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Steven Weinberg

94 quotes

• “There is one constant that seems to be fine tuned...and that is dark energy.”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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?”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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.”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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...”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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 .”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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.”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

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

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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...”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

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

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “[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 =”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “[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}]”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “[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...”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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.”

  Steven Weinberg (1933–2021) first seen 1956 wikiquote, CC BY-SA 4.0 source

  Recorded in: Ref: W. Rindler, Mon. Not. Roy. Astron. Soc. 116, 663 (1956).

• “[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.”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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.”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

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

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

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

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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.”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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.”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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.”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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.”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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 (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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.”

  Steven Weinberg (1933–2021) first seen 1989 wikiquote, CC BY-SA 4.0 source

  Recorded in: Testing Quantum Mechanics", Annals of Physics (1989)

• “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.”

  Steven Weinberg (1933–2021) first seen 1997 wikiquote, CC BY-SA 4.0 source

  Recorded in: What is quantum field theory, and what did we think it is?", arXiv preprint hep-th/9702027 (1997) (pp. 12–13)

• “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.”

  Steven Weinberg (1933–2021) first seen 2001 wikiquote, CC BY-SA 4.0 source

  Recorded in: Facing Up: Science and Its Cultural Adversaries pp. 47–48 (2001)

• “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.”

  Steven Weinberg (1933–2021) first seen 2006 wikiquote, CC BY-SA 4.0 source

  Recorded in: Closing statements of presentation at Beyond Belief : Science, Religion, Reason and Survival (5 November 2006)

• “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.”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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?”

  Steven Weinberg (1933–2021) first seen 2012 wikiquote, CC BY-SA 4.0 source

  Recorded in: The Big Higgs Question", The New York Review of Books, 9 July 2012

• “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?”

  Steven Weinberg (1933–2021) first seen 2017 wikiquote, CC BY-SA 4.0 source

  Recorded in: Reminiscences of the Standard Model" - Special Colloquium by Steven Weinberg, 17 October 2017, YouTube video at 1:02:17 of 1:39:24

• “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 ...”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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.”

  Steven Weinberg (1933–2021) first seen 1993 wikiquote, CC BY-SA 4.0 source

  Recorded in: (1993), Epilogue, p. 154

• “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.”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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...”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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...”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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...”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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 ...”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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.”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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.”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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.”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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.”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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.”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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.”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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.”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source

• “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.”

  Steven Weinberg (1933–2021) said by 2021 at the latest wikiquote, CC BY-SA 4.0 source