Max Born in the context of Halogen

Indeterminism is the idea that events (or certain events, or events of certain types) are not caused, or are not caused deterministically.

It is the opposite of determinism and related to chance. It is highly relevant to the philosophical problem of free will, particularly in the form of metaphysical libertarianism. In science, most specifically quantum theory in physics, indeterminism is the belief that no event is certain and the entire outcome of anything is probabilistic. Heisenberg's uncertainty principle and the "Born rule", proposed by Max Born, are often starting points in support of the indeterministic nature of the universe. Indeterminism is also asserted by Sir Arthur Eddington, and Murray Gell-Mann. Indeterminism has been promoted by the French biologist Jacques Monod's essay "Chance and Necessity".The physicist-chemist Ilya Prigogine argued for indeterminism in complex systems.

The University of Göttingen, officially the Georg August University of Göttingen (German: Georg-August-Universität Göttingen, commonly referred to as Georgia Augusta), is a public research university in the city of Göttingen, Lower Saxony, Germany. Founded in 1734 by George II, King of Great Britain and Elector of Hanover, it began instruction in 1737 and is recognized as the oldest university in Lower Saxony. Recognized for its historic and traditional significance, the university has affiliations with 47 Nobel Prize winners by its own count.

The University of Göttingen reached its academic peak from the late 19th to early 20th century, establishing itself as a major international center for mathematics and physics. During this period, scholars such as David Hilbert, Felix Klein, Max Born, and Ludwig Prandtl conducted influential research in mathematics, quantum mechanics, and aerodynamics. The university attracted international students, including prominent Americans such as Edward Everett, George Bancroft, John Lothrop Motley, and J. Robert Oppenheimer. This prominence was severely disrupted by the Nazi rise to power in 1933, when the "great purge" resulted in the dismissal or emigration of numerous faculty members, including many of Jewish origin or those opposed to the regime. The university was subsequently reopened under British control in 1945 and began a process of academic reconstruction.

Goethe University Frankfurt (German: Johann Wolfgang Goethe-Universität Frankfurt am Main) is a public research university located in Frankfurt am Main, Germany. It was founded in 1914 as a citizens' university, which means it was founded and funded by the wealthy and active liberal citizenry of Frankfurt. The original name in German was Universität Frankfurt am Main (University of Frankfurt am Main). In 1932, the university's name was extended in honour of one of the most famous native sons of Frankfurt, the poet, philosopher and writer/dramatist Johann Wolfgang von Goethe. The university currently has around 48,000 students, distributed across four major campuses within the city.

The university celebrated its 100th anniversary in 2014. The first female president of the university, Birgitta Wolff, was sworn into office in 2015, and was succeeded by Enrico Schleiff in 2021. 20 Nobel Prize winners have been affiliated with the university, including Max von Laue and Max Born. The university is also affiliated with 18 winners of the Gottfried Wilhelm Leibniz Prize.

Werner Karl Heisenberg (/ˈhaɪ.zən.bɜːrɡ/; German: [ˈvɛʁnɐ ˈhaɪzn̩bɛʁk] ; 5 December 1901 – 1 February 1976) was a German theoretical physicist, one of the main pioneers of the theory of quantum mechanics and a principal scientist in the German nuclear program during World War II.

Heisenberg published his Umdeutung paper in 1925, a major reinterpretation of old quantum theory. In the subsequent series of papers with Max Born and Pascual Jordan, during the same year, his matrix formulation of quantum mechanics was substantially elaborated. He is known for the uncertainty principle, which he published in 1927. He received the Nobel Prize in Physics in 1932 "for the creation of quantum mechanics".

The Born rule is a postulate of quantum mechanics that gives the probability that a measurement of a quantum system will yield a given result. In one commonly used application, it states that the probability density for finding a particle at a given position is proportional to the square of the amplitude of the system's wavefunction at that position. It was formulated and published by German physicist Max Born in July 1926.

The Copenhagen interpretation is a collection of views about the meaning of quantum mechanics, stemming from the work of Niels Bohr, Werner Heisenberg, Max Born, and others. While "Copenhagen" refers to the city where Bohr and Heisenberg worked, the use as an "interpretation" was apparently coined by Heisenberg during the 1950s to refer to ideas developed in the 1925–1927 period, glossing over his disagreements with Bohr. Consequently, there is no definitive historical statement of what the interpretation entails.

Features common across versions of the Copenhagen interpretation include the idea that quantum mechanics is intrinsically indeterministic, with probabilities calculated using the Born rule, and the principle of complementarity, which states that objects have certain pairs of complementary properties that cannot all be observed or measured simultaneously. Moreover, the act of "observing" or "measuring" an object is irreversible, and no truth can be attributed to an object except according to the results of its measurement (that is, the Copenhagen interpretation rejects counterfactual definiteness). Copenhagen-type interpretations hold that quantum descriptions are objective, in that they are independent of physicists' personal beliefs and other arbitrary mental factors.

J. Robert Oppenheimer (born Julius Robert Oppenheimer /ˈɒpənhaɪmər/ OP-ən-hy-mər; April 22, 1904 – February 18, 1967) was an American theoretical physicist who served as the director of the Manhattan Project's Los Alamos Laboratory during World War II. He is often called the "father of the atomic bomb" for his role in overseeing the development of the first nuclear weapons.

Born in New York City, Oppenheimer obtained a degree in chemistry from Harvard University in 1925 and a doctorate in physics from the University of Göttingen in Germany in 1927, studying under Max Born. After research at other institutions, he joined the physics faculty at the University of California, Berkeley, where he was made a full professor in 1936.

The history of quantum mechanics is a fundamental part of the history of modern physics. The major chapters of this history begin with the emergence of quantum ideas to explain individual phenomena—blackbody radiation, the photoelectric effect, solar emission spectra—an era called the Old or Older quantum theories.

Building on the technology developed in classical mechanics, the invention of wave mechanics by Erwin Schrödinger and expansion by many others triggers the "modern" era beginning around 1925. Paul Dirac's relativistic quantum theory work led him to explore quantum theories of radiation, culminating in quantum electrodynamics, the first quantum field theory. The history of quantum mechanics continues in the history of quantum field theory. The history of quantum chemistry, theoretical basis of chemical structure, reactivity, and bonding, interlaces with the events discussed in this article.

In quantum mechanics, a probability amplitude is a complex number used for describing the behaviour of systems. The square of the modulus of this quantity at a point in space represents a probability density at that point.

Probability amplitudes provide a relationship between the quantum state vector of a system and the results of observations of that system, a link that was first proposed by Max Born, in 1926. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding, and the probability thus calculated is sometimes called the "Born probability". These probabilistic concepts, namely the probability density and quantum measurements, were vigorously contested at the time by the original physicists working on the theory, such as Schrödinger and Einstein. It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics—topics that continue to be debated even today.

Fritz Jakob Haber (German: [ˈfʁɪt͡s ˈhaːbɐ] ; 9 December 1868 – 29 January 1934) was a German chemist who received the Nobel Prize in Chemistry in 1918 for his invention of the Haber process, a method used in industry to synthesize ammonia from nitrogen gas and hydrogen gas. This invention is important for the large-scale synthesis of fertilizers and explosives. It is estimated that a third of annual global food production uses ammonia from the Haber–Bosch process, and that this food supports nearly half the world's population. For this work, Haber has been called one of the most important scientists and industrial chemists in human history. Haber also, along with Max Born, proposed the Born–Haber cycle as a method for evaluating the lattice energy of an ionic solid.

Haber, a known German nationalist, is also considered the "father of chemical warfare" for his years of pioneering work developing and weaponizing chlorine and other poisonous gases during World War I. He first proposed the use of the heavier-than-air chlorine gas as a weapon to break the trench deadlock during the Second Battle of Ypres. His work was later used, without his direct involvement, to develop the Zyklon B pesticide used for the killing of more than 1 million Jews in gas chambers in the greater context of the Holocaust.

Walther Wilhelm Georg Bothe (German: [ˈvaltɐ ˈboːtə] ; 8 January 1891 – 8 February 1957) was a German experimental physicist who shared the 1954 Nobel Prize in Physics with Max Born "for the coincidence method and his discoveries made therewith."

Bothe served in the military during World War I from 1914, and he was a prisoner of war of the Russians, returning to Germany in 1920. Upon his return to the laboratory, he developed and applied coincidence circuits to the study of nuclear reactions, such as the Compton effect, cosmic rays, and the wave–particle duality of radiation.

In quantum chemistry and molecular physics, the Born–Oppenheimer (BO) approximation is the assumption that the wave functions of atomic nuclei and electrons in a molecule can be treated separately, based on the fact that the nuclei are much heavier than the electrons. Due to the larger relative mass of a nucleus compared to an electron, the coordinates of the nuclei in a system are approximated as fixed, while the coordinates of the electrons are dynamic. The approach is named after Max Born and his 23-year-old graduate student J. Robert Oppenheimer, the latter of whom proposed it in 1927 during a period of intense foment in the development of quantum mechanics.

The approximation is widely used in quantum chemistry to speed up the computation of molecular wavefunctions and other properties for large molecules. There are cases where the assumption of separable motion no longer holds, which make the approximation lose validity (it is said to "break down"), but even then the approximation is usually used as a starting point for more refined methods.

The Born–Haber cycle is an approach to analyze reaction energies. It was named after two German scientists, Max Born and Fritz Haber, who developed it in 1919. It was also independently formulated by Kazimierz Fajans and published concurrently in the same journal. The cycle is concerned with the formation of an ionic compound from the reaction of a metal (often a Group I or Group II element) with a halogen or other non-metallic element such as oxygen.

Born–Haber cycles are used primarily as a means of calculating lattice energy (or more precisely enthalpy), which cannot otherwise be measured directly. The lattice enthalpy is the enthalpy change involved in the formation of an ionic compound from gaseous ions (an exothermic process), or sometimes defined as the energy to break the ionic compound into gaseous ions (an endothermic process). A Born–Haber cycle applies Hess's law to calculate the lattice enthalpy by comparing the standard enthalpy change of formation of the ionic compound (from the elements) to the enthalpy required to make gaseous ions from the elements.

Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually autonomous and logically consistent formulation of quantum mechanics. Its account of quantum jumps supplanted the Bohr model's electron orbits. It did so by interpreting the physical properties of particles as matrices that evolve in time. It is equivalent to the Schrödinger wave formulation of quantum mechanics, as manifest in Dirac's bra–ket notation.

In some contrast to the wave formulation, it produces spectra of (mostly energy) operators by purely algebraic, ladder operator methods. Relying on these methods, Wolfgang Pauli derived the hydrogen atom spectrum in 1926, before the development of wave mechanics.

Klaus Emil Julius Fuchs (29 December 1911 – 28 January 1988) was a German theoretical physicist, atomic spy, and communist who supplied information from the American, British, and Canadian Manhattan Project to the Soviet Union during and shortly after World War II. While at the Los Alamos Laboratory, Fuchs was responsible for many significant theoretical calculations relating to the first nuclear weapons and, later, early models of the hydrogen bomb. After his conviction in 1950, he served nine years in prison in the United Kingdom, then migrated to East Germany where he resumed his career as a physicist and scientific leader.

The son of a Lutheran pastor, Fuchs attended the University of Leipzig, where his father was a professor of theology, and became involved in student politics, joining the student branch of the Social Democratic Party of Germany (SPD), and the Reichsbanner Schwarz-Rot-Gold, an SPD-allied paramilitary organisation. He was expelled from the SPD in 1932, and joined the Communist Party of Germany (KPD). He went into hiding after the 1933 Reichstag fire and the subsequent persecution of communists in Nazi Germany, and fled to the United Kingdom, where he received his PhD from the University of Bristol under the supervision of Nevill Francis Mott, and his DSc from the University of Edinburgh, where he worked as an assistant to Max Born.