37,190 research outputs found
The Mathematical Universe
I explore physics implications of the External Reality Hypothesis (ERH) that
there exists an external physical reality completely independent of us humans.
I argue that with a sufficiently broad definition of mathematics, it implies
the Mathematical Universe Hypothesis (MUH) that our physical world is an
abstract mathematical structure. I discuss various implications of the ERH and
MUH, ranging from standard physics topics like symmetries, irreducible
representations, units, free parameters, randomness and initial conditions to
broader issues like consciousness, parallel universes and Godel incompleteness.
I hypothesize that only computable and decidable (in Godel's sense) structures
exist, which alleviates the cosmological measure problem and help explain why
our physical laws appear so simple. I also comment on the intimate relation
between mathematical structures, computations, simulations and physical
systems.Comment: Replaced to match accepted Found. Phys. version, 31 pages, 5 figs;
more details at http://space.mit.edu/home/tegmark/toe.htm
The Algebraic View of Computation
We argue that computation is an abstract algebraic concept, and a computer is
a result of a morphism (a structure preserving map) from a finite universal
semigroup.Comment: 13 pages, final version will be published elsewher
Second quantization of the elliptic Calogero-Sutherland model
We use loop group techniques to construct a quantum field theory model of
anyons on a circle and at finite temperature. We find an anyon Hamiltonian
providing a second quantization of the elliptic Calogero-Sutherland model. This
allows us to prove a remarkable identity which is a starting point for an
algorithm to construct eigenfunctions and eigenvalues of the elliptic
Calogero-Sutherland Hamiltonian (this algorithm is elaborated elsewhere).
This paper contains a detailed introduction, technical details and proofs.Comment: 36 page
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