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Tony Rothman

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Deep(est) Paradox of Physics: Physics is Time Symmetric Nature is Not

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Fundamental Theories of Physics Dont Care Which Way Time Goes Newtonian Physics Newtonian Physics Electromagnetism Electromagnetism Relativity Relativity Quantum Mechanics Quantum Mechanics

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Nevertheless, Nature Cares

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Roger Penrose lists seven ways in which Nature distinguishes past from future, seven arrows of time

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Seven Arrows of Time 1. Memory Arrow 2. Electromagnetic Arrow 3. Quantum Arrow 4. Black Hole Arrow 5. Cosmological Arrow 6. Kaon Arrow 7. Entropy Arrow

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1. Memory Arrow Memory only works backwards (We don't remember the future)

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2. Electromagnetic Arrow Electromagnetic Causes Precede Effects

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3. Quantum Arrow Wave Functions Collapse But Dont Uncollapse

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4. Black Hole Arrow Black Holes Exist But White Holes Dont (Apparently)

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5. Cosmological Arrow We live in an expanding universe, not a contracting one. Would time change direction if universe started contracting?

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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!

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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

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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

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7. Entropy Arrow Entropy always increases (second law of thermodynamics)

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Question: Are arrows independent? Hawking: Memory and entropy arrows linked (Requires energy to read one bit, increases entropy by certain amount)

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Rothman to Penrose: One arrow arbitrary; only six independent signs.

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Sudarshan to Rothman: All particle decay CPT invariant but Irreversible: Particle-decay arrow. Rothman to Rothman: Temperature dependent?

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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

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Second Law: Entropy of a system always increases under realistic (irreversible) process Only law of nature that exhibits direction of time!

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Thermodynamic system: System with lots of particles (Gas) Obeys second law But individual particles obey Newtonian physics

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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?

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Boltzmann attempts to derive increase of entropy from Newtonian Physics H-Theorem

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Loschmidt Strikes Back

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Boltzmann goes to probabilistic theory An ordered deck of cards becomes disordered on shuffling

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Gibbs strikes back

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Another Problem: Entropy should not always be equated with disorder

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Prigogines Solution: Second Law is fundamental. Cant derive. Chaotic systems manifest irreversible Behavior. Entropy increase tied up with chaos

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Objection: Chaotic systems are time-symmetric. If a system is chaotic into the future, it is also chaotic into the past

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Conclusion : To date no satisfactory explanation for direction of time

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