The Mathematical Universe

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.

Replaced to match accepted Found. Phys. version, 31 pages, 5 figs; more details at http://space.mit.edu/home/tegmark/toe.html

References in corpus (30)

• de Sitter Vacua in String Theory
• Quantization of Four-form Fluxes and Dynamical Neutralization of the Cosmological Constant
• Semiclassicality and Decoherence of Cosmological Perturbations
• Dimensionless constants, cosmology and other dark matters
• Counting Flux Vacua
• Why the Universe is Just So
• What does inflation really predict?
• Saltatory Relaxation of the Cosmological Constant
• Can the universe afford inflation?
• Holographic probabilities in eternal inflation
• Is "the theory of everything'' merely the ultimate ensemble theory?
• An Alternative to Inflation
• Inflationary Theory and Alternative Cosmology
• A relational solution to the problem of time in quantum mechanics and quantum gravity induces a fundamental mechanism for quantum decoherence
• Is Our Universe Natural?
• Multiverses and physical cosmology
• Emergence of classicality for primordial fluctuations: Concepts and analogies
• Counting Pockets with World Lines in Eternal Inflation
• Freak observers and the measure of the multiverse
• Does the universe in fact contain almost no information?
• Many worlds in one
• Feynman-Weinberg Quantum Gravity and the Extended Standard Model as a Theory of Everything
• On Math, Matter and Mind
• Anthropic predictions for vacuum energy and neutrino masses
• Towards a Coherent Theory of Physics and Mathematics: The Theory-Experiment Connection
• Universe creation on a computer
• Why Occam's Razor
• Cosmology and Local Physics
• The Representation of Natural Numbers in Quantum Mechanics
• From new states of matter to a unification of light and electrons

Cited by in corpus (75)

• $H_0$ tension as a hint for a transition in gravitational theory
• The Beginning and the End: The Meaning of Life in a Cosmological Perspective
• Physical limits of inference
• Direct detection of dark matter: a critical review
• The Born Rule Dies
• A Complete Theory of Everything (will be subjective)
• The Physical World as a Virtual Reality
• New Gauge Field from Extension of Space Time Parallel Transport of Vector Spaces to the Underlying Number Systems
• Some comments on "The Mathematical Universe"
• Landauer's principle as a special case of Galois connection
• No-Bang Quantum State of the Cosmos
• The Arrow Of Time In The Landscape
• Cosmology at the Crossroads of the Natural and Human Sciences: is demarcation possible?
• Pure quantum interpretations are not viable
• Implementation of classical communication in a quantum world
• Typicality, Freak Observers and the Anthropic Principle of Existence
• The informational physics indeed can help to understand Nature?
• Yet another time about time - Part I
• Fiber bundle description of number scaling in gauge theory and geometry
• Physics from scratch. Letter on M. Tegmark's ``The Mathematical Universe''
• Effects of a scalar scaling field on quantum mechanics
• The Computable Universe Hypothesis
• Space and time dependent scaling of numbers in mathematical structures: Effects on physical and geometric quantities
• "The Information as Absolute" Concept and Basic Physics
• Simulating space and time
• The emergence of the physical world from information processing
• Informaticology: combining Computer Science, Data Science, and Fiction Science
• A Representation of Real and Complex Numbers in Quantum Theory
• Minkowski Spacetime and QED from Ontology of Time
• Spurious, Emergent Laws in Number Worlds
• Some Subtle Concepts in Fundamental Physics
• On the Philosophical Foundations of Physics: An Experimentalist's Perspective
• Nothing happens in the Universe of the Everett Interpretation
• Can quantum gravity be both consistent and complete?
• Constraints on physical reality arising from a formalization of knowledge
• Some remarks on the mathematical structure of the multiverse
• Is the Quilted Multiverse Consistent with a Thermodynamic Arrow of Time?
• Extending cosmological natural selection
• Local Lorentz Transformation and "Lorentz Violation"
• A Possible Mathematical Structure for Physics
• Why there is something rather than nothing: The finite, infinite and eternal
• The Last Scientific Revolution
• Reality and super-reality: properties of a mathematical multiverse
• Multiverse Predictions for Habitability: Origin of Life Scenarios
• Effects of mathematical locality and number scaling on coordinate chart use
• Principal fiber bundle description of number scaling for scalars and vectors: Application to gauge theory
• The Algebraic View of Computation
• A Pedestrian Approach to the Measurement Problem in Quantum Mechanics
• The Final Theory of Physics - a Tautology?
• Quantum panprotopsychism and the combination problem
• The non-unique Universe
• Many Worlds Model resolving the Einstein Podolsky Rosen paradox via a Direct Realism to Modal Realism Transition that preserves Einstein Locality
• A Possible Approach to Inclusion of Space and Time in Frame Fields of Quantum Representations of Real and Complex Numbers
• The Computational Status of Physics: A Computable Formulation of Quantum Theory
• Disentangling Boltzmann brains, the time-asymmetry of memory, and the second law
• Possible link between the distribution of atomic spectral lines and the radiation-matter-equilibrium in the early universe
• Against Absolute Actualization: Three "Non-Localities" and Failure of Model-External Randomness made easy with Many-Worlds Models including Stronger Bell-Violation and Correct QM Probability
• What do kets represent?
• On the objective existence of physical processes: a physicist's philosophical view
• Physical Relativism as an Interpretation of Existence
• The utterly prosaic connection between physics and mathematics
• The Relativity of Existence
• Bayesian Methods and Universal Darwinism
• The Preferred System of Reference Reloaded
• The Observer Class Hypothesis
• Temporal Platonic Metaphysics
• Ontological Foundations of the Variational Principles and the Path Integral Formalism
• On the foundations and necessity of classical gauge invariance
• A Natural Introduction to Fine-Tuning
• Deriving Ontological Statements from the Unnatural Higgs Mass
• The Standard Model Symmetry and Qubit Entanglement
• Godel's Incompleteness Theorems and Platonic Metaphysics
• Falsifiability of Isolated Spacetime Regions
• Finite Computational Structures and Implementations
• The Level I Multiverse is not the same as the Level III Multiverse