In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing problems can be generalised to consider unequal spheres, n-dimensional Euclidean space (where the problem becomes circle packing in two dimensions, or hypersphere packing in higher dimensions) or to non-Euclidean spaces such as hyperbolic space.

A typical sphere packing problem is to find an arrangement in which the spheres fill as large a proportion of the space as possible. The proportion of space filled by the spheres is called the density of the arrangement. As the density of an arrangement can vary depending on the volume over which it is measured, the problem is usually to maximise the average or asymptotic density, measured over a large enough volume.

A lattice arrangement (commonly called a regular arrangement) is one in which the centers of the spheres form a very symmetric pattern which only needs n vectors to be uniquely defined (in n-dimensional Euclidean space). Lattice arrangements are periodic. Arrangements in which the spheres do not form a lattice (often referred to as irregular) can still be periodic, but also aperiodic (properly speaking non-periodic) or random. Lattice arrangements are easier to handle than irregular ones—their high degree of symmetry makes it easier to classify them and to measure their densities.

Regular packing

Dense packing

In three-dimensional Euclidean space, the densest packing of equal spheres is achieved by a family of structures called close-packed structures. One method for generating such a structure is as follows. Consider a plane with a compact arrangement of spheres on it. For any three neighbouring spheres, a fourth sphere can be placed on top in the hollow between the three bottom spheres. If we do this "everywhere" in a second plane above the first, we create a new compact layer. A third layer can be placed directly above the first one, or the spheres can be offset, vertically above another set of hollows of the first layer. There are thus three types of planes, called A, B and C.

Two simple arrangements within the close-packed family correspond to regular lattices. One is called cubic close packing (or face centred cubic) — where the layers are alternated in the ABCABC… sequence. The other is called hexagonal close packing — where the layers are alternated in the ABAB… sequence. But many layer stacking sequences are possible (ABAC, ABCBA, ABCBAC, etc.), and still generate a close-packed structure. In all of these arrangements each sphere is surrounded by 12 other spheres, and the average density is :$\backslash frac\{\backslash pi\}\{\backslash sqrt\{18\}\}\; \backslash simeq\; 0.74048.$

Gauss proved in 1831 that these packings have the highest density amongst all possible lattice packings.

In 1611 Johannes Kepler had conjectured that this is the maximum possible density amongst both regular and irregular arrangements — this became known as the Kepler conjecture. In 1998 Thomas Callister Hales, following the approach suggested by László Fejes Tóth in 1953, announced the proof of the Kepler conjecture. Hales' proof is a proof by exhaustion involving checking of many individual cases using complex computer calculations. Referees have said that they are "99% certain" of the correctness of Hales' proof, so the Kepler conjecture has almost certainly been proved.

Jammed packings with a low density

Packings where all spheres are constrained by their neighbours to stay in one location are called rigid or jammed. The jammed sphere packing with the lowest density has a density of only 0.0555.

Irregular packing

If we attempt to build a densely packed collection of spheres we will be tempted to always place the next sphere in a hollow between three packed spheres. If five spheres are assembled in this way, they will be consistent with one of the regularly packed arrangements described above. However, the sixth sphere placed in this way will render the structure inconsistent with any regular arrangement. (Chaikin, 2007). This results in the possibility of a random close packing of spheres which is stable against compression.

When spheres are randomly added to a container and then compressed, they will generally form what is known as an "irregular" or "jammed" packing configuration when they can be compressed no more. This irregular packing will generally have a density of about 64%. Recent research predicts analytically that it cannot exceed a density limit of 63.4% This situation is unlike the case of one or two dimensions, where compressing a collection of 1-dimensional or 2-dimensional spheres (i.e. line segments or disks) will yield a regular packing.

Hypersphere packing

In dimensions higher than three, the densest regular packings of hyperspheres are known up to 8 dimensions. Very little is known about irregular hypersphere packings; it is possible that in some dimensions the densest packing may be irregular. Some support for this conjecture comes from the fact that in certain dimensions (e.g. 10) the densest known irregular packing is denser than the densest known regular packing.

Dimension 24 is special due to the existence of the Leech lattice, which has the best kissing number and is the densest lattice packing. No better irregular packing is known, and at best an irregular packing could improve over the Leech lattice packing by only 2.

Another line of research in high dimensions is trying to find asymptotic bounds for the density of the densest packings. Currently the best known result is that there exists a lattice in dimension n with density bigger or equal to $cn2^\{-n\}$ for some number c.

Unequal sphere packing

Many problems in the chemical and physical sciences can be related to packing problems where more than one size of sphere is available. Here there is a choice between separating the spheres into regions of close-packed equal spheres, or combining the multiple sizes of spheres into a compound or interstitial packing. When many sizes of spheres (or a distribution) are available, the problem quickly becomes untractable, but some studies of binary hard spheres (two sizes) are available.

When the second sphere is much smaller than the first, it is possible to arrange the large spheres in a close-packed arrangement, and then arrange the small spheres within the octahedral and tetrahedral gaps. The density of this interstitial packing depends sensitively on the radius ratio, but in the limit of extreme size ratios, the smaller spheres can fill the gaps with the same density as the larger spheres filled space.

When the smaller sphere has a radius greater than 0.4142 of the radius of the larger sphere, it is no longer possible to fit into even the octahedral holes of the close-packed structure. Thus, beyond this point, either the host structure must expand to accommodate the interstitials (which compromises the overall density), or rearrange into a more complex crystalline compound structure. Structures are known which exceed the close packing density for radius ratios up to 0.623.

Hyperbolic space

Although the concept of circles and spheres can be extended to hyperbolic space, finding the densest packing becomes much more difficult. In a hyperbolic space there is no limit to the number of spheres that can surround another sphere (for example, Ford circles can be thought of as an arrangement of identical hyperbolic circles in which each circle is surrounded by an infinite number of other circles). The concept of average density also becomes much more difficult to define accurately. The densest packings in any hyperbolic space are almost always irregular.

Other spaces

Sphere packing on the corners of a hypercube (with the spheres defined by Hamming distance) corresponds to designing error-correcting codes: if the spheres have radius d, then their centers are codewords of a d-error-correcting code. Lattice packings correspond to linear codes. There are other, subtler relationships between Euclidean sphere packing and error-correcting codes; thus, the binary Golay code is closely related to the 24-dimensional Leech lattice.

See also

Packing problem

Apollonian sphere packing

Hermite constant

Kissing number problem

Close-packing of spheres

Sphere-packing bound

References

Bibliography

T. Aste and D. Weaire "The Pursuit of Perfect Packing" (Institute Of Physics Publishing London 2000) ISBN 0-7503-0648-3

Chaikin, Paul "Reference Frame", Physics Today, June 2007 p8.

Conway, J.H. & Sloane, N.J.H. (1998) "Sphere Packings, Lattices and Groups" (Third Edition). ISBN 0-387-98585-9

External links

Dana Mackenzie (May 2002) A fine mess"">"A fine mess" (New Scientist)

:A non-technical overview of packing in hyperbolic space.

"Kugelpackungen (Sphere Packing)" (T.E. Dorozinski)

"3D Sphere Packing Applet" Sphere Packing java applet

"Densest Packing of spheres into a sphere" java applet

Category:Discrete geometry Category:Crystallography Category:Spheres

ar:تعبئة الكرات de:Dichteste Kugelpackung es:Empaquetamiento de esferas fr:Empilement compact it:Impacchettamento di sfere nl:Hexagonale dichtste stapeling ja:球充填 ru:Упаковка шаров sv:Tätpackade kristallstrukturer zh:最密堆积

Coordinates	43°35′07″N39°43′13″N
name	Max Planck
birth date	April 23, 1858
birth place	Kiel, Duchy of Holstein
death date	October 04, 1947
death place	Göttingen, Lower Saxony, Germany
nationality	German
field	Physics
alma mater	Ludwig Maximilian University of Munich
work institutions	University of KielUniversity of BerlinUniversity of GöttingenKaiser-Wilhelm-Gesellschaft
doctoral advisor	Alexander von Brill
doctoral students	Gustav Ludwig HertzErich KretschmannWalther MeißnerWalter SchottkyMax von LaueMax AbrahamMoritz SchlickWalther BotheJulius Edgar Lilienfeld
known for	Planck constantPlanck postulatePlanck's law of black body radiation
Awards
Religion	Lutheran
Signature	Max Planck signature.svg
Footnotes	He is the father of Erwin Planck who was executed in 1945 by the Gestapo for his part in the July 20 plot. }}

Max Karl Ernst Ludwig Planck, ForMemRS, (April 23, 1858 – October 4, 1947) was a German physicist who is regarded as the founder of the quantum theory, for which he received the Nobel Prize in Physics in 1918.

Life and career

Planck came from a traditional, intellectual family. His paternal great-grandfather and grandfather were both theology professors in Göttingen; his father was a law professor in Kiel and Munich; and his paternal uncle was a judge.

Planck was born in Kiel, Holstein, to Johann Julius Wilhelm Planck and his second wife, Emma Patzig. He was baptised with the name of Karl Ernst Ludwig Marx Planck; of his given names, Marx (a now obsolete variant of Markus or maybe simply an error for Max, which is actually short for Maximilian) was indicated as the primary name. However, by the age of ten he signed with the name Max and used this for the rest of his life.

He was the sixth child in the family, though two of his siblings were from his father's first marriage. Among his earliest memories was the marching of Prussian and Austrian troops into Kiel during the Danish-Prussian war of 1864. In 1867 the family moved to Munich, and Planck enrolled in the Maximilians gymnasium school, where he came under the tutelage of Hermann Müller, a mathematician who took an interest in the youth, and taught him astronomy and mechanics as well as mathematics. It was from Müller that Planck first learned the principle of conservation of energy. Planck graduated early, at age 17. This is how Planck first came in contact with the field of physics.

Planck was gifted when it came to music. He took singing lessons and played piano, organ and cello, and composed songs and operas. However, instead of music he chose to study physics.

The Munich physics professor Philipp von Jolly advised Planck against going into physics, saying, "in this field, almost everything is already discovered, and all that remains is to fill a few holes." Planck replied that he did not wish to discover new things, but only to understand the known fundamentals of the field, and so began his studies in 1874 at the University of Munich. Under Jolly's supervision, Planck performed the only experiments of his scientific career, studying the diffusion of hydrogen through heated platinum, but transferred to theoretical physics.

In 1877 he went to Berlin for a year of study with physicists Hermann von Helmholtz and Gustav Kirchhoff and mathematician Karl Weierstrass. He wrote that Helmholtz was never quite prepared, spoke slowly, miscalculated endlessly, and bored his listeners, while Kirchhoff spoke in carefully prepared lectures which were dry and monotonous. He soon became close friends with Helmholtz. While there he undertook a program of mostly self-study of Clausius's writings, which led him to choose heat theory as his field.

In October 1878 Planck passed his qualifying exams and in February 1879 defended his dissertation, Über den zweiten Hauptsatz der mechanischen Wärmetheorie (On the second law of thermodynamics). He briefly taught mathematics and physics at his former school in Munich.

In June 1880 he presented his habilitation thesis, Gleichgewichtszustände isotroper Körper in verschiedenen Temperaturen (Equilibrium states of isotropic bodies at different temperatures).

Academic career

With the completion of his habilitation thesis, Planck became an unpaid private lecturer in Munich, waiting until he was offered an academic position. Although he was initially ignored by the academic community, he furthered his work on the field of heat theory and discovered one after another the same thermodynamical formalism as Gibbs without realizing it. Clausius's ideas on entropy occupied a central role in his work.

In April 1885 the University of Kiel appointed Planck as associate professor of theoretical physics. Further work on entropy and its treatment, especially as applied in physical chemistry, followed. He proposed a thermodynamic basis for Svante Arrhenius's theory of electrolytic dissociation.

Within four years he was named the successor to Kirchhoff's position at the University of Berlin — presumably thanks to Helmholtz's intercession — and by 1892 became a full professor. In 1907 Planck was offered Boltzmann's position in Vienna, but turned it down to stay in Berlin. During 1909, as University of Berlin professor, eight of his lectures were used by the Ernest Kempton Adams Fund for Physical Research in Theoretical Physics at Columbia University in New York City for a series of lectures translated by Columbia University professor A. P. Wills. He retired from Berlin on January 10, 1926, and was succeeded by Erwin Schrödinger.

Family

In March 1887 Planck married Marie Merck (1861–1909), sister of a school fellow, and moved with her into a sublet apartment in Kiel. They had four children: Karl (1888–1916), the twins Emma (1889–1919) and Grete (1889–1917), and Erwin (1893–1945).

After the apartment in Berlin, the Planck family lived in a villa in Berlin-Grunewald, Wangenheimstraße 21. Several other professors of Berlin University lived nearby, among them theologian Adolf von Harnack, who became a close friend of Planck. Soon the Planck home became a social and cultural centre. Numerous well-known scientists, such as Albert Einstein, Otto Hahn and Lise Meitner were frequent visitors. The tradition of jointly performing music had already been established in the home of Helmholtz.

After several happy years, in July 1909 Marie Planck died, possibly from tuberculosis. In March 1911 Planck married his second wife, Marga von Hoesslin (1882–1948); in December his third son Hermann was born.

During the First World War Planck's second son Erwin was taken prisoner by the French in 1914, while his oldest son Karl was killed in action at Verdun. Grete died in 1917 while giving birth to her first child. Her sister died the same way two years later, after having married Grete's widower. Both granddaughters survived and were named after their mothers. Planck endured these losses stoically.

In January 1945, Erwin, to whom he had been particularly close, was sentenced to death by the Nazi Volksgerichtshof because of his participation in the failed attempt to assassinate Hitler in July 1944. Erwin was executed on 23 January 1945.

Wives: Marie Merck (m. 1887), Marga von Hoesslin (m. 1910)

Children: Karl (1888–1916), twins Emma (1889–1919) and Grete (1889–1917), Erwin (1893–1945), Hermann (1911–1954)

Professor at Berlin University

In Berlin, Planck joined the local Physical Society. He later wrote about this time: "In those days I was essentially the only theoretical physicist there, whence things were not so easy for me, because I started mentioning entropy, but this was not quite fashionable, since it was regarded as a mathematical spook". Thanks to his initiative, the various local Physical Societies of Germany merged in 1898 to form the German Physical Society (Deutsche Physikalische Gesellschaft, DPG); from 1905 to 1909 Planck was the president.

Planck started a six-semester course of lectures on theoretical physics, "dry, somewhat impersonal" according to Lise Meitner, "using no notes, never making mistakes, never faltering; the best lecturer I ever heard" according to an English participant, James R. Partington, who continues: "There were always many standing around the room. As the lecture-room was well heated and rather close, some of the listeners would from time to time drop to the floor, but this did not disturb the lecture". Planck did not establish an actual "school"; the number of his graduate students was only about 20, among them:

:1897 Max Abraham (1875–1922) :1904 Moritz Schlick (1882–1936) :1906 Walther Meißner (1882–1974) :1906 Max von Laue (1879–1960) :1907 Fritz Reiche (1883–1960) :1912 Walter Schottky (1886–1976) :1914 Walther Bothe (1891–1957)

Black-body radiation

In 1894 Planck turned his attention to the problem of black-body radiation. He had been commissioned by electric companies to create maximum light from lightbulbs with minimum energy. The problem had been stated by Kirchhoff in 1859: "how does the intensity of the electromagnetic radiation emitted by a black body (a perfect absorber, also known as a cavity radiator) depend on the frequency of the radiation (i.e., the color of the light) and the temperature of the body?". The question had been explored experimentally, but no theoretical treatment agreed with experimental values. Wilhelm Wien proposed Wien's law, which correctly predicted the behaviour at high frequencies, but failed at low frequencies. The Rayleigh–Jeans law, another approach to the problem, created what was later known as the "ultraviolet catastrophe", but contrary to many textbooks this was not a motivation for Planck.

Planck's first proposed solution to the problem in 1899 followed from what Planck called the "principle of elementary disorder", which allowed him to derive Wien's law from a number of assumptions about the entropy of an ideal oscillator, creating what was referred-to as the Wien–Planck law. Soon it was found that experimental evidence did not confirm the new law at all, to Planck's frustration. Planck revised his approach, deriving the first version of the famous Planck black-body radiation law, which described the experimentally observed black-body spectrum well. It was first proposed in a meeting of the DPG on October 19, 1900 and published in 1901. This first derivation did not include energy quantisation, and did not use statistical mechanics, to which he held an aversion. In November 1900, Planck revised this first approach, relying on Boltzmann's statistical interpretation of the second law of thermodynamics as a way of gaining a more fundamental understanding of the principles behind his radiation law. As Planck was deeply suspicious of the philosophical and physical implications of such an interpretation of Boltzmann's approach, his recourse to them was, as he later put it, "an act of despair ... I was ready to sacrifice any of my previous convictions about physics." The central assumption behind his new derivation, presented to the DPG on 14 December 1900, was the supposition, now known as the Planck postulate, that electromagnetic energy could be emitted only in quantized form, in other words, the energy could only be a multiple of an elementary unit $E\; =\; h\; \backslash nu$, where $h$ is Planck's constant, also known as Planck's action quantum (introduced already in 1899), and $\backslash nu$ (the Greek letter nu, not the Roman letter v) is the frequency of the radiation. Note that the elementary units of energy discussed here are represented by $h\; \backslash nu$ and not simply by $h$. Physicists now call these quanta photons, and a photon of frequency $\backslash nu$ will have its own specific and unique energy. The amplitude of energy at that frequency is then a function of the number of photons of that frequency being produced per unit of time.

At first Planck considered that quantisation was only "a purely formal assumption ... actually I did not think much about it..."; nowadays this assumption, incompatible with classical physics, is regarded as the birth of quantum physics and the greatest intellectual accomplishment of Planck's career (Ludwig Boltzmann had been discussing in a theoretical paper in 1877 the possibility that the energy states of a physical system could be discrete). Further interpretation of the implications of Planck's work was advanced by Albert Einstein in 1905 in connection with his work on the photoelectric effect—for this reason, the philosopher and historian of science Thomas Kuhn argued that Einstein should be given credit for quantum theory more so than Planck, since Planck did not understand in a deep sense that he was "introducing the quantum" as a real physical entity. Be that as it may, it was in recognition of Planck's monumental accomplishment that he was awarded the Nobel Prize in Physics in 1918.

The discovery of Planck's constant enabled him to define a new universal set of physical units (such as the Planck length and the Planck mass), all based on fundamental physical constants.

Subsequently, Planck tried to grasp the meaning of energy quanta, but to no avail. "My unavailing attempts to somehow reintegrate the action quantum into classical theory extended over several years and caused me much trouble." Even several years later, other physicists like Rayleigh, Jeans, and Lorentz set Planck's constant to zero in order to align with classical physics, but Planck knew well that this constant had a precise nonzero value. "I am unable to understand Jeans' stubbornness — he is an example of a theoretician as should never be existing, the same as Hegel was for philosophy. So much the worse for the facts if they don't fit."

Max Born wrote about Planck: "He was by nature and by the tradition of his family conservative, averse to revolutionary novelties and skeptical towards speculations. But his belief in the imperative power of logical thinking based on facts was so strong that he did not hesitate to express a claim contradicting to all tradition, because he had convinced himself that no other resort was possible."

Einstein and the theory of relativity

In 1905 the three epochal papers of the hitherto completely unknown Albert Einstein were published in the journal Annalen der Physik. Planck was among the few who immediately recognized the significance of the special theory of relativity. Thanks to his influence this theory was soon widely accepted in Germany. Planck also contributed considerably to extend the special theory of relativity.

Einstein's hypothesis of light quanta (photons), based on Philipp Lenard's 1902 discovery of the photoelectric effect, was initially rejected by Planck. He was unwilling to discard completely Maxwell's theory of electrodynamics. "The theory of light would be thrown back not by decades, but by centuries, into the age when Christian Huygens dared to fight against the mighty emission theory of Isaac Newton ..."

In 1910 Einstein pointed out the anomalous behavior of specific heat at low temperatures as another example of a phenomenon which defies explanation by classical physics. Planck and Nernst, seeking to clarify the increasing number of contradictions, organized the First Solvay Conference (Brussels 1911). At this meeting Einstein was able to convince Planck.

Meanwhile Planck had been appointed dean of Berlin University, whereby it was possible for him to call Einstein to Berlin and establish a new professorship for him (1914). Soon the two scientists became close friends and met frequently to play music together.

World War I

At the onset of the First World War Planck endorsed the general excitement of the public, writing that, "Besides much that is horrible, there is also much that is unexpectedly great and beautiful: the smooth solution of the most difficult domestic political problems by the unification of all parties (and) ... the extolling of everything good and noble."

Nonetheless, Planck refrained from the extremes of nationalism. In 1915, at a time when Italy was about to join the Allied Powers, he voted successfully for a scientific paper from Italy, which received a prize from the Prussian Academy of Sciences, where Planck was one of four permanent presidents.

Planck also signed the infamous "Manifesto of the 93 intellectuals", a pamphlet of polemic war propaganda (while Einstein retained a strictly pacifistic attitude which almost led to his imprisonment, being spared by his Swiss citizenship). But in 1915 Planck, after several meetings with Dutch physicist Lorentz, he revoked parts of the Manifesto. Then in 1916 he signed a declaration against German annexationism.

Post War and Weimar Republic

In the turbulent post-war years, Planck, now the highest authority of German physics, issued the slogan "persevere and continue working" to his colleagues.

In October 1920 he and Fritz Haber established the Notgemeinschaft der Deutschen Wissenschaft (Emergency Organization of German Science), aimed at providing financial support for scientific research. A considerable portion of the monies the organization would distribute were raised abroad.

Planck also held leading positions at Berlin University, the Prussian Academy of Sciences, the German Physical Society and the Kaiser-Wilhelm-Gesellschaft (which in 1948 became the Max-Planck-Gesellschaft). During this time economic conditions in Germany were such that he was hardly able to conduct research.

During the interwar period, Planck became a member of the Deutsche Volks-Partei (German People's Party), the party of Nobel Peace Prize laureate Gustav Stresemann, which aspired to liberal aims for domestic policy and rather revisionistic aims for international politics.

Planck disagreed with the introduction of universal suffrage and later expressed the view that the Nazi dictatorship resulted from "the ascent of the rule of the crowds".

Quantum mechanics

At the end of the 1920s Bohr, Heisenberg and Pauli had worked out the Copenhagen interpretation of quantum mechanics, but it was rejected by Planck, as well as Schrödinger, Laue, and Einstein. Planck expected that wave mechanics would soon render quantum theory—his own child—unnecessary. This was not to be the case, however. Further work only cemented quantum theory, even against his and Einstein's philosophical revulsions. Planck experienced the truth of his own earlier observation from his struggle with the older views in his younger years: "A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it."

Nazi dictatorship and The Second World War

When the Nazis seized power in 1933, Planck was 74. He witnessed many Jewish friends and colleagues expelled from their positions and humiliated, and hundreds of scientists emigrated from Germany. Again he tried the "persevere and continue working" slogan and asked scientists who were considering emigration to remain in Germany. He hoped the crisis would abate soon and the political situation would improve. There was also a deeper argument against emigration. Emigrating German non-Jewish scientists would need to look for academic positions abroad, but these positions better served Jewish scientists, who had no chance of continuing to work in Germany.

Hahn asked Planck to gather well-known German professors in order to issue a public proclamation against the treatment of Jewish professors, but Planck replied, "If you are able to gather today 30 such gentlemen, then tomorrow 150 others will come and speak against it, because they are eager to take over the positions of the others." Under Planck's leadership, the Kaiser-Wilhelm-Gesellschaft (KWG) avoided open conflict with the Nazi regime, except concerning Fritz Haber. Planck tried to discuss the issue with Adolf Hitler but was unsuccessful. In the following year, 1934, Haber died in exile.

One year later, Planck, having been the president of the KWG since 1930, organized in a somewhat provocative style an official commemorative meeting for Haber. He also succeeded in secretly enabling a number of Jewish scientists to continue working in institutes of the KWG for several years. In 1936, his term as president of the KWG ended, and the Nazi government pressured him to refrain from seeking another term.

As the political climate in Germany gradually became more hostile, Johannes Stark, prominent exponent of Deutsche Physik ("German Physics", also called "Aryan Physics") attacked Planck, Sommerfeld and Heisenberg for continuing to teach the theories of Einstein, calling them "white Jews." The "Hauptamt Wissenschaft" (Nazi government office for science) started an investigation of Planck's ancestry, but all they could find out was that he was "1/16 Jewish."

In 1938 Planck celebrated his 80th birthday. The DPG held a celebration, during which the Max-Planck medal (founded as the highest medal by the DPG in 1928) was awarded to French physicist Louis de Broglie. At the end of 1938 the Prussian Academy lost its remaining independence and was taken over by Nazis (Gleichschaltung). Planck protested by resigning his presidency. He continued to travel frequently, giving numerous public talks, such as his talk on Religion and Science, and five years later he was sufficiently fit to climb 3,000-meter peaks in the Alps.

During the Second World War, the increasing number of Allied bombing campaigns against Berlin forced Planck and his wife to leave the city temporarily and live in the countryside. In 1942 he wrote: "In me an ardent desire has grown to persevere this crisis and live long enough to be able to witness the turning point, the beginning of a new rise." In February 1944 his home in Berlin was completely destroyed by an air raid, annihilating all his scientific records and correspondence. Finally, he got into a dangerous situation in his rural retreat because of the rapid advance of the Allied armies from both sides. After the end of the war he was brought to a relative in Göttingen.

Planck endured many personal tragedies after the age of 50. In 1909, his first wife died after 22 years of marriage, leaving him with two sons and twin daughters. Planck's oldest son, Karl, was killed in action in 1916. His daughter Margarete died in childbirth in 1917, and another daughter, Emma, married her late sister's husband and then also died in childbirth, in 1919. During World War II, Planck's house in Berlin was completely destroyed by bombs in 1944 and his youngest son, Erwin, was implicated in the attempt made on Hitler's life in the July 20 plot. Consequently, Erwin died at the hands of the Gestapo in 1945. Erwin's death destroyed Planck's will to live. By the end of the war, Planck, his second wife and his son by her, moved to Göttingen where he died on October 4, 1947.

Religious view

Planck was very tolerant towards alternative views and religions, and so was discontented with the Nazi church organizations' demands for unquestioning belief.

In a lecture on 1937 entitled "Religion und Naturwissenschaft" he suggested the importance of these symbols and rituals related directly with a believer's ability to worship god, but that one must be mindful that the symbols provide an imperfect illustration of divinity. He criticised atheism for being focussed on the derision of such symbols, while at the same time warned of the over-estimation of the importance of such symbols by believers.

Max Planck said "All matter originates and exists only by virtue of a force which brings the particle of an atom to vibration and holds this most minute solar system of the atom together. We must assume behind this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter" in 1944, indicating that he believed in some kind of God.

Planck regarded the scientist as a man of imagination and faith, "faith" interpreted as being similar to "having a working hypothesis". For example the causality principle isn't true or false, it is an act of faith. Thereby Planck may have indicated a view that points toward Imre Lakatos' research programs process descriptions, where falsification is mostly tolerable, in faith of its future removal.

On the other hand, Planck wrote, "...'to believe' means 'to recognize as a truth,' and the knowledge of nature, continually advancing on incontestably safe tracks, has made it utterly impossible for a person possessing some training in natural science to recognize as founded on truth the many reports of extraordinary contradicting the laws of nature, of miracles which are still commonly regarded as essential supports and confirmations of religious doctrines, and which formerly used to be accepted as facts pure and simple, without doubt or criticism.. The belief in miracles must retreat step by step before relentlessly and reliably progressing science and we cannot doubt that sooner or later it must vanish completely."

Six months before his death a rumour started that Planck had converted to Catholicism, but when questioned what had brought him to make this step, he declared that, although he had always been deeply religious, he did not believe "in a personal God, let alone a Christian God."

Honors and awards

"Pour le Mérite" for Science and Arts 1915 (in 1930 he became chancellor of this order)

Nobel Prize in Physics 1918 (awarded 1919)

Lorentz Medal 1927

Franklin Medal (1927)

Adlerschild des Deutschen Reiches (1928), an award from the German Reich President

Max Planck medal (1929, together with Einstein)

Copley Medal (1929)

Planck received honorary doctorates from the universities of Frankfurt, Munich (TH), Rostock, Berlin (TH), Graz, Athens, Cambridge, London, and Glasgow.

The asteroid 1069 was named "Stella Planckia" by the International Astronomical Union (1938)

Publications

Planck, Max. (1897). Vorlesungen über Thermodynamik

Planck, Max. (1900). “Entropy and Temperature of Radiant Heat.” Annalen der Physik, vol. 1. no 4. April, pg. 719–37.

Planck, Max. (1901). "On the Law of Distribution of Energy in the Normal Spectrum". Annalen der Physik, vol. 4, p. 553 ff.

See also

{| |- |valign="top"|

Planck units

*Planck length

*Planck mass

*Planck time

*Planck temperature

*Planck charge

Derived Planck units

*Planck current

*Planck power

*Planck density

|valign="top"|

Planck's law of black body radiation

Planck epoch

Planck particle

Planck postulate

Max-Planck-Gesellschaft

Planck (crater)

Max Planck Society

Planck Surveyor

Photon polarization

|}

German inventors and discoverers

References

Bibliography

Aczel, Amir D. Entanglement, Chapter 4. (Penguin, 2003) ISBN 9780452284579

Pickover, Clifford A. Archimedes to Hawking: Laws of Science and the Great Minds Behind Them, Oxford University Press, 2008, ISBN 978-0195336115

Rosenthal-Schneider, Ilse Reality and Scientific Truth: Discussions with Einstein, von Laue, and Planck (Wayne State University, 1980) ISBN 0-8143-1650-6

External links

Biographies

Annotated bibliography for Max Planck from the Alsos Digital Library for Nuclear Issues

Max Planck – Encyclopædia Britannica article

Max Planck Biography – www.nobel-prize-winners.com

Max Planck Institutes of Natural Science and Astrophysics

Cinematic self portrait of Max Planck, Berlin-Brandenburgische Akademie der Wissenschaften, 1942

Nobel Biography

Articles

Life–Work–Personality – Exhibition on the 50th anniversary of Planck's death

Max Planck, Planck's constant, and Schrodinger's Cat

Category:1858 births Category:1947 deaths Category:People from Kiel Category:People from the Duchy of Holstein Category:German Nobel laureates Category:German physicists Category:Members of the Pontifical Academy of Sciences Category:Members of the Prussian Academy of Sciences Category:Nobel laureates in Physics Category:Recipients of the Copley Medal Category:Quantum physicists Category:Optical physicists Category:Recipients of the Pour le Mérite (civil class) Category:Theoretical physicists Category:Thermodynamicists Category:German People's Party politicians Category:Sondershäuser Verband members Category:Ludwig Maximilian University of Munich alumni Category:Ludwig Maximilian University of Munich faculty Category:Humboldt University of Berlin alumni Category:Humboldt University of Berlin faculty Category:University of Kiel faculty Category:German Christians Category:Fellows of the Leopoldina Category:Members of the Bavarian Maximilian Order for Science and Art

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