our normal lives because the speeds involved are insignificant.

Newton’s recipe for measuring the speed of a body moving through space involved simply timing it as it passed between two fixed points. This is based on the assumptions that time is flowing at the same rate for everyone – that there is such a thing as ‘absolute’ time, and that two observers would always agree on the distance between any two points in space.
The implications of this principle if the observers are moving at different speeds are bizarre and normal indicators of velocity such as distance and time become warped. Absolute space and time do not exist. The faster an object is moving the slower time moves. Objects appear to become shorter in the direction of travel. Mass increases as the speed of an object increases. Ultimately nothing may move faster than or equal to the speed of light because at that point it would have infinite mass, no length and time would stand still.

‘The energy (E) of a body equals its mass (m) times the speed of light (c) squared’

This equation shows that mass and energy are mutually convertible under certain conditions.

The mass-energy equation is a consequence of Einstein’s theory of special relativity and declares that only a small amount of atomic mass could unleash huge amounts of energy.

Two of his early papers described Brownian motion and the ‘photoelectric’ effect (employing PLANCK’s quantum theory and helping to confirm Planck’s ideas in the process).

1915 – Germany

‘Objects do not attract each other by exerting pull, but the presence of matter in space causes space to curve in such a manner that a gravitational field is set up. Gravity is the property of space itself’

From 1907 to 1915 Einstein developed his special theory into a general theory that included equating accelerating forces and gravitational forces. This implies light rays would be bent by gravitational attraction and electromagnetic radiation wavelengths would be increased under gravity. Moreover, mass and the resultant gravity, warps space and time, which would otherwise be ‘flat’, into curved paths that other masses (e.g. the moons of planets) caught within the field of the distortion follow. The predictions from special and general relativity were gradually proven by experimental evidence.

Einstein spent much of the rest of his life trying to devise a unified theory of electromagnetic, gravitational and nuclear fields.   TIMELINE QUANTUM MECHANICS

# NIELS BOHR (1885-1962)

1913 – Denmark

‘Electrons in atoms are restricted to certain orbits but they can move from one orbit to another’

Bohr’s was the first quantum model for the internal structure of the atom.

Bohr worked with RUTHERFORD in Manchester and improved upon Rutherford’s model, which said that electrons were free to orbit the nucleus at random.

Classical physics insisted that electrons moving around the nucleus would eventually expire and collapse into the nucleus as they radiated energy. Bohr resolved the issue surrounding Rutherford’s atomic structure by applying the concept of quantum physics set out by MAX PLANCK in 1900.
He suggested that the electrons would have to exist in one of a number of specific orbits, each being defined by specific levels of energy. From the perspective of quantum theory, electrons only existed in these fixed orbits where they did not radiate energy. The electrons could move to higher-level orbits if energy was added, or fall to lower ones if they gave out energy. The innermost orbit contains up to two electrons. The next may contain up to eight electrons. If an inner orbit is not full, an electron from an outer orbit can jump into it. Energy is released as light (a photon) when this happens. The energy that is released is a fixed amount, a quantum.

Quanta of radiation would only ever be emitted as an atom made the transition between states and released energy. Electrons could not exist in between these definite steps. This quantised theory of the electrons’ orbits had the benefits of explaining why atoms always emitted or absorbed specific frequencies of electromagnetic radiation and of providing an understanding of why atoms are stable.

Bohr calculated the amount of radiation emitted during these transitions using Planck’s constant. It fitted physical observations and made sense of the spectral lines of a hydrogen atom, observed when the electromagnetic radiation (caused by the vibrations of electrons) of the element was passed through a prism.
The prism breaks it up into spectral lines, which show the intensities and frequencies of the radiation – and therefore the energy emissions and absorptions of the electrons.

Each of the elements has an atomic number, starting with hydrogen, with an atomic number of one. The atomic number corresponds to the number of protons in the element’s atoms. Bohr had already shown that electrons inhabit fixed orbits around the nucleus of the atom.
Atoms strive to have a full outer shell (allowed orbit), which gives a stable structure. They may share, give away or receive extra electrons to achieve stability. The way that atoms will form bonds with others, and the ease with which they will do it, is determined by the configuration of electrons.
As elements are ordered in the periodic table by atomic number, it can be seen that their position in the table can be used to predict how they will react.

In addition to showing that electrons are restricted to orbits, Bohr’s model also suggested that

• the orbit closest to the nucleus is lowest in energy, with successively higher energies for more distant orbits.
• when an electron jumps to a lower orbit it emits a photon.
• when an electron absorbs energy, it jumps to a higher orbit.

Although it contained elements of quantum theory, the Bohr model had its flaws. It ignored the wave character of the electron. Work by WERNER KARL HEISENBERG later tackled these weaknesses.

Bohr’s theory of complementarity states that electrons may be both a wave and a particle, but that we can only experience them as one or the other at any given time. He showed that contradictory characteristics of an electron could be proved in separate experiments and none of the results can be accepted singly – we need to hold all the possibilities in mind at once. This requires a slight adjustment to the original model of atomic structure, we can no longer say that an electron occupies a particular orbit, but can only give the probability that it is there.

In 1939 he developed a theory of nuclear fission with Jon Archibald Wheeler (b.1911) and realised that the 235uranium isotope would be more susceptible to fission than the more commonly used 238uranium.
The element bohrium is named after him.   TIMELINE QUANTUM MECHANICS

# LOUIS DE BROGLIE (1892-1987)

1924 – France

‘The wave-particle duality of matter.
Like photons, particles such as electrons also show wave-particle duality, that is, they also behave like light waves’

Einstein had suggested in one of his 1905 papers that the ‘photoelectric’ effect could be explained by an interpretation that included electromagnetic waves behaving like particles. De Broglie simply reversed the argument and asked: ‘if waves can behave like particles (a stream of quanta or photons), why should particles not behave like waves?’

By applying quantum theory de Broglie was able to show that an electron could act as if it were a wave with its wavelength calculated by dividing PLANCK‘s constant by the electron’s momentum at any given instant. His proposal was found to be plausible by experimental evidence shortly afterwards.

BORN, SCHRODINGER and HEISENBERG offered arguments to the debate. NIELS BOHR provided some context in 1927 by pointing out that the equipment used in experiments to prove the case one way or another greatly influenced the outcome of the results. A principle of ‘complementarity’ had to be applied suggesting the experimental proof to be a series of partially correct answers, which have to be interpreted side by side for the most complete picture. Uncertainty and Complementarity together became known as the ‘Copenhagen interpretation’ of quantum mechanics.

Eventually, the ‘probabilistic’ theories of Heisenberg and Born largely won out. At this juncture, cause and effect had logically been removed from atomic physics and de Broglie, like Einstein and Schrödinger, began to question the direction quantum theory was taking and rejected many of its findings.   TIMELINE QUANTUM MECHANICS

# ERWIN SCHRODINGER (1887-1961)

1926 Austria

‘The complex mathematical equation describing the changing wave pattern of a particle such as an electron in an atom. The solution of the equation gives the probability of finding the particle at a particular place’

This equation provides a mathematical description of the wave-like properties of particles. Schrödinger developed what became known as ‘wave mechanics, although like others, including EINSTEIN, he later became uncomfortable with the direction quantum theory took. His own proposal was built upon that of LOUIS DE BROGLIE – that particles could, in quantum theory, behave like waves. Schrödinger felt that de Broglie’s equations were too simplistic and did not offer a detailed enough analysis of the behaviour of matter, particularly at the sub-atomic level. He removed the idea of the particle completely and argued that everything is a form of wave.

PLANCK’s work had shown that light came in different colours because the photons had different amounts of energy. If you divided that energy by the frequency at which that colour of light was known to oscillate, you always arrived at the same value, the so-called Planck’s constant.

Between 1925 and 1926 Schrödinger calculated a ‘wave equation’ that mathematically underpinned his argument. When the theory was applied against known values for the hydrogen atom, for example in calculating the level of energy in an electron, it overcame some of the elements of earlier quantum theory developed by NIELS BOHR and addressed the weaknesses of de Broglie’s thesis.
Schrödinger stated that the quantum energies of electrons did not correspond to fixed orbits, as Bohr had stated, but to the vibration frequency of the ‘electron-wave’ around the nucleus. Just as a piano string has a fixed tone, so an electron wave has a fixed quantum of energy.

Having done away with particles, it was required that a physical explanation for the properties and nature of matter be found. The Austrian came up with the concept of ‘wave packets’ which would give the impression of the particle as seen in classical physics, but would actually be a wave.

The probabilistic interpretation of quantum theory based on the ideas of HEISENBERG and BORN proposed that matter did not exist in any particular place at all, being everywhere at the same time until one attempted to measure it. At that point, the equations offered the best ‘probability’ of finding the matter in a given location. Wave mechanics used much simpler mathematics than Heisenberg’s matrix mechanics, and was easier to visualise.
Schrödinger showed that in mathematical terms, both theories were the same and the rival theories together formed the basis for quantum mechanics.

Schrödinger joined Einstein and others in condemning the probabilistic view of physics where nothing was explainable for certain and cause and effect did not exist.

Ironically, PAUL ADRIAN MAURICE DIRAC went on to prove that Schrödinger’s wave thesis and the probabilistic interpretation were, mathematically at least, the equivalent of each other. Schrödinger shared a Nobel Prize for Physics with Dirac in 1933.   TIMELINE QUANTUM ELECTRODYNAMICS