Some arguments, based on the possible spontaneous violation of the cosmological principle (represented by the observed large-scale structures of galaxies), on the Cartan geometry of simple spinors, and on the Fock formulation of hydrogen atom wave equation in momentum space, are presented in favor of the hypothesis that space-time and momentum space should be both conformally compactified and should both originate from the two four-dimensional homogeneous spaces of the conformai group, both isomorphic (S 3 ×S 1)/Z (...) 2 and correlated by conformal inversion, but should not necessarily be identified with them. Within this framework, the possible common origin for the SO(4) symmetry underlying the geometrical structure of the Universe, of Kepler orbits, and of the H atom is discussed. One of the consequences of the proposed hypothesis could be that any quantum field theory should be naturally free from both infrared and ultraviolet divergences. But then physical spaces defined as those where physical phenomena may be best described through some set of fields, could be different from those homogeneous spaces. A simple, exactly soluble, toy model, valid for a two-dimensional spacetime, is presented where the conjectured conformally compactified homogeneous spaces are both isomorphic to (S 1 ×S 1)/Z 2,while the possible physical spaces could be two finite lattices which are dual since Fourier transforms, represented by finite, discrete, sums, may be well defined on them. (shrink)

It is argued that physics must eventually expand to accommodate mind and consciousness but that this will require a new paradigm. The paradigm required will impinge on two problems on the borders of physics and philosophy: the relationship between physical space and perceptual space and the nature of the passage of time. It is argued that the resolution of both these problems may involve a 5-dimensional model, with the 5th dimension being associated with mental time, and this proposal (...) may relate to recent developments in brane cosmology. A description of consciousness must also entail a proper understanding of the specious present, the minimum timescale of conscious experience, this possibly being associated with a compactified extra dimension. There could even be a hierarchy of levels of consciousness, associated with a hierarchy of extra dimensions. (shrink)

The mathematical and physical aspects of the conformal symmetry of space-time and of physical laws are analyzed. In particular, the group classification of conformally flat space-times, the conformal compactifications of space-time, and the problem of imbedding of the flat space-time in global four-dimensional curved spaces with non-trivial topological and geometrical structure are discussed in detail. The wave equations on the compactified space-times are analyzed also, and the set of their elementary solutions constructed. Finally, the (...) implications of global compactified space-times for cosmology are discussed. It is argued that the recent discovery of periodic structure of matter distribution on large distances strongly suggests that the global cosmological space-time should be close. Next we analyze the inflation scalar field in the inflationary model of universe evolution considered on the spatially compact Robertson-Walker space-time. It is shown that the energy distribution in this model is periodic and the periods and density decrease with increasing distance, in striking agreement with experimental data. Our model of the universe also provides a definite predictions for the energy distribution, polar and azimuthal, considered as a function of angles θ and φ. These predictions should be tested with the new astronomical data. (shrink)

Spontaneous transitions between bound states of an atomic system, “Lamb Shift” of energy levels and many other phenomena in real nonrelativistic quantum systems are connected within the influence of the quantum vacuum fluctuations (fundamental environment (FE)) which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system “quantum system (QS) + FE” is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger (L-Sch) type, and is defined on the extended space R 3 (...) ⊗ R {ξ}, where R 3 and R {ξ} are the Euclidean and functional spaces, respectively. The density matrix for single QS in FE is defined. The entropy of QS entangled with FE is defined and investigated in detail. It is proved that as a result of interaction of QS with environment there arise structures of various topologies which are a new quantum property of the system. (shrink)

Compactified Minkowski spacetime is suggested by conformal covariance of Maxwell equations, while E. Cartan's definition of simple spinors leads to the idea of compactified momentum space. Assuming both diffeomorphic to (S 3 × S 1 )/Z 2 , one may obtain in the conformally flat stereographic projection field theories both infrared and ultraviolet regularized. On the compact manifold themselves instead, Fourier integrals of wave-field oscillations would have to be replaced by Fourier series summed over indices of spherical (...) eigenfunctions: n, l, m, m′. Tentatively identifying those wave structures with spacetime itself (in the frame of Big-Bang) and/or with matter and radiation distribution, some large-scale (hydrogenic) and small-scale (lattice) space structures are conjectured. (shrink)

We construct a world model consisting of a matter field living in 4 dimensional spacetime and a gravitational field living in 11 dimensional spacetime. The seven hidden dimensions are compactified within a radius estimated by reproducing the particle–wave characteristics of diffraction experiments. In the presence of matter fields the gravitational field develops localized modes with elementary excitations called gravonons which are induced by the sources. The final world model treated here contains only gravonons and a scalar matter field. The (...) gravonons are localized in the environment of the massive particles which generate them. The solution of the Schrödinger equation for the world model yields matter fields which are localized in the 4 dimensional subspace. The localization has the following properties: There is a chooser mechanism for the selection of the localization site. The chooser selects one site on the basis of minor energy differences and differences in the gravonon structure between the sites, which at present cannot be controlled experimentally and therefore let the choice appear statistical. The changes from one localization site to a neighbouring one take place in a telegraph-signal like manner. The times at which telegraph like jumps occur depend on subtleties of the gravonon structure which at present cannot be controlled experimentally and therefore let the telegraph-like jumps appear statistical. The fact that the dynamical law acts in the configuration space of fields living in 11 dimensional spacetime lets the events observed in 4 dimensional spacetime appear non-local. In this way the phenomenology of CQM is obtained without the need of introducing the process of collapse and a probabilistic interpretation of the wave function. Operators defining observables need not be introduced. All experimental findings are explained in a deterministic way as a consequence of the time development of the wave function in configuration space according to Schrödinger’s equation without the need of introducing a probabilistic interpretation. (shrink)

We investigate a theory in which fundamental objects are branes described in terms of higher grade coordinates $X^{\mu{_1}\ldots \mu{_n}}$ encoding both the motion of a brane as a whole, and its volume evolution. We thus formulate a dynamics which generalizes the dynamics of the usual branes. Geometrically, coordinates $X^{\mu{_1} \ldots \mu{_n}}$ and associated coordinate frame fields { ${\gamma_{\mu{_1}\ldots\mu{_n}}}$ } extend the notion of geometry from spacetime to that of an enlarged space, called Clifford space or C-space. If (...) we start from four-dimensional spacetime, then the dimension of C-space is 16. The fact that C-space has more than four dimensions suggests that it could serve as a realization of Kaluza-Klein idea. The “extra dimensions” are not just the ordinary extra dimensions, they are related to the volume degrees of freedom, therefore they are physical, and need not be compactified. Gauge fields are due to the metric of Clifford space. It turns out that amongst the latter gauge fields there also exist higher grade, antisymmetric fields of the Kalb–Ramond type, and their non-Abelian generalization. All those fields are naturally coupled to the generalized branes, whose dynamics is given by a generalized Howe–Tucker action in curved C-space. (shrink)

Contemporary physics is in a great need of a unified theoretical framework allowing for a comprehensive physical description of particles and interactions. One of the leading candidates for such a framework, the superstring theory, has recently provoked immense critics due to the lack of its experimental verification (L. Smolin, R. Penrose). The survey of the specificity of the unification mechanisms that are operative within the superstring theory shows that, in comparison with such a successful paradigm as that of the general (...) theory of relativity, the unification model of the theory does not follow the strict relation between the formalism and a unifying physical idea. The critical analysis of the superstring theory, presented by Lee Smolin in his book The Trouble with Physics, offers a detailed re-evaluation of theory's physical foundations but remains insensitive to issues of methodological, ontological and epistemological import. In particular, Smolin seems to be aware of the lack of the background independence as well as the need to compactify extra space-time dimensions that are hoped to be alleviated in the future M-theory. He treats purely mathematical criteria such as that of renormalizability on an equal footing with the physical interpretation of the theory. Such a methodological disarray leads to Smolin's biased estimate of the true drawbacks of the superstring theory. (shrink)

The Cartesian concept of nature, which has determined modern thinking until the present time, has become obsolete. It shall be shown that Hegel's objective-idealistic conception of nature discloses, in comparison to that of Descartes, new perspectives for the comprehension of nature and that this, in turn, results in possibilities of actualizing Hegel's philosophy of nature. If the argumentation concerning philosophy of nature is intended to catch up with the concrete Being-of-nature and to meet it in its concretion, then this is (...) impossible for the finite spirit in a strictly a priori sense – this is the thesis supported here which is not at all close to Hegel. As the argumentation rather has to consider the conditions of realization concerning the Being-of-nature, too, it is compelled to take up empirical elements – concerning the organism, for instance, system-theoretical aspects, physical and chemical features of the nervous system, etc. With that, on the one hand, empirical-scientific premises are assumed (e.g. the lawlikeness of nature), which on the other hand become (now close to Hegel) possibly able to be founded in the frame of a Hegelian-idealistic conception. In this sense, a double strategy of empirical-scientific concretization and objective-idealistic foundation is followed up, which represents the methodical basic principle of the developed considerations. In the course of the undertaking, the main aspects of the whole Hegelian design concerning the philosophy of nature are considered – space and time, mass and motion, force and law of nature, the organism, the pro-blem of evolution, psychic being – as well as Hegel's basic thesis concerning the philosophy of nature, that therein a tendency toward coherence and idealization manifests itself in the sense of a (categorically) gradually rising succession of nature: from the separateness of space to the ideality of sensation. In the sense of the double strategy of concretization and foundation it is shown that on the one hand possibilities of philosophical penetration concerning actual empirical-scientific results are opened, and on the other hand – in turn – a re-interpretation of Hegel's theorem on the basis of physical, evolution-theoretical and system-theoretical argumentation also becomes possible. In this mutual crossing-over and elucidation of empirical and Hegelian argumentation not only do perspectives of a new comprehension of nature become visible, but also, at the same time – as an essential consequence of this methodical principle – thoughts on the possibilities of actualizing Hegel's philosophy of nature. (shrink)

What is space? And why are questions of space important to social theory? Society, Action and Space is the first English translation of a book which has been widely recognized in Europe as a major contribution to the interface between geography and social theory. Benno Werlen focuses on the issues which are at the heart of the most important debates in human and social geography today. One of the most significant recent developments in social analysis has been (...) the increasing interchange among geographers, sociologists, anthropologists and social philosophers concerning "the spatial." This debate involves the work of Giddens, Foucault, Bourdieu, Lefebvre, Harvey, Gregory, Soja, and many others. From these new developments a whole series of new forms and empirical work, as well as theoretical innovations, have come into being. Spatial considerations are no longer confined to the realm of geography, but are now seen as fundamental to all forms of social theorizing, especially under conditions of late modernity and globalization. Society, Action and Space links discussions in the philosophy of social science with theories of action which have direct relevance to concepts of space. Benno Werlen provides a discussion of Popper's critical rationalism, and connects it to ideas drawn from phenomenology. This epistemological debate is linked with the sociological action theories of Pareto, Weber, Parsons, and Schutz. The book closes with an evaluation of how "the spatial" can be systematically integrated into action theory. Ambitious, original, and persuasive in its arguments, it raises exciting new implications for the study of space and social theory. (shrink)

Assembled here for the first time in English translation, Sigrid Weigel and Georgina Paul offer illuminating new insights into Benjamin's theory, combining impulses from post-structuralism, feminism, cultural anthropology and psychoanalysis.

‘Space does not exist fundamentally: it emerges from a more fundamental non-spatial structure.’ This intriguing claim appears in various research programs in contemporary physics. Philosophers of physics tend to believe that this claim entails either that spacetime does not exist, or that it is derivatively real. In this article, I introduce and defend a third metaphysical interpretation of the claim: reductionism about space. I argue that, as a result, there is no need to subscribe to fundamentality, layers of (...) reality and emergence in order to analyse the constitution of space by non-spatial entities. It follows that space constitution, if borne out, does not provide empirical evidence in favour of a stratified, Aristotelian in spirit, metaphysics. The view will be described in relation to two particular research programs in contemporary physics: wave function realism and loop quantum gravity. (shrink)

Presenting the history of space-time physics, from Newton to Einstein, as a philosophical development DiSalle reflects our increasing understanding of the connections between ideas of space and time and our physical knowledge. He suggests that philosophy's greatest impact on physics has come about, less by the influence of philosophical hypotheses, than by the philosophical analysis of concepts of space, time and motion, and the roles they play in our assumptions about physical objects and physical measurements. This way (...) of thinking leads to interpretations of the work of Newton and Einstein and the connections between them. It also offers ways of looking at old questions about a priori knowledge, the physical interpretation of mathematics, and the nature of conceptual change. Understanding Space-Time will interest readers in philosophy, history and philosophy of science, and physics, as well as readers interested in the relations between physics and philosophy. (shrink)

In this book, Lawrence Sklar demonstrates the interdependence of science and philosophy by examining a number of crucial problems on the nature of space and ...

Quality-space theory (QST) explains the nature of the mental qualities distinctive of perceptual states by appeal to their role in perceiving. QST is typically described in terms of the mental qualities that pertain to color. Here we apply QST to the olfactory modalities. Olfaction is in various respects more complex than vision, and so provides a useful test case for QST. To determine whether QST can deal with the challenges olfaction presents, we show how a quality space (QS) (...) could be constructed relying on olfactory perceptible properties and the olfactory mental qualities then defined by appeal to that QS of olfactory perceptible properties. We also consider how to delimit the olfactory QS from other modalities. We further apply QST to the role that experience plays in refining our olfactory discriminative abilities and the occurrence of olfactory mental qualities in non-conscious olfactory states. QST is shown to be fully applicable to and useful for understanding the complex domain of olfaction. (shrink)

In this book John Campbell shows that the general structural features of human thought can be seen as having their source in the distinctive ways in which we...

PREFACE: - BY his theory of relativity Albert Einstein has provoked a revolution of thought in physical science. The achievement consists essentially in this Einstein has succeeded in separating far more completely than hitherto the share of the observer and the share of external nature in the things we see happen. The perception of an object by an observer depends on his own situation and circumstances for example, distance will make it appear smaller and dimmer. We make allowance for this (...) almost unconsciously in interpreting what we see. But it now appears that the allowance made for the motion of the observer has hitherto been too crude a fact overlooked because in practice all observers share nearly the same motion, that of the earth. Physical space and time are found to be closely bound up with this motion of the observer and only an amorphous combination of the two is left inherent in the external world. When space and time are relegated to their proper source the observer the world of nature which remains appears strangely unfamiliar but it is in reality simplified, and the underlying unity of the principal phenomena is now clearly revealed. The deductions from this new outlook have, with one doubtful exception, been confirmed when tested by experiment. It is my aim to give an account of this work without intro ducing anything very technical in the way of mathematics, physics, or philosophy. The new view of space and time, so opposed to our habits of thought, must in any case demand unusual mental exercise. The results appear strange and the incongruity is not without a humorous side. For the first nine chapters the task is one of interpreting a clear-cut theory, accepted in all its essentials by a large and growing school of physicists although perhaps not everyone would accept the authors views of its meaning. Chapters x and xi deal with very recent advances, with regard to which opinion is more fluid. As for the last chapter, containing the authors specula tions on the meaning of nature, since it touches on the rudiments of a philosophical system, it is perhaps too sanguine to hope that it can ever be other than controversial. A non-mathematical presentation has necessary limitations and the reader who wishes to learn how certain exact result follow from Einsteins, or even Newtons, law of gravitation m bound to seek the reasons in a mathematical treatise. But thj limitation of range is perhaps less serious than the limitation of intrinsic truth. There is a relativity of truth, as there is a relativity of space. For is and IS-NOT though with Rule and Line And UP-AND-DOWK without, I could define, Alas It is not so simple. We abstract from the phenomena that which is peculiar to the position and motion of the observer but can we abstract that which is peculiar to the limited imagina tion of the human brain We think we can, but only in the symbolism of mathematics. As the language of a poet rings with a truth that eludes the clumsy explanations of his commentators, so the geometry of relativity in its perfect harmony expresses a truth of form and type in nature, which my bowdlerised version misses. But the mind is not content to leave scientific Truth in a dry husk of mathematical symbols, and demands that it shall be alloyed with familiar images. The mathematician, who handles x so lightly, may fairly be asked to state, not indeed the in scrutable meaning of a in nature, but the meaning which x conveys to him. Although primarily designed for readers without technical knowledge of the subject, it is hoped that the book may also appeal to those who have gone into the subject more deeply. A few notes have been added in the Appendix mainly to bridge the gap between this and more mathematical treatises, and to indicate the points of contact between the argument in the text and the parallel analytical investigation. It is impossible adequately to express my debt to con temporary literature and discussion... (shrink)

Our aim in this paper is to take quite seriously Heinz Post’s claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set theory, we avoid working within a label-tensor-product-vector-space-formalism, to use Redhead and Teller’s words, and get a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified. We (...) build a vector space with inner product, the Q-space, using the non-classical part of quasi-set theory, to deal with indistinguishable elements. Vectors in Q-space refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the fact of unobservability of permutations. Thus, this paper can be regarded as a tentative to follow and enlarge Heinsenberg’s suggestion that new phenomena require the formation of a new “closed” (that is, axiomatic) theory, coping also with the physical theory’s underlying logic and mathematics. (shrink)

This volume explores the multiple ways in which people experience time-space compression in varying historical and geographical circumstances.

In his argument for the possibility of knowledge of spatial objects, in the Transcendental Deduction of the B-version of the Critique of Pure Reason, Kant makes a crucial distinction between space as “form of intuition” and space as “formal intuition.” The traditional interpretation regards the distinction between the two notions as reflecting a distinction between indeterminate space and determinations of space by the understanding, respectively. By contrast, a recent influential reading has argued that the two notions (...) can be fused into one and that space as such is first generated by the understanding through an act of synthesis of the imagination. Against this reading, this article argues that a key characteristic of space as a form of intuition is its nonconceptual unity, which defines the properties of space and is as such necessarily independent of determination by the understanding through the transcendental synthesis of the imagination. The conceptual unity that the understanding prescribes to the manifold in intuition, by means of the categories, defines the formal intuition. Furthermore, this article argues that it is the sui generis, nonconceptual unity of space, when takenas a unity for the understanding by means of conceptual determination, that first enables geometric knowledge and knowledge of spatially located particulars. (shrink)

We live today within a system in which state and corporate power aim to render space flat, transparent, and uniform, for only then can it be truly controlled. The gaze of power and the commodity form are capable of infiltrating even the darkest of corners, and often, we invite them into our most private spaces. We do so as a matter of convenience, but also to placate ourselves and cope with the alienation inherent in our everyday lives. The resulting (...) dominant space can best be termed totalitarian. It is space stripped of uniqueness, deprived of the “spatial aura” necessary for authentic experience. In Totalitarian Space and the Destruction of Aura, Saladdin Ahmed sets out to help us grasp what has been lost before no trace remains. He draws attention to that which we might prefer not to see, but despite the bleakness of this indictment of reality, the book also offers a message of hope. Namely, it is only once we comprehend the magnitude of the threat to our spatial experience and our own complicity in sustaining this system that we can begin to resist the totalizing forces at work. (shrink)

Space, Time, and Stuff is an attempt to show that physics is geometry: that the fundamental structure of the physical world is purely geometrical structure. Along the way, he examines some non-standard views about the structure of spacetime and its inhabitants, including the idea that space and time are pointless, the idea that quantum mechanics is a completely local theory, the idea that antiparticles are just particles travelling back in time, and the idea that time has no structure (...) whatsoever. The main thrust of the book, however, is that there are good reasons to believe that spaces other than spacetime exist, and that it is the existence of these additional spaces that allows one to reduce all of physics to geometry. Philosophy, and metaphysics in particular, plays an important role here: the assumption that the fundamental laws of physics are simple in terms of the fundamental physical properties and relations is pivotal."--P. [4] of cover. (shrink)

The aim of this book is to give an account of Einstein's work without introducing anything very technical in the way of mathematics, physics, or philosophy.

Ian Stoner has recently argued that we ought not to colonize Mars because doing so would flout our pro tanto obligation not to violate the principle of scientific conservation, and there is no countervailing considerations that render our violation of the principle permissible. While I remain agnostic on, my primary goal in this article is to challenge : there are countervailing considerations that render our violation of the principle permissible. As such, Stoner has failed to establish that we ought not (...) to colonize Mars. I close with some thoughts on what it would take to show that we do have an obligation to colonize Mars and related issues concerning the relationship between the way we discount our preferences over time and projects with long time horizons, like space colonization. (shrink)

There is a growing body of scholarship that is addressing the ethics, in particular, the bioethics of space travel and colonisation. Naturally, a variety of perspectives concerning the ethical issues and moral permissibility of different technological strategies for confronting the rigours of space travel and colonisation have emerged in the debate. Approaches ranging from genetically enhancing human astronauts to modifying the environments of planets to make them hospitable have been proposed as methods. This paper takes a look at (...) a critique of human bioenhancement proposed by Mirko Garasic who argues that the bioenhancement of human astronauts is not only functional but necessary and thus morally permissible. However, he further claims that the bioethical arguments proposed for the context of space do not apply to the context of Earth. This paper forwards three arguments for how Garasic’s views are philosophically dubious: (1) when he examines our responsibility towards future generations he refers to a moral principle (which we will call the principle of mere survival) which, besides being vague, is not morally acceptable; (2) the idea that human bioenhancement is not natural is not only debatable but morally irrelevant; and (3) it is not true that the situations that may arise in space travel cannot occur on Earth. We conclude that not only is the (bio)enhancement of humans on Earth permissible but perhaps even necessary in certain circumstances. (shrink)

INTRODUCTION In Einstein's theory of gravitation matter and its dynamical interaction are based on the notion of an intrinsic geometric structure of the space -time continuum. The ideal aspiration, the ultimate aim, of the theory is not more and ...

The essays in Rhetorical Spaces grow out of Lorraine Code's ongoing commitment to engaging philosophical issues as they figure in people's everyday lives. The arguements in this book are informed at once by the moral-political implications of how knowledge is produced and circulated and by issues of gendered subjectivity. In their critical dimension, these lucid essays engage with the incapacity of the philosophical mainstream's dominant epistemologies to offer regulative principles that guide people in the epistemic projects that figure centrally in (...) their lives. In its constructive dimension, Rhetorical Spaces focuses on developing productive, case-by-case analyses of knowing other people in situations where social-political inequalities create asymmetrical patterns of epistemic power and privilege. Framing all of the essays is the conception of rhetorical spaces which shows that prevailing intellectual-political climates can work to enhance or to thwart possibilities of establishing cognitive authority for the members of a society who belong to groups other than the dominant ones. Finally, bridging the gap between theory and practice, Lorraine Code shows how the issue of reconfiguring structures of authority and expertise are not just matters of individual responsibility, but require a radical restructuring of the communities and social orders in which people know and act. (shrink)

In this paper I argue that empty space can be heard. This position contrasts with the generally held view that the only things that can be heard are sounds, their properties, echoes, and perhaps sound sources. Specifically, I suggest that when sounds reverberate in enclosed environments we auditorily represent the volume of space surrounding us. Clearly, we can learn the approximate size of an enclosed space through hearing a sound reverberate within it, and so any account that (...) denies that we hear empty space must instead show how beliefs about volumes of space can be derived indirectly from what is heard. That is, if space is not auditorily represented when we hear sounds reverberate, what is? I consider whether hearing reverberation can be thought of as hearing a distinct sound, hearing echoes, or hearing a property of a sound. I argue that experiences of reverberation cannot be reduced to the perception of any of these types and that therefore empty space is represented in auditory perceptual content. In the final section I outline two ways in which space might be represented. (shrink)

Branching space-time is a simple blend of relativity and indeterminism. Postulates and definitions rigorously describe the causal order relation between possible point events. The key postulate is a version of everything has a causal origin; key defined terms include history and choice point. Some elementary but helpful facts are proved. Application is made to the status of causal contemporaries of indeterministic events, to how splitting of histories happens, to indeterminism without choice, and to Einstein-Podolsky-Rosen distant correlations.

This paper provides a method for characterizing space events using the framework of conceptual spaces. We focus specifically on estimating and ranking the likelihood of collisions between space objects. The objective is to design an approach for anticipatory decision support for space operators who can take preventive actions on the basis of assessments of relative risk. To make this possible our approach draws on the fusion of both hard and soft data within a single decision support framework. (...) Contextual data is also taken into account, for example data about space weather effects, by drawing on the Space Domain Ontologies, a large system of ontologies designed to support all aspects of space situational awareness. The framework is coupled with a mathematical programming scheme that frames a mathematically optimal approach for decision support, providing a quantitative basis for ranking potential for collision across multiple satellite pairs. The goal is to provide the broadest possible information foundation for critical assessments of collision likelihood. (shrink)