Falsification of Einstein’s relativity

In 1915, Einstein published general relativity. In 1916, he published a German language book about relativity, which contained his marble table thought experiment for explaining a continuum. Without realizing it, Einstein introduced a quantized two-dimensional discontinuum geometry and inadvertently falsified the marble table thought experiment continuum, which falsified relativity. The foundations of physics do not now (and never did) include a fundamentally sound relativistic theory to account for macroscopic phenomena. It is well known the success of relativity and its singularity problem indicate general relativity is a first approximation of a more fundamental theory. Combine that indication with the falsification of relativity and it is apparent, without speculation, that relativity is now and always was a first approximation of a more fundamental theory. A possible way forward to the more fundamental theory is developing a discontinuum physics based on the quantized two-dimensional discontinuum geometry or an algebraic version of it. Such discontinuum physics is not presented, because it is beyond the scope of this paper.

Branching Space-Times

This book develops a rigorous theory of indeterminism as a local and modal concept. Its crucial insight is that our world contains events or processes with alternative, really possible outcomes. The theory aims at clarifying what this assumption involves, and it does it in two ways. First, it provides a mathematically rigorous framework for local and modal indeterminism. Second, we support that theory by spelling out the philosophically relevant consequences of this formulation and by showing its fruitful applications in metaphysics. To this end, we offer a formal analysis of modal correlations and of causation, which is applicable in indeterministic and non-local contexts as well. We also propose a rigorous theory of objective single-case probabilities, intended to represent degrees of possibility. In a third step, we link our theory to current physics, investigating how local and modal indeterminism relates to issues in the foundations of physics, in particular, quantum non-locality and spatio-temporal relativity. The book also ventures into the philosophy of time, showing how the theory’s resources can be used to explicate the dynamic concept of the past, present, and future based on local indeterminism.

On Russell’s 1927 Book The Analysis of Matter

The goal of this article is to bring into wider attention the often neglected important work by Bertrand Russell on the philosophy of nature and the foundations of physics, published in the year 1927. It is suggested that the idea of what could be named Russell space, introduced in Part III of that book, may be viewed as more fundamental than many other types of spaces since the highly abstract nature of the topological ordinal space proposed by Russell there would incorporate into its very fabric the emergent nature of spacetime by deploying event assemblages, but not spacetime or particles, as the fundamental building blocks of the world. We also point out the curious historical fact that the book The Analysis of Matter can be chronologically considered the earliest book-length generic attempt to reflect on the relation between quantum mechanics, just emerging by that time, and general relativity.

Proof of Euclid’s fifth postulate and the establishment of the metaphysical foundations of the so-called space (metametry)

Euclid’s fifth postulate has been accepted as a theorem since the time of ancient Greece. The efforts to prove it have been going on for nearly 2 000 years. Non-Euclidean geometry, based on its rejection, emerged in the first half of the 19th century. The author of the present article returns to the problem by addressing the metaphysical foundations of physics. The author has found the ideal instrument for analyzing infinity to be an infinitely small unit, which cannot be divided further. With the help of this instrument, the fundamental properties of the so-called space were found. It was concluded that there are no oblique or curved lines on the basic level. The apparent curved and oblique lines are stairs with negligibly fluent changing or constant steps, correspondingly. Hence, the refutation of non-Euclidean geometries and seeking a new proof of the postulate. Inter alia, it was found that the requirement to conclude the proof from Euclid’s other four axioms only diverted the attention of mathematicians from the true problem. The author proved the fifth postulate on a plane. Its application to a pair of skew lines is considered. In conclusion, the author describes the basic properties of the so-called space.