1、Tony Rothman,Deep(est) Paradox of Physics:,Physics is Time Symmetric Nature is Not,Fundamental Theories of Physics Dont Care Which Way Time Goes,Newtonian Physics Electromagnetism Relativity Quantum Mechanics,Nevertheless, Nature Cares,Roger Penrose lists seven ways in which Nature distinguishes pas
2、t from future, seven “arrows of time”,Seven Arrows of Time,Memory Arrow Electromagnetic Arrow Quantum Arrow Black Hole Arrow Cosmological Arrow Kaon Arrow Entropy Arrow,1. Memory Arrow,Memory only works backwards (We dont remember the future),2. Electromagnetic Arrow,Electromagnetic Causes Precede E
3、ffects,3. Quantum Arrow,Wave Functions “Collapse” But Dont “Uncollapse”,4. Black Hole Arrow,Black Holes Exist But White Holes Dont (Apparently),5. Cosmological Arrow,We live in an expanding universe, not a contracting one. Would time change direction if universe started contracting?,6. Kaon Arrow,Ka
4、on decay not time symmetric Ko In a time-reversed world this particle decays at a different rate than in our world!,CPT theorem,“Charge-Parity-Time” Change electric charge of all particles in world (Change all particles to antiparticles); Reflect it in mirror; Run time backwards: New world is indist
5、inguishable from old,Princeton 1964 Experiment:,Kaon decay not invariant under CP-reversal Must also change under T-reversal,7. Entropy Arrow,Entropy always increases (second law of thermodynamics),Question: Are arrows independent?,Hawking: Memory and entropy arrows linked (Requires energy to read o
6、ne bit, increases entropy by certain amount),Rothman to Penrose: One arrow arbitrary; only six independent signs.,Sudarshan to Rothman: All particle decay CPT invariant but Irreversible: Particle-decay arrow.Rothman to Rothman: Temperature dependent?,Entropy,Entropy can be thought of as waste heat g
7、enerated in any realistic process “Disorder” in a system,Second Law: Entropy of a system always increases under realistic (“irreversible”) process,Only law of nature that exhibits direction of time!,“Thermodynamic system”: System with lots of particles (Gas) Obeys second law,But individual particles
8、 obey Newtonian physics,Central Paradox: Gas is a thermodynamic system; obeys second law. But if gas particles individually obey time-symmetric Newtonian physics, how can arrow of time arise?,Boltzmann attempts to derive increase of entropy from Newtonian Physics H-Theorem,Loschmidt Strikes Back,Bol
9、tzmann goes to probabilistic theory,An ordered deck of cards becomes disordered on shuffling,Gibbs strikes back,Another Problem: Entropy should not always be equated with disorder,Prigogines Solution:,Second Law is fundamental. Cant derive.Chaotic systems manifest irreversible Behavior.Entropy increase tied up with chaos,Objection:,Chaotic systems are time-symmetric.If a system is chaotic into the future, it is also chaotic into the past,Conclusion:,To date no satisfactory explanation for direction of time,
