Related papers: A Chorus of Bells
This is an expository article discussing some of the work of Uhlenbeck, focusing mainly on work concerning harmonic maps and Yang-Mills fields.
From its earliest days nearly a century ago, quantum mechanics has proven itself to be a tremendously accurate yet intellectually unsatisfying theory to many. Not the least of its problems is that it is a theory about the results of…
a 10-page biography of Raoul Bott followed by a 25-page discussion of his major papers
A short essay on the life and mathematical heritage of Coble. A substantially edited version will be part of the series of biographical memoirs of past members of the National Academy of Sciences. Version 2: minor changes. Version 3. Typo…
John S. Bell is well known for the result now referred to simply as "Bell's theorem," which removed from serious consideration by physics of local hidden-variable theories. Under these circumstances, if quantum theory is to serve as a truly…
In 1976, I met John Bell several times in CERN and we talked about a possible violation of optical theorem, purity tests, EPR paradox, Bell inequalities and their violation. I review our discussions, and explain how they were related to my…
John Bell's inequalities have already been considered by Boole in 1862. Boole established a one-to-one correspondence between experimental outcomes and mathematical abstractions of his probability theory. His abstractions are two-valued…
In this paper we derive congruences expressing Bell numbers and derangement numbers in terms of each other modulo any prime.
We correct a 1957 combinatorial enumeration by the linguist J. Greenberg. The desired count, the Bell number B(25), supported using his Mass Comparison method for language classification. In 1987, he used this method to classify indigenous…
These are the preparatory notes for a Science & Music essay, "Playing by numbers", appeared in Nature 453 (2008) 988-989.
In the first half we show an interesting relation between coherent states and the Bell states in the case of spin 1/2, which was suggested by Fivel. In the latter half we treat generalized coherent states and try to generalize this relation…
A few remarks on how mathematics quests for freedom.
The aim of this chapter is to describe two situations where positive noise correlations can be directly monitored using a transport experiment, either with a superconductor or with a correlated electron system. To be more precise, the…
A review article on perturbation theory
About Conway's surreal numbers: A letter to a friend (written in French). In memoriam John Horton Conway.
In writing this biographical memoir of John Hammersley, we have tried to communicate something of the character of the person, and of the impact of his scientific achievements across lattice models (for example, percolation, self-avoiding…
In a recent article (Found Sci (2020) https://doi.org/10.1007/s10699-020-09666-0) Marek Czachor claims that the Bell inequality cannot be proved because variables of complementary measurements cannot be added or multiplied. Even though he…
The relation between the boolean functions and Bell inequalities for qubits is analyzed. The connection between the maximal quantum violation of a Bell inequality and the nonlinearity of the corresponding boolean function is discussed. A…
"Bell's theorem" can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976. His 1964 theorem is the incompatibility of quantum phenomena with the joint assumptions of Locality and Predetermination.…
Summary of results and overall conclusions on my works in the field of Bell inequalities and QM's alleged non-locality.