User talk:Smarter than u09

Welcome!

Hello,, and welcome to Wikipedia! I hope you like the place and decide to stay. Unfortunately, one or more of the pages you created may not conform to some of Wikipedia's guidelines for page creation, and may soon be deleted.

There's a page about creating articles you may want to read called Your first article. If you are stuck, and looking for help, please come to the New contributors' help page, where experienced Wikipedians can answer any queries you have! Or, you can just type   on this page, and someone will show up shortly to answer your questions. Here are a few other good links for newcomers: I hope you enjoy editing here and being a Wikipedian! Please sign your name on talk pages using four tildes ( ~ ); this will automatically produce your name and the date. If you have any questions, check out Where to ask a question or ask me on. Again, welcome! Accounting4Taste: talk 20:42, 12 January 2010 (UTC)
 * Your first article
 * Biographies of living persons
 * How to write a great article
 * The five pillars of Wikipedia
 * Help pages
 * Tutorial

Albert Einstein

From Wikipedia, the free encyclopedia Jump to: navigation, search "Einstein" redirects here. For other uses, see Einstein (disambiguation).

Albert Einstein

Albert Einstein, 1921 Born	14 March 1879 Ulm, Kingdom of Württemberg, German Empire Died	18 April 1955 (aged 76) Princeton, New Jersey, USA Residence	Germany, Italy, Switzerland, USA Citizenship	Württemberg/Germany (1879–96) Stateless (1896–1901) Switzerland (1901–55) Austria (1911–12) Germany (1914–33) United States (1940–55)[1] Ethnicity	Jewish Fields	Physics Institutions	Swiss Patent Office (Bern) University of Zurich Charles University in Prague ETH Zurich Prussian Academy of Sciences Kaiser Wilhelm Institute University of Leiden Institute for Advanced Study Alma mater	ETH Zurich University of Zurich Doctoral advisor	Alfred Kleiner Other academic advisors	Heinrich Friedrich Weber Notable students	Ernst G. Straus Nathan Rosen Leo Szilard Raziuddin Siddiqui[2] Known for	General relativity Special relativity Photoelectric effect Brownian motion Mass-energy equivalence Einstein field equations Unified Field Theory Bose–Einstein statistics Notable awards	Nobel Prize in Physics (1921) Copley Medal (1925) Max Planck Medal (1929) Time Person of the Century Signature

Albert Einstein (pronounced /ˈælbərt ˈaɪnstaɪn/; German: [ˈalbɐt ˈaɪ̯nʃtaɪ̯n] ( listen); 14 March 1879–18 April 1955) was a theoretical physicist who is widely regarded as one of the most influential scientists of all time. His many contributions to physics include the special and general theories of relativity, the founding of relativistic cosmology, the first post-Newtonian expansion, explaining the perihelion advance of Mercury, prediction of the deflection of light by gravity and gravitational lensing, the first fluctuation dissipation theorem which explained the Brownian movement of molecules, the photon theory and wave-particle duality, the quantum theory of atomic motion in solids, the zero-point energy concept, the semiclassical version of the Schrödinger equation, and the quantum theory of a monatomic gas which predicted Bose–Einstein condensation.

Einstein is best known for his theories of special relativity and general relativity. He received the 1921 Nobel Prize in Physics “for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect.”[3]

Einstein published more than 300 scientific and over 150 non-scientific works.[4] He is often regarded as the father of modern physics.[5]

Contents

1 Early life and education 2 Marriages and children 3 Patent office 4 Scientific career 4.1 Physics in 1900 4.2 Thermodynamic fluctuations and statistical physics 4.3 Thought experiments and a-priori physical principles 4.4 Special relativity 4.5 Photons 4.6 Quantized atomic vibrations 4.7 Adiabatic principle and action-angle variables 4.8 Wave-particle duality 4.9 Theory of Critical Opalescence 4.10 Zero-point energy 4.11 Principle of equivalence 4.12 Hole argument and Entwurf theory 4.13 General relativity 4.14 Cosmology 4.15 Modern quantum theory 4.16 Bose–Einstein statistics 4.17 Energy momentum pseudotensor 4.18 Unified field theory 4.19 Wormholes 4.20 Einstein–Cartan theory 4.21 Einstein–Podolsky–Rosen paradox 4.22 Equations of motion 4.23 Einstein’s mistakes 5 Collaboration with other scientists 5.1 Einstein-de Haas experiment 5.2 Schrödinger gas model 5.3 Einstein refrigerator 6 Bohr versus Einstein 7 Religious views 8 Politics 9 Death 10 Legacy 11 In popular culture 12 Awards 13 Honors 14 See also 15 Publications 16 Notes 17 Further reading 18 External links Early life and education

Einstein at the age of 4. His father showed him a pocket compass, and Einstein realized that there must be something causing the needle to move, despite the apparent “empty space.”[6] Albert Einstein was born in Ulm, in the Kingdom of Württemberg in the German Empire on 14 March 1879.[7] His father was Hermann Einstein, a salesman and engineer. His mother was Pauline Einstein (née Koch). In 1880, the family moved to Munich, where his father and his uncle founded Elektrotechnische Fabrik J. Einstein & Cie, a company that manufactured electrical equipment based on direct current.[7]

Albert Einstein in 1893 (age 14). From Euclid, Einstein began to understand deductive reasoning, and by the age of twelve, he had learned Euclidean geometry. Soon after he began to investigate infinitesimal calculus. At age 16, he performed the first of his famous thought experiments in which he visualized traveling alongside a beam of light.[8] The Einsteins were non-observant Jews. Their son attended a Catholic elementary school from the age of five until ten.[9] Although Einstein had early speech difficulties, he was a top student in elementary school.[10][11] As he grew, Einstein built models and mechanical devices for fun and began to show a talent for mathematics.[7] In 1889 Max Talmud (later changed to Max Talmey) introduced the ten-year old Einstein to key texts in science, mathematics and philosophy, including Kant’s Critique of Pure Reason and Euclid’s Elements (which Einstein called the "holy little geometry book").[12] Talmud was a poor Jewish medical student from Poland. The Jewish community arranged for Talmud to take meals with the Einsteins each week on Thursdays for six years. During this time Talmud wholeheartedly guided Einstein through many secular educational interests.[13][14]

In 1894, his father’s company failed: Direct current (DC) lost the War of Currents to alternating current (AC). In search of business, the Einstein family moved to Italy, first to Milan and then, a few months later, to Pavia. When the family moved to Pavia, Einstein stayed in Munich to finish his studies at the Luitpold Gymnasium. His father intended for him to pursue electrical engineering, but Einstein clashed with authorities and resented the school’s regimen and teaching method. He later wrote that the spirit of learning and creative thought were lost in strict rote learning. In the spring of 1895, he withdrew to join his family in Pavia, convincing the school to let him go by using a doctor’s note.[7] During this time, Einstein wrote his first scientific work, "The Investigation of the State of Aether in Magnetic Fields".[15]

Einstein applied directly to the Eidgenössische Polytechnische Schule (later Eidgenössische Technische Hochschule (ETH)) in Zürich, Switzerland. Lacking the requisite Matura certificate, he took an entrance examination, which he failed, although he got exceptional marks in mathematics and physics.[16] The Einsteins sent Albert to Aarau, in northern Switzerland to finish secondary school.[7] While lodging with the family of Professor Jost Winteler, he fell in love with the family’s daughter, Marie. (His sister Maja later married the Winteler son, Paul.)[17] In Aarau, Einstein studied Maxwell’s electromagnetic theory. At age 17, he graduated, and, with his father’s approval, renounced his citizenship in the German Kingdom of Württemberg to avoid military service, and enrolled in 1896 in the mathematics and physics program at the Polytechnic in Zurich. Marie Winteler moved to Olsberg, Switzerland for a teaching post.

In the same year, Einstein’s future wife, Mileva Marić, also entered the Polytechnic to study mathematics and physics, the only woman in the academic cohort. Over the next few years, Einstein and Marić’s friendship developed into romance. In a letter to her, Einstein called Marić “a creature who is my equal and who is as strong and independent as I am.”[18] Einstein graduated in 1900 from the Polytechnic with a diploma in mathematics and physics;[19] Although historians have debated whether Marić influenced Einstein’s work, the majority of academic historians of science agree that she did not.[20][21][22]

Marriages and children

It has been suggested that Lieserl Einstein be merged into this article or section. (Discuss) In early 1902, Einstein and Mileva Marić had a daughter they called Lieserl in their correspondence, who was born in Novi Sad where the parents of Mileva lived.[23] Her full name is not known, and her fate is uncertain after 1903.[24] Einstein and Marić married in January 1903, and in May 1904 the couple’s first son, Hans Albert Einstein, was born in Bern, Switzerland. Their second son, Eduard, was born in Zurich in July 1910. In 1914, Einstein moved to Berlin, while his wife remained in Zurich with their sons. Marić and Einstein divorced on 14 February 1919, having lived apart for five years. Einstein married Elsa Löwenthal (née Einstein) on 2 June 1919, after having had a relationship with her since 1912. She was his first cousin maternally and his second cousin paternally. In 1933, they emigrated permanently to the United States. In 1935, Elsa Einstein was diagnosed with heart and kidney problems and died in December, 1936.[25]

Patent office

The Einsteinhaus on the Kramgasse in Bern, where Einstein lived with his wife during his Annus Mirabilis

Left to right: Conrad Habicht, Maurice Solovine and Einstein, who founded the Olympia Academy After graduating, Einstein spent almost two frustrating years searching for a teaching post, but a former classmate’s father helped him secure a job in Bern, at the Federal Office for Intellectual Property, the patent office, as an assistant examiner.[26] He evaluated patent applications for electromagnetic devices. In 1903, Einstein’s position at the Swiss Patent Office became permanent, although he was passed over for promotion until he "fully mastered machine technology".[27]

Much of his work at the patent office related to questions about transmission of electric signals and electrical-mechanical synchronization of time, two technical problems that show up conspicuously in the thought experiments that eventually led Einstein to his radical conclusions about the nature of light and the fundamental connection between space and time.[28]

With friends he met in Bern, Einstein formed a weekly discussion club on science and philosophy, which he jokingly named "The Olympia Academy." Their readings included Henri Poincaré, Ernst Mach, and David Hume, who influenced Einstein’s scientific and philosophical outlook. The next year, Einstein published a paper in the prestigious Annalen der Physik on the capillary forces of a straw.[29]

Scientific career

Throughout his life, Einstein published hundreds of books and articles. Most were about physics, but a few expressed leftist political opinions about pacifism, socialism, and zionism.[4][7] In addition to the work he did by himself he also collaborated with other scientists on additional projects including the Bose–Einstein statistics, the Einstein refrigerator and others.[30]

Physics in 1900

Einstein’s early papers all come from attempts to demonstrate that atoms exist and have a finite nonzero size. At the time of his first paper in 1902, it was not yet completely accepted by physicists that atoms were real, even though chemists had good evidence ever since Antoine Lavoisier’s work a century earlier. The reason physicists were skeptical was because no 19th century theory could fully explain the properties of matter from the properties of atoms.

Ludwig Boltzmann was a leading 19th century atomist physicist, who had struggled for years to gain acceptance for atoms. Boltzmann had given an interpretation of the laws of thermodynamics, suggesting that the law of entropy increase is statistical. In Boltzmann’s way of thinking, the entropy is the logarithm of the number of ways a system could be configured inside. The reason the entropy goes up is only because it is more likely for a system to go from a special state with only a few possible internal configurations to a more generic state with many. While Boltzmann’s statistical interpretation of entropy is universally accepted today, and Einstein believed it, at the turn of the 20th century it was a minority position.

The statistical idea was most successful in explaining the properties of gases. James Clerk Maxwell, another leading atomist, had found the distribution of velocities of atoms in a gas, and derived the surprising result that the viscosity of a gas should be independent of density. Intuitively, the friction in a gas would seem to go to zero as the density goes to zero, but this is not so, because the mean free path of atoms becomes large at low densities. A subsequent experiment by Maxwell and his wife confirmed this surprising prediction. Other experiments on gases and vacuum, using a rotating slitted drum, showed that atoms in a gas had velocities distributed according to Maxwell’s distribution law.

In addition to these successes, there were also inconsistencies. Maxwell noted that at cold temperatures, atomic theory predicted specific heats that are too large. In classical statistical mechanics, every spring-like motion has thermal energy kBT on average at temperature T, so that the specific heat of every spring is Boltzmann’s constant kB. A monatomic solid with N atoms can be thought of as N little balls representing N atoms attached to each other in a box grid with 3N springs, so the specific heat of every solid is 3NkB, a result which became known as the Dulong–Petit law. This law is true at room temperature, but not for colder temperatures. At temperatures near zero, the specific heat goes to zero.

Similarly, a gas made up of a molecule with two atoms can be thought of as two balls on a spring. This spring has energy kBT at high temperatures, and should contribute an extra kB to the specific heat. It does at temperatures of about 1000 degrees, but at lower temperature, this contribution disappears. At zero temperature, all other contributions to the specific heat from rotations and vibrations also disappear. This behavior was inconsistent with classical physics.

The most glaring inconsistency was in the theory of light waves. Continuous waves in a box can be thought of as infinitely many spring-like motions, one for each possible standing wave. Each standing wave has a specific heat of kB, so the total specific heat of a continuous wave like light should be infinite in classical mechanics. This is obviously wrong, because it would mean that all energy in the universe would be instantly sucked up into light waves, and everything would slow down and stop.

These inconsistencies led some people to say that atoms were not physical, but mathematical. Notable among the skeptics was Ernst Mach, whose positivist philosophy led him to demand that if atoms are real, it should be possible to see them directly.[31] Mach believed that atoms were a useful fiction, that in reality they could be assumed to be infinitesimally small, that Avogadro’s number was infinite, or so large that it might as well be infinite, and kB was infinitesimally small. Certain experiments could then be explained by atomic theory, but other experiments could not, and this is the way it will always be.

Einstein opposed this position. Throughout his career, he was a realist. He believed that a single consistent theory should explain all observation, and that this theory would be a description what was really going on, underneath it all. So he set out to show that the atomic point of view was correct. This led him first to thermodynamics, then to statistical physics, and to the theory of specific heats of solids.

In 1905, while he was working in the patent office, the leading German language physics journal Annalen der Physik published four of Einstein’s papers. The four papers eventually were recognized as revolutionary, and 1905 became known as Einstein’s "Miracle Year", and the papers, as the Annus Mirabilis Papers.

Main article: Annus Mirabilis Papers

Albert Einstein, 1905, The Miracle Year. On 30 April 1905, Einstein completed his thesis with Alfred Kleiner, Professor of Experimental Physics, serving as pro-forma advisor. Einstein was awarded a PhD by the University of Zurich. His dissertation was entitled A New Determination of Molecular Dimensions. [32] Thermodynamic fluctuations and statistical physics

Main article: statistical physics Einstein’s earliest papers were concerned with thermodynamics. He wrote a paper establishing a thermodynamic identity in 1902, and a few other papers which attempted to interpret phenomena from a statistical atomic point of view.

His research in 1903 and 1904 was mainly concerned with the effect of finite atomic size on diffusion phenomena. As in Maxwell’s work, the finite nonzero size of atoms leads to effects which can be observed. This research, and the thermodynamic identity, were well within the mainstream of physics in his time. They would eventually form the content of his PhD thesis.[33]

His first major result in this field was the theory of thermodynamic fluctuations. When in equilibrium, a system has a maximum entropy and according to the statistical interpretation, it can fluctuate a little bit. Einstein pointed out that the statistical fluctuations of a macroscopic object, like a mirror suspended on spring, would be completely determined by the second derivative of the entropy with respect to the position of the mirror.

Searching for ways to test this relation, his great breakthrough came in 1905. The theory of fluctuations, he realized, would have a visible effect for an object which could move around freely. Such an object would have a velocity which is random, and would move around randomly, just like an individual atom. The average kinetic energy of the object would be kBT, and the time decay of the fluctuations would be entirely determined by the law of friction.

The law of friction for a small ball in a viscous fluid like water was discovered by George Stokes. He showed that for small velocities, the friction force would be proportional to the velocity, and to the radius of the particle (see Stokes’ law). This relation could be used to calculate how far a small ball in water would travel due to its random thermal motion, and Einstein noted that such a ball, of size about a micron, would travel about a few microns per second. This motion could be easily detected with a microscope and indeed, as Brownian motion, had actually been observed by the botanist Robert Brown. Einstein was able to identify this motion with that predicted by his theory. Since the fluctuations which give rise to Brownian motion are just the same as the fluctuations of the velocities of atoms, measuring the precise amount of Brownian motion using Einstein’s theory would show that Boltzmann’s constant is non-zero and would measure Avogadro’s number.

These experiments were carried out a few years later, and gave a rough estimate of Avogadro’s number consistent with the more accurate estimates due to Max Planck’s theory of blackbody light, and Robert Millikan’s measurement of the charge of the electron.[34] Unlike the other methods, Einstein’s required very few theoretical assumptions or new physics, since it was directly measuring atomic motion on visible grains.

Einstein’s theory of Brownian motion was the first paper in the field of statistical physics. It established that thermodynamic fluctuations were related to dissipation. This was shown by Einstein to be true for time-independent fluctuations, but in the Brownian motion paper he showed that dynamical relaxation rates calculated from classical mechanics could be used as statistical relaxation rates to derive dynamical diffusion laws. These relations are known as Einstein relations.

The theory of Brownian motion was the least revolutionary of Einstein’s Annus mirabilis papers, but it had an important role in securing the acceptance of the atomic theory by physicists.

Thought experiments and a-priori physical principles

Main article: Thought experiment Einstein’s thinking underwent a transformation in 1905. He had come to understand that quantum properties of light mean that Maxwell’s equations were only an approximation. He knew that new laws would have to replace these, but he did not know how to go about finding those laws. He felt that guessing formal relations would not go anywhere.

So he decided to focus on a-priori principles instead, which are statements about physical laws which can be understood to hold in a very broad sense even in domains where they have not yet been shown to apply. A well accepted example of an a-priori principle is rotational invariance. If a new force is discovered in physics, it is assumed to be rotationally invariant almost automatically, without thought. Einstein sought new principles of this sort, to guide the production of physical ideas. Once enough principles are found, then the new physics will be the simplest theory consistent with the principles and with previously known laws.

The first general a-priori principle he found was the principle of relativity, that uniform motion is indistinguishable from rest. This was understood by Hermann Minkowski to be a generalization of rotational invariance from space to space-time. Other principles postulated by Einstein and later vindicated, are the principle of equivalence and the principle of adiabatic invariance of the quantum number. Another of Einstein’s general principles, Mach’s principle is fiercely debated, and whether it holds in our world or not is still not definitively established.

The use of a-priori principles is a distinctive unique signature of Einstein’s early work, which has become a standard tool in modern theoretical physics.

Special relativity

Main article: History of special relativity His 1905 paper on the electrodynamics of moving bodies introduced his theory of special relativity, which showed that the observed independence of the speed of light on the observer’s state of motion required fundamental changes to the notion of simultaneity. Consequences of this include the time-space frame of a moving body slowing down and contracting (in the direction of motion) relative to the frame of the observer. This paper also argued that the idea of a luminiferous aether – one of the leading theoretical entities in physics at the time – was superfluous.[35] In his paper on mass–energy equivalence, which had previously considered to be distinct concepts, Einstein deduced from his equations of special relativity what has been called the twentieth century’s best-known equation: E = mc2.[36][37] This equation suggests that tiny amounts of mass could be converted into huge amounts of energy and presaged the development of nuclear power.[38] Einstein’s 1905 work on relativity remained controversial for many years, but was accepted by leading physicists, starting with Max Planck.[39][40]

Photons

Main article: Photon In a 1905 paper,[41] Einstein postulated that light itself consists of localized particles (quanta). Einstein’s light quanta were nearly universally rejected by all physicists, including Max Planck and Niels Bohr. This idea only became universally accepted in 1919, with Robert Millikan’s detailed experiments on the photoelectric effect, and with the measurement of Compton scattering.

Einstein’s paper on the light particles was almost entirely motivated by thermodynamic considerations. He was not at all motivated by the detailed experiments on the photoelectric effect, which did not confirm his theory until fifteen years later. Einstein considers the entropy of light at temperature T, and decomposes it into a low-frequency part and a high-frequency part. The high-frequency part, where the light is described by Wien’s law, has an entropy which looks exactly the same as the entropy of a gas of classical particles.

Since the entropy is the logarithm of the number of possible states, Einstein concludes that the number of states of short wavelength light waves in a box with volume V is equal to the number of states of a group of localizable particles in the same box. Since (unlike others) he was comfortable with the statistical interpretation, he confidently postulates that the light itself is made up of localized particles, as this is the only reasonable interpretation of the entropy.

This leads him to conclude that each wave of frequency f is associated with a collection of photons with energy hf each, where h is Planck’s constant. He does not say much more, because he is not sure how the particles are related to the wave. But he does suggest that this idea would explain certain experimental results, notably the photoelectric effect.[42]

Quantized atomic vibrations

Main article: Einstein solid Einstein continued his work on quantum mechanics in 1906, by explaining the specific heat anomaly in solids. This was the first application of quantum theory to a mechanical system. Since Planck’s distribution for light oscillators had no problem with infinite specific heats, the same idea could be applied to solids to fix the specific heat problem there. Einstein showed in a simple model that the hypothesis that solid motion is quantized explains why the specific heat of a solid goes to zero at zero temperature.

Einstein’s model treats each atom as connected to a single spring. Instead of connecting all the atoms to each other, which leads to standing waves with all sorts of different frequencies, Einstein imagined that each atom was attached to a fixed point in space by a spring. This is not physically correct, but it still predicts that the specific heat is 3NkB, since the number of independent oscillations stays the same.

Einstein then assumes that the motion in this model are quantized, according to the Planck law, so that each independent spring motion has energy which is an integer multiple of hf, where f is the frequency of oscillation. With this assumption, he applied Boltzmann’s statistical method to calculate the average energy of the spring. The result was the same as the one that Planck had derived for light: for temperatures where kBT is much smaller than hf, the motion is frozen, and the specific heat goes to zero.

So Einstein concluded that quantum mechanics would solve the main problem of classical physics, the specific heat anomaly. The particles of sound implied by this formulation are now called phonons. Because all of Einstein’s springs have the same stiffness, they all freeze out at the same temperature, and this leads to a prediction that the specific heat should go to zero exponentially fast when the temperature is low. The solution to this problem is to solve for the independent normal modes individually, and to quantize those. Then each normal mode has a different frequency, and long wavelength vibration modes freeze out at colder temperatures than short wavelength ones. This was done by Debye, and after this modification, Einstein’s quantization method reproduced quantitatively the behavior of the specific heats of solids at low temperatures.

This work was the foundation of condensed matter physics.

Adiabatic principle and action-angle variables

Main article: Old quantum theory Throughout the 1910s, quantum mechanics expanded in scope to cover many different systems. After Ernest Rutherford discovered the nucleus and proposed that electrons orbit like planets, Niels Bohr was able to show that the same quantum mechanical postulates introduced by Planck and developed by Einstein would explain the discrete motion of electrons in atoms, and the periodic table of the elements.

Einstein contributed to these developments by linking them with the 1898 arguments Wilhelm Wien had made. Wien had shown that the hypothesis of adiabatic invariance of a thermal equilibrium state allows all the blackbody curves at different temperature to be derived from one another by a simple shifting process. Einstein noted in 1911 that the same adiabatic principle shows that the quantity which is quantized in any mechanical motion must be an adiabatic invariant. Arnold Sommerfeld identified this adiabatic invariant as the action variable of classical mechanics. The law that the action variable is quantized was the basic principle of the quantum theory as it was known between 1900 and 1925.

Wave-particle duality

Main article: Wave-particle duality Although the patent office promoted Einstein to Technical Examiner Second Class in 1906, he had not given up on academia. In 1908, he became a privatdozent at the University of Bern.[43] In "über die Entwicklung unserer Anschauungen über das Wesen und die Konstitution der Strahlung" ("The Development of Our Views on the Composition and Essence of Radiation"), on the quantization of light, and in an earlier 1909 paper, Einstein showed that Max Planck’s energy quanta must have well-defined momenta and act in some respects as independent, point-like particles. This paper introduced the photon concept (although the name photon was introduced later by Gilbert N. Lewis in 1926) and inspired the notion of wave-particle duality in quantum mechanics.

Theory of Critical Opalescence

Main article: critical opalescence Einstein returned to the problem of thermodynamic fluctuations, giving a treatment of the density variations in a fluid at its critical point. Ordinarily the density fluctuations are controlled by the second derivative of the free energy with respect to the density. At the critical point, this derivative is zero, leading to large fluctuations. The effect of density fluctuations is that light of all wavelengths is scattered, making the fluid look milky white. Einstein relates this to Raleigh scattering, which is what happens when the fluctuation size is much smaller than the wavelength, and which explains why the sky is blue.[44]

Einstein at the Solvay conference in 1911. That year he became an associate professor at the University of Zurich and shortly afterward, he accepted a full professorship at the German Charles-Ferdinand University in Prague. Zero-point energy

Main article: Zero-point energy Einstein’s physical intuition led him to note that Planck’s oscillator energies had an incorrect zero point. He modified Planck’s hypothesis by stating that the lowest energy state of an oscillator is equal to 1⁄2hf, to half the energy spacing between levels. This argument, which was made in 1913 in collaboration with Otto Stern, was based on the thermodynamics of a diatomic molecule which can split apart into two free atoms.

Principle of equivalence

Main article: Principle of equivalence In 1907, while still working at the patent office, Einstein had what he would call his "happiest thought". He realized that the principle of relativity could be extended to gravitational fields. He thought about the case of a uniformly accelerated box not in a gravitational field, and noted that it would be indistinguishable from a box sitting still in an unchanging gravitational field.[45] He used special relativity to see that the rate of clocks at the top of a box accelerating upward would be faster than the rate of clocks at the bottom. He concludes that the rates of clocks depend on their position in a gravitational field, and that the difference in rate is proportional to the gravitational potential to first approximation.

Although this approximation is crude, it allowed him to calculate the deflection of light by gravity, and show that it is nonzero. This gave him confidence that the scalar theory of gravity proposed by Gunnar Nordström was incorrect. But the actual value for the deflection that he calculated was too small by a factor of two, because the approximation he used doesn’t work well for things moving at near the speed of light. When Einstein finished the full theory of general relativity, he would rectify this error, and predict the correct amount of light deflection by the sun.

From Prague, Einstein published a paper about the effects of gravity on light, specifically the gravitational redshift and the gravitational deflection of light. The paper challenged astronomers to detect the deflection during a solar eclipse.[46] German astronomer Erwin Finlay-Freundlich publicized Einstein’s challenge to scientists around the world.[47]

Einstein thought about the nature of the gravitational field in the years 1909–1912, studying its properties by means of simple thought experiments. A notable one is the rotating disk. Einstein imagined an observer making experiments on a rotating turntable. He noted that such an observer would find a different value for the mathematical constant pi than the one predicted by Euclidean geometry. The reason is that the radius of a circle would be measured with an uncontracted ruler, but according to special relativity, the circumference would seem to be longer, because the ruler would be contracted.

Since Einstein believed that the laws of physics were local, described by local fields, he concluded from this that spacetime could be locally curved. This led him to study Riemannian geometry, and to formulate general relativity in this language.

Hole argument and Entwurf theory

Main article: Hole argument While developing general relativity, Einstein became confused about the gauge invariance in the theory. He formulated an argument that led him to conclude that a general relativistic field theory is impossible. He gave up looking for fully generally covariant tensor equations, and searched for equations that would be invariant under general linear transformations only.

The Entwurf ("draft") theory was the result of these investigations. As its name suggests, it was a sketch of a theory, with the equations of motion supplemented by additional gauge fixing conditions. Simultaneously less elegant and more difficult than general relativity, Einstein abandoned the theory after realizing that the hole argument was mistaken.

General relativity

See also: History of general relativity In 1912, Einstein returned to Switzerland to accept a professorship at his alma mater, the ETH. Once back in Zurich, he immediately visited his old ETH classmate Marcel Grossmann, now a professor of mathematics, who introduced him to Riemannian geometry and, more generally, to differential geometry. On the recommendation of Italian mathematician Tullio Levi-Civita, Einstein began exploring the usefulness of general covariance (essentially the use of tensors) for his gravitational theory. For a while Einstein thought that there were problems with the approach, but he later returned to it and, by late 1915, had published his general theory of relativity in the form in which it is used today.[48] This theory explains gravitation as distortion of the structure of spacetime by matter, affecting the inertial motion of other matter. During World War I, the work of Central Powers scientists was available only to Central Powers academics, for national security reasons. Some of Einstein’s work did reach the United Kingdom and the United States through the efforts of the Austrian Paul Ehrenfest and physicists in the Netherlands, especially 1902 Nobel Prize-winner Hendrik Lorentz and Willem de Sitter of Leiden University. After the war ended, Einstein maintained his relationship with Leiden University, accepting a contract as an Extraordinary Professor; for ten years, from 1920 to 1930, he travelled to Holland regularly to lecture.[49]

In 1917, several astronomers accepted Einstein ’s 1911 challenge from Prague. The Mount Wilson Observatory in California, U.S., published a solar spectroscopic analysis that showed no gravitational redshift.[50] In 1918, the Lick Observatory, also in California, announced that it too had disproved Einstein’s prediction, although its findings were not published.[51]

Eddington’s photograph of a solar eclipse, which confirmed Einstein’s theory that light “bends.” On 7th November 1919, the leading British newspaper The Times printed a banner headline that read: “Revolution in Science – New Theory of the Universe – Newtonian Ideas Overthrown.”[52] However, in May 1919, a team led by the British astronomer Arthur Stanley Eddington claimed to have confirmed Einstein’s prediction of gravitational deflection of starlight by the Sun while photographing a solar eclipse with dual expeditions in Sobral, northern Brazil, and Príncipe, a west African island.[47] Nobel laureate Max Born praised general relativity as the "greatest feat of human thinking about nature";[53] fellow laureate Paul Dirac was quoted saying it was "probably the greatest scientific discovery ever made".[54] The international media guaranteed Einstein’s global renown.

There have been claims that scrutiny of the specific photographs taken on the Eddington expedition showed the experimental uncertainty to be comparable to the same magnitude as the effect Eddington claimed to have demonstrated, and that a 1962 British expedition concluded that the method was inherently unreliable.[52] The deflection of light during a solar eclipse was confirmed by later, more accurate observations.[55] Some resented the newcomer’s fame, notably among some German physicists, who later started the Deutsche Physik (German Physics) movement.[56][57]

Cosmology

Main article: Cosmology In 1917, Einstein applied the General theory of relativity to model the structure of the universe as a whole. He wanted the universe to be eternal and unchanging, but this type of universe is not consistent with relativity. To fix this, Einstein modified the general theory by introducing a new notion, the cosmological constant. With a positive cosmological constant, the universe could be an eternal static sphere[58]

Einstein believed a spherical static universe is philosophically preferred, because it would obey Mach’s principle. He had shown that general relativity incorporates Mach’s principle to a certain extent in frame dragging by gravitomagnetic fields, but he knew that Mach’s idea would not work if space goes on forever. In a closed universe, he believed that Mach’s principle would hold.

Mach’s principle has generated much controversy over the years.

After her husband’s many relocations, Mileva established a permanent home with the children in Zürich in 1914. Einstein went alone to Berlin, where he became a member of the Prussian Academy of Sciences and a professor at the Humboldt University of Berlin, although with a special clause in his contract that freed him from most teaching obligations. Einstein was president of the German Physical Society (1916–1918).[59] and also directed the Kaiser Wilhelm Institute for Physics (1914–1932).[60] Modern quantum theory

Main article: Schrödinger equation In 1917, at the height of his work on relativity, Einstein published an article in Physikalische Zeitschrift that proposed the possibility of stimulated emission, the physical process that makes possible the maser and the laser.[61] This article showed that the statistics of absorption and emission of light would only be consistent with Planck’s distribution law if the emission of light into a mode with n photons would be enhanced statistically compared to the emission of light into an empty mode. This paper was enormously influential in the later development of quantum mechanics, because it was the first paper to show that the statistics of atomic transitions had simple laws. Einstein discovered Louis de Broglie’s work, and supported his ideas, which were received skeptically at first. In another major paper from this era, Einstein gave a wave equation for de Broglie waves, which Einstein suggested was the Hamilton–Jacobi equation of mechanics. This paper would inspire Schrödinger’s work of 1926.

Bose–Einstein statistics

Main article: Bose–Einstein condensation In 1924, Einstein received a description of a statistical model from Indian physicist Satyendra Nath Bose, based on a counting method that assumed that light could be understood as a gas of indistinguishable particles. Einstein noted that Bose’s statistics applied to some atoms as well as to the proposed light particles, and submitted his translation of Bose’s paper to the Zeitschrift für Physik. Einstein also published his own articles describing the model and its implications, among them the Bose–Einstein condensate phenomenon that some particulates should appear at very low temperatures.[62] It was not until 1995 that the first such condensate was produced experimentally by Eric Allin Cornell and Carl Wieman using ultra-cooling equipment built at the NIST–JILA laboratory at the University of Colorado at Boulder.[63] Bose–Einstein statistics are now used to describe the behaviors of any assembly of bosons. Einstein’s sketches for this project may be seen in the Einstein Archive in the library of the Leiden University.[30]

Energy momentum pseudotensor

Main article: Stress-energy-momentum pseudotensor General relativity includes a dynamical spacetime, so it is difficult to see how to identify the conserved energy and momentum. Noether’s theorem allows these quantities to be determined from a Lagrangian with translation invariance, but general covariance makes translation invariance into something of a gauge symmetry. The energy and momentum derived within general relativity by Noether’s presecriptions do not make a real tensor for this reason.

Einstein argued that this is true for fundamental reasons, because the gravitational field could be made to vanish by a choice of coordinates. He maintained that the noncovariante energy momentum pseudotensor was in fact the best description of the energy momentum distribution in a gravitational field. This approach has been echoed by Lev Landau and Evgeny Lifshitz, and others, and has become standard.

The use of non-covariant objects like pseudotensors was heavily criticized in 1917 by Erwin Schrödinger and others.

Unified field theory

Main article: Classical unified field theories Following his research on general relativity, Einstein entered into a series of attempts to generalize his geometric theory of gravitation, which would allow the explanation of electromagnetism. In 1950, he described his "unified field theory" in a Scientific American article entitled "On the Generalized Theory of Gravitation." [64] Although he continued to be lauded for his work, Einstein became increasingly isolated in his research, and his efforts were ultimately unsuccessful. In his pursuit of a unification of the fundamental forces, Einstein ignored some mainstream developments in physics, most notably the strong and weak nuclear forces, which were not well understood until many years after his death. Mainstream physics, in turn, largely ignored Einstein’s approaches to unification. Einstein’s dream of unifying other laws of physics with gravity motivates modern quests for a theory of everything and in particular string theory, where geometrical fields emerge in a unified quantum-mechanical setting.

Wormholes

Main article: Wormhole Einstein collaborated with others to produce a model of a wormhole. His motivation was to model elementary particles with charge as a solution of gravitational field equations, in line with the program outlined in the paper "Do Gravitational Fields play an Important Role in the Constitution of the Elementary Particles?". These solutions cut and pasted Schwarzschild black holes to make a bridge between two patches.

If one end of a wormhole was positively charged, the other end would be negatively charged. These properties led Einstein to believe that pairs of particles and antiparticles could be described in this way.

Einstein–Cartan theory

Main article: Einstein–Cartan theory In order to incorporate spinning point particles into general relativity, the affine connection needed to be generalized to include an antisymmetric part, called the torsion. This modification was made by Einstein and Cartan in the 1920s.

Einstein–Podolsky–Rosen paradox

Main article: EPR paradox In 1935, Einstein returned to the question of quantum mechanics. He considered how a measurement on one of two entangled particles would affect the other. He noted, along with his collaborators, that by performing different measurements on the distant particle, either of position or momentum, different properties of the entangled partner could be discovered without disturbing it in any way.

He then used a hypothesis of local realism to conclude that the other particle had these properties already determined. The principle he proposed is that if it is possible to determine what the answer to a position or momentum measurement would be, without in any way disturbing the particle, then the particle actually has values of position or momentum.

This principle distilled the essence of Einstein’s objection to quantum mechanics. As a physical principle, it has since been shown to be incompatible with experiments.

Equations of motion

Main article: Einstein–Infeld–Hoffmann equation The theory of general relativity has two fundamental laws – the Einstein equations which describe how space curves, and the geodesic equation which describes how particles move.

Since the equations of general relativity are non-linear, a lump of energy made out of pure gravitational fields, like a black hole, would move on a trajectory which is determined by the Einstein equations themselves, not by a new law. So Einstein proposed that the path of a singular solution, like a black hole, would be determined to be a geodesic from general relativity itself.

This was established by Einstein, Infeld and Hoffmann for pointlike objects without angular momentum, and by Roy Kerr for spinning objects.

Einstein’s mistakes

This section needs additional citations for verification. Please help improve this article by adding reliable references. Unsourced material may be challenged and removed. (January 2010) In addition to his well-accepted results, some of Einstein’s papers contain mistakes:

1905: In the original German version of the special relativity paper, and in some English translations, Einstein gives a wrong expression for the transverse mass of a fast moving particle. The transverse mass is the antiquated name for the ratio of the 3-force to the 3-acceleration when the force is perpendicular to the velocity. Einstein gives this ratio as, while the actual value is (corrected by Max Planck). 1905: In his PhD dissertation, the friction in dilute solutions has a miscalculated numerical prefactor, which makes the estimate of Avogadro’s number off by a factor of 3. The mistake is corrected by Einstein in a later publication. 1905: An expository paper explaining how airplanes fly includes an example which is incorrect. There is a wing which he claims will generate lift. This wing is flat on the bottom, and flat on the top, with a small bump at the center. It is designed to generate lift by Bernoulli’s principle, and Einstein claims that it will. Simple action reaction considerations, though, show that the wing will not generate lift, at least if it is long enough. 1911: Einstein predicted how much the sun’s gravity would deflect nearby starlight, but used an approximation which gives an answer which is half as big as the correct one.[65] 1913: Einstein started writing papers based on his belief that the hole argument made general covariance impossible in a theory of gravity. 1922: Einstein published a qualitative theory of superconductivity based on the vague idea of electrons shared in orbits. This paper predated modern quantum mechanics, and is well understood to be completely wrong. The correct BCS theory of low temperature superconductivity was only worked out in 1957, thirty years after the establishing of modern quantum mechanics. 1937: Einstein believed that the focusing properties of geodesics in general relativity would lead to an instability which causes plane gravitational waves to collapse in on themselves. While this is true to a certain extent in some limits, because gravitational instabilities can lead to a concentration of energy density into black holes, for plane waves of the type Einstein and Rosen considered in their paper, the instabilities are under control. Einstein retracted this position a short time later, but until his death his collaborator Nathan Rosen maintained that gravitational waves are unstable. 1939: Einstein denied several times that black holes could form, the last time in print. He published a paper that argues that a star collapsing would spin faster and faster, spinning at the speed of light with infinite energy well before the point where it is about to collapse into a black hole. This paper received no citations, and the conclusions are well understood to be wrong. Einstein’s argument itself is inconclusive, since he only shows that stable spinning objects have to spin faster and faster to stay stable before the point where they collapse. But it is well understood today (and was understood well by some even then) that collapse cannot happen through stationary states the way Einstein imagined. In addition to these well established mistakes, there are other arguments whose deduction is considered correct, but whose interpretation or philosophical conclusion is considered to have been incorrect:

In the Bohr–Einstein debates and the papers following this, Einstein tries to poke holes in the uncertainty principle, ingeniously, but unsuccessfully. In the EPR paper, Einstein concludes that quantum mechanics must be replaced by local hidden variables. The measured violations of Bell’s inequality show that hidden variables, if they exist, must be nonlocal. Einstein himself considered the use of the "fudge factor" lambda in his 1917 paper founding cosmology as a "blunder".[65] The theory of general relativity predicted an expanding or contracting universe, but Einstein wanted a universe which is an unchanging three dimensional sphere, like the surface of a three dimensional ball in four dimensions. He wanted this for philosophical reasons, so as to incorporate Mach’s principle in a reasonable way. He stabilized his solution by introducing a cosmological constant, and when the universe was shown to be expanding, he retracted the constant as a blunder. This is not really much of a blunder – the cosmological constant is necessary within general relativity as it is currently understood, and it is widely believed to have a nonzero value today. Einstein took the wrong side in a few scientific debates.

He briefly flirted with transverse and longitudinal mass concepts, before rejecting them. Einstein initially opposed Minkowski’s geometrical formulation of special relativity, changing his mind completely a few years later. Based on his cosmological model, Einstein rejected expanding universe solutions by Friedman and Lemaitre as unphysical, changing his mind when the universe was shown to be expanding a few years later. Finding it too formal, Einstein believed that Heisenberg’s matrix mechanics was incorrect. He changed his mind when Schrödinger and others demonstrated that the formulation in terms of the Schrödinger equation, based on Einstein’s wave-particle duality was equivalent to Heisenberg’s matrices. Einstein rejected work on black holes[66] by Chandrasekhar, Oppenheimer, and others, believing, along with Eddington, that collapse past the horizon (then called the ’Schwarzschild singularity’) would never happen. So big was his influence, that this opinion was not rejected until the early 1960s, almost a decade after his death. Einstein believed that some sort of nonlinear instability could lead to a field theory whose solutions would collapse into pointlike objects which would behave like quantum particles. While there are many field theories with point-like particle solutions, none of them behave like quantum particles. It is widely believed that quantum mechanics would be impossible to reproduce from a local field theory of the type Einstein considered, because of Bell’s inequality. In addition to these well known mistakes, it is sometimes claimed that the general line of Einstein’s reasoning in the 1905 relativity paper is flawed, or the photon paper, or one or another of the most famous papers. None of these claims are widely accepted.

Collaboration with other scientists

In addition to long time collaborators Leopold Infeld, Nathan Rosen, Peter Bergmann and others, Einstein also had some one-shot collaborations with various scientists.

Einstein-de Haas experiment

Main article: Einstein-de Haas effect Einstein and De Haas demonstrated that magnetization is due to the motion of electrons, nowadays known to be the spin. In order to show this, they reversed the magnetization in an iron bar suspended on a torsion pendulum. They confirmed that this leads the bar to rotate, because the electron’s angular momentum changes as the magnetization changes. This experiment needed to be sensitive, because the angular momentum associated with electrons is small, but it definitively established that electron motion of some kind is responsible for magnetization.

Schrödinger gas model

Einstein suggested to Erwin Schrödinger that he might be able to reproduce the statistics of a Bose–Einstein gas by considering a box. Then to each possible quantum motion of a particle in a box associate an independent harmonic oscillator. Quantizing these oscillators, each level will have an integer occupation number, which will be the number of particles in it.

This formulation is a form of second quantization, but it predates modern quantum mechanics. Erwin Schrödinger applied this to derive the thermodynamic properties of a semiclassical ideal gas. Schrödinger urged Einstein to add his name as co-author, although Einstein declined the invitation.[67]

Einstein refrigerator

Main article: Einstein refrigerator In 1926, Einstein and his former student Leó Szilárd co-invented (and in 1930, patented) the Einstein refrigerator. This Absorption refrigerator was then revolutionary for having no moving parts and using only heat as an input.[68] On 11 November 1930, U.S. Patent 1,781,541 was awarded to Albert Einstein and Leó Szilárd for the refrigerator. Although the refrigerator was not immediately put into commercial production, the most promising of their patents being quickly bought up by the Swedish company Electrolux to protect its refrigeration technology from competition.[69]

Bohr versus Einstein

Einstein and Niels Bohr. Einstein’s disagreement with Bohr revolved around the idea of scientific determinism. See also: Bohr–Einstein debates In the 1920s, quantum mechanics developed into a more complete theory. Einstein was unhappy with the Copenhagen interpretation of quantum theory developed by Niels Bohr and Werner Heisenberg. In this interpretation, quantum phenomena are inherently probabilistic, with definite states resulting only upon interaction with classical systems. A public debate between Einstein and Bohr followed, lasting on and off for many years (including during the Solvay Conferences). Einstein formulated thought experiments against the Copenhagen interpretation, which were all rebutted by Bohr. In a 1926 letter to Max Born, Einstein wrote: "I, at any rate, am convinced that He [God] does not throw dice." [70]

Einstein was never satisfied by what he perceived to be quantum theory’s intrinsically incomplete description of nature, and in 1935 he further explored the issue in collaboration with Boris Podolsky and Nathan Rosen, noting that the theory seems to require non-local interactions; this is known as the EPR paradox.[71] The EPR experiment has since been performed, with results confirming quantum theory’s predictions.[72] Repercussions of the Einstein–Bohr debate have found their way into philosophical discourse.

Religious views

Main article: Religious views of Albert Einstein I'm not an atheist and I don't think I can call myself a pantheist. We are in the position of a little child entering a huge library filled with books in many different languages. The child knows someone must have written those books. It does not know how. The child dimly suspects a mysterious order in the arrangement of the books but doesn't know what it is. That, it seems to me, is the attitude of even the most intelligent human being toward God. —Albert Einstein[73] The question of scientific determinism gave rise to questions about Einstein’s position on theological determinism, and whether or not he believed in God, or in a god. In 1929, Einstein told Rabbi Herbert S. Goldstein "I believe in Spinoza’s God, who reveals Himself in the lawful harmony of the world, not in a God Who concerns Himself with the fate and the doings of mankind."[74] In a 1954 letter, he wrote, "I do not believe in a personal God and I have never denied this but have expressed it clearly.”[75] In a letter to philosopher Erik Gutkind, Einstein remarked, "The word God is for me nothing more than the expression and product of human weakness, the Bible a collection of honorable, but still purely primitive, legends which are nevertheless pretty childish."[76]

Politics

Main article: Political views of Albert Einstein

Einstein with Indian poet and Nobel laureate Rabindranath Tagore during their widely publicized 14 July 1930 conversation Throughout the November Revolution in Germany Einstein signed an appeal for the foundation of a nationwide liberal and democratic party,[77][78] which was published in the Berliner Tageblatt on 16 November 1918,[79] and became a member of the German Democratic Party.[80]

Einstein flouted the ascendant Nazi movement, tried to be a voice of moderation in the tumultuous formation of the State of Israel and braved anti-communist politics and resistance to the civil rights movement in the United States. He participated in the 1927 congress of the League against Imperialism in Brussels.[81] He was a socialist Zionist who supported the creation of a Jewish national homeland in the British mandate of Palestine.[82]

After World War II, as enmity between the former allies became a serious issue, Einstein wrote, “I do not know how the third World War will be fought, but I can tell you what they will use in the Fourth – rocks!”[83] In a 1949 Monthly Review article entitled “Why Socialism?”[84] Albert Einstein described a chaotic capitalist society, a source of evil to be overcome, as the “predatory phase of human development” (Einstein 1949). With Albert Schweitzer and Bertrand Russell, Einstein lobbied to stop nuclear testing and future bombs. Days before his death, Einstein signed the Russell–Einstein Manifesto, which led to the Pugwash Conferences on Science and World Affairs.[85]

Einstein was a member of several civil rights groups, including the Princeton chapter of the NAACP. When the aged W. E. B. Du Bois was accused of being a Communist spy, Einstein volunteered as a character witness, and the case was dismissed shortly afterward. Einstein’s friendship with activist Paul Robeson, with whom he served as co-chair of the American Crusade to End Lynching, lasted twenty years.[86]

Death

On 17 April 1955, Albert Einstein experienced internal bleeding caused by the rupture of an abdominal aortic aneurysm, which had previously been reinforced surgically by Dr. Rudolph Nissen in 1948.[87] He took the draft of a speech he was preparing for a television appearance commemorating the State of Israel’s seventh anniversary with him to the hospital, but he did not live long enough to complete it.[88] Einstein refused surgery, saying: "I want to go when I want. It is tasteless to prolong life artificially. I have done my share, it is time to go. I will do it elegantly."[89] He died in Princeton Hospital early the next morning at the age of 76, having continued to work until near the end. Einstein’s remains were cremated and his ashes were scattered around the grounds of the Institute for Advanced Study, Princeton, New Jersey.[90][91] During the autopsy, the pathologist of Princeton Hospital, Thomas Stoltz Harvey removed Einstein’s brain for preservation, without the permission of his family, in hope that the neuroscience of the future would be able to discover what made Einstein so intelligent.[92]

Legacy

While travelling, Einstein had written daily to his wife Elsa and adopted stepdaughters, Margot and Ilse, and the letters were included in the papers bequeathed to The Hebrew University. Margot Einstein permitted the personal letters to be made available to the public, but requested that it not be done until twenty years after her death (she died in 1986[93]). Barbara Wolff, of The Hebrew University’s Albert Einstein Archives, told the BBC that there are about 3,500 pages of private correspondence written between 1912 and 1955.[94]

Einstein bequeathed the royalties from use of his image to The Hebrew University of Jerusalem. Corbis, successor to The Roger Richman Agency, licenses the use of his name and associated imagery, as agent for the Hebrew University.[95][96]

In popular culture

Main article: Albert Einstein in popular culture In the period before World War II, Albert Einstein was so well-known in America that he would be stopped on the street by people wanting him to explain "that theory." He finally figured out a way to handle the incessant inquiries. He told his inquirers "Pardon me, sorry! Always I am mistaken for Professor Einstein."[97]

Albert Einstein has been the subject of or inspiration for many novels, films, and plays. Einstein is a favorite model for depictions of mad scientists and absent-minded professors; his expressive face and distinctive hairstyle have been widely copied and exaggerated. Time magazine’s Frederic Golden wrote that Einstein was "a cartoonist’s dream come true."[98]

Einstein’s association with great intelligence and originality has made the name Einstein synonymous with genius.[99]

Awards

Max Planck presents Albert Einstein with the Max Planck medal of the German Physical Society, 28 June 1929, in Berlin, Germany In 1922, Einstein was awarded the 1921 Nobel Prize in Physics,[100] "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect". This refers to his 1905 paper on the photoelectric effect, "On a Heuristic Viewpoint Concerning the Production and Transformation of Light", which was well supported by the experimental evidence by that time. The presentation speech began by mentioning "his theory of relativity [which had] been the subject of lively debate in philosophical circles [and] also has astrophysical implications which are being rigorously examined at the present time." (Einstein 1923)

It was long reported that Einstein gave the Nobel prize money directly to his first wife, Mileva Marić, in compliance with their 1919 divorce settlement. However, personal correspondence made public in 2006[101] shows that he invested much of it in the United States, and saw much of it wiped out in the Great Depression.

Einstein traveled to New York City in the United States for the first time on 2 April 1921. When asked where he got his scientific ideas, Einstein explained that he believed scientific work best proceeds from an examination of physical reality and a search for underlying axioms, with consistent explanations that apply in all instances and avoid contradicting each other. He also recommended theories with visualizable results (Einstein 1954).[102]

In 1999, Albert Einstein was named Person of the Century by Time magazine. [98] [103] A Gallup poll recorded him as the fourth most admired person of the 20th century in the U.S. [104]

Honors

See also: List of things named after Albert Einstein Albert Einstein has been recognized numerous times for his achievements. The International Union of Pure and Applied Physics named 2005 the “World Year of Physics” in commemoration of the 100th anniversary of the publication of the Annus Mirabilis Papers.[105]

The Albert Einstein Memorial in central Washington, D.C. is a monumental bronze statue depicting Einstein seated with manuscript papers in hand. The statue commissioned in 1979, is located in a grove of trees at the southwest corner of the grounds of the National Academy of Sciences on Constitution Avenue.

The chemical element 99, einsteinium, was named for him in August 1955, four months after Einstein’s death.[106][107]

In 1999 Time magazine named him the Person of the Century, beating contenders like Mahatma Gandhi and Franklin Roosevelt, and in the words of a biographer, “to the scientifically literate and the public at large, Einstein is synonymous with genius.”[108] Also in 1999, an opinion poll of 100 of today's leading physicists ranked Einstein the "greatest physicist ever".[109]

2001 Einstein is an inner main belt asteroid discovered on 5 March 1973.[110]

The Albert Einstein Award (sometimes called the Albert Einstein Medal because it is accompanied with a gold medal) is an award in theoretical physics, that was established to recognize high achievement in the natural sciences. It was endowed by the Lewis and Rosa Strauss Memorial Fund in honor of Albert Einstein’s 70th birthday. It was first awarded in 1951 and included a prize money of $ 15,000,[111][112] which was later reduced to $ 5,000.[113][114] The winner is selected by a committee (the first of which consisted of Einstein, Oppenheimer, von Neumann and Weyl[115]) of the Institute for Advanced Study, which administers the award.[112] Lewis L. Strauss used to be one of the trustees of the institute.[116]

The Albert Einstein Peace Prize is an award that is given yearly by the Chicago, Illinois-based Albert Einstein Peace Prize Foundation. Winners of the prize receive $50,000.[117]

In 1990, his name was added to the Walhalla temple for "laudable and distinguished Germans",[118] which is located east of Regensburg, in Bavaria, Germany.[119]

See also

Book:Albert Einstein Books are collections of articles which can be downloaded or ordered in print. Heinrich Burkhardt Hermann Einstein History of gravitational theory Introduction to special relativity List of coupled cousins Relativity priority dispute Sticky bead argument Summation convention The Einstein Theory of Relativity (educational film about the theory of relativity) German inventors and discoverers Historical Museum of Bern (Einstein museum) Science Odyssey People And Discoveries Publications

The following publications by Albert Einstein are referenced in this article. A more complete list of his publications may be found at List of scientific publications by Albert Einstein. Einstein, Albert (1901). "Folgerungen aus den Capillaritätserscheinungen (Conclusions Drawn from the Phenomena of Capillarity)". Annalen der Physik 4: p. 513. doi:10.1002/andp.19013090306. Einstein, Albert (1905a). "On a Heuristic Viewpoint Concerning the Production and Transformation of Light" ([dead link]). Annalen der Physik 17: 132–148.. This annus mirabilis paper on the photoelectric effect was received by Annalen der Physik 18th March. Einstein, Albert (1905b). A new determination of molecular dimensions.. This PhD thesis was completed 30th April and submitted 20th July. Einstein, Albert (1905c). "On the Motion – Required by the Molecular Kinetic Theory of Heat – of Small Particles Suspended in a Stationary Liquid". Annalen der Physik 17: 549–560.. This annus mirabilis paper on Brownian motion was received 11th May. Einstein, Albert (1905d). "On the Electrodynamics of Moving Bodies". Annalen der Physik 17: 891–921.. This annus mirabilis paper on special relativity was received 30th June. Einstein, Albert (1905e). "Does the Inertia of a Body Depend Upon Its Energy Content?". Annalen der Physik 18: 639–641.. This annus mirabilis paper on mass-energy equivalence was received 27th September. Einstein, Albert (1915). "Die Feldgleichungen der Gravitation (The Field Equations of Gravitation)". Königlich Preussische Akademie der Wissenschaften: 844–847. Einstein, Albert (1917a). "Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie (Cosmological Considerations in the General Theory of Relativity)". Königlich Preussische Akademie der Wissenschaften. Einstein, Albert (1917b). "Zur Quantentheorie der Strahlung (On the Quantum Mechanics of Radiation)". Physikalische Zeitschrift 18: 121–128. Einstein, Albert (11th July 1923). "Fundamental Ideas and Problems of the Theory of Relativity". Nobel Lectures, Physics 1901–1921. Amsterdam: Elsevier Publishing Company. Retrieved 25 March 2007. Einstein, Albert (1924). "Quantentheorie des einatomigen idealen Gases (Quantum theory of monatomic ideal gases)". Sitzungsberichte der Preussichen Akademie der Wissenschaften Physikalisch-Mathematische Klasse: 261–267.. First of a series of papers on this topic. Einstein, Albert (1926). "Die Ursache der Mäanderbildung der Flussläufe und des sogenannten Baerschen Gesetzes". Die Naturwissenschaften 14: 223–224. doi:10.1007/BF01510300.. On Baer’s law and meanders in the courses of rivers. Einstein, Albert; Podolsky, Boris; Rosen, Nathan (15th May 1935). "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?". Physical Review 47 (10): 777–780. doi:10.1103/PhysRev.47.777. Einstein, Albert (1940). On Science and Religion. 146. Edinburgh: Scottish Academic. 605. doi:10.1038/146605a0. ISBN 0707304539. Einstein, Albert et al. (4th December 1948). To the editors. Melville, NY: AIP, American Inst. of Physics. ISBN 0735403597. Einstein, Albert (May 1949). "Why Socialism?". Monthly Review. Retrieved 16 January 2006. Einstein, Albert (1950). "On the Generalized Theory of Gravitation". Scientific American CLXXXII (4): 13–17. Einstein, Albert (1954). Ideas and Opinions. New York: Random House. ISBN 0-517-00393-7. Einstein, Albert (1969) (in German). Albert Einstein, Hedwig und Max Born: Briefwechsel 1916–1955. Munich: Nymphenburger Verlagshandlung. ISBN 388682005X. Einstein, Albert (1979). Autobiographical Notes (Centennial ed.). Chicago: Open Court. ISBN 0-875-48352-6.. The chasing a light beam thought experiment is described on pages 48–51. Collected Papers: Stachel, John, Martin J. Klein, a. J. Kox, Michel Janssen, R. Schulmann, Diana Komos Buchwald and others (Eds.) (1987–2006). The Collected Papers of Albert Einstein, Vol. 1–10. Princeton University Press. Further information about the volumes published so far can be found on the webpages of the Einstein Papers Project and on the Princeton University Press Einstein Page Notes

^ Hans-Josef, Küpper (2000). "Various things about Albert Einstein". einstein-website.de. Retrieved 18 July 2009. ^ http://www.ias.ac.in/currsci/apr25/articles32.htm ^ "The Nobel Prize in Physics 1921". Nobel Foundation. Archived from the original on 5 October 2008. Retrieved 6 March 2007. ^ a b Paul Arthur Schilpp, editor (1951). Albert Einstein: Philosopher-Scientist, Volume II. New York: Harper and Brothers Publishers (Harper Torchbook edition). pp. 730–746. His non-scientific works include: About Zionism: Speeches and Lectures by Professor Albert Einstein (1930), “Why War?” (1933, co-authored by Sigmund Freud), The World As I See It (1934), Out of My Later Years (1950), and a book on science for the general reader, The Evolution of Physics (1938, co-authored by Leopold Infeld). ^ Zahar, Élie (2001). Poincaré's Philosophy. From Conventionalism to Phenomenology. Carus Publishing Company. p. 41. ISBN 0-8126-9435-X., Chapter 2, p. 41 ^ Schilpp (Ed.), P. A. (1979). Albert Einstein – Autobiographical Notes. Open Court Publishing Company. pp. 8–9. ^ a b c d e f "Albert Einstein – Biography". Nobel Foundation. Retrieved 7 March 2007. ^ (Einstein 1979) ^ Einstein: the life and times, By Ronald William Clark ^ Rosenkranz, Ze’ev (2005). Albert Einstein – Derrière l’image. Neue Zürcher Zeitung. p. 29. ISBN 3-03823-182-7. ^ Sowell, Thomas (2001). The Einstein Syndrome: Bright Children Who Talk Late. Basic Books. pp. 89–150. ISBN 0-465-08140-1. ^ Dudley Herschbach, "Einstein as a Student," Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA, page 3, web: HarvardChem-Einstein-PDF: Max Talmud visited on Thursdays for six years. ^ www.chem.harvard.edu/herschbach/Einstein_Student.pdf Albert’s intellectual growth was strongly fostered at home. His mother, a talented pianist, ensured the children’s musical education. His father regularly read Schiller and Heine aloud to the family. Uncle Jakob challenged Albert with mathematical problems, which he solved with "a deep feeling of happiness."Most remarkable was Max Talmud, a poor Jewish medical student from Poland, "for whom the Jewish community had obtained free meals with the Einstein family." Talmud came on Thursday nights for about six years, and "invested his whole person in examining everything that engaged [Albert’s] interest." Talmud had Albert read and discuss many books with him. These included a series of twenty popular science books that convinced Albert "a lot in the Bible stories could not be true," and a textbook of plane geometry that launched Albert on avid self-study of mathematics, years ahead of the school curriculum. Talmud even had Albert read Kant; as a result Einstein began preaching to his schoolmates about Kant, with "forcefulness" ^ Einstein’s greatest intellectual stimulation came from a poor student who dined with his family once a week. It was an old Jewish custom to take in a needy religious scholar to share the Sabbath meal; the Einsteins modified the tradition by hosting instead a medical student on Thursdays. His name was Max Talmud, and he began his weekly visits when he was 21 and Einstein was 10. ^ Mehra, Jagdish (2001). "Albert Einstein’s first paper" (PDF). The Golden Age of Physics. World Scientific. ISBN 9810249853. Retrieved 4 March 2007. ^ Highfield, Roger; Carter, Paul (1993). The Private Lives of Albert Einstein. London: Faber and Faber. p. 21. ISBN 0-571-17170-2. ^ Highfield & Carter (1993, pp. 21,31,56–57) ^ Letter Einstein to Marić on 3 October 1900 (Collected Papers Vol. 1, document 79). ^ "A Brief Biography of Albert Einstein". April 2005. Retrieved 11 June 2007. ^ Alberto A Martínez (April 2004). "Arguing about Einstein’s wife". Physics World. Retrieved 21 November 2005. ^ Allen Esterson. "Mileva Marić: Einstein’s Wife". Retrieved 23 February 2007. ^ John Stachel. "“Albert Einstein and Mileva Maric. A Collaboration That Failed to Develop.” In: Creative Couples in the Sciences, H. M. Pycior et al. (ed)" (PDF). Retrieved 23 February 2007. ^ This conclusion is from Einstein’s correspondence with Marić. Lieserl is first mentioned in a letter from Einstein to Marić (who was staying with her family in or near Novi Sad at the time of Lieserl’s birth) dated 4 February 1902 (Collected papers Vol. 1, document 134). ^ Albrecht Fölsing (1998). Albert Einstein: A Biography. Penguin Group. ISBN 0140237194; see section I, II, ^ Highfield & Carter 1993, p. 216 ^ Now the "Swiss Federal Institute of Intellectual Property". Retrieved 16 October 2006.. See also their "FAQ about Einstein and the Institute". ^ Peter Galison, "Einstein’s Clocks: The Question of Time" Critical Inquiry 26, no. 2 (Winter 2000): 355–389. ^ Gallison, Question of Time. ^ Galison, Peter (2003). Einstein’s Clocks, Poincaré’s Maps: Empires of Time. New York: W.W. Norton. ISBN 0393020010. ^ a b "Einstein archive at the Instituut-Lorentz." Instituut-Lorentz. 2005. Retrieved on 21 November 2005. ^ This did not become possible until the development of alpha particle scintillation detectors early in the twentieth century. Rutherford invited Mach to take a look at the scintillation screen in a dark room, where the impact of individual alpha particles (Helium nuclei) are directly visible to the dark adapted eye. ^ (Einstein 1905b) ^ an account may be found here ^ The charge of a mole of electrons was known and measured as Faraday’s constant. Dividing by the charge of a single electron, measured by Millikan, gives Avogadro’s number. ^ (Einstein 1905d) ^ Hawking, S. W. (2001). The Universe in a Nutshell. Bantam Books. ISBN 0-55-380202-X. ^ Schwartz, J.; McGuinness, M. (1979). Einstein for Beginners. Pantheon Books. ISBN 0-39-450588-3. ^ (Einstein 1905e) ^ For a discussion of the reception of relativity theory around the world, and the different controversies it encountered, see the articles in Thomas F. Glick, ed., The Comparative Reception of Relativity (Kluwer Academic Publishers, 1987), ISBN 9027724989. ^ Pais, Abraham (1982). Subtle is the Lord. The Science and the Life of Albert Einstein. Oxford University Press. pp. 382–386. ISBN 019853907X. ^ Einstein, Albert (1905). "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt". Annalen der Physik 17: 132–148. Retrieved 27 June 2009. ^ (Einstein 1905a). ^ Pais, Abraham (1982). Subtle is the Lord. The Science and the Life of Albert Einstein. Oxford University Press. p. 522. ISBN 019853907X. ^ Levenson, Thomas. "Einstein’s Big Idea." Public Broadcasting Service. 2005. Retrieved on 25 February 2006. ^ Einstein, A.. "Relativitätsprinzip und die aus demselben gezogenen Folgerungen (On the Relativity Principle and the Conclusions Drawn from It)". Jahrbuch der Radioaktivität (Yearbook of Radioactivity) 4: 411–462. page 454 (Wir betrachen zwei Bewegung systeme ...) ^ Einstein, Albert (1911). "On the Influence of Gravity on the Propagation of Light". Annalen der Physik 35: 898–908. doi:10.1002/andp.19113401005. (also in Collected Papers Vol. 3, document 23) ^ a b Crelinsten, Jeffrey. "Einstein’s Jury: The Race to Test Relativity." Princeton University Press. 2006. Retrieved on 13 March 2007. ISBN 9780691123103 ^ (Einstein 1915) ^ "Two friends in Leiden". Retrieved 11 June 2007. ^ Crelinsten, Jeffrey (2006). Einstein’s Jury: The Race to Test Relativity. Princeton University Press. pp. 103–108. ISBN 978-0-691-12310-3. Retrieved 13 March 2007. ^ Crelinsten, Jeffrey (2006). Einstein’s Jury: The Race to Test Relativity. Princeton University Press. pp. 114–119. ISBN 978-0-691-12310-3. Retrieved 13 March 2007. ^ a b Andrzej, Stasiak (2003). "Myths in science". EMBO reports 4 (3): 236. doi:10.1038/sj.embor.embor779. Retrieved 31 March 2007. ^ "The genius of space and time". The Guardian. 17 September 2005. Retrieved 31 March 2007. ^ Schmidhuber, Jürgen. "Albert Einstein (1879–1955) and the ’Greatest Scientific Discovery Ever’." 2006. Retrieved on 4 October 2006. ^ See the table in MathPages Bending Light ^ Hentschel, Klaus and Ann M. (1996). Physics and National Socialism: An Anthology of Primary Sources. Birkhaeuser Verlag. xxi. ISBN 3-76-435312-0. ^ For a discussion of astronomers’ attitudes and debates about relativity, see Crelinsten, Jeffrey (2006). Einstein’s Jury: The Race to Test Relativity. Princeton University Press. ISBN 0691123101., especially chapters 6, 9, 10 and 11. ^ (Einstein 1917a) ^ Heilbron, 2000, p. 84. ^ Kant, Horst. “Albert Einstein and the Kaiser Wilhelm Institute for Physics in Berlin.” in Renn, Jürgen. “Albert Einstein – Chief Engineer of the Universe: One Hundred Authors for Einstein.” Ed. Renn, Jürgen. Wiley-VCH. 2005. pp. 166–169. ISBN = 3527405747 ^ (Einstein 1917b) ^ (Einstein 1924) ^ "Cornell and Wieman Share 2001 Nobel Prize in Physics". 9 October 2001. Retrieved 11 June 2007. ^ (Einstein 1950) ^ a b Wright, Karen (30 September 2004). "The Master’s Mistakes". Discover Magazine. Retrieved 15 October 2009. ^ Wright, Karen (30 September 2004). "The Master’s Mistakes". Discover Magazine. Retrieved 15 October 2009. ^ Moore, Walter (1989). Schrödinger: Life and Thought. Cambridge: Cambridge University Press. ISBN 0-521-43767-9. ^ Goettling, Gary. Einstein’s refrigerator Georgia Tech Alumni Magazine. 1998. Retrieved on 21 November 2005. Leó Szilárd, a Hungarian physicist who later worked on the Manhattan Project, is credited with the discovery of the chain reaction ^ In September 2008 it was reported that Malcolm McCulloch of Oxford University was heading a three-year project to develop more robust appliances that could be used in locales lacking electricity, and that his team had completed a prototype Einstein refrigerator. He was quoted as saying that improving the design and changing the types of gases used might allow the design’s efficiency to be quadrupled.Alok, Jha (21 September 2008). "Einstein fridge design can help global cooling". The Guardian. ^ (Einstein 1969). A reprint of this book was published by Edition Erbrich in 1982, ISBN 388682005X ^ (Einstein 1935) ^ Aspect, Alain; Dalibard, Jean; Roger, Gérard (1982). "Experimental test of Bell’s inequalities using time-varying analyzers". Physical Review Letters 49 (25): 1804–1807. doi:10.1103/PhysRevLett.49.1804. The first of many experimental tests relating to EPR. ^ [refspace.com/quotes/s%253A0 "refpace | Popular quotes"], [[Refpace. Retrieved December 20, 2009. ^ Brian, Dennis (1996). Einstein: A Life. New York: John Wiley & Sons. p. 127. ISBN 0471114596. ^ "Belief in God a 'product of human weaknesses': Einstein letter", CBC News. Retrieved December 16, 2009. ^ "Letters of Note: The word God is a product of human weakness", Letters of Note. Retrieved December 16, 2009. ^ Pulzer, Peter G.J. (2003). "Jews and the German state: the political history of a minority, 1848–1933". Blackwell Publishers. Retrieved 21 October 2009. ^ Leonhard, Elke (1993). "Von postrevolutionärer Scheinblüte zum politischen Bankrott; Weimars liberale Parteien DDP und DVP" (in German). Sozialdemokratischer Pressedienst. Retrieved 21 October 2009. ^ Holborn, Hajo (1971). "Deutsche Geschichte in der Neuzeit, III" (in German). R. oldenbourg. Retrieved 21 October 2009. ^ Geller, Jay Howard (2005). "Jews in post-Holocaust Germany, 1945–1953". Cambridge University Press. Retrieved 21 October 2009. ^ "Nationalist-Communist Civil War 1927–1937". Retrieved 3 October 2007. ^ Zionism and Israel Information Center. "Albert Einstein and Zionism". Retrieved 14 August 2008. ^ Calaprice, Alice (2005). The new quotable Einstein. Princeton University Press. p. 173. ISBN 0-691-12075-7. Other versions of the quote exist. ^ "Why Socialism?". Retrieved 30 June 2007. ^ Butcher, Sandra Ionno (May 2005). "The Origins of the Russell–Einstein Manifesto" (PDF). Council of the Pugwash Conferences on Science and World Affairs. Retrieved 2 May 2007. ^ Ken Gewertz (12 April 2007). "Albert Einstein, Civil Rights activist". Harvard University Gazette. Retrieved 11 June 2007. ^ "The Case of the Scientist with a Pulsating Mass". 14 June 2002. Retrieved 11 June 2007. ^ Albert Einstein Archives (April 1955). "Einstein Archives Online". Retrieved 14 March 2007. ^ Cohen, Jr; Graver, Lm (november 1995). "The ruptured abdominal aortic aneurysm of Albert Einstein". Surgery, gynecology & obstetrics 170 (5): 455–8. ISSN 0039-6087. . edit ^ O’Connor, J.J.; Robertson, E.F. (1997). "Albert Einstein". The MacTutor History of Mathematics archive. School of Mathematics and Statistics, University of St. Andrews. Retrieved 14 March 2007. ^ "Dr. Albert Einstein Dies in Sleep at 76. World Mourns Loss of Great Scientist.". New York Times. 19 April 1955, Tuesday. "Princeton, New Jersey, 18 April 1955. Dr. Albert Einstein, one of the great thinkers of the ages, died in his sleep here early today." ^ "The Long, Strange Journey of Einstein’s Brain". Retrieved 3 October 2007. ^ New York Times obituary ^ BBC (11 July 2006). "Letters Reveal Einstein Love Life". BBC News (BBC). Retrieved 14 March 2007. ^ Roger Richman Agency (2007). "Albert Einstein Licensing". Retrieved 25 March 2007.; Archive copy at the Internet Archive ^ "Einstein". Corbis Rights Representation. Retrieved 8 August 2008. ^ The New Yorker April 1939 pg 69 Disguise ^ a b Golden, Frederic (3 January 2000). "Person of the Century: Albert Einstein". Time. Retrieved 25 February 2006. ^ [1] ^ "Albert Einstein – Frequently Asked Questions". Nobelprize.org. 18 April 1955. Retrieved 7 January 2009. ^ BBC (11 July 2006). "Letters Reveal Einstein Love Life". BBC News (BBC). Retrieved 25 November 2008. ^ See Albert Einstein, "Geometry and Experience," (1921), reprinted in Ideas and Opinions. ^ Isaacson, Walter (3 January 2000). "Person of the Century: Why We Chose Einstein". Time. Retrieved 16 July 2007. ^ "Mother Teresa Voted by American People as Most Admired Person of the Century". 31 December 1999. Retrieved 13 August 2008. ^ "World Year of Physics 2005". Retrieved 3 October 2007. ^ "Einsteinium and Fermium". Retrieved 6 June 2009. ^ "History of the International Atomic Energy Agency – The First Forty Years" (pdf). International Atomic Energy Agency. p. 30. Retrieved 6 June 2009. ^ Howard, Don, and Stachel, John J. Einstein: The Formative Years, 1879–1909, p. 159, Springer (2000) ^ Einstein voted "greatest physicist ever" by leading physicists: BBC news, Monday, 29 November 1999, http://news.bbc.co.uk/2/hi/science/nature/541840.stm ^ Spratt, Christopher E. (April 1990). "The Hungaria group of minor planets". Royal Astronomical Society of Canada, Journal (ISSN 0035-872X) 84 (2): 123–131. ^ Biography of J. Schwinger from University of St Andrews, MacTutor History of Mathematics Archive (Last accessed 17 December 2006). ^ a b The Month at Caltech, April 1954 issue, p. 20 (Last accessed on 4 September 2007). ^ The Americana Annual 1962: An Encyclopedia of the Events of 1961. Americana Corporation. 1962. ISSN 0196-0180. ^ Astronautics and Aeronautics, 1967. Scientific and Technical Information Branch, NASA. 1968. ISSN 0519-2366. ^ Sigmund, Dawson, Muhlberger (2006). Kurt Godel: The Album. Wiesbaden: Vieweg. ISBN 3834801739. ^ Report of the Director for 1948–53, Institute for Advanced Study, p. 30 (1954). (pdf file last accessed on 6 September 2007). ^ "Pugwash Online". Retrieved 20 December 2009. ^ Walhalla, official guide booklet. p. 3. Translated by Helen Stellner and David Hiley, Bernhard Bosse Verlag Regensburg, 2002 ^ "Walhalla Ruhmes- und Ehrenhalle" (in German). Retrieved 3 October 2007.