A BRIEF BIOGRAPHY OF MAX PLANCK

It is our experience that all objects become luminous when heated to a sufficiently high temperature. For instance, a bar of iron placed in a hot flame will, at first, show little effect, but after a while it will begin to glow dark red, then bright red, orange, yellowish-white and eventually, if the temperature of the flame is high enough, white-hot before it melts. Indeed, this was how light was produced by the flame of an old-fashioned gas burner playing on a 'mantle', made of a high temperature oxide. Now, light is produced by the hot filament of an electric light bulb, and on the cosmic scale our Sun and all stars emit light because of their surface are very hot. A heating coil on a typical kitchen range when red-hot is at a temperature of about 600-700oC, the filament of an electrical light bulb, at about 2000oC, emits a bright, white light (although an electric arc at 3000-4000oC looks even 'whiter') and our Sun has a surface temperature of about 5800oC. On the other hand even though visible light may not be apparent we know that one can still get and feel radiant heat. Thus, one concludes that

There is a characteristic distribution of intensity between the various wavelengths, with a maximum intensity at some wavelength characteristic of the temperature of the object. This observation led to two important laws discovered in the final decades of the 19th century.

In 1879 Josef Stefan (1835-1893) pointed out that some measurements by John Tyndall (1820-1893) of the rate of loss of heat from a hot wire, showed that

Several years later, Ludwig Boltzmann (1844-1906) was able to derive this relationship, now known as the Stefan-Boltzmann law, by applying thermodynamic reasoning to Maxwell's electromagnetic theory. Wien's displacement law was established by the German physicist Wilhelm Wien (1864-1928) in 1893. He concluded that:

It was verified in the final years of the 19th century and partly for this work, Wien was awarded the Nobel Prize in 1911. By measuring the intensity distribution of wavelengths of the radiation emitted from a hot object one can determine its surface temperature; the surface temperature of the Sun inferred by this method is about 5800 K. At very high temperatures, for example, at the surfaces of some stars, the maximum wavelength may be much shorter than the visible region and fall in the ultra-violet region. Similarly, because of their (lower) temperature, some stars emit only invisible infrared radiation.

Above, reference was made to a 'black body'. A black body, defined by the German physicist Gustav Kirchoff (1824-1887), is an object which at all temperatures absorbs completely all the radiation falling on it. Furthermore, as we have seen above, at any given temperature it emits a characteristic continuous spectrum of wavelengths of radiation that depends only on the temperature of the black body and not what it's made of. While an ideal black body is not really found in practice, it can be approximated by a hollow enclosure, painted black on the inside, with a very small opening in the wall. So, radiation entering the hole has little chance of escaping; rather it is gradually absorbed by repeated contact with the internal surfaces of the object. Similarly, if the enclosure is heated, the radiation coming from the hole is effectively black body radiation.

The kinetic theory of gases was reasonably developed at that time also. In particular, it considered heat to be the result of the random motion of the numerous individual molecules of which all material bodies are made of. Since it would not be possible (and indeed senseless) to follow the motion of each individual molecule, the mathematical description was necessarily statistical, i.e., averages taken over a large number. One of the basic laws of Statistical Mechanics, which is the study of the average properties of large ensembles (collections) of particles involved in random motion, is the equipartition theorem that states that:

So, if all the particles are identical (as in a pure gas) they will all have on the average equal velocities and equal kinetic energies [1]. However, while the equipartition theorem governs the average distribution of energies and velocities among the members of a large ensemble, one must remember that the energies and velocities of individual particles may deviate from the averages, a phenomenon known as statistical fluctuations. Maxwell calculated these fluctuations mathematically - called a Maxwellian distribution - and the use of these ideas was very successful in explaining the thermal properties of gases.

Here the successes of the individual ideas of thermal radiation and the statistical methods ended. The principles of Newton's mechanics, Maxwell's electromagnetic theory and thermodynamics could not account for the distribution of energy in black body radiation. The classical approach was straightforward; the emission of radiation was believed to be due to the oscillating charges within the body. It was assumed that the vibrations occurred at different frequencies and it was the variation of their relative intensities that determined the shape of the characteristic black body spectrum. The general idea therefore was to consider a very large number of oscillators having all possible frequencies, impose the condition that they be in thermal equilibrium with one another at the temperature in question and then determine what the distribution of intensities among the different oscillators satisfied these requirements. Wien proposed one variant that agreed with experiment at short wavelengths. Lord Rayleigh (John William Strutt, 1842-1919) suggested another based on the modes of vibration of the electromagnetic field within an enclosure, later developed by James Jeans (1877-1946), that matched the spectrum only at long wavelengths and resulted in the so-called 'ultra-violet catastrophe'. So, neither one was able to provide a completely proper account and the paradoxes remained.

In a historic paper entitled On the law of Distribution of Energy in the Normal Spectrum, which was reported to the German Physical Society at the end of 1900, Max Planck made an extraordinary proposal. He states that if UN is the total vibrational energy of the system of oscillators then:

Here, he breaks away from the idea of 'classical' physics where the energy of an oscillator depends only on the frequency and amplitude, with no restrictions whatsoever on either. Later in the paper Planck says:

This statement is the well-known expression for the energy of a quantum of radiation and h is now known as Planck's constant. Planck deduced a value for h (=6.55 x 10-34 J.s) that was a little smaller than today's accepted value (=6.626 x 10-34 J.s).

It is, perhaps, difficult to realize that these simple statements - the quantum postulates - completely revolutionized physics! At the time, the idea that processes could be discontinuous was not easy to accept. It was not until the hypothesis proved successful in many applications that it was properly accepted in spite of the awkward philosophical questions it posed. In 1938, Niels Bohr (1885-1962) wrote:

Planck received the Nobel prize for physics in 1918 at the age of forty-two for the discovery of the quantum of energy.

Max Karl Ernst Ludwig Planck was born in Kiel, Germany on April 23, 1858, into an academic family. His father was a professor of constitutional law at the University and both his grandfather and great-grandfather had been professors of theology at Göttingen. Planck lived through several chapters of German history; as Max von Laue said in his memorial address on Planck's death:

The family moved to Munich in 1867 and Planck attended the Maximilian Gymnasium (high school) where he developed an interest in physics. Apparently, his early life was uneventful. At age seventeen he entered the University of Munich, where he studied physics for three years. He says he chose physics because:

The following year he went to the University of Berlin and came into contact with several influential and distinguished scientists of that period; Hermann von Helmholtz (1821-1894), Gustav Kirchoff - he wrote that he admired Kirchoff greatly but found him dry and monotonous as a teacher - and Rudolph Clausius (1822-1888). He became interested in theory of heat - thermodynamics - while in Berlin and in 1879 he returned to the University of Munich and presented his Ph.D dissertation in the Second Law of Thermodynamics. He received his degree summa cum laude and became an instructor at the University in 1880. In 1885 he accepted an associate professor position in theoretical physics at the University of Kiel. Following the death of Kirchoff in 1889 Planck was invited to take his place at the University of Berlin. In 1892 he became a full professor, a position he kept until his retirement at age seventy. He continued his studies of thermodynamics publishing a classical treatise on the subject in 1897. By 1900 his studies in thermodynamics and electromagnetic radiation brought him to the problem of the distribution of energy from a black body, which he solved by introducing the quantum hypothesis; the climax of his work.

Planck continued teaching and writing for many years and was gratified to see that the early opposition to his revolutionary idea gradually turned into cautious acceptance, then enthusiastic and widespread approval. In 1905 Albert Einstein (1879-1955) adopted the quantum hypothesis to account for the photoelectric effect [2] and in 1907 he used it to explain the variation of the specific heat of solids with temperature; each of these theories contributed significantly to the acceptance of Planck's idea. However, probably the most important use occurred in 1913 when Niels Bohr proposed his theory of atomic structure and the origin of atomic spectra. Planck himself explains how despite having invented quantum theory he did not really understand it at first:

He held a number of distinguished professional positions during his life, including permanent secretary to the Prussian Academy of Science (1912-1943), elected as a foreign member of the Royal Society (1926), and president of the Kaiser Wilhelm Institute for the Advancement of Science (1930-1937), the main German research organization.

Planck's latter years were rather unhappy ones. He remained in Germany during WWII suffering several personal losses, including a son, Erwin, who was executed for alleged complicity in the ill-fated plot to assassinate Hitler and overthrow the Nazi regime towards the end of the war. He witnessed the efforts of this regime, including those of some colleagues, to create German Physics in which the discoveries of Einstein and other Jewish scientists were to play only a minor role. The war had a very serious impact on Planck; Heilbron [3] writes:

After WWII Planck again became President of the Kaiser Wilhelm Institute in 1945-1946 and for the second time defended German science through another period of exceptional difficulty. When he died on October 4, 1947 he could probably find little consolation in the knowledge that the attempts to establish a German dictatorship in science had failed, for the Third Reich had all but destroyed the great tradition of physics in Germany. Although he made no contribution to astronomy, one of the recently discovered asteroids was named Planckiana in his honor.

FOOTNOTES

[1] If E is the total energy of the gas and there are N particles, then the average energy per particle is E/N. If we have a mixture made up of two different gases, the more massive molecules will have smaller velocities, and vice versa, so that all the molecules will have the same average kinetic energy. Thus, in a mixture of hydrogen and oxygen, the oxygen atoms, which are 16 times more massive than hydrogen atoms, will have a velocity that is times smaller than the latter.

[2] Einstein received the Nobel prize in 1921 for his explanation of the photoelectric effect. He introduced the concept of photons, i.e., that light travels in discrete bundles of energy that sometimes behave as waves and sometimes as particles; each photon is a packet of electromagnetic waves of the same frequency, hence the same energy.

[3] J.L. Heilbron, The dilemmas of an upright man: Max Plank as spokesman for German Science (Berkeley, 1986).

REFERENCES

Books

M. Shamos Great Experiments in Physics (Dover Publications Inc., New York - 1987).

George Gamow Thirty Years that Shook Physics (Dover Publications Inc., New York - 1985).

Web-sites