A Zenonian supertask involving an infinite number of colliding balls is considered, under the restriction that the total mass of all the balls is finite. Classical mechanics leads to the conclusion that momentum, but not necessarily energy, must be conserved. Relativistic mechanics, on the other hand, implies that energy and momentum conservation are always violated. Quantum mechanics, however, seems to rule out the Zeno configuration as an inconsistent system.

Ever since Copernicus, scientists have continually adjusted their view of human nature, moving it further and further from its ancient position at the center of Creation. But in recent years, a startling new concept has evolved that places it more firmly than ever in a special position. Known as the Anthropic Cosmological Principle, this collection of ideas holds that the existence of intelligent observers determines the fundamental structure of the Universe. In its most radical version, the Anthropic Principle asserts that (...) "intelligent information-processing must come into existence in the Universe, and once it comes into existence, it will never die out." This wide-ranging and detailed book explores the many ramifications of the Anthropic Cosmological Principle, covering the whole spectrum of human inquiry from Aristotle to Z bosons. Bringing a unique combination of skills and knowledge to the subject, John D. Barrow and Frank J. Tipler--two of the world's leading cosmologists--cover the definition and nature of life, the search for extraterrestrial intelligence, and the interpretation of the quantum theory in relation to the existence of observers. The book will be of vital interest to philosophers, theologians, mathematicians, scientists, and historians, as well as to anyone concerned with the connection between the vastness of the universe of stars and galaxies and the existence of life within it on a small planet out in the suburbs of the Milky Way. (shrink)

This column is about a new alternative to standard Big Bang cosmology that reaches back in time to the era before the Big Bang in an effort to remove some of the arbitrary assumptions from the model. It's in part the work of Gabriele Veneziano, a theorist at CERN, and it is called pre-Big-Bang cosmology. We'll begin by reviewing the standard scenario of the origin of the universe.

Alternate View Column AV-02 Keywords: cosmology, bubble, universe, inflation Published in the September-1984 issue of Analog Science Fiction & Fact Magazine; This column was written and submitted 2/10/84 and is copyrighted ©1984, John G. Cramer. All rights reserved. No part may be reproduced in any form without the explicit permission of the author.

This column is about the end of the universe and of time itself, as implied by a new variant of the standard model of Big Bang cosmology. But before considering the destruction of the universe-as-we-know-it, we will need to review the most startling development in modern cosmology: the discovery that the expansion of the universe is increasing due to "dark energy" contained in space itself. The best evidence for dark energy comes from studies of Type Ia supernovas.

In this column I want to describe a new possible description of the universe, a cosmological paradigm proposing a universe that is infinite, eternal, and that recycles itself from Big Bang to Big Crunch at regular time intervals. This new model of cosmology is the work of Paul J. Steinhardt of Princeton and Neil Turok of Cambridge, and is inspired by string theory and based on Steinhardt’s own ekpyrotic cosmology, as described in a previous AV column (“Brane Bashing: Big Bang (...) or Big Clap?”, Analog, April-2002 ). (shrink)

Recent models in quantum cosmology make use of the concept of imaginary time. These models all conjecture a join between regions of imaginary time and regions of real time. We examine the model of James Hartle and Stephen Hawking to argue that the various no-boundary attempts to interpret the transition from imaginary to real time in a logically consistent and physically significant way all fail. We believe this conclusion also applies to quantum tunneling models, such as that proposed by Alexander (...) Vilenkin. We conclude, therefore, that the notion of emerging from imaginary time is incoherent. A consequence of this conclusion seems to be that the whole class of cosmological models appealing to imaginary time is thereby refuted. (shrink)

In the literature on the compatibility between the time of our experience and the time of physics, the special theory of relativity has enjoyed central stage. By bringing into the discussion the general theory of relativity, I suggest a new analysis of the misunderstood notion of becoming, developed from hints in Gödel’s published and unpublished arguments for the ideality of time. I claim that recent endorsements of such arguments, based on Gödel’s own “rotating” solution to Einstein’s field equation, fail: once (...) understood in the right way, becoming can be shown to be both mind-independent and compatible with spacetime physics. Being a needed tertium quid between views of time traditionally regarded as in conflict, such a new approach to becoming should also help to dissolve a crucial aspect of the century-old debate between the so-called A and B theories of time. (shrink)

The cosmological constant is back. Several lines of evidence point to the conclusion that either there is a positive cosmological constant or else the universe is filled with a strange form of matter (“quintessence”) that mimics some of the effects of a positive lambda. This paper investigates the implications of the former possibility. Two senses in which the cosmological constant can be a constant are distinguished: the capital Λ sense in which lambda is a universal constant on a par with (...) the charge of the electron, and the lower case λ sense in which lambda is a humble constant of integration. The latter interpretation has been touted as the means to a solution to various problems in physics. These claims are critically examined with an eye to discerning the implications for philosophy of science and foundations of physics. (shrink)

Modern cosmology treats space and time, or rather space-time, as concrete particulars. The General Theory of Relativity combines the distribution of matter and energy with the curvature of space-time. Here space-time appears as a concrete entity which affects matter and energy and is affected by the things in it. I question the idea that space-time is a concrete existing entity which both substantivalism and reductive relationism maintain. Instead I propose an alternative view, which may be called non-reductive relationism, by arguing (...) that space and time are abstract entities based on extension and changes. (shrink)

Present physics is a mix of theories of time, logic, and matter. These may have a common origin in a unitary quantum cosmology founded on process alone. A quantum theory of sets, or something like it, is helpful for such a cosmology, and one is constructed by adding superposition to a slightly reformulated classical set theory. There is an elementary or atomic process in such theories. The size of its characteristic time is estimated from the mass spectrum, although this gives (...) a much larger time than is usually accepted. In a discussion of the foundations of quantum theory, the problem of the collapsing state-vector is attributed to statism, the ideology, alien to quantum theory, that the system under study has a state. The origin of metrical and gauge structure is considered. Using von Neumann's work on the lattices of algebras, we may represent almost any gauge structure by enlarging the ring of c-numbers of quantum theory beyond the complex (or quaternion) field. Ultimately the gauge structure and c-numbers may express a transport relation defined by the discrete network of the world. (shrink)

Einstein's special and general theory of relativity abolished the Newtonian concept of absolute time. Moreover, Einsteinian physics revealed the mutual interdependence of space, time, and matter. Applying general relativity to cosmology leads again to the existence of a preferred time coordinate among the homogeneous and isotropic cosmological models. Einstein referred to this time coordinate as ,,almost absolute time." What is the exact relation between absolute time in relativistic cosmology and absolute time in Newtonian physics? To answer this question firstly we (...) investigate which features are characteristic of Newtonian absolute time. Secondly we show how the preferred time in relativistic cosmology is related to the cosmological principle. After that we compare the two concepts of time. Finally, we consider the concept of time in particular cosmological models like the static Einstein universe, the relation between cosmic time and the evolution of the universe and different possibilities to introduce the time coordinate in oscillating cosmological models. German Die Spezielle und Allgemeine Relativitätstheorie Einsteins räumten mit dem Konzept einer absoluten Zeit, wie es von Newton für seine Physik vorausgesetzt worden war, auf und zeigten die wechselseitige Abhängigkeit von Raum, Zeit und Materie. In Anwendung der Allgemeinen Relativitätstheorie auf das kosmologische Problem ergibt sich jedoch für die üblicherweise herangezogene Klasse der homogenen und isotropen Weltmodelle die Möglichkeit, eine ausgezeichnete Zeitkoordinate einzuführen, die Einstein als ,,quasi-absolute Zeit bezeichnete. Wie verhält sich die absolute Zeit der relativistischen Kosmologie zur absoluten Zeit Newtons? Diese Frage wird beantwortet, indem die wichtigsten Momente der absoluten Zeit Newtons herausgestellt werden, die auf dem Kosmologischen Prinzip basierende Möglichkeit der Einführung einer ausgezeichneten Zeit in der Kosmologie erörtert wird und anschließend beide Zeitkonzepte konfrontiert werden. Abschließend wird der Begriff der Zeit im Rahmen bestimmter kosmologischer Modelle weiter untersucht, vor allem seine Bedeutung im statischen Einstein-Universum, seine Verknüpfung mit der Evolution des Universums und die verschiedenen Möglichkeiten, die Zeit in oszillierenden bzw. zyklischen Modellen zu definieren. (shrink)

Excerpts: The wider the range of a piece of research the less adequately can any one worker deal with each of its specialized aspects.

Recent developments in cosmology indicate that every history having a non-zero probability is realized in infinitely many distinct regions of spacetime. Thus, it appears that the universe contains infinitely many civilizations exactly like our own, as well as infinitely many civilizations that differ from our own in any way permitted by physical laws. We explore the implications of this conclusion for ethical theory and for the doomsday argument. In the infinite universe, we find that the doomsday argument applies only to (...) effects which change the average lifetime of all civilizations, and not those which affect our civilization alone. (shrink)

In recent decades, there has been astonishing growth in scientific theorizing about multiverses. Once considered outré or absurd, multiple universe theories appear to be gaining considerable scientific respectability. There are, of course, many such theories, including (i) Everett’s (1957) many worlds interpretation of quantum mechanics, defended by Deutsch (1997) and others; (ii) Linde’s (1986) eternal inflation view, which suggests that universes form like bubbles in a chaotically inflating sea; (iii) Smolin’s (1997) fecund universe theory, which proposes that universes are generated (...) through black holes; (iv) the cyclic model, recently defended using string/M theory by Steinhardt and Turok (2007), which holds that distinct universes are formed in a never-ending sequence of Big Bangs and Big Crunches; and (v) Tegmark’s (2007) “Level IV” multiverse, which contains many universes governed by distinct mathematical and scientific laws. While not all of these preclude each other, the details and implications of each one are hotly contested.1 In one area within the philosophy of religion (the debate concerning the “fine-tuning” argument), scientific multiverse theories are widely held to be hostile to theism. This is because such theories appear to account for the relevant data – the biophilic parameters of the universe we inhabit – without appeal to an intelligent designer. Yet, in recent years, several philosophers2 and one physicist3 have offered reasons for thinking that if theism is true, the actual world comprises (or probably comprises) many universes. I first set out some requirements – both scientific and otherwise – for such a theory. I then survey some problems such theories are held to face, and some prospects they are thought to have. Finally, I examine arguments both for and against the claim that multiverse theories can help theists respond to the problem of evil.. (shrink)

The case of Fred Hoyle’s prediction of a resonance state in carbon-12, unknown in 1953 when it was predicted, is often mentioned as an example of anthropic prediction. An investigation of the historical circumstances of the prediction and its subsequent experimental confirmation shows that Hoyle and his contemporaries did not associate the level in the carbon nucleus with life at all. Only in the 1980s, after the emergence of the anthropic principle, did it become common to see Hoyle’s prediction as (...) anthropically significant. At about the same time mythical accounts of the prediction and its history began to abound. Not only has the anthropic myth no basis in historical fact, it is also doubtful if the excited levels in carbon-12 and other atomic nuclei can be used as an argument for the predictive power of the anthropic principle, such as has been done by several physicists and philosophers. (shrink)

The cosmos exists just because of the ethical need for it We, and all the intricate structures of our universe, exist as thoughts in a divine mind that knows everything worth knowing. There could also be infinitely many other universes in this mind....It may be hard to believe that the universe is as Leslie says it is--but it is also hard to resist his compelling ideas and arguments.

One of the first books to address what has come to be known as the philosophy of cosmology, Universes asks, "Why does the universe exist?", arguing that the universe is "fine tuned for producing life." For example, if the universe's early expansion speed had been smaller by one part in a million, then it would have recollapsed rapidly; with an equivalently tiny speed increase, no galaxies would have formed. Either way, this universe would have been lifeless.

Quentin Smith has argued that quantum-cosmological theory is incompatible with theism. The two claims that Smith argues render theism inconsistent with Hawking’s theory are that of the initial creation of the universe by God and His continued conservation of it. His primary argument is that divine decision and Hawking’s wave function entail contradictory probabilities that the universe begin to exist and continue to evolve in a certain way. I attempt to refute the argument by providing a schema that accommodates probabilities (...) conditioned on divine decision as well as those conditioned on the wave function with respect to these two issues. (shrink)

Ellis and Murphy show how contemporary sciences actually support a religiously based ethic of nonviolence, not by appealing to the Enlightment's mechanismic ...

In a recent essay, Quentin Smith revisits a question of philosophical cosmology. Why does the universe exist? This is one way of asking the existence question EQ. Smith notes that all theistic philosophical cosmologists have answered this question in terms of God’s creative choice. Smith favors an “atheistic” philosophical answer: “The universe exists because it has an unconditional probability of existing based on a fundamental law of nature.” He further declares: “This law of nature ... is inconsistent with theism and (...) implies that God does not exist.” The structure of Smith's reasoning in defense of these claims is the following: (1) The answer to EQ of theistic philosophical cosmologists is logically inconsistent with the answer of atheistic philosophical cosmologists. (2) Therefore, theistic and atheistic philosophical cosmologies are logically inconsistent with each other. (3) The atheistic answer to EQ is a complete answer to EQ. (4) Therefore, theism is demonstrably false. I shall argue that Smith’s reasoning in defense of (1) is not sound. From that, it follows that (2) is not a proven truth. Assumption (3) is controversial, and in the present context question-begging. It presupposes that materialism is true. Therefore, (4) is not a proven truth. (shrink)

Probabilities in quantum theory are traditionally given by Born’s rule as the expectation values of projection operators. Here it is shown that Born’s rule is insufficient in universes so large that they contain identical multiple copies of observers, because one does not have definite projection operators to apply. Possible replacements for Born’s rule include using the expectation value of various operators that are not projection operators, or using vari-.

The revolution in science inaugurated by quantum physics has made us aware of the role of observation in the construction of data. Eugene Wigner remarked that in quantum physics we no longer have observables (invariants), only observations. Tongue in cheek, I asked him whether that meant that quantum physics is really psychology, expecting a gruff reply to my sassiness. Instead, Wigner beamed understanding and replied "Yes, yes, that's exactly correct." David Bohm pointed out that were we to look at the (...) cosmos without the lenses of our telescopes we would see a hologram. I extend Bohm's insight to the lens in the optics of the eye. The receptor processes of the ear and skin work in a similar fashion. Without these lenses and lenslike operations all of our perceptions would be entangled as in a hologram. Furthermore, the retina absorbs quanta of radiation so that quantum physics uses the very perceptions that become formed by it. In turn, higher-order brain systems send signals to the sensory receptors so that what we perceive is often as much a result of earlier rather than just immediate experience. This influence from inside out becomes especially relevant to our interpretation of how we experience the contents and bounds of cosmology that come to us by way of radiation. (shrink)

This radical reinterpretation of the formative stages of Chinese culture and history traces the central role played by cosmology in the formation of China's early empires. It crosses the disciplines of history, social anthropology, archaeology, and philosophy to illustrate how cosmological systems, particularly the Five Elements, shaped political culture. By focusing on dynamic change in early cosmology, the book undermines the notion that Chinese cosmology was homogenous and unchanging. By arguing that cosmology was intrinsic to power relations, it also challenges (...) prevailing theories of political and intellectual history. (shrink)

Avoiding the seductive trap of utopianism, Whyte approaches this challenge by defining the terms of a potentially worldwide consensus of heart, mind, and will ...

Philosophical considerations have been essentially involved in the origin and development of the steady-state cosmological theory (SST). These considerations include an explicit uniformitarian methodology and implicit metaphysical views concerning the status of natural laws in a changing universe. I shall examine the foundations of SST by reconstructing its early history. Whereas the strong uniformitarian methodology of SST found no support in the subsequent development of cosmology, the idea of a possible influence the global structure of the universe may have on (...) the laws of physics operative in it has been assimilated by the standard big bang theory as it made its remarkable progress in recent decades. (shrink)