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 Kaon decay not time symmetric K o ππ 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 indistinguishable from old
Princeton 1964 Experiment: Kaon decay not invariant under CP-reversal Kaon decay not invariant under CP-reversal Must also change under T- 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 one 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 generated in any realistic process Entropy can be thought of as waste heat generated in any realistic process Disorder in a system 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 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
Boltzmann 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