Physicists From Germany

"... Newton’s revelations about gravity were motivated by the availability of quantitative observational data of the . His theory seemed to be a complete and well-proven concept and it held for centuries. It was not until the last century that Einstein derived gravitation from the underlying spacetime concept. Einstein’s work was not provoked by observational facts, but was motivated on a purely theoretical basis, which makes his formalism and prediction particularly elegant. General Relativity presented a big change in concept beyond Newton and it predicted specific phenomena. These effects have been verified experimentally and to this date are being tested to higher and higher accuracy. The classical tests were: and . Einstein’s General Relativity corrections are now being used on an everyday basis. A typical example is the , where General Relativity effects yield a combined effect of 38 per day. The accuracy to which General Relativity can be confirmed is entirely limited by experimental uncertainties and none of the uncertainty originates from the theoretical description, since General Relativity has no adjustable parameters. It seems that to date, gravity is exactly described by General Relativity."

"We report the first results from a new that uses a 3 ton source mass which slowly rotates around the . The highly symmetric pendulum consists of a - composition suspended from a thin torsion fiber. The counter-balanced source is shaped to minimize s."

"The past fifteen years of laboratory-scale gravitational experimentation have been marked by many new and exciting developments. The field received a lot of impetus by the hypothesis of a ”” ... in 1986. This very testable new force would have been a blatant violation of the equivalence principle. The evidence for the 5th force was partially based on a reanalysis of the torsion balance data of of the early 1900’s. Immediately several groups around the world started to do . The availability of new technologies combined with many new and creative ideas quickly led to several refined measurements by which the 5th force in its postulated form could be conclusively ruled out. However, the physics community was once again reminded of the importance of the equivalence principle which lies at the foundation of general relativity. Tests of the equivalence principle become particularly important for , most of which predict an equivalence principle breakdown at some level. In addition it is generally believed that the can only be complete with the existence of new particles which could exist at high masses as well as at the ultra low energies. The latter frontier being covered by laboratory-gravity tests."

"... On my father’s side, I come from a family of artists and architects. My grandfather was a Bauhaus architect in Germany and my grandmother was a painter. When my father as a child was tinkering around in the basement with chemistry sets, his mother said to him, “You’ll never make a living in science. Why don’t you go into the family business, the arts?” Well, he defied that advice. He was actually a PhD student with Heisenberg in Göttingen, and then a post-doc with Enrico Fermi in Chicago. After that he went to Caltech where he switched to biology and became one of the founders of the field of molecular biology. He founded the department of molecular biology at the . My mother was from a town on the Swiss-German border called , and she actually got her PhD in biology at age 22."

"... in the seventies the work of and Rubin ... looked at galaxies and found evidence for dark matter in every single one."

"s and massive s in the mass range 2–20 have been proposed as candidates to provide the in the halo of our galaxy."

""What is the Universe made of?" The question is one of the deepest unanswered mysteries in all of human existence. Solving the puzzle has been my life's work and is the hottest research topic in cosmology and particle physics today."

"At about this same time Dirac wrote a paper that proposed a general theory of how measurements should be described in quantum mechanics. Similar work was also done by P. Jordan in Göttingen. These two papers constitute what is called transformation theory, because they show how one can transform information gained by measuring one quantity into predicting information about another."

"Born approximation is a familiar and convenient approximation in handling scattering problems. It is adequate, or at least informative, in so many cases that we tend to develop the habit of using its first-order term without always checking the conditions for its applicability."

"Richard Dalitz, in: (quote from page v)"

"After the war, Bethe went back to Cornell, where he helped build an outstanding research center in high-energy physics. Peierls returned to Birmingham, where he created the outstanding school of theoretical physics in Western Europe. The two physicists established a pipeline between the two institutions and offered their generous evaluations of the young postdocs and colleagues—Hugh McManus, Edwin Salpeter, Stuart Butler, Richard Dalitz, Freeman Dyson, and others—that they sent to one another. Their correspondence likewise gives perceptive overviews of advances in high-energy physics, especially of the progress made after 1955 in the nuclear many-body problem on which Bethe was concentrating. Their letters also concern policy challenges posed by, for example, the cold war, nuclear weaponry, nuclear test ban treaties, and antiballistic missiles."

"It is Rudi's genius to show the reader in concrete terms how to do the predicting after some organized thinking."

"An important episode for my understanding of conduction problems arose from a paper by Kretschmann, ... who attacked the then accepted theory of conductivity and claimed that the basis of the papers by Bloch and others was quite wrong. He had a number of objections which were mostly not very well conceived, but he claimed, in particular, that in the usual derivation of the Boltzmann equation one had made unjustified use of perturbation theory. In trying to defend the theory I therefore set out to prove that perturbation theory was in order, and to my amazement I found that this was very questionable, if not exactly for the reasons given by Kretschmann. It appeared that the usual application of Fermi's 'golden rule' depended on the inequality ħ/τ ≪ kT, where τ is the collision time. This was not satisfied for many metals. Indeed Landau's dimensional analysis made them comparable. ..."

"Any theoretical physicist has met, in his introduction to the subject, the simplest examples of Schrödinger's equation, including the harmonic oscillator. In demonstrating its solution, it is usually shown that for energies satisfying the usual quantum condition, E = (n + ½)ħω (1.1.1) where n is a non-negative integer and ω the frequency, the equation has a solution satisfying the correct boundary conditions. It is equally important to know that these are the only solutions, i.e., that for an energy not equal to (1.1.1) no admissible solution exists. This negative statement is not usually proved in elementary treatments, or else it is deduced from quite elaborate discussions of the convergence and behavior of a certain infinite series. It is therefore surprising to find that the result can be seen without any complicated algebra."

"The atoms which constitute a solid consist of nuclei and electrons. For a description of the state of the solid it is not, however, necessary to specify the state of all the Z electrons of each atom, since we can eliminate most or all of them by a principle that is familiar from the theory of molecules. ... Since the atomic nuclei are much heavier than the electrons, they move much more slowly, and it is therefore reasonable to start from the approximation in which they are taken to be taken to be at rest, though not necessarily in the regular positions."

"When I arrived in Leipzig, Heisenberg was working on the theory of ferromagnetism. It was known the magnetism of such substances as iron was due to the "spin" of the electrons inside the substance. Each electron spins like a little top, and in the iron there is a "molecular field", a force that tends to align the spin of each electron with that of its neighbors. But the nature of this field was unknown. It could not be a magnetic effect because magnetic forces are much too weak to account for the observed behaviour. Heisenberg saw that the answer lay in the Pauli exclusion principle, which says that no two electrons can be in exactly the same state. Thus two electrons with the same spin orientation keep out of each other's way; while this repulsion may increase their energy of motion, it diminishes their mutual repulsion, and can therefore lead to a decrease in total energy, making the parallel alignment of the electron spins energetically favourable. He had encountered this mechanism in the theory of atomic spectra and concluded that it was also responsible for ferromagnetism."

"1.4 Types of binding ... The most important types of force are as follows: (a) Electrostatic forces. In an ionic crystal the attraction is mainly due to the Coulomb interaction between point charges. This is particularly amenable to calculation, and a great deal of work has been done on it. The force is a 'two-body' force, i.e. the interaction between two given ions is independent of the positions of any other ions that may be present. ... (b) Van der Waals forces. This name describes the effect that a neutral and isotropic atom can acquire a polarization under the influence of an electric field, and even two neutral isotropic atoms will induce small dipole moments in each other, due to the fluctuating moments which they possess because of the existence of virtual excited states. ... (c) Homopolar binding. These are forces like those effective in homopolar molecules, and we know they are due to the exchange of electrons between the atoms. In molecular crystals (H2, Cl2, etc.) these bonds can easily be localized and we can start from a description of the molecular by the methods of quantum chemistry and then add the relatively weak forces between different molecules. In other cases, however, such as diamond or graphite, each atom shares some valence electrons with each of its neighbors, and it is therefore not possible to single out any given groups of atoms that may be regarded as chemically saturated. The quantitative discussion of such forces is not easy. ... (d) Overlap. If two atoms approach so closely that their electron shells overlap, then there is a strong repulsive force between them. ... (e) Metallic bond. ... it is worth noting that in the case of a metal the presence and motion of the conduction electrons is an important factor in holding the crystal together and in determining its structure."

"His contributions to condensed matter physics were largely on fundamental questions, establishing the principles of this subject. Most of this work was done during the years 1928–37, but much of it could not be tested until the experimental techniques needed for this had become sufficiently developed. ... Rudolf Peierls's work in nuclear physics began in 1933, when James Chadwick challenged him and Hans Bethe to explain his first measurements of the cross-section for photo-disintegration of the deuteron. Peierls's experience in this field developed rapidly within the next few years, on both practical questions and academic research, to the point where he and Otto Frisch could confidently conclude that the construction of an atomic bomb would be quite possible using 235U, which could be obtained obtained from natural uranium by a feasible separation process, and they pointed this out in the famous Frisch-Peierls Memorandum of 1940 which they sent to the British government. This led to the Atomic Bomb Project, at first in Britain under the name "Tube Alloys Project" and later in USA as the "Manhattan District Project", which many of the UK scientists, including both Peierls and Frisch, were sent to join at the end of 1943."

"With both light and electrons, one was faced with the so-called "wave-particle duality"; both could be regarded as waves for some purposes and as particles for others. An important step in resolving this paradox was a paper by Max Born in July 1926, in which he suggested that the waves determine the probability of finding the particle in a particular place. This idea was already considered much earlier by Einstein, but it was rejected by him. This interpretation of the theory was further developed in the spring of 1927 by Heisenberg, who formulated his "uncertainty principle" ..."

"The combination of interest in physics and in philosophy was uncommon in the United States, and physicists who deviated from the narrow path were looked down upon by their colleagues. Philosophy of physics was definitely regarded as an aberrant, evasive sort of discipline, practiced by physicists who 'could not make it' in their straight profession and, in somewhat greater numbers, by philosophers whose knowledge of physics was inadequate."

"Philosophy shows itself to be alive when it raises, again and again, the deep concerns that plague man's reason; it dies when it presumes to have resolved them with finality. Determinism and freedom in their conjunction pose one of the eternal questions ..."

"... during the last two decades, there has been introduced into physical methodology a principle of utmost philosophical importance, easily rivaling that of relativity, and, in some respects, indeed that of causality. Discovered by Pauli in 1925, it immediately elucidate a whole realm of physical facts and was accepted by physicists with wide acclaim. Called the exclusion principle—or Pauli principle, or principle of anti-symmetry—it was embodied in the axiomatics of quantum mechanics; its pecular methodological significance passed out of view."

"There are 10500 or more metastable vacua, which can be thought of as local minima in a huge, multidimensional potential landscape. They differ not only in the value of their vacuum energy, but in their entire low-energy effective field theory, which is determined by local properties near the foot of a valley and thus only very indirectly by the fundamental building blocks of the landscape. Different vacua will have different matter content, coupling constants, and forces. We will not predict the standard model uniquely. We will have to predict many of the features of our universe statistically, from their relative abundance in the landscape."

"The vacua with positive cosmological constant trap the universe in eternal inflation. They decay only locally, by producing bubbles of new vacua. Thus, every vacuum in the landscape will be realized an infinite number of times in different, causally disconnected regions. Each bubble expands to become an infinite open universe embedded in the global spacetime."

"In our search for new ideas, beauty plays many roles. It's a guide, a reward, a motivation. It's also a systematic bias."

"The Standard Model is based on a principle called "gauge symmetry". According to this principle, every particle has a direction in an internal space, much like the needle in a compass, except that the needle doesn't point anywhere you can look."

"The logic of arguments from naturalness resembles the attempt to predict the plot of a long-running TV series. If the hero -- here, naturalness --is in a pickle, certainly he will survive, so something must happen to turn around a situation that looks bleak."

"If you want to rely on non-empirical assessment, you have to make really sure that scientists’ judgment is as objective as humanly possible. And the environment in academia presently is absolutely unsuitable for this. You just can’t be sure how much sociology affects judgment. And no physicist I know makes any effort to consciously address cognitive biases, such as wishful thinking, loss aversion, or the use of aesthetic criteria. It’s just not something that they pay attention to because it’s never been necessary before. As long as you have data for guidance, you’ll be swiftly corrected."

"To make predictions with inflation one cannot just say “there once was exponential expansion and it ended somehow.” No, to be able to calculate something, one needs a mathematical model. The current models for inflation work by introducing a new field – the “inflaton” – and give this field a potential energy. The potential energy depends on various parameters. And these parameters can then be related to observations. The scientific approach to the situation would be to choose a model, determine the parameters that best fit observations, and then revise the model as necessary – ie, as new data comes in. But that’s not what cosmologists presently do. Instead, they have produced so many variants of models that they can now “predict” pretty much anything that might be measured in the foreseeable future."

"if you pile up enough of it, even shit can look beautiful."

"In no other type of warfare does the advantage lie so heavily with the aggressor."

"It is difficult to compare a differential geometer with a function theorist, or those working on ordinary and partial differential equations with numerical analysts. Christoffel not only contributed to all these fields, but his interests extended to orthogonal polynomials and continued fractions, and the applications of his work to the foundations of tensor analysis, to geodetical science, to the theory of shock waves, to the dispersion of light. Nevertheless, it is widely recognised, at least in the German speaking countries of Europe, that Riemann was the best mathematician of the 19th century, behind Gauss and ahead of Weierstrass. In our opinion Christoffel's teacher Dirichlet, belongs to the next most important group of mathematicians which includes (in chronological order of birth) Jacobi, Kummer, Kronecker, Dedekind, Cantor and Klein. Christoffel himself should be placed in a second group following these. This second group, which may partly overlap with the former, would include such illustrious names as Möbius, von Staudt, Plücker, Heine, Du Bois-Reymond, Carl Neumann, Lipschitz, Fuchs, Schwarz, Hurwitz and Minkowski."

"The development of abstract algebra, which is one of the most distinctive innovations of twentieth century mathematics, is largely due to her—in published papers, in lectures, and in personal influence on her contemporaries."

"I do not see that the sex of the candidate is an argument against her admission as Privatdozent [teaching assistant]. After all, we are a university and not a bathing establishment."

"[I]t surely is not much of an exaggeration to call her the mother of modern algebra."

"A keen mind and infectious enthusiasm for mathematical research made Emmy Noether an effective teacher. Her classroom technique, like her thinking, was strongly conceptual. Rather than simply lecturing, she conducted discussion sessions in which she would explore a topic with her students. ...Outstanding mathematicians often make their greatest contributions early in their careers. Emmy Noether was an exception: she began to produce her most powerful and creative work around the age of 40. ...She never attained the top rank of full professor, although she contributed so much to making Göttingen the premier mathematical center in Europe—many would say in the world. When the Nazis seized power in 1932, one of their first acts was to deprive non-Aryan[s]... of their positions. ...For a time Emmy Noether continued to meet informally with students and colleagues, inviting groups to her apartment... In the meantime, efforts were being made on her behalf... and she secured a temporary position at , a new college for women near Philadelphia."

"In the judgement of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began. In the realm of algebra, in which the most gifted mathematicians have been busy for centuries, she discovered methods which have proved of enormous importance in the development of the present-day generation of younger mathematicians."

"s were old acquaintances from classical physics. ... asserts that any continuous symmetry leads to a conservation law. It is rather intuitive... After all, symmetry reflects invariance under a transformation, and therefore there must exist a quantity that remains invariant or, in other words, that is conserved. For instance, a circle is invariant under rotations about its centre. ...Hence, the symmetry of a circle is associated with the conservation of distance ...The power of Noether's theorem was to show that this intuitive concept is valid for any continuous symmetry ...from Noether's theorem we discover that the conservation of electric charge is the consequence of the special rotational symmetry of QED... [acting upon] an abstract space defined by the quantum fields."

"The first "modern" text in algebra, van der Waerden's Modern Algebra, which appeared in 1931, was heavily influenced by Emmy Noether. It is an enlightening exercise to compare this work with algebra books of just a few decades earlier to see the profound influence that she had on our present conception of algebra. Nevertheless, even Noether realized that one needs to be familiar with a wide variety of concrete examples from all parts of mathematics before one can understand the value of the generalizations she was able to make."

"Following ['s] work, Emmy Noether, in 1921, transferred s for ideals in algebraic number fields to those for ideals in arbitrary rings. ...Noether and her students made other major contributions to ring theory before she turned to a treatment of finite group representations from an ideal-theoretic point of view. ...Chain conditions had been used since the days of Hölder and Dedekind but were brought to the fore in the 1921 paper [above]. Through Noether's influence... algebraic notions were linked to topology in the work of and ..."

"With the appearance of Einstein's general theory of relativity, Hilbert turned to that subject, which also occupied his colleague Felix Klein. Interestingly, the most lasting mathematical contribution out of this effort came from an algebraist who had recently engaged in studies of differential invariants. This was Emmy Noether... the daughter of the algebraic geometer , whom Hilbert and Klein brought to Göttingen to assist them in research. Her results were published in 1918; best known as ""..."

"She continually advised her students to read and re-read Dedekind's works, in which she saw an inexhaustible source of inspiration. When praised for her own innovations, she used to repeat: "Es steht alles schon bei Dedekind.""

"The third and last exception to general sterility connects the arithmetic of forms with that other major outgrowth of ancient diophantine analysis, the Gaussian concept of congruence. Dickson in 1907 began the congruencial theory of forms, in which the coefficients of the forms are either natural integers reduced modulo p, p prime, or elements of a Galois field. The linear transformations in the theory, corresponding to those in the classical problem of equivalence, were similarly reduced, and hence modular invariants and covariants were defineable. By 1923 the theory was practically worked out, except for two central difficulties, by Dickson and his pupils. Simplified derivations for some of the results were given (1926) by E. Noether by an application of her methods in abstract algebra."

"[Noether] taught us to think in terms of simple and general algebraic concepts—homomorphic mappings, groups and rings with operators, ideals—and not in cumbersome algebraic computations; and she thereby opened up the path to finding algebraic principles in places where such principles had been obscured by some complicated special situation."

"The third great epoch in the extension of arithmetic is that of the twentieth century after 1910. To anticipate, the introduction of general methods into , beginning in the first decade of the twentieth century, prepared that vast field of mathematics, first opened up by Hamilton and Grassman in the 1840s, for partial arithmetization in the second and third decades of the century. In 1910, E. Steinitz... proceeding from, and partly generalizing, Kronecker's theory (1881) of "algebraic magnitudes," made a fundamental contribution to the modern theory of (commutative) fields. His work was one of the strongest impulses to the abstract algebra of the 1920s and 1930s, with its accompanying generalized arithmetic. The outstanding figure in the later phase of this development is usually considered to be Emmy Noether... who, with her numerous pupils, laid down the broad foundations of the modern abstract theory of ideals, also a great deal more in the domain of modern algebra. The application of this work to the 'integers' of linear s affords the ultimate extension up to 1940 of common arithmetic."

"Dedekind's concern with algebra goes back to the 1850s, when he attended Dirichlet's lectures on number theory... and pursued intensive studies of . ...[H]e developed an abstract treatment of elementary group theory at that time. After Dirichlet's death, Dedekind was charged with publishing Dirichlet's lectures on number theory. In appendices he presented... his ideal theory... The most axiomatic approach [1894]... was the one that especially influenced Emmy Noether and her school of algebraists in the 1920s."

"demonstrates that wherever there is symmetry in nature, there is also a conservation law, and vice versa. In other words, the symmetries of space and time are not only linked with conservation of energy, momentum, and angular momentum, but each implies the other. Conservation laws are necessary consequences of symmetries, and symmetries necessarily entail conservation laws. The simplicity, power, and depth of Noether's theorem only slowly became apparent. Today, it is an indispensable part of the groundwork of modern physics... [with] over a dozen important conservation laws and their associated symmetries..."

"Emmy Noether introduced the notion of a representation space— a vector space upon which the elements of the algebra operate as linear transformations, the composition of the linear transformations reflecting the multiplication in the algebra. By doing so she enables us to use our geometric intuition. Her point of view stresses the essential fact about a simple algebra, namely, that it has only one type of irreducible space and that it is faithfully represented by its operation on this space. 's statement that the simple algebra is a total matrix algebra over a quasifield is now more understandable. It simply means that all transformations of this space which are linear with respect to a certain quasifield are produced by the algebra. This treatment of algebras may be found in 's '. Recently it has been discovered that this last described treatment of simple algebras is capable of generalization to a far wider class of rings."

"The work of Galois and his successors showed that the nature, or explicit definition, of the roots of an is reflected in the structure of the group of the equation for the field of its coefficients. This group can be determined non-tentatively in a finite number of steps, although, as Galois himself emphasized, his theory is not intended to be a practical method for solving equations. But, as stated by Hilbert, the and the theory of s have their common root in that of algebraic fields. The last was initiated by Galois, developed by Dedekind and Kronecker in the mid-nineteenth century, refined and extended in the late nineteenth century by Hilbert and others, and finally, in the twentieth century, given new direction by the work of Steinitz in 1910, and in that of E. Noether and her school since 1920."

"Her thesis ends with a table of the complete system of covariant forms for a given ternary quartic consisting of not less than 331 forms in symbolic representation. It is an awe-inspiring piece of work; but today I am afraid we should be inclined to rank it among those achievements with regard to which Gordan himself once said when asked about the use of the theory of invariants: "Oh, it is very useful indeed; one can write many theses about it.""