Week 5: INTERNAL CRISIS Armahedi Mahzar ICAS Jacarta 2010 PHILOSOPHY of SCIENCE Week 5: INTERNAL CRISIS Armahedi Mahzar ICAS Jacarta 2010

Internal Crisis of Science Physics Mathematics

Internal Crisis of Science Empirical Objectivism Theory of Relativity Quantum Theory Mathematical Rationalism Meta-mathematics Computationalism

Internal Crisis of Science Principle of Relativity (Einstein) Relativity of Space Time Matter Energy Equivalence

Special Theory of Relativity 1905, Albert Einstein resolved the Michelson-Morley crisis by discarding the ether concept and asserting the principle of relativity —that the laws of physics are the same for all observers in uniform motion. Shortly after publishing his 1905 paper on special relativity, Einstein realized that his theory required a fundamental equivalence between mass and energy, which he expressed in the equation E=mc2.

Special Theory of Relativity As the consequence of his theory, we have to admit the relativity of space and time Accordingly, two twins would age at different rates if one left on a high-speed journey to a distant star and then returned. This experiment has actually been done, not with twins, but with an atomic clock flown around the world. time slows as speed increases comes from measuring muons at the top and bottom of mountains.

General Theory of Relativity Historically, the path to general relativity followed Einstein's attempt to incorporate gravity into relativity theory gravity is not a force, but a local curvature manifestation of space-time geometry.

General Theory of Relativity the expansion of the universe predicted by the theory of general relativity is now a known rate. the existence of black holes, objects that warp space and time so that not even light can escape.

Indeterminacy of Observation Quantum Theory Indeterminacy of Observation Wave Particle Duality

Heisenberg Principle of Uncertainty Indeterminacy of Observation We can not observe both the position and the momentum of a particle with the same accuracy

Wave-Particle Duality Photo-electric Effect of Light as photon Electron diffraction Diffraction of Light as wave Electron as Particle

Foundation of Mathematics Logicism Intuitionism Formalism

Locicism Bertrand Russel mathematics is an extension of logic and therefore some or all mathematics is reducible to logic

Intuitionism Brouwer Mathematics as the constructive mental activity of humans. Mathematics does not consist of analytic activities wherein deep properties of existence are revealed and applied. logic and mathematics are the application of internally consistent methods to realize more complex mental constructs.

Formalism Hilbert statements of mathematics and logic can be thought of as statements about the consequences of certain string manipulation rules.

Criticism of Mathematical Reductionism Kurt Godel Theorem of Incompleteness Alan Turing Theorem of Indecidability

Theorem of Incompleteness (Godel) Incompleteness of Consistent Axiom System Inconsistency of Complete Axiom System

Undecidability Theorem there is no algorithm which can be applied to any arbitrary program and input to decide whether the program stops when run with that input

Conclusion Objects can not be separated from subject Mathematical rationality can not be reduced