Institute for Experimental Physics University of Vienna Institute
- Slides: 8
Institute for Experimental Physics University of Vienna Institute for Quantum Optics and Quantum Information Austrian Academy of Sciences Mathematical Undecidability & Quantum Complementarity Časlav Brukner (in collaboration with Tomasz Paterek) Reykjavik, Iceland July 2007
Information-theoretical formulation of quantum physics: The most elementary system contains one bit of information. → Irreducible Randomness Zeilinger, 1999 Brukner, Zeilinger 2002 quant-ph/0212084 Information-theoretical formulation of Gödel’s theorem: If a theorem contains more information than a given set of axioms, then it is impossible for theorem to be derived from the axioms. Chaitin, 1982 Are the two related to each other?
Undecidability: Simple Example Axiom: “f(0)= 0” 1 bit Can be neither proved Theorem: “f(0)=0 and f(0) = f(1)”. nor disproved: needs 2 bits Theorem: “f(0)=0 and f(1)=0” Independent Statements: “f(0)= 0”, “f(1)= 0”, “f(0)=f(1)”
Closer look … 1 bit available → 3 logically complementary statements 1 2 3
„Experimental Test of Theorems“ 1 2 3 Axiom Theorem
How to represent mathematical functions physically?
Testing theorems using quantum mechanics
Testing Undecidable Theorems x y z State Preparation Measurement Bases 1. Systems give answers when asked (detectors “click”) 2. The question asked is undecidable → Random results! Is quantum randomness physical expression for mathematical undecidability?
Experimental vs non experimental
What is quasi experimental research
Disadvantages of experimental research
Experimental vs non experimental
Nonexperimental study
University physics with modern physics fifteenth edition
Experimental physics and industrial control system
"controls engineering"
Experimental physics and industrial control system
