Physicists From The United States

"Religion was not an issue in my family; indeed, it was never discussed. My only religious training came because the Minta required that all students take classes in their respective religions. My family celebrated one holiday, the Day of Atonement, when we all fasted. Yet my father said prayers for his parents on Saturdays and on all the Jewish holidays. The idea of God that I absorbed was that it would be wonderful if He existed: We needed Him desperately but had not seen Him in many thousands of years."

"We must learn to live with contradictions, because they lead to deeper and more effective understanding."

"No, I'm the infamous Edward Teller."

"Physics is, hopefully, simple. Physicists are not."

"Two paradoxes are better than one; they may even suggest a solution."

"A fact is a simple statement that everyone believes. It is innocent, unless found guilty. A hypothesis is a novel suggestion that no one wants to believe. It is guilty, until found effective."

"There's no system foolproof enough to defeat a sufficiently great fool."

"The preservation of peace and the improvement of the lot of all people require us to have faith in the rationality of humans. If we have this faith and if we pursue understanding, we have not the promise but at least the possibility of success. We should not be misled by promises. Humanity in all its history has repeatedly escaped disaster by a hair's breadth. Total security has never been available to anyone. To expect it is unrealistic; to imagine that it can exist is to invite disaster. What we do have in our technological capacities is an opportunity to use our inventiveness, our creativity, our wisdom and our understanding of our fellow beings to create a future world that is a little better than the one in which we live today."

"By having simplified what is known, physicists have been led into realms which as yet are anything but simple. That at some time, they, too, will appear as simple consequences of a theory of which no one has yet dreamed is not a statement of fact. It is a statement of faith."

"On May 7, a few weeks after the accident at Three-Mile Island, I was in Washington. I was there to refute some of that propaganda that Ralph Nader, Jane Fonda and their kind are spewing to the news media in their attempt to frighten people away from nuclear power. I am 71 years old, and I was working 20 hours a day. The strain was too much. The next day, I suffered a heart attack. You might say that I was the only one whose health was affected by that reactor near Harrisburg. No, that would be wrong. It was not the reactor. It was Jane Fonda. Reactors are not dangerous."

"At present the carbon dioxide in the atmosphere has risen by 2 per cent over normal. By 1970, it will be perhaps 4 per cent, by 1980, 8 per cent, by 1990, 16 per cent [about 360 parts per million, by Teller’s accounting], if we keep on with our exponential rise in the use of purely conventional fuels. By that time, there will be a serious additional impediment for the radiation leaving the earth. Our planet will get a little warmer. It is hard to say whether it will be 2 degrees Fahrenheit or only one or 5. But when the temperature does rise by a few degrees over the whole globe, there is a possibility that the icecaps will start melting and the level of the oceans will begin to rise. Well, I don’t know whether they will cover the Empire State Building or not, but anyone can calculate it by looking at the map and noting that the icecaps over Greenland and over Antarctica are perhaps five thousand feet thick."

"Ladies and gentlemen, I am to talk to you about energy in the future. I will start by telling you why I believe that the energy resources of the past must be supplemented. First of all, these energy resources will run short as we use more and more of the fossil fuels. But I would [...] like to mention another reason why we probably have to look for additional fuel supplies. And this, strangely, is the question of contaminating the atmosphere. [....] Whenever you burn conventional fuel, you create carbon dioxide. [....] The carbon dioxide is invisible, it is transparent, you can’t smell it, it is not dangerous to health, so why should one worry about it? Carbon dioxide has a strange property. It transmits visible light but it absorbs the infrared radiation which is emitted from the earth. Its presence in the atmosphere causes a greenhouse effect [....] It has been calculated that a temperature rise corresponding to a 10 per cent increase in carbon dioxide will be sufficient to melt the icecap and submerge New York. All the coastal cities would be covered, and since a considerable percentage of the human race lives in coastal regions, I think that this chemical contamination is more serious than most people tend to believe."

"I don't want to kill anybody. I am passionately opposed to killing, but I'm even more passionately fond of freedom. The freedom of Dr. Pauling and of myself expressing our opinions freely on any subject, however broad, however far removed of our proper competence, but particularly, to be able to express our opinions in the fields we really know; this would not be possible in Russia."

"If we stay strong, then I believe we can stabilize the world and have peace based on force. Now, peace based on force is not as good as peace based on agreement, but in the terrible world in which we live, in the world where the Russians have enslaved many millions of human beings, in the world where they have killed men, I think that for the time being the only peace we can have is the peace based on force. Furthermore, I do not think that this peace based on force is, can be, or should be, an ultimate end. Our ultimate end must be precisely what Dr. Pauling says, peace based on agreement, on understanding, on universally agreed and enforced law. I think this is a wonderful idea, but peace based on force buys the necessary time, and in this time we can work for better understanding, for closer collaboration, first with the countries which are closest to us, which we understand better, our allies, the western countries, the NATO countries, which believe in human liberties as we do. Then, as soon as possible, with the rest of the free world, and eventually, I hope, with the whole world, including Russia, even though it may take many years to come."

"It is not even impossible to imagine that the effects of an atomic war fought with greatly perfected weapons and pushed by the utmost determination will endanger the survival of man."

"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."

"... 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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"Perhaps the most important immediate consequence of Planck’s work was to provide long-sought values for atomic constants."

"The principles of quantum mechanics are so contrary to ordinary intuition that they can best be motivated by taking a look at their prehistory."

"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."

"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."

"[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."

"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."

"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."

"[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..."

"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]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}]"

"[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 ="

"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."

"Almost all of modern cosmology is based on this Robert-Walker metric, at least as a first approximation."

"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..."

"I hope the readers will let me know of any mistakes... I will post them on... zippy.ph.utexas.edu/~weinberg/corrections.html."

"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 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 ."

"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 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."

"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'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?"

"There is one constant that seems to be fine tuned...and that is dark energy."

"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."