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The Mathematical Universe and the External Reality Hypothesis (ERH)
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The Mathematical Universe

Authors: Max Tegmark (MIT)

(Submitted on 5 Apr 2007 (v1), last revised 8 Oct 2007 (this version, v2))

Abstract: 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.

Comments: Replaced to match accepted Found. Phys. version, 31 pages, 5 figs; more details at this http URL

Subjects: General Relativity and Quantum Cosmology (gr-qc); Astrophysics (astro-ph); High Energy Physics - Theory (hep-th)

Cite as: arXiv:0704.0646v2 [gr-qc]

Submission history

From: Max Tegmark [view email]

[v1] Thu, 5 Apr 2007 14:47:46 GMT (533kb)

[v2] Mon, 8 Oct 2007 22:59:39 GMT (538kb)

http://arxiv.org/abs/0704.0646

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