The history and philosophy of science are destined to play a fundamental role in an epoch marked by a major scientific revolution. This ongoing revolution, principally affecting mathematics and physics, entails a profound upheaval of our conception of space, space–time, and, consequently, of natural laws themselves. Briefly, this revolution can be summarized by the following two trends: by the search for a unified theory of the four fundamental forces of nature, which are known, as of now, as gravity, electromagnetism, and (...) strong and weak nuclear forces; by the search for new mathematical concepts capable of elucidating and therefore explaining such a relationship. In fact, the first search is essentially dependent on the second; that is to say, that in order for a new theory of physics to come to light, the development of a deeper geometric theory capable of explaining the structure of space–time on a quantum scale appears to be necessary. On careful consideration, we notice that both of these developments converge in the direction of a unitary and fundamental tendency of modern science—which is the geometrization of theoretical physics and of natural sciences. This new emergent situation carries within it a profound conceptual change, affecting the way in which relations are conceived of, first and foremost, between mathematics and physics. This new paradigm can be summed up by the intimately interdependent points: the immense variety of physical phenomena and of natural forms follows from the equally infinite variety of geometric and topological objects that can be made out in space and from which space is made up; the second point, which ensues from the former one and which is of great historical and epistemological significance, is that mathematics is involved in rather than applied to phenomena. In other words, phenomena are effects that emerge from the geometrical structure of space–time. There is no doubt that this new conception of the relationship between the universe of mathematical ideas and objects and the world of natural phenomena is the true scientific revolution of our century, of great conceptual importance, and consequently, capable of changing our view of science and of nature at one and the same time. It is all at once of a scientific, philosophical and aesthetic order. (shrink)

The reconcilability of gravitational with electromagnetic clocks suggests that a rigorous analysis of time will provide understanding of the unity of gravity and electromagnetism. Time is found to be fundamentally a property of elementary particles, only derivatively a property of clocks. A declaration is made: that the flow of an elementary particle's timeis the change of its radius, that time is therefore illusory. The de Sitter expanding universe is derived from this principle by treating elementary particles as spheres in Euclidean (...) space. The hyperspheres of de Sitter space call up a five-dimensional metric manifold whose geometry models gravity, electromagnetism, and other phenomena tied to the structure of matter; neutrinos are provided for. Distance in this manifold is related to a secondary time, not correlated to primary time, but just as illusory. A particle's inertial rest mass is the relative rate of its two proper times; mass and charge are jointly, not individually, conserved. (shrink)

Before the discovery of the expanding universe, one of the challenges faced in early relativistic cosmology was the determination of the finite and constant curvature radius of space-time by using astronomical observations. Great interest in this specific question was shown by de Sitter, Silberstein, and Lundmark. Their ideas and methods for measuring the cosmic curvature radius, at that time interpreted as equivalent to the size of the universe, contributed to the development of the empirical approach to relativistic cosmology. Their works (...) are a noteworthy example of the efforts made by modern cosmologists toward the understanding of the universe as a whole, its properties, and its content. (shrink)

I critically discuss a controversial ‘trans-Planckian censorship’ conjecture, which has recently been introduced to researchers working at the intersection of fundamental physics and cosmology. My focus explicitly avoids any appeals to contingent research within string theory or regarding the more general gravitational ‘swampland’. Rather, I concern myself with the conjecture’s foundations in our current, well-trodden physics of quantized fields, spacetime, and gravity. In doing so, I locate what exactly within trans-Planckian censorship amounts to a departure from current physics—identifying what is, (...) ultimately, so conjectural about the conjecture. (shrink)

When applied to a dipole source subjected to acceleration which is violent and long lasting (“extreme acceleration”), Maxwell's equations predict radiative power which augments Larmor's classical radiation formula by a nontrivial amount. The physical assumptions behind this result are made possible by the kinematics of a system of geometrical clocks whose tickings are controlled by cavities which are expanding inertially. For the purpose of measuring the radiation from such a source we take advantage of the physical validity of a spacetime (...) coordinate framework (“inertially expanding frame”) based on such clocks. They are compatible and commensurable with the accelerated clocks of the accelerated source. By contrast, a common Lorentz frame with its mutually static clocks won't do: It lacks that commensurability. Inertially expanding clocks give a physicist a window into the frame of a source with extreme acceleration, and thus can locate that source and measure radiation from it without being subjected to such acceleration himself. The conclusion is that inertially expanding reference frames reveal qualitatively distinct aspects of nature which would not be accessible if inertial frames were the only admissible frames. (shrink)