Related papers: Open problems in mathematical physics
For more than half a century, dualities have been at the heart of modern physics. From quantum mechanics to statistical mechanics, condensed matter physics, quantum field theory and quantum gravity, dualities have proven useful in solving…
A major question in philosophy of science involves the unreasonable effectiveness of mathematics in physics. Why should mathematics, created or discovered, with nothing empirical in mind be so perfectly suited to describe the laws of the…
What follows is a broad-brush overview of the recent synergistic interactions between mathematics and theoretical physics of quantum field theory and string theory. The discussion is forward-looking, suggesting potentially useful and…
We acuminate the idea of a final theory of physics in order to analyze its logical implications and consequences. It is argued that the rationale of a final theory is the principle of sufficient reason. This implies that a final theory of…
What is physics? What are the limits of what physics can say about the world? In seeking ever-broader theoretical `umbrellas' for physical phenomena, we are seeking unifying principles. Emergent phenomena have turned out to be some of the…
A tradition handed down among physicists maintains that classical physics is a perfectly deterministic theory capable of predicting the future with absolute certainty, independently of any interpretations. It also tells that it was quantum…
Quantum physics has intrigued scientists and philosophers alike, because it challenges our notions of reality and locality--concepts that we have grown to rely on in our macroscopic world. It is an intriguing open question whether the…
We introduce PHYSICS, a comprehensive benchmark for university-level physics problem solving. It contains 1297 expert-annotated problems covering six core areas: classical mechanics, quantum mechanics, thermodynamics and statistical…
I give a pedagogical explanation of what it is about quantization that makes general relativity go from being a nearly perfect classical theory to a very problematic quantum one. I also explain why some quantization of gravity is…
We review current theoretical cosmology, including fundamental and mathematical cosmology and physical cosmology (as well as cosmology in the quantum realm), with an emphasis on open questions.
Should physicists deal with the question of the reality of Minkowski space (or any relativistic spacetime)? It is argued that they should since this is a question about the dimensionality of the world at the macroscopic level and it is…
Quantum mechanics has enjoyed a multitude of successes since its formulation in the early twentieth century. At the same time, it has generated puzzles that persist to this day. These puzzles have inspired a large literature in physics and…
An introductory guide to mathematical cosmology is given focusing on the issue of the genericity of various important results which have been obtained during the last thirty or so years. Some of the unsolved problems along with certain new…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
We give a brief overview of 20 open theoretical questions in supersymmetric particle physics. The 20 questions we have chosen range from the GeV scale to the Planck scale, and include issues pertaining to the Minimal Supersymmetric Standard…
It is rare to succeed in getting mathematics into ordinary conversation without meeting all kinds of reservations. In order to raise public awareness of mathematics effectively, it is necessary to modify such attitudes. In this paper, we…
Since its inception at the beginning of the twentieth century, quantum mechanics has challenged our conceptions of how the universe ought to work; however, the equations of quantum mechanics can be too computationally difficult to solve…
The hard problem in consciousness is the problem of understanding how physical processes in the brain could give rise to subjective conscious experience. In this paper, I suggest that in order to understand the relationship between…
Partially or totally unsolved questions in number theory and geometry especially, such as coloration problems, elementary geometric conjectures, partitions, generalized periods of a number, length of a generalized period, arithmetic and…
Two questions are suggested as having priority when trying to bring together Quantum Mechanics and General Relativity. Both questions have a scope which goes well beyond Physics, and in particular Quantum Mechanics and General Relativity.