22,286 research outputs found
Are black holes about information?
Information theory is increasingly invoked by physicists concerned with
fundamental physics, including black hole physics. But to what extent is the
application of information theory in those contexts legitimate? Using the case
of black hole thermodynamics and Bekenstein's celebrated argument for the
entropy of black holes, I will argue that information-theoretic notions are
problematic in the present case. Bekenstein's original argument, as suggestive
as it may appear, thus fails. This example is particularly pertinent to the
theme of the present collection because the Bekenstein-Hawking formula for
black hole entropy is widely accepted as 'empirical data' in notoriously
empirically deprived quantum gravity, even though the laws of black hole
thermodynamics have so far evaded empirical confirmation.Comment: 20 pages; forthcoming in Richard Dawid, Radin Dardashti, and Karim
Th\'ebault (eds.), Epistemology of Fundamental Physics, Cambridge University
Press; minor changes and additions of reference
The concept of "character" in Dirichlet's theorem on primes in an arithmetic progression
In 1837, Dirichlet proved that there are infinitely many primes in any
arithmetic progression in which the terms do not all share a common factor. We
survey implicit and explicit uses of Dirichlet characters in presentations of
Dirichlet's proof in the nineteenth and early twentieth centuries, with an eye
towards understanding some of the pragmatic pressures that shaped the evolution
of modern mathematical method
Spectral asymptotics for first order systems
This is a review paper outlining recent progress in the spectral analysis of
first order systems. We work on a closed manifold and study an elliptic
self-adjoint first order system of linear partial differential equations. The
aim is to examine the spectrum and derive asymptotic formulae for the two
counting functions. Here the two counting functions are those for the positive
and the negative eigenvalues. One has to deal with positive and negative
eigenvalues separately because the spectrum is, generically, asymmetric.Comment: Edited in accordance with referee's recommendation
- …