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Max Tegmark, MIT Why I think that we live in a mathematical object

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Can we describe reality purely mathematically? But can we understand all this in terms of a fundamental “theory of everything”? gr-qc/9704009 0704.0646 [gr-qc]

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 Do you yearn for a TOE with an intuitive interpretation?

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 Do you yearn for a TOE with an intuitive interpretation? Opposition is good, in the dialectic spirit

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 Do you yearn for a TOE with an intuitive interpretation? Thus spake the bards: Forget it! Opposition is good, in the dialectic spirit “It’s all just the equations”

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 External Reality Hypothesis (ERH): There exists an external physical reality completely independent of us humans. External Reality Hypothesis (ERH): There exists an external physical reality completely independent of us humans. Mathematical Universe Hypothesis (MUH): Or external physical reality is a mathematical structure. Mathematical Universe Hypothesis (MUH): Or external physical reality is a mathematical structure.

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 External Reality Hypothesis (ERH): There exists an external physical reality completely independent of us humans. External Reality Hypothesis (ERH): There exists an external physical reality completely independent of us humans.

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 External Reality Hypothesis (ERH): There exists an external physical reality completely independent of us humans. External Reality Hypothesis (ERH): There exists an external physical reality completely independent of us humans.

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 TOE External Reality Hypothesis (ERH): There exists an external physical reality completely independent of us humans. External Reality Hypothesis (ERH): There exists an external physical reality completely independent of us humans.

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 TOE External Reality Hypothesis (ERH): There exists an external physical reality completely independent of us humans. External Reality Hypothesis (ERH): There exists an external physical reality completely independent of us humans. For this description of the external physical reality to be complete, it must be devoid of human “baggage”.

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 TOE External Reality Hypothesis (ERH): There exists an external physical reality completely independent of us humans. External Reality Hypothesis (ERH): There exists an external physical reality completely independent of us humans. We humans have a common understanding of words like“object”, “experiment”, “observation”, “cause”, “particle”, “string”, but computers don’t!

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 Big Bang Zoom

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 Big Bang Zoom Tegmark & Wheeler 2001, quant-ph/0101077 Less baggage More baggage

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 Big Bang Zoom Tegmark 1997, gr-qc/9704009, Ann. Phys, 270, 151 A mathematical structure: abstract entities with relations between them

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 External Reality Hypothesis (ERH): There exists an external physical reality completely independent of us humans. External Reality Hypothesis (ERH): There exists an external physical reality completely independent of us humans. Mathematical Universe Hypothesis (MUH): Or external physical reality is a mathematical structure. Mathematical Universe Hypothesis (MUH): Or external physical reality is a mathematical structure.

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Phenomenology implications

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 Big Bang Zoom Tegmark 1997, gr-qc/9704009, Ann. Phys, 270, 151

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Big Bang Zoom Tegmark 1997, gr-qc/9704009, Ann. Phys, 270, 151 Bird’s view: Frog’s view:

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Emergence implications

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 Is it really possible to derive “physics from scratch”, i.e., frog’s view from bird’s view? How would physics emerge from the mathematical structure? Promising 1st steps: automorphism group, symmetries, irracs & irreps, etc. G ö del completeness/Church-Turing computability may help explain why the laws of our universe are so simple.

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Parallel universe implications

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 This isn’t science! It’s inevitable

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 I hate it! Makes sense! Why not?

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 Party on!

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If our frog’s view of our observable universe… …requires more bits to describe than… …the bird’s view of our mathematical structure… …then we’re in a multiverse! 10 100 bits? 10 3 bits? So if you’re looking for a simple mathematical TOE, you’re looking for a multiverse theory.

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 Big Bang Zoom Where are the parallel universes? 1)Far away in space 2)Infinitely far away in space 3)Elsewhere in Hilbert space 4)Elsewhere in “math space”

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Big Bang Zoom What are the 4 multiverse levels like? 1)Same effective laws of physics, different initial conditions 2)Same fundamental laws of physics, different effective laws (“bylaws”) 3)Nothing qualitatively new 4)Different fundamental laws of physics The bigger the multiverse, the simpler the theory. 10 100 bits? 10 3 bits? 0 bits! 10 2 bits?

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 More MUH support

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 We’re not taking this guy seriously enough!

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 The strongest form of the anthropic principle: “The Universe must be such that we like it.”

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Max Tegmark Dept. of Physics, MIT tegmark@mit.edu FQXi Symposium July 22, 2007 The strongest form of the anthropic principle: “The Universe must be such that we like it.”

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0704.0646 [gr-qc]

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