Related papers: How not to factor a miracle
Classical mathematics (involving such notions as infinitely small/large and continuity) is usually treated as fundamental while finite mathematics is treated as inferior which is used only in special applications. We first argue that the…
The unique and beautiful character of certain mathematical results and proofs is often considered one of the most gratifying aspects of engaging with mathematics. We study whether this perception of mathematical arguments having an…
Einstein initially objected to the probabilistic aspect of quantum mechanics - the idea that God is playing at dice. Later he changed his ground, and focussed instead on the point that the Copenhagen Interpretation leads to what Einstein…
Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial…
While quantum computers are expected to yield considerable advantages over classical devices, the precise features of quantum theory enabling these advantages remain unclear. Contextuality--the denial of a notion of classical physical…
The physics of matter in the condensed state is concerned with problems in which the number of constituent particles is vastly greater than can be easily comprehended. The inherent physical limitations of the human mind are fundamental and…
What is fundamentally quantum? We argue that most of the features, problems, and paradoxes -- such as the measurement problem, the Wigner's friend paradox and its proposed solutions, single particle nonlocality, and no-cloning -- allegedly…
Quantum mechanics (QM) has attracted a considerable amount of mysticism, in public opinion and even among academic researches, due to some of its conceptually puzzling features, such as the modification of reality by the observer and…
Despite the success of modern physics in formulating mathematical theories that can predict the outcome of experiments, we have made remarkably little progress towards answering the most fundamental question of: why is there a universe at…
Courses in mathematical methods for physics students are not known for including too much in the way of mathematical rigour and, in some ways, understandably so. However, the conditions under which some quite commonly used mathematical…
An influential argument for scientific realism posits that, if scientific theories were not true, their empirical success would be a coincidence. Here, I show that the false Drude's theory succeeds in explaining the Wiedemann-Franz law by…
We discuss views about whether the universe can be rationally comprehended, starting with Plato, then Leibniz, and then the views of some distinguished scientists of the previous century. Based on this, we defend the thesis that…
Despite the extraordinary successes the two great bastions of $20^{th}$ century science (Quantum Theory and General Relativity) are troubled with serious conceptual and mathematical difficulties. As a result, further growth of fundamental…
There has been a surge of recent interest in the Wigner's Friend paradox, sparking several novel thought experiments and no-go theorems. The main narrative has been that Wigner's Friend highlights a counterintuitive feature that is unique…
When we want to predict the future, we compute it from what we know about the present. Specifically, we take a mathematical representation of observed reality, plug it into some dynamical equations, and then map the time-evolved result back…
Mathematicians occasionally discover interesting truths even when they are playing with mathematical ideas with no thoughts about possible consequences of their actions. This paper describes two specific instances of this phenomenon. The…
In physics, there is the prevailing intuition that we are part of a unique external world, and that the goal of physics is to understand and describe this world. This assumption of the fundamentality of objective reality is often seen as a…
Physics is formulated in terms of timeless classical mathematics. A formulation on the basis of intuitionist mathematics, built on time-evolving processes, would offer a perspective that is closer to our experience of physical reality.
The way Leibniz applied his philosophy to mathematics has been the subject of longstanding debates. A key piece of evidence is his letter to Masson on bodies. We offer an interpretation of this often misunderstood text, dealing with the…
It is becoming common to hear teaching advice about spending more time on the "physics of the problem" so that students will get more physical insight and develop a stronger intuition that can be very helpful when thinking about physics…