US-amerikanischer Physiker und Nobelpreisträger
106 quotes found
"Das Bemühen, das Universum zu verstehen, ist eines der ganz wenigen Dinge, die das menschliche Leben ein wenig über die Stufe einer Farce erheben, und gibt ihm etwas von der Anmut der Tragödie."
"„Je begreiflicher uns das Universum wird, desto sinnloser erscheint es auch.“"
"„Dass Elementarteilchenphysik in unseren Augen fundamentaler als andere Zweige der Physik erscheint, liegt daran, dass sie tatsächlich fundamentaler ist.“"
"Eine der größten Errungenschaften der Wissenschaft ist nicht, es intelligenten Leuten unmöglich zu machen, religiös zu sein, sondern es ihnen zumindest zu ermöglichen, nicht religiös zu sein. Dahinter sollten wir nicht zurückfallen."
"„Mit oder ohne Religion würden gute Menschen Gutes tun und böse Menschen Böses. Aber damit gute Menschen Böses tun, bedarf es der Religion.“"
"„Ich denke, dass ein enormer Schaden von der Religion angerichtet wurde – nicht nur im Namen der Religion, sondern tatsächlich von der Religion.“ – The Atheism Tapes, BBC, 2004."
"... most physicists would probably agree that the place of local fields is nowhere so secure as in the theory of photons and gravitons, whose properties seem indissolubly linked with the space-time concepts of gauge invariance (of the second kind) and/or Einstein's equivalence principle."
"As everyone today knows, in specifying the value of a gauge coupling constant it is necessary to say not only what its value is but where — that is at what normalization scale — it has that value."
"Elementary particles are terribly boring, which is one reason why we're so interested in them."
"Considering the pervasive importance of quantum mechanics in modern physics, it is odd how rarely one hears of efforts to test quantum mechanics experimentally with high precision.…The trouble is that it is very difficult to find any logically consistent generalization of quantum mechanics. One obvious target for generalization is the linearity of quantum mechanics, but if we arbitrarily add nonlinear terms to the Schrodinger equation, how do we know that the theory we obtain will have a sensible physical interpretation? At least in part, it is the dearth of generalized versions of quantum mechanics that has made it so hard to plan experimental tests of quantum mechanics."
"The more the universe seems comprehensible, the more it also seems pointless."
"So what happens to the effective field theories of electroweak, strong, and gravitational interactions at energies of order 1015–1018 GeV? I know of only two plausible alternatives. One possibility is that the theory remains a quantum field theory, but one in which the finite or infinite number of renormalized couplings do not run off to infinity with increasing energy, but hit a fixed point of the renormalizable group equations. ... The other possibility, which I have to admit is a priori more likely, is that at very high energy we will run into really new physics, not describable in terms of a quantum field theory. I think that by far the most likely possibility is that this will be something like a string theory."
"Either by God you mean something definite or you don't mean something definite. If by God you mean a personality who is concerned about human beings, who did all this out of love for human beings, who watches us and who intervenes, then I would have to say in the first place how do you know, what makes you think so? And in the second place, is that really an explanation? If that's true, what explains that? Why is there such a God? It isn't the end of the chain of whys, it just is another step, and you have to take the step beyond that."
"If you have bought one of those T-shirts with Maxwell's equations on the front, you may have to worry about its going out of style, but not about its becoming false. We will go on teaching Maxwellian electrodynamics as long as there are scientists."
"Religion is an insult to human dignity. With or without it you would have good people doing good things and evil people doing evil things. But for good people to do evil things, that takes religion."
"One of the great achievements of science has been, if not to make it impossible for intelligent people to be religious, then at least to make it possible for them not to be religious. We should not retreat from this accomplishment."
"In trying to get votes for the Superconducting Super Collider, I was very much involved in lobbying members of Congress, testifying to them, bothering them, and I never heard any of them talk about postmodernism or social constructivism. You have to be very learned to be that wrong."
"It seems to me that we are in the position of a company of players who have by chance found their way into a great theater. Outside, the city streets are dark and lifeless, but in the theater the lights are on, the air is warm, and the walls are wonderfully decorated. However, no scripts are found, so the players begin to improvise—a little psychological drama, a little poetry, whatever comes to mind. Some even set themselves to explain the stage machinery. The players do not forget that they are just amusing themselves, and that they will have to return to the darkness outside the theater, but while on the stage they do their best to give a good performance. I suppose that this is a rather melancholy view of human life, but melancholy is one of the distinctive creations of our species, and not without its own consolations."
"It seems that scientists are often attracted to beautiful theories in the way that insects are attracted to flowers — not by logical deduction, but by something like a sense of smell."
"There are those whose views about religion are not very different from my own, but who nevertheless feel that we should try to damp down the conflict, that we should compromise it. … I respect their views and I understand their motives, and I don't condemn them, but I'm not having it. To me, the conflict between science and religion is more important than these issues of science education or even environmentalism. I think the world needs to wake up from its long nightmare of religious belief; and anything that we scientists can do to weaken the hold of religion should be done, and may in fact be our greatest contribution to civilization."
"A superconductor of any kind is nothing more or less than a material in which a particular symmetry of the laws of nature, electromagnetic gauge invariance, is spontaneously broken. ... These rotations act on a two-dimensional vector, whose two components are the real and imaginary parts of the electron field, the quantum mechanical operator that in quantum field theories of matter destroys electrons. The rotation angle of the broken symmetry group can vary with location in the superconductor, and then the symmetry transformations also affect the electromagnetic potentials ... The symmetry breaking in a superconductor leaves unbroken a rotation by 180°, which simply changes the sign of the electron field. In consequence of this spontaneous symmetry breaking, products of any even number of electron fields have non-vanishing expectation values in a superconductor, though a single electron field does not. All of the dramatic exact properties of superconductors – zero electrical resistance, the expelling of magnetic fields from superconductors known as the Meissner effect, the quantization of magnetic flux through a thick superconducting ring, and the Josephson formula for the frequency of the AC current at a junction between two superconductors with different voltages – follow from the assumption that electromagnetic gauge invariance is broken in this way, with no need to inquire into the mechanism by which the symmetry is broken."
"If there is no point in the universe that we discover by the methods of science, there is a point that we can give the universe by the way we live, by loving each other, by discovering things about nature, by creating works of art. And that—in a way, although we are not the stars in a cosmic drama, if the only drama we're starring in is one that we are making up as we go along, it is not entirely ignoble that faced with this unloving, impersonal universe we make a little island of warmth and love and science and art for ourselves. That's not an entirely despicable role for us to play."
"There is a hope, which I nurse but I don't see being realized, that eventually we'll find that quantum mechanics as we know it now is just an approximation ..."
"'s kindness to me and my wife went beyond his help with this research. He had my wife and me to dinner at his house and at that dinner I went to the bathroom and I learned something about Källén that I don't think anyone knows. And that is that he had hand towels embroidered with the . And I mentioned this to Mrs. Källén and she said they were a present from Pauli."
"A theorist today is hardly considered respectable if he or she has not introduced at least one new particle for which there is no experimental evidence."
"In fact, there is something puzzling about the Higgs mass we now do observe. It is generally known as the “hierarchy problem.” Since it is the Higgs mass that sets the scale for the masses of all other known elementary particles, one might guess that it should be similar to another mass that plays a fundamental role in physics, the so-called Planck mass, which is the fundamental unit of mass in the theory of gravitation. (It is the mass of hypothetical particles whose gravitational attraction for one another would be as strong as the electric force between two electrons separated by the same distance.) But the Planck mass is about a hundred thousand trillion times larger than the Higgs mass. So, although the Higgs particle is so heavy that a giant particle collider was needed to create it, we still have to ask, why is the Higgs mass so small?"
"There’s something I’ve been working on for more than a year — maybe it’s just an old man’s obsession, but I’m trying to find an approach to quantum mechanics that makes more sense than existing approaches. I’ve just finished editing the second edition of my book, Lectures on Quantum Mechanics, in which I think I strengthen the argument that none of the existing interpretations of quantum mechanics are entirely satisfactory."
"It doesn't work to build half an accelerator. The particles need to go all the way around."
"Having taught quantum mechanics and written a book about it recently — a technical treatise — I find that I am not as happy about quantum mechanics as I used to be — not as dismissive of the critics. And it's a bad sign in particular that those physicists who are happy about quantum mechanics — who don't see anything wrong with it — don't agree with each other about what it means. ... And the problem has specifically to do with the act of measurement."
"Symmetry is not enough by itself. In electromagnetism, for example, if you write down all the symmetries we know, such as Lorentz invariance and gauge invariance, you don’t get a unique theory that predicts the magnetic moment of the electron. The only way to do that is to add the principle of renormalisability – which dictates a high degree of simplicity in the theory and excludes these additional terms that would have changed the magnetic moment of the electron from the value Schwinger calculated in 1948."
"One of the things that excited me so much about quantum chromodynamics after the work of Gross and Wilczek and Politzer was that it seemed to provide a rational explanation for what had always been mysterious to me — the fact that there were symmetries, like parity conservation, charge conjugation invariance, and strangeness conservation, that were very good symmetries of the strong and electromagnetic interactions — as far as we knew exact — and yet were not respected by the weak interactions. Why should nature have ... symmetries that are symmetries of part of nature but not other parts of nature?"
"... I found that I was unable to explain the foundations of quantum mechanics in a way that I found entirely satisfactory."
"In the Standard Model the masses of quarks and leptons take values proportional to the coupling constants in the interaction of these fermions with scalar fields, constants that in the context of this model are entirely arbitrary. But the peculiar hierarchical pattern of lepton and quark masses seems to call for a larger theory, in which in some leading approximation the only quarks and leptons with non-zero mass are those of the third generation, the tau, top, and bottom, with the other lepton and quark masses arising from some sort of radiative correction. Such theories were actively considered ... soon after the completion of the Standard Model, but interest in this program seems to have lapsed subsequently ..."
"... there are particles ... that we have never seen in a laboratory but astronomers tell us make up most of the matter in the universe — the so-called . It's dark because it doesn't radiate — it doesn't interact with light. We just know about it because of its gravitational field. What is the dark matter? ... We have a lot of ideas — all going in different directions. We don't know which is the right idea."
"Our mistake is not that we take our theories too seriously, but that we do not take them seriously enough. It is always hard to realize that these numbers and equations we play with at our desks have something to do with the real world. ...The most important thing accomplished by the three-degree radiation background in 1965 was to force us to take seriously the idea that there was an early universe."
"It is almost irresistible for humans to believe that we have some special relation to the universe, that human life is not just a more-or-less farcical outcome of a chain of accidents reaching back to the first three minutes, but that we were somehow built in from the beginning. ... It is very hard to realise that this is all just a tiny part of an overwhelmingly hostile universe. It is even harder to realise that this present universe has evolved from an unspeakably unfamiliar early condition, and faces a future extinction of endless cold or intolerable heat. The more the universe seems comprehensible, the more it also seems pointless."
"The effort to understand the universe is one of the very few things which lifts human life a little above the level of farce and gives it some of the grace of tragedy."
"This book is written for readers who may not be familiar with classical physics, but who are willing to pick up enough... to be able to understand the rich tangle of ideas and experiments that make up the history of twentieth century physics. This background is provided in a number of "flashback"sections on the nature of electricity, Newton's laws of motion, electric and magnetic forces, conservation of energy, atomic weights and so on... inserted wherever... needed to allow the reader to understand the next point in the history. ...Generally ...the student or reader is ...is offered only one path ...ideal for ...physicists, but for many ...an impassable desert ...I invite the reader to plunge immediately into... key topics ...using each ...as an entreé into just those concepts and methods ...needed to understand that topic. ...Most of what I know about physics and mathematics I have learned only when there was no alternative ...in order to get on with my work. ...So the plan of this book may be closer to the actual education of working scientists than many ...My hope ...that this book may contribute to a radical revision in the way ...science is brought to the nonscientists. ...This book is intended to be comprehensible to readers who have no prior background in science, and no familiarity with mathematics beyond arithmetic. ...Appendices present some of the calculations that underlie the reasoning in the main text. ...The great scientific achievements described here form the a large part of the soil from which our... recent harvest of discoveries have sprung. ...I hope that scientists find some ...enlightening. I also hope that this book will be enjoyed by students and practitioners of the history of science."
"This is not intended to be yet another popular book that offers... the latest news in physics. Still, it would be a pity not to show the links between the historic discoveries... and the work of fundamental physics today. I have therefore taken the opportunity... of this new edition to point out these links... I now carry the story of the discovery of elementary particles... to the present day."
"By the end of the nineteenth century the idea of the atom had become familiar... but not yet universally accepted. Partly because of the heritage of Newton and Dalton, there was a disposition to use atomic theories in England. ...Resistance to atomism persisted in Germany ...under the influence of an empiricist school... centered on Ernst Mach... many [German physicists and chemists] held back from incorporating into... theories anything that—like atoms—could not be observed directly. ...It is said that the opposition to Boltzmann's work by the followers of Mach contributed to Boltzmann's suicide..."
"Under ordinary circumstances, visible light is absorbed or emitted when the electrons in an atom or molecule are excited into orbits of higher energy, or sink back into orbits of lower energy, respectively."
"The s and s in nuclei, like the electrons surrounding the nuclei, can be excited to states of higher energy or... fall back to a state of lower energy, but the energies... are typically a million times those need to excite the electrons..."
"Electrons are believed to be absolutely stable, and protons and neutrons (when bound...) live at least 1030 years. With few exceptions, all other particles have very short lifetimes..."
"The reader may... wonder why when amber is rubbed with fur the electrons go from the fur to the amber, but when glass is rubbed with silk the electrons go from the glass to the silk? ...[W]e still don't know. The question involves the physics of surfaces of complex solids... In a purely empirical way, there has been developed... the triboelectric sequence... The electrification is most intense for objects... well separated in the... sequence. ...It is ironic that we still do not have a detailed understanding of frictional electrification, even though it was the first... to be studied... But... often... science progresses... by selecting problems that are as free as possible from irrelevant complications and... provide opportunities to get at fundamental principles..."
"In 1709 Hauksbee observed that when air inside a glass vessel was evacuated... [to] 1/60 normal air pressure and the vessel was attached to... frictional electricity, a strange light would be seen... Flashes... similar... had... been noticed in the partial vacuum above... mercury in barometers. ...[T]oday we know ...[w]hen an electric current flows through a gas, the electrons knock into the gas atoms and give up some... energy... reemitted as as light. Today's fluorescent lights and neon signs are based on the same principle... but even at 1/60 atmospheric pressure the air interfered too much with the flow of electrons to allow their nature to be discovered. Real progress became possible only when the gas... could be removed..."
"In 1858 Johann Heinrich Geissler... invented a pump that used columns of mercury as pistons and consequently needed no gaskets. ...Geissler's pump was used... by ... [M]etal plates inside a glass tube were connected to a powerful source of electricity. ...[W]hen almost all of the air was evacuated ...the light disappeared through most of the tube, but a greenish glow appeared ...near the cathode. ...A few years later, ... introduced a name... s. We know now that these rays are streams of electrons. ...But this was far from obvious to nineteenth century physicists. ...Plücker ...observed that the position of the glow on the walls of the tube could be moved by ...a magnet ..."
"Plücker's student J. W. Hittorf... observed that solid bodies... near a small cathode would cast shadows... [and] deduced... the rays travel... in straight lines."
"Hertz showed... the... rays were not appreciably deflected by electrified metal plates. This seemed to rule out... electrically charged particles... Hertz concluded the rays were some sort of wave... the nature of light was... not well understood, and a magnetic deflection did not seem impossible. In 1891 Hertz made a further observation... to support the wave theory... The rays could penetrate thin foils of gold and other metals, much as light penetrates glass. ...We know now that... the... particles were traveling so fast, and the electric forces were so weak... the deflection was too small to observe."
"Perrin... showed in 1895 that the rays deposit negative electrical charge on a charge collector... inside... the tube."
"[I]n 1897 Thomson... detected a deflection... by electric forces between the rays and the electrified metal plates. ...due largely to the use of better vacuum pumps ...to where the effects of residual gas ...became negligible. (Some evidence for... deflection was [also] found... by Goldstein.) [D]eflection was toward the positively charged plate... away from the negatively charged one, confirming Perrin... that the rays carry negative electric charge."
"Thomson... exerted electric and magnetic forces on the rays and measured the amount... deflected."
"The laws of motion... were set out by... Newton at the beginning of... the Principia. ...[T]he key principle is ...in the Second Law... paraphrased as... the force to give an object a certain acceleration is proportional to the product of the and the ."
"Acceleration is the rate of change of . ...The units are ...velocity per unit time, or distance-per-time per time. ...[F]alling bodies ...near ...earth fall with an acceleration or 9.8 meters-per-second per second ...after the first second ...falling at speed ...9.8 meters per second, after two seconds... 19.6 ...and so on. [T]he units of velocity are length/time... and units of acceleration... (distance/time)/time, or equivalently distance/time2 ...[T]he acceleration near... Earth would be written 9.8 m/sec2 for short."
"As a special case of Newton's Second Law, a body... when acted on by zero force, will experience zero acceleration—that is, it will move with constant velocity. Newton listed this... as the First Law... The Third Law... action equals reaction: If one body exerts a force on another... the second... exerts an equal force in the opposite direction on the first."
"When the velocity and the acceleration are changing, we can define the instantaneous velocity or acceleration at any moment as the average values... over a vanishingly small time interval centered on that moment. Newton's Law actually relates the force to the instantaneous acceleration."
"Velocity, acceleration, and force are vectors... they have direction as well as magnitude. It is often convenient to describe... [vectors] in terms of their components along specified directions. ...Components of vectors can be negative as well as positive ...Newton's Second Law applies separately to each component... it says... the component of force in any direction is equal to the mass times the corresponding component of acceleration."
"When several forces act... the total force is the sum... each component of the total force is the sum of the corresponding components of the individual forces."
"Thomson used Newton's Second Law to obtain a general formula... to interpret measurements of the cathode-ray deflection... produced by... electric or magnetic forces... In his cathode ray tube, the ray particles pass through... the deflection region... subjected to electric and magnetic forces... at right angles to their original direction... then through a much longer force-free... drift region... in which they drift freely until they hit the end of the tube... [a] glowing spot... The forces exerted on the cathode ray particles give them an acceleration at right angles to the axis of the tube, so... the particles have a small component of velocity at right angles to their original motion... equal to the product of the acceleration and the time... in the [very short] deflection region... [T]he downward displacement of the ray when it hits the end of the tube is the downward velocity produced in the deflection region times the length of time... in the drift region... [T]he electric force... on a particle is proportional to the [particle's] electric charge... [U]nlike the electric force, the magnetic force... on a particle is proportional to the particle's velocity as well as its charge. By measuring... deflections due to... [both] forces, Thomson... could determine both the ray-particle velocities and the ratio of their charge and mass."
"Early speculation on about electric forces relied... on an analogy with Newton's theory of gravitational forces. At the end of Principia, Newton described gravitation as a cause that acts on the sun and the planets "according to the quantity of solid matter which they contain and propagates on all sides to immense distances, decreasing always as the inverse square of the distances." ...It was irresistible to guess that the electric force might obey a similar law, also proportional to the inverse square of the distance... with charge playing the role that mass plays..."
"(...Newton's theory... is now known only to be an approximation... for particles... not moving too fast and gravitational forces... not too strong. ...It is one of the consequences of General Relativity that gravitation is produced by and acts on energy as well as mass, so that it even affects particles of zero mass, like the photon."
"Coulomb used a... device of his own invention, the torsion balance, to measure forces between small pith balls. The inverse-square law was found to hold accurately..."
"It is... convenient to state Coulomb's law in modern terms, first used... by James Clerk Maxwell. The electric force... is always proportional to the electric charge... We call the factor of proportionality the electric field so...Electric force... = Electric charge... x Electric field"
"The years since the mid-1970s have been the most frustrating in the history of particle physics. We are paying the price of our own success: theory has advanced so far that further progress will require the study of processes at energies far beyond the reach of existing facilities. In order to break out of this impasse, physicists began in 1982 to develop plans for a scientific project of unprecedented size and cost, known as the Superconducting Super Collider."
"It is with Isaac Newton that the modern dream of a final theory really begins."
"The last thirty years of Einstein's life were largely devoted to a search for a so-called unified field theory that would unify James Clerk Maxwell's theory of electromagnetism with the general theory of relativity, Einstein's theory of gravitation. Einstein's attempt was not successful, and with hindsight we can now see that it was misconceived. Not only did Einstein reject quantum mechanics; the scope of his effort was too narrow. ... Nevertheless Einstein's struggle is our struggle today. It is the search for a final theory."
"The best military historians in fact do recognize the difficulty in stating rules of generalship. They do not speak of a science of war, but rather of a pattern of military behavior that cannot be taught or stated precisely but that somehow or other sometimes helps in winning battles. This is called the art of war. In the same spirit I think that one should not hope for a science of science, the formulation of any definite rules about how scientists do or ought to behave, but only aim at a description of the sort of behavior that historically has led to scientific progress—an art of science."
"I managed to get a quick PhD — though when I got it I knew almost nothing about physics. But I did learn one big thing: that no one knows everything, and you don't have to."
"Another lesson to be learned, to continue using my oceanographic metaphor, is that while you are swimming and not sinking you should aim for rough water."
"As you will never be sure which are the right problems to work on, most of the time that you spend in the laboratory or at your desk will be wasted. If you want to be creative, then you will have to get used to spending most of your time not being creative, to being becalmed on the ocean of scientific knowledge."
"Finally, learn something about the history of science, or at a minimum the history of your own branch of science. The least important reason for this is that the history may actually be of some use to you in your own scientific work."
"Many people do simply awful things out of sincere religious belief, not using religion as a cover the way that Saddam Hussein may have done, but really because they believe that this is what God wants them to do, going all the way back to Abraham being willing to sacrifice Isaac because God told him to do that. Putting God ahead of humanity is a terrible thing."
"Maybe at the very bottom of it... I really don't like God. You know, it's silly to say I don't like God because I don't believe in God, but in the same sense that I don't like Iago, or the Reverend Slope or any of the other villains of literature, the god of traditional Judaism and Christianity and Islam seems to me a terrible character. He's a god who will... who obsessed the degree to which people worship him and anxious to punish with the most awful torments those who don't worship him in the right way. Now I realise that many people don't believe in that any more who call themselves Muslims or Jews or Christians, but that is the traditional God and he's a terrible character. I don't like him."
"I have a friend — or had a friend, now dead — Abdus Salam, a very devout Muslim, who was trying to bring science into the universities in the Gulf states and he told me that he had a terrible time because, although they were very receptive to technology, they felt that science would be a corrosive to religious belief, and they were worried about it... and damn it, I think they were right. It is corrosive of religious belief, and it's a good thing too."
"There is one constant that seems to be fine tuned...and that is dark energy."
"I'm offended by the kind of smarmy religiosity that's all around us, perhaps more in America than in Europe, and not really that harmful because it's not really that intense or even that serious, but just... you know after a while you get tired of hearing clergymen giving the invocation at various public celebrations and you feel, haven't we outgrown all this? Do we have to listen to this?"
"In 1999 I finished my three volume book on the quantum theory of fields (..."QTF"), and... set... the task of learning... the theory underlying the great progress in cosmology in the previous two decades. ...Review articles ...gave good summaries of the data, but ...often quoted formulas without ...derivation, and sometimes ...without reference to the original derivation. Occasionally the formulas were wrong, and extremely difficult for me to rederive. ...[O]riginal ...articles sometimes had gaps in their arguments, or relied on hidden assumptions, or used unexplained notation. Often massive computer programs had taken the place of analytic studies. In many cases... it was easiest to work out the relevant theory myself. This book is the result. Its aim... self-contained explanations of the ideas and formulas... used and tested in modern cosmological observations."
"I have tried... to present analytic calculations of cosmological phenomena, and not just report results obtained elsewhere by numerical computation. The calculations... in the literature... necessarily take many details into account, which either make an analytic treatment impossible, or obscure the main physical features of the calculation. Where this is the case, I have not hesitated to sacrifice some degree of accuracy for greater transparency."
"So much has happened in cosmology since the 1960s that this book... bears little resemblance to... Gravitation and Cosmology. On occasion I refer back to (..."G&C") for material that does not seem worth repeating... Classical general relativity has not changed much since 1972 (apart from a great strengthening of its experimental verification) so it did not seem necessary to cover gravitation... I provide a brief introduction in Appendix B. Other appendices deal with technical material... I have also supplied a glossary of symbols..."
"I decided to exclude material that was highly speculative... cosmological theory in higher dimensions... anthropic reasoning... holographic cosmology... conjectures about the details of inflation, or many other new ideas. ...The present book is largely concerned with ...mainstream cosmology: ...inflation driven by one or more scalar fields ...followed by a big bang dominated by radiation, , baryonic matter, and ."
"Where I knew them I have included references to... the Cornell archive, ...arxiv.org, as well as to the published literature. ...I have quoted the latest measurements of cosmological s known to me, in part... to give the reader a sense of what is... observationally possible. ...I have not tried to combine measurements from observations of different types because... it would [not] add... additional physical insight and any... cosmological concordance would... soon be out of date."
"I hope the readers will let me know of any mistakes... I will post them on... zippy.ph.utexas.edu/~weinberg/corrections.html."
"The visible universe seems the same in all directions... larger than about 300 million light years. The ... (...[~]one part in 105) in the cosmic microwave background... radiation... traveling... [~]14 billion years, supporting the conclusion..."
"Almost all of modern cosmology is based on this Robert-Walker metric, at least as a first approximation."
"Consider the geometry of a three-dimensional homogeneous and isotropic space. ...[G]eometry is encoded in a metric g_{ij}(\mathbf{x}) (with i and j running over the three coordinate directions), or equivalently a line element ds^2 \equiv g_{ij} dx^i dx^j, with summation over repeated indices... ds is the proper distance between \mathbf{x} and \mathbf{x}+\mathbf{dx}, meaning... the distance measured by a surveyor who uses a... Cartesian [coordinate system] in a small neighborhood of... point \mathbf{x}.) One... homogeneous isotropic three-dimensional space with positive definite lengths is flat space, with line elementds^2=d\mathbf{x}^2...The coordinate transformations that leave this invariant are... ordinary three-dimensional rotations and translations. ...Another ...possibility is a four-dimensional with some radius a, with line elementds^2=d \mathbf{x}^2+dz^2,\;\;z^2 + \mathbf{x}^2 = a^2,...Here the transformations that leave the line element invariant are four-dimensional rotations; the direction of \mathbf{x} can be changed to any other direction by a four-dimensional rotation that does not change z. ...[T]he only other possibility (up to a coordinate transformation) is a hyperspherical surface in four-dimensional , with line elementds^2 = d\mathbf{x}^2 - dz^2,\;\;z^2 - \mathbf{x}^2 = a^2,...where a^2 is (so far) an arbitrary positive constant. The coordinate transformations that leave this invariant are four-dimensional pseudo-rotations, just like s, but with z instead of time."
"[In] the case of Euclidean space...ds^2 = a^2[d\mathbf{x}^2 + K \frac{(\mathbf{x} \cdot d\mathbf{x}^2)}{1-K\mathbf{x}^2}]...where K ="
"[T]o extend this to the geometry of spacetime... include a term... in the spacetime line element, with a now an arbitrary function of time (known as the Robertson-Walker scale factor):d\tau^2 \equiv -g_{\mu\nu}(x) dx^\mu dx^\nu = dt^2-a^2(t)[d\mathbf{x}^2 + K \frac{(\mathbf{x} \cdot d\mathbf{x}^2)}{1-K\mathbf{x}^2}]"
"Consider... [the formula given by special relativity for the magnitude of the ]P \equiv m_0 \sqrt{g_{ij}\frac{dx^i}{d\tau}\frac{dx^j}{d\tau}}...where d\tau^2 = dt^2 - g_{ij} dx^i dx^j. [This holds because in] a locally inertial Cartesian coordinate system, for which g_{ij} = \delta_{ij}, we have d\tau = dt\sqrt{1 - \mathbf {v}^2} where v^i = \frac{dx^i}{dt}... [The P] is evidently invariant under arbitrary changes in the spatial coordinates, so we can evaluate it... in Robertson-Walker coordinates. ...[T]o save work ...adopt a spatial coordinate system in which the particle position is near the origin x^i = 0, where \tilde{g}_{ij} = \delta_{ij} + \mathit0(\mathbf{x}), and we can therefore ignore the purely spatial components of \Gamma_{jk}^i of the . General relativity gives [the momentum]... with a metric g_{ij} = a^2(t)\delta_{ij}...P(t) \propto 1/a(t)... for any non-zero mass, however small... Hence, although for photons both m_0 and d\tau vanish... [the momentum relation] is still valid."
"[T]he property of being a geodesic is invariant under coordinate transformations... so the path of the photon or particle will... be a geodesic in any spatial coordinate system..."
"In 1929 Hubble announced... a "roughly linear" relation between and distance. ...His data points ...did not really support a linear relation. But in the early 1930s he had measured redshifts and distances out to the , with a redshift z \eqsim 0.02, corresponding to... 7,000 km/sec and a linear relation... was evident. The conclusion... the universe is really expanding. ...At the time of writing, the largest... z=6.96. It may eventually become possible to measure the expansion rate H(t) \equiv \dot{a}(t)/a(t) at times t earlier than the present, by observing the change in very accurately measured redshifts of individual galaxies over times as short as a decade."
"Modern cosmological theories can exhibit horizons of two... types. which limit the distances at which past events can be observed or at which it will ever be possible to observe future events. These are called Rindler s and s, respectively."
"[T]he distance at present isd_{\mathrm{max}}(t_0) = \frac{1}{H_0} \int_{0}^{1} \frac{dx}{x^2 \sqrt{\Omega_\Lambda+\Omega_K x^{-2}+\Omega_M x^{-3}}}...[T]here may have been a time before the radiation-dominated era in which there was nothing in the universe but , in which case the particle horizon distance would... be infinite. But as far as telescopic observations... [d_{max}(t_0)] gives the proper distance beyond which we cannot now see."
"In the case where the universe does not recollapse, the proper distance to the is...d_{MAX}(t) = a(t) \int_{0}^{r_{MAX}(t)} \frac{dr}{\sqrt{1-Kr^2}} = a(t)\int_{0}^{\infty} \frac{dt'}{a(t')}... In the absence of a cosmological constant, a(t) grows like t^{\frac{2}{3}}, and the integral diverges, so there is no event horizon. But with a cosmological constant, a(t) will eventually grow as exp(Ht) with H = H_0 \Omega^{1/2}_\Lambda constant and... an event horizon... approaches... d_{MAX}(\infty) = 1/H. As time passes all sources of light outside our gravitationally bound will move beyond this... and become unobservable. The same is true for the quintessence theory... In that case a(t) eventually grows as exp(const \times\, t^{2/{(2+\frac{\alpha}{2})}}), so for any \alpha \ge 0 the integral... [d_{MAX}(t)] converges."
"The development of quantum mechanics in the 1920s was the greatest advance in physical science since the work of Isaac Newton. It was not easy; the ideas of quantum mechanics present a profound departure from ordinary human intuition. Quantum mechanics has won acceptance through its success. It is essential to modern atomic, molecular, nuclear, and elementary particle physics, and to a great deal of chemistry and condensed matter physics as well."
"The principles of quantum mechanics are so contrary to ordinary intuition that they can best be motivated by taking a look at their prehistory."
"Perhaps the most important immediate consequence of Planck’s work was to provide long-sought values for atomic constants."
"Planck’s quantization assumption applied to the matter that emits and absorbs radiation, not to radiation itself. As George Gamow later remarked, Planck thought that radiation was like butter; butter itself comes in any quantity, but it can be bought and sold only in multiples of one quarter pound. It was Albert Einstein (1879–1955) who in 1905 proposed that the energy of radiation of frequency ν was itself an integer multiple of hν."
"In this derivation Bohr had relied on the old idea of classical radiation theory, that the frequencies of spectral lines should agree with the frequency of the electron’s orbital motion, but he had assumed this only for the largest orbits, with large n. The light frequencies he calculated for transitions between lower states, such as n=2 → n=1, did not at all agree with the orbital frequency of the initial or final state. So Bohr’s work represented another large step away from classical physics."
"Heisenberg’s starting point was the philosophical judgment, that a physical theory should not concern itself with things like electron orbits in atoms that can never be observed. This is a risky assumption, but in this case it served Heisenberg well."
"To start, we will consider a single particle moving in three space dimensions under the influence of a general central potential. Later we will specialize to the case of a Coulomb potential, and work out the spectrum of hydrogen. One other classic problem, the harmonic oscillator, will be treated at the end of this chapter."
"My own conclusion is that today there is no interpretation of quantum mechanics that does not have serious flaws. This view is not universally shared. Indeed, many physicists are satisfied with their own interpretation of quantum mechanics. But different physicists are satisfied with different interpretations. In my view, we ought to take seriously the possibility of finding some more satisfactory other theory, to which quantum mechanics is only a good approximation."
"Steven Weinberg is famous as a scientist, but he thinks deeply and writes elegantly about many other things besides science.… he is not only preeminent as a mathematical physicist. He has also made important contributions to the discussion of history and politics."
"Asked what single mystery, if he could choose, he would like to see solved in his lifetime, Weinberg doesn’t have to think for long: he wants to be able to explain the observed pattern of quark and lepton masses."
"Weinberg’s paper “A Model of Leptons”, published in Physical Review Letters (PRL) on 20 November 1967, determined the direction of high-energy particle physics through the final decades of the 20th century. Just two and a half pages long, it is one of the most highly cited papers in the history of theoretical physics. Its contents are the core of the Standard Model of particles physics, now almost half a century old and still passing every experimental test."
"Here he unwittingly puts his finger on what I believe is the actual source of the near-century of discomfort and disagreement. There is an implicit assumption, shared by almost all physicists, that the scientist must be separated from the science. The usual appeals to measurement with classical outcomes, it seems to me, are unsuccessful attempts to objectify and impersonalize processes in which an individual scientist acts on and is reacted upon by the world. The collapse of the wavefunction after measurement represents nothing more than the updating of that scientist’s expectations, based on his or her experience of the world’s response to the measurement. Weinberg hopes to keep the scientist out of the laws of nature, but our chronic failure to agree on the meaning of quantum mechanics demonstrates the futility of his hope. Nor does Weinberg’s hope make sense to me. Science is a highly developed form of human language. Embedded in books and papers, it is a distillation of the communicated individual experiences of all scientists. Why insist that science should make no reference to the process that has established it? The laws of quantum mechanics are exactly the same for everyone who uses them. In that important sense they are entirely objective. If a scientific law involves both the scientist and the world, it does not mean that science can tell us nothing about people, as Weinberg mysteriously worries, any more than it means that science can tell us nothing about the world."
"By inclination, Weinberg is an extreme reductionist. But he is also a realist and acknowledges when something is not working the way he might want it to. In 1987 the arch-reductionist concluded that certain facts seemed to be inconsistent with any explanation based on the usual kind of mathematical reasoning. Instead, it seemed they might be true only because if they were not, we observers could not be here to observe them. Weinberg undoubtedly disliked such anthropic-principle explanations. But when, to his disappointment, he found that the anthropic principle might explain the apparent vanishing of the cosmological constant, he said so loudly and clearly, despite the great hostility of the physics community toward the principle."
"... I vividly remember sitting in front of Wheeler, who told me his opinion of the leading particle theorists at various major universities and ended with the pronouncement that Steve Weinberg was the best of the upcoming generation."