Related papers: Infinities in Physics and Transfinite numbers in M…
What do we do when cosmology raises questions it cannot answer? These include the existence of a multiverse and the universality of the laws of physics. We cannot settle any of these issues by experiment, and this is where philosophers…
In this paper we analyze the status of some `unbelievable results' presented in the paper `On Some Contradictory Computations in Multi-Dimensional Mathematics' [1] published in Nonlinear Analysis, a journal indexed in the Science Citation…
This article critically reappraises arguments in support of Cantor's theory of transfinite numbers. The following results are reported: i) Cantor's proofs of nondenumerability are refuted by analyzing the logical inconsistencies in…
There is a problem with the foundations of classical mathematics, and potentially even with the foundations of computer science, that mathematicians have by-and-large ignored. This essay is a call for practicing mathematicians who have been…
Much of Mathematics, and therefore Physics as well, have been limited by four rather consequential restrictions. Two of them are ancient taboos, one is an ancient and no longer felt as such bondage, and the fourth is a surprising omission…
Here we continue with the ideas expressed in "On the strangeness of quantum mechanics" aiming to demonstrate more concretely how this philosophical outlook might be used as a key for resolving the measurement problem. We will address in…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
The quantitative aspirations of economists and financial analysts have for many years been based on the belief that it should be possible to build models of economic systems - and financial markets in particular - that are as predictive as…
Georg Cantor was the genuine discoverer of the Mathematical Infinity, and whatever he claimed, suggested, or even surmised should be taken seriously -- albeit not necessary at its face value. Because alongside his exquisite in beauty…
Is the universe digital or analog? In this essay I argue that both classical and quantum physics include limits that prevent us from definitively answering that question. That quantum physics does so is no surprise. That classical physics…
A well-known topic within the philosophy of physics is the problem of fine-tuning: the fact that the universal constants seem to take non-arbitrary values in order for live to thrive in our Universe. In this paper we will talk about this…
We show that for an infinite, uniformly charged plate no well defined electric field exists in the framework of electrostatics, because it cannot be defined as a mathematically consistent limit of a solution for a finite plate. We discuss…
This is a short text covering some topics on the Foundations of Quantum Theory and it includes some comments on the recent Nature article by D. Frauchiger and R. Renner. The so-called "paradox" is simply due to a misunderstanding on the…
The dynamics of physical theories is usually described by differential equations. Difference equations then appear mainly as an approximation which can be used for a numerical analysis. As such, they have to fulfill certain conditions to…
The 20th century has revealed two important limitations of scientific knowledge. On the one hand, the combination of Poincar\'e's nonlinear dynamics and Heisenberg's uncertainty principle leads to a world picture where physical reality is,…
The theories of quantum mechanics and relativity dramatically altered our understanding of the universe ushering in the era of modern physics. Quantum theory deals with objects probabilistically at small scales, whereas relativity deals…
Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum…
More than hundred years ago the 'classic physics' was it in its full power, with just a few unexplained phenomena; which however led to a revolution and the development of the 'modern physics'. Today the computing is in a similar position:…
We formulate physically-motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to Quantum Mechanics as the only nontrivial consistent theory. Complex numbers and the existence of…
Mathematical core of quantum mechanics is the theory of unitary representations of symmetries of physical systems. We argue that quantum behavior is a natural result of extraction of "observable" information about systems containing…