cosmology

"If a distant galaxy is moving relative to us, its entire is Doppler-shifted in frequency. Its s are displaced relative to those of stationary light sources. Thanks to this effect, we know that distant galaxies recede from the solar system at speeds proportional to their distances from us. That's the effect that told us of the expanding universe, and of its birth, long ago, in the Big Bang."

"All kinds of questions remain. Many have to do with cosmology. How did the universe originate? How did the galaxies become distributed in space like the suds in the kitchen sink..? Why is the cosmological constant apparently very tiny but non-zero and has a peculiar value that leads the universe to expand more rapidly?"

"Red-shifts are produced either in the nebulae, where the light originates, or in the intervening space through which the light travels. If the source is in the nebulae, then red-shifts are probably velocity-shifts and the nebulae are receding. If the source lies in the intervening space, the explanation of red-shifts is unknown, but the nebulae are sensibly stationary."

"A book, too, can be a star, explosive material, capable of stirring up fresh life endlessly, a living fire to lighten the darkness, leading out into the expanding universe."

"This model of the expanding universe I shall call the substratum. It achieves in the private Euclidean space of each fundamental observer the objects for which Einstein developed his closed spherical space. Although it is finite in volume, in the measures of any chosen observer, it has all the properties of an infinite space in that its boundary is forever inaccessible and its contents comprise an infinity of members. It is also homogeneous in the sense that each member stands in the same relation to the rest. This description of the substratum holds good in the scale of time in which the galaxies or fundamental particles are receding from one another with uniform velocities. This choice of the scale of time, together with the theory of equivalent time-keepers... makes possible the application of the Lorentz formulae to the private Euclidean spaces of the various observers. It thus brings the theory of the expanding universe into line with other branches of physics, which use the Lorentz formulæ and adopt Euclidean private spaces. ...[T]here is no more need to require a curvature for space itself in the field of cosmology than in any other department of physics. The observer at the origin is fully entitled to select a private Euclidean space in which to describe phenomena, and when he concedes a similar right to every other equivalent observer and imposes the condition of the same world-view of each observer, he is inevitably led to the model of the substratum which we have discussed."

"The ideas that prove to be of lasting interest are likely to build on the framework of the now standard world picture, the hot big bang model of the expanding universe. The full extent and richness of this picture is not as well understood as I think it ought to be, even among those making some of the most stimulating contributions to the flow of ideas."

"If the general picture, however, of a Big Bang followed by an expanding Universe is correct, what happened before that? Was the Universe devoid of all matter and then the matter suddenly somehow created? How did that happen? In many cultures, the customary answer is that a God or Gods created the Universe out of nothing. But if we wish to pursue this question courageously, we must of course ask the next question: where did God come from? If we decide that this is an unanswerable question, why not save a step and conclude that the origin of the Universe is an unanswerable question? Or, if we say that God always existed, why not save a step, and conclude that the Universe always existed? That there's no need for a creation, it was always here. These are not easy questions. Cosmology brings us face to face with the deepest mysteries, questions that were once treated only in religion and myth."

"The most far-reaching implication of general relativity... is that the universe is not static, as in the orthodox view, but is dynamic, either contracting or expanding. Einstein, as visionary as he was, balked at the idea... One reason... was that, if the universe is currently expanding, then... it must have started from a single point. All space and time would have to be bound up in that "point," an infinitely dense, infinitely small "singularity." ...this struck Einstein as absurd. He therefore tried to sidestep the logic of his equations, and modified them by adding... a "cosmological constant." The term represented a force, of unknown nature, that would counteract the gravitational attraction of the mass of the universe. That is, the two forces would cancel... it is the kind of rabbit-out-of-the-hat idea that most scientists would label ad-hoc. ...Ironically, Einstein's approach contained a foolishly simple mistake: His universe would not be stable... like a pencil balanced on its point."

"[W]e stress... the wide range of validity exhibited by s in theoretical physics. ...[I]t has ...been demonstrated how they can be employed to derive equations of optics, dynamics of particles and rigid bodies, and electromagnetism. In addition, physicists have succeeded in formulating the laws of elasticity and hydrodynamics as variational principles, and even Einstein's law of gravitation was included in this category by Hilbert, who found a scaler function... for which \partial\int\mathfrak{h}\,dx_0\,dx_1\,dx_2\,dx_3=0 is equivalent to Einstein's law. This function has been called the "curvature," an identification which induced Whittaker to describe Hilbert's principle in the laconic words, "gravitation simply represents a continual effort of the universe to straighten itself out.""

"The general theory of relativity considers physical space-time as a four-dimensional manifold whose line element coefficients g_{\mu \nu} satisfy the differential equationsG_{\mu \nu} = \lambda g_{\mu \nu} \qquad .\;.\;.\;.\;.\;.\; (1)in all regions free from matter and electromagnetic field, where G_{\mu \nu} is the contracted Riemann-Christoffel tensor associated with the fundamental tensor g_{\mu \nu}, and \lambda is the ."

"In considerations involving the nature of the world as a whole the irregularities caused by the aggregation of matter into stars and stellar systems may be ignored; and if we further assume that the total matter in the world has but little effect on its macroscopic properties, we may consider them as being determined by the solution of an empty world."

"The solution of (1), which represents a homogeneous manifold, may be written in the form:ds^2 = \frac{d\rho^2}{1 - \kappa^2\rho^2} - \rho^2 (d\theta^2 + sin^2 \theta \; d\phi^2) + (1 - \kappa^2 \rho^2)\; c^2 d\tau^2, \qquad (2)where \kappa = \sqrt \frac{\lambda}{3}. If we consider \rho as determining distance from the origin... and \tau as measuring the proper-time of a clock at the origin, we are led to the de Sitter spherical world..."

"Now it is the practice of astronomers to assume that brightness falls off inversely with the square of the "distance" of an object—as it would do in Euclidean space, if there were no absorption... We must therefore examine the relation between this astronomer's "distance" d... and the distance r which appears as an element of the geometry."

"In all these congruence geometries, except the Euclidean, there is at hand a natural unit of length R = \frac{1}{K^\frac{1}{2}}; this length we shall, without prejudice, call the "radius of curvature" of the space."

"All change is relative. The universe is expanding relatively to our common material standards; our material standards are shrinking relatively to the size of the universe. The theory of the "expanding universe" might also be called the theory of the "shrinking atom". ...[T]ake the... universe as our standard of constancy... he sees us shrinking... only the intergalactic spaces remain the same. The earth spirals round the sun in an ever‑decreasing orbit. ...Our years will ...decrease in geometrical progression in the cosmic scale of time. ... Owing to the property of geometrical progressions an infinite number of our years will add up to a finite cosmic time; so that what we should call the end of eternity is an ordinary finite date in the cosmic calendar. But on that date the universe has expanded to infinity in our reckoning, and we have shrunk to nothing in the reckoning of the cosmic being. ...When the last act opens the curtain rises on midget actors rushing through their parts at frantic speed. Smaller and smaller. Faster and faster. One last microscopic blurr of intense agitation. And then nothing."

"I have said the repulsion is proportional to the distance... Distance from what? From anywhere you like. ...Cosmical repulsion is a dispersing force tending to make a system expand uniformly—not diverging from any centre in particular, but such that all internal distances increase at the same rate. That corresponds precisely to the kind of expansion we observe in the system of the galaxies."

"What is needed is a homely experiment which could be carried out in the basement with parts from an old sewing machine and an Ingersoll watch, with an old file of Popular Mechanics standing by for reference! This I am, alas, afraid we have not achieved, but I do believe that the following example... is adequate to expose the principles..."

"If you think... the shattering of the bubble universe is... tragic... [W]hen the worst has happened our galaxy... will be left intact. ...not so bad a prospect."

"The really amazing thing is not that life on Earth is balanced on a knife-edge, but that the entire universe is balanced on a knife-edge. You see, even if you dismiss mankind as just a mere hiccup in the great scheme of things, the fact remains that the entire universe seems unreasonably suited to the existence of life — almost contrived — you might say a "put-up job"."

"Matter in quantum mechanics is not an inert substance but an active agent, constantly making choices between alternative possibilities according to probabilistic laws. ...It appears that mind, as manifested by the capacity to make choices, is to some extent inherent in every electron. ...Our brains appear to be devices for the amplification of the mental component of the quantum choices made by molecules inside our heads. ...There is evidence from peculiar features of the laws of nature that the universe as a whole is hospitable to the growth of mind. ...an extension of the Anthropic Principle up to a universal scale."

"This is the way the world ends This is the way the world ends This is the way the world ends Not with a bang but a whimper."

"Some say the world will end in fire, Some say in ice. From what I’ve tasted of desire I hold with those who favor fire. But if it had to perish twice, I think I know enough of hate To know that for destruction ice Is also great And would suffice."

"Science does not accept Aristotelian styles of explanation, that a stone falls because of its nature... it likes to be on Earth... Within science, all causes must be local and instrumental. Purpose is not acceptable as an explanation... Action at a distance, either in space or time, is forbidden. Especially, teleological influences of final goals upon phenomena are forbidden. ...The choice of laws of nature, and the choice of initial conditions for the universe, are questions belonging to meta-science and not to science. Science is restricted to the explanation of phenomena within the universe. Teleology is not forbidden when explanations go beyond ...into meta-science. The most familiar example of a meta-scientific explanation is the so-called Anthropic Principle. ...It accords with the spirit of modern science that we have two complementary styles of explanation, the teleological style allowing a role for purpose in the universe at large, and the non-teleological style excluding purpose..."

"The gap between a dumb and a clever person may appear large from an anthropocentric perspective, yet in a less parochial view the two have nearly indistinguishable minds."

"What we hear about eternal inflation or the string landscape, seems somehow unavoidably to lead to some kind of multiverse. However, it seems to me there is a fundamental problem there. Once of course you have the multiverse, then you can start playing around and try to find probability or getting to the anthropic principle, or whatever. But the point is that the picture is essentially a classical one, and it is difficult to see that if you have many universes, coming essentially with an inflationary state, that there would not be plenty of horizons in this. Now the quantum mechanics of horizons is, I think, perfectly not understood. The simplest example is the black hole, where after all nobody knows really if the problem lies in the singularity or if it lies really already in the horizon."

"Blow, winds, and crack your cheeks! rage! blow! You cataracts and hurricanoes, spout Till you have drench’d our steeples, drown’d the cocks! You sulphurous and thought-executing fires, Vaunt-couriers to oak-cleaving thunderbolts, Singe my white head! And thou, all-shaking thunder, Smite flat the thick rotundity o’ the world! Crack nature’s moulds, all germins spill at once That make ingrateful man!"

"The soul, secur’d in her existence, smiles At the drawn dagger, and defies its point. The stars shall fade away, the sun himself Grow dim with age, and nature sink in years, But thou shalt flourish in immortal youth, Unhurt amidst the war of elements, The wreck of matter, and the crush of worlds."

"To say that Nature displays intelligence doesn't make you a Christian fundamentalist. Einstein said as much, and a fascinating theory called the anthropic principle has been seriously considered by Stephen Hawking, among others."

"Whitrow... proposed an anthropic resolution of the venerable philosophical question Why physical space has three dimensions? (arguing that with a space of different dimensionality there would be no living being to pose the question) and, similarly to [Grigory Moiseevich] Idlis, alluded around 1955 to an anthropic explanation of the size of the observable universe. Anyway, he never published these last ideas, which were developed years later by Wheeler. The only reference to Whitrow’s argument that appeared in print during the 1950s seems to be that due to the philosopher of religion Eric Lionel Mascall, who attributed to the English’s mathematician thatit may be necessary for the universe to have the enormous size and complexity which modern astronomy has revealed, in order for the earth to be a possible habitation for living beings."

"Whereas originally the hopes for string theory, and its descendants, were that some kind of uniqueness would be arrived at, whereby the theory would supply mathematical explanations for the measured numbers of experimental physics, the string theorists were driven to find refugee in the strong anthropic argument in an attempt to narrow down an absolutely vast number of alternatives. In my own view, this a very sad and unhelpful place for a theory to find itself."

"In fact Sax was suspicious of all the current cosmology, placing humanity as it did right at the center of things, time after time. It suggested to Sax that all these formulations were artifacts of human perception only, the strong anthropic principle seeping into everything they saw, like color."

"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."

"What the anthropic principle depends upon is the idea that whatever is the nature of the universe, or universe portion that we see about us, being subject to whatever dynamical laws govern its actions, this must be strongly favourable to our very existence."

"... when non-perturbative phenomena are included, there is no problem from the string theory point of view in effecting continuous transitions between Calabi-Yau spaces of different topology. This shows that stringy ideas about geometry are really more general than those found in classical Riemannian geometry. The moduli space of Calabi-Yau manifolds should thus be regarded as a continuously connected whole, rather than a series of different ones individually associated with different topological objects ... Thus, questions about the topology of Calabi-Yau spaces must be treated on the same footing as questions about the metric on the spaces. That is, the issue of topology is another aspect of the the moduli fields. These considerations are relevant to understanding the ground state of the universe."

"Many scientists are still ashamed of using the . Just as the friends of were afraid of using the name , the opponents of the anthropic principle often say that they do not want to use the 'A' in their research."

"Once one starts to admit anthropic interpretations of fine-tuning problems like the cosmological constant, it is clear that such a proposal might be made for other fine-tuning problems, such as the problem of the Higgs boson mass. Certainly, we would not be here if the Higgs boson mass, and hence also the and and and masses, were greatly bigger. If they were near the , for example, any collection of more than a few elementary particles would collapse into a Black Hole. More generally, if the elementary particle masses were scaled up by a factor N, the number of elementary particles in a star or planet would scale down like N–3, and for very modest N the stars would stop shining."

"The old cosmological constant problem is to understand why the is so small; the new problem is to understand why it is comparable to the present mass density. ... does not help with either; anthropic considerations offer a possibility of solving both. In theories with a that takes random initial values, the anthropic principle may apply to the cosmological constant, but probably to nothing else."

"The theory of the inflationary multiverse changes the way we think about our place in the world. According to its most popular version, our world may consist of infinitely many exponentially large parts, exhibiting different sets of low-energy laws of physics. Since these parts are extremely large, the interior of each of them behaves as if it were a separate universe, practically unaffected by the rest of the world. This picture, combined with the theory of eternal inflation and anthropic considerations, may help to solve many difficult problems of modern physics, including the cosmological constant problem."

"I think the Anthropic Cosmological Principle brings to us an idea perhaps as old as humanity itself: that we are not at all just an accidental anomaly, the microscopic caprice of a tiny particle whirling in the endless depth of the universe. Instead, we are mysteriously connected to the entire universe, we are mirrored in it, just as the entire evolution of the universe is mirrored in us."

"Until recently, it might have seemed that we were an unhappy bit of mildew on a heavenly body whirling in space among many that have no mildew on them at all. this was something that classical science could explain. Yet, the moment it begins to appear that we are deeply connected to the entire universe, science reaches the outer limits of its powers. Because it is founded on the search for universal laws, it cannot deal with singularity, that is, with uniqueness. The universe is a unique event and a unique story, and so far we are the unique point of that story. But unique events and stories are the domain of poetry, not science. With the formulation of the Anthropic Cosmological Principle, science has found itself on the border between formula and story, between science and myth. In that, however, science has paradoxically returned, in a roundabout way, to man, and offers him — in new clothing — his lost integrity. It does so by anchoring him once more in the cosmos."

"We are participators in bringing into being not only the near and here but the far away and long ago. We are in this sense, participators in bringing about something of the universe in the distant past and if we have one explanation for what's happening in the distant past why should we need more?"

"What makes the Anthropic Principle and the Gaia Hypothesis so inspiring? One simple thing: Both remind us, in modern language, of what we have long suspected, of what we have long projected into our forgotten myths and perhaps what has always lain dormant within us as archetypes. That is, the awareness of our being anchored in the earth and the universe, the awareness that we are not here alone nor for ourselves alone, but that we are an integral part of higher, mysterious entities against whom it is not advisable to blaspheme. This forgotten awareness is encoded in all religions. All cultures anticipate it in various forms. It is one of the things that form the basis of man's understanding of himself, of his place in the world, and ultimately of the world as such."

"There ought to be something very special about the boundary conditions of the universe and what can be more special than that there is no boundary?"

"Why was there a Big Bang? What, if anything, came before? What mechanisms generated the exponential inflation of the early Universe? What are dark matter and dark energy, which dominate today's Universe? How did the first stars and galaxies form? Why are the fundamental constants of nature what they are? Must we depend on the Cosmic Anthropic Principle to 'answer' such questions? Is our Universe unique, or must we appeal to a Multiverse? What will be the ultimate fate of our Universe?"

"Once one starts to admit anthropic interpretations of fine-tuning problems like the cosmological constant, it is clear that such a proposal might be made for other fine-tuning problems, such as the problem of the Higgs boson mass. Certainly, we would not be here if the Higgs boson mass, and hence also the and and and masses, were greatly bigger. If they were near the , for example, any collection of more than a few elementary particles would collapse into a Black Hole. More generally, if the elementary particle masses were scaled up by a factor N, the number of elementary particles in a star or planet would scale down like N–3, and for very modest N the stars would stop shining."

"There seems to be a vast landscape of possible universes. ... We live in one in which life is possible, but if the universe were only slightly different, beings like us could not exist. What are we to make of this fine-tuning? Is it evident that the universe, after all, was designed by a benevolent creator? Or does science offer a different explanation?"

"The old cosmological constant problem is to understand why the is so small; the new problem is to understand why it is comparable to the present mass density. ... does not help with either; anthropic considerations offer a possibility of solving both. In theories with a that takes random initial values, the anthropic principle may apply to the cosmological constant, but probably to nothing else."

"Talk of the sublime, the exalted, the eternal, the passionate, of glory, challenge, or majesty fills some of us with bewilderment, discomfort, and embarrassment; others with sour resentment or scornful disbelief. To reinstate such values seems to us like trying to reinstate Ptolemaic astronomy—equally misguided, incomprehensible, and inimical to our perceived interests."

"It became clear that our Galaxy is only one system among many, and that the universe is far vaster than the particular stellar system to which the Sun and planets belong. Since then developments have been more rapid than at any time since the days of Copernicus, Digges and Bruno when the geocentric hypothesis of the cosmos received its death-blow."

"These seven bodies were the Sun, the Moon, Mercury, Venus, Mars, Jupiter, and Saturn, all of which were documented by the Babylonians over three thousand years ago. Until the sixteenth century, the most commonly held view was that the Earth was at the centre of the Universe and that the seven bodies revolved around the Earth."