Tony Rothman

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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
• Electromagnetism
• Relativity
• 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 Ko pp
• 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 mirrorRun time backwards
• New world is indistinguishable from old

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Princeton 1964 Experiment

• Kaon decay not invariant under CP-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
• Disorder in a system

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Second LawEntropy of a system always increases
under realistic (irreversible) process

• Only law of nature that exhibits direction of
  time!

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Thermodynamic systemSystem with lots of
particles(Gas)Obeys second law

• But individual particles obey
• Newtonian physics

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Central ParadoxGas is a thermodynamic
systemobeys second law.But if gas particles
individually obey time-symmetric Newtonian
physics, how canarrow of time arise?
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Boltzmann attempts to deriveincrease of entropy
from Newtonian PhysicsH-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 alwaysbe
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