Infinities as natural places

Written from a very untutored and limited viewpoint in terms of physics and mathematics, this essay ventures some thoughts that should therefore be regarded as only very tentative. Especially as they address a long established idea that sits right at the heart of the scientific discipline of physics. This is the idea of naturally moving reference systems, a notion closely linked to the classical principles of both inertia and relativity. Such inertial reference systems played a key role in some thought experiments published over a century ago, by Albert Einstein. It is a critical

This essay is a contribution to the historical phenomenology of science, taking as its point of departure husserl's later philosophy of science and Jacob klein's seminal work on the emergence of the symbolic conception of number in european mathematics during the late sixteenth and seventeenth centuries. since neither husserl nor klein applied their ideas to actual theories of modern mathematical physics, this essay attempts to do so through a case study of the concept of "spacetime." in §1, i sketch klein's account of the emergence of the symbolic conception of number, beginning with Vieta in the late sixteenth century. in §2, through a series of historical illustrations, i show how the principal impediment to assimilating the new symbolic algebra to mathematical physics, namely, the dimensionless character of symbolic number, is overcome via the translation of the traditional language of ratio and proportion into the symbolic language of equations. in § §3-4, i critically examine the concept of "minkowski spacetime," specifically, the purported analogy between the Pythagorean distance formula and the minkowski "spacetime interval." finally, in §5, i address the question of whether the concept of minkowski spacetime is, as generally assumed, indispensable to einstein's general theory of relativity.

The exploration on the origin of the universe by human-beings' has never stopped. Whether it is from the theory that everything is number to atomism, the Tao and " Wu(nothingness)"in the East, the emergence of God in the West, from nature being God to the ideal of the grand unified theory of physics, they are all the steps of this exploration. Geometry originally started from a few axioms and established the mathematical foundation of the entire Euclidean space, thus laying the foundation of classical physics. The thinking and revision of the axioms of Euclidean geometry established non-Euclidean geometry/Riemannian geometry, which became the cornerstone of modern/modern physics. Might this suggest that the world is geometric, and the universe is just a manifold? Whether or not possible to understand the ultimate universe through the least assumptions. The real space hypothesis attempts to bridge the gap between relativity and quantum mechanics in the name of geometry and explain the nature of "existence". The ultimate understanding of science and philosophy-why does everything exist, where does time come from, and does consciousness transcend matter?-Providing a possible unified framework. As Albert Einstein said, "The most incomprehensible thing about the universe is that it could be understood." The key to understanding may lie in an unmeasured high-dimensional manifold. Why does time have a special place? It was never made clear. Mathematical tools provide proof that at least one dimension is unidirectionally irreversible when a high-dimensional space is projected onto a lowdimensional space. This provides an explanation of the unidirectionality of time based on the projection of spatial dimensions, closely linking time with the structure and nature of space, and deepening the understanding of the nature of time. From this point of view, it is believed that there is a real space that encompasses all existences, and that all finite dimensional spaces are their subspaces or phase spaces, and that all dimensions in the real space are equal, and that time has no special status. It possibly provides new perspectives for existing theories such as the unification of the Big Bang theory, the four fundamental forces, string theory, and the weighted cosmology. Understand the basic laws and phenomena of the universe from a higher-dimensional perspective, and eliminate the barriers between theories. However, the overly abstract nature may be beyond the scope of existing knowledge, and it is almost impossible to design experiments to verify its authenticity. At the same time, the real space hypothesis could not predict specific theoretical results, making it difficult to meet the falsifiability of the "scientific" theoretical category, and it is difficult to incorporate it into the category of scientific cognition and make practical application progress. 1．The Real-Space hypothesis The real space hypothesis assumes as following: a) That the ultimate form of existence in the universe is a real space; Or it could be called absolute space; b) That both matter and force are expressions of the geometry of space; c) Time is the result of the projection/observation process.

The basic thesis is that the problem of infinity underlies the current dilemma in modern theoretical physics. The traditional and set-theoretic conceptions of infinity are considered. It is demonstrated that standard mathematical analysis is dependent on the complete relativity of the infinite. In examining the domains of modern physics, infinity is found to lose its entirely relative character and, therefore, to be less amenable to classical analysis. Complementary aspects of microworld infinity are identified and are associated with the equivalent features (inertial and gravitational mass) of Einstein's macroworld theory. The persisting effort to treat essentially non-classical phenomena in classical terms is critically discussed. A new attitude toward the infinite is recommended, one that might lead to establishing a second principle of the relativity of the infinite. The prospect for implementing the suggested approach through a "transanalytic" meta-theory of dimensional generation is briefly entertained.

Aquinas Review, 1994

In the article I compare and contrast the two concepts of place or space in the light of the fundamental principles of natural philosophy.

2016

We consider to what extent the fundamental question of spacetime singularities is relevant for the philosophical debate about the nature of spacetime. After reviewing some basic aspects of the spacetime singularities within general relativity, we argue that the well known difficulty to localize them in a meaningful way may challenge the received metaphysical view of spacetime as a set of points possessing some intrinsic properties together with some spatiotemporal relations. Considering the algebraic for-mulation of general relativity, we argue that the spacetime singularities highlight the philosophically misleading dependence on the standard geometric representation of spacetime. 1. Introduction. Despite Earman’s (1995) invitation to consider more carefully the question of spacetime singularities, only a little literature in spacetime philosophy has been devoted to this foundational issue. (Some notable exceptions are Earman 1996, Curiel 1999, and Mattingly 2001.) This paper aims ...

The Routledge Handbook of Emergence, 2019

Research in quantum gravity strongly suggests that our world in not fundamentally spatiotemporal, but that spacetime may only emerge in some sense from a non-spatiotemporal structure, as this paper illustrates in the case of causal set theory and loop quantum gravity. This would raise philosophical concerns regarding the empirical coherence and general adequacy of theories in quantum gravity. If it can be established, however, that spacetime emerges in the appropriate circumstances and how all its relevant aspects are explained in fundamental non-spatiotemporal terms, then the challenge is fully met. It is argued that a form of spacetime functionalism offers the most promising template for this project. Space and time, it seems, must be part and parcel of the ontology of any physical theory; of any theory with a credible claim to being a physical theory, that is. After all, physics is the science of the fundamental constitution of the material bodies, their motion in space and time, and indeed of space and time themselves. Usually implicit, Larry has given expression to this common intuition: What could possibly constitute a more essential, a more ineliminable, component of our conceptual framework than that ordering of phenomena which places them in space and time? The spatiality and temporality of things is, we feel, the very condition of their existing at all and having other, less primordial, features... We could imagine a world without electric charge, without the atomic constitution of matter, perhaps without matter at all. But a world not in time? A world not spatial? Except to some Platonists, I suppose, such a world seems devoid of real being altogether. (45) The worry here, I take it, goes beyond a merely epistemic concern regarding the inconceivability of a non-spatiotemporal world; rather, it is that such a world would violate some basic necessary condition of physical existence. It is contended that space and time partially ground a material world. The alternative to a spatiotemporal world, it is suggested, is a realm of merely abstract entities. 1 Part of what it means to be 'physically salient' (Huggett and Wüthrich 2013) is to be in space and time. In other words, what it is to give a physical explanation of aspects of our manifest world is, among other things, to offer a theory of how objects are and move in space and time. * I thank Robin Hendry and Tom Lancaster for their insightful and challenging comments on an earlier draft of this paper. This work was partly performed under a collaborative agreement between the University of Illinois at Chicago and the University of Geneva and made possible by grant number 56314 from the John Templeton Foundation and its content are solely the responsibility of the author and do not represent the official views of the John Templeton Foundation. 1 The defenders of the claim that the world is purely abstract, formal, or mathematical-as opposed to partly abstract, formal, or mathematical-are usually referred to as 'Pythagoreans', rather than as 'Platonists'.

This essay is a contribution to the historical phenomenology of science, taking as its point of departure husserl's later philosophy of science and Jacob klein's seminal work on the emergence of the symbolic conception of number in european mathematics during the late sixteenth and seventeenth centuries. since neither husserl nor klein applied their ideas to actual theories of modern mathematical physics, this essay attempts to do so through a case study of the concept of "spacetime." in §1, i sketch klein's account of the emergence of the symbolic conception of number, beginning with Vieta in the late sixteenth century. in §2, through a series of historical illustrations, i show how the principal impediment to assimilating the new symbolic algebra to mathematical physics, namely, the dimensionless character of symbolic number, is overcome via the translation of the traditional language of ratio and proportion into the symbolic language of equations. in § §3-4, i critically examine the concept of "minkowski spacetime," specifically, the purported analogy between the Pythagorean distance formula and the minkowski "spacetime interval." finally, in §5, i address the question of whether the concept of minkowski spacetime is, as generally assumed, indispensable to einstein's general theory of relativity.