Tony Rothman

Deep(est) Paradox of Deep(est) Paradox of Physics:Physics:

Physics is Time SymmetricPhysics is Time Symmetric

Nature is NotNature is Not

Fundamental Theories of Physics Fundamental Theories of Physics Don’t Care Which Way Time GoesDon’t Care Which Way Time Goes

• Newtonian PhysicsNewtonian Physics• ElectromagnetismElectromagnetism• RelativityRelativity• Quantum MechanicsQuantum Mechanics

Nevertheless, Nature CaresNevertheless, Nature Cares

Roger Penrose lists seven waysRoger Penrose lists seven ways in which Nature in which Nature

distinguishes past from future,distinguishes past from future,seven “arrows of time”seven “arrows of time”

Seven Arrows of TimeSeven Arrows of Time

1.1. Memory ArrowMemory Arrow

2.2. Electromagnetic ArrowElectromagnetic Arrow

3.3. Quantum ArrowQuantum Arrow

4.4. Black Hole ArrowBlack Hole Arrow

5.5. Cosmological ArrowCosmological Arrow

6.6. Kaon ArrowKaon Arrow

7.7. Entropy ArrowEntropy Arrow

1. Memory Arrow1. Memory Arrow

Memory onlyMemory only

works backwardsworks backwards

(We don't remember(We don't remember

the future)the future)

2. Electromagnetic Arrow2. Electromagnetic Arrow

Electromagnetic Causes Precede EffectsElectromagnetic Causes Precede Effects

3. Quantum Arrow3. Quantum Arrow

Wave Functions “Collapse”Wave Functions “Collapse”

But Don’t “Uncollapse”But Don’t “Uncollapse”

4. Black Hole Arrow4. Black Hole Arrow

Black Holes Exist But White Holes Black Holes Exist But White Holes Don’t (Apparently)Don’t (Apparently)

5. Cosmological Arrow5. Cosmological Arrow

We live in an expanding We live in an expanding universe, not a contracting one.universe, not a contracting one.

Would time change direction if Would time change direction if universe started contracting?universe started contracting?

6. Kaon Arrow6. Kaon Arrow

Kaon decay not time symmetric Kaon decay not time symmetric KKo o ππππ

In a time-reversed world this In a time-reversed world this particle decays at a different particle decays at a different

rate than in our world!rate than in our world!

CPT theoremCPT theorem

““Charge-Parity-Time”Charge-Parity-Time”Change electric charge of all particles in Change electric charge of all particles in

world (Change all particles to world (Change all particles to antiparticles);antiparticles);Reflect it in mirror;Reflect it in mirror;Run time backwards:Run time backwards:

New world is indistinguishable New world is indistinguishable from oldfrom old

Princeton 1964 Experiment:Princeton 1964 Experiment:

• Kaon decay not invariant under Kaon decay not invariant under CP-reversalCP-reversal

• Must also change under T-Must also change under T-reversalreversal

7. Entropy Arrow7. Entropy Arrow

Entropy always increasesEntropy always increases

(second law of thermodynamics)(second law of thermodynamics)

Question:Question: Are arrows independent? Are arrows independent?

Hawking: Memory and entropy Hawking: Memory and entropy arrows linkedarrows linked

(Requires energy to read one bit, (Requires energy to read one bit, increases entropy by certain increases entropy by certain

amount)amount)

Rothman to Penrose:Rothman to Penrose:

One arrow arbitrary; only six One arrow arbitrary; only six independent signs.independent signs.

Sudarshan to Rothman:Sudarshan to Rothman:

All particle decay CPT invariant All particle decay CPT invariant butbut

Irreversible:Irreversible:

Particle-decay arrow.Particle-decay arrow.

Rothman to Rothman:Rothman to Rothman:

Temperature dependent?Temperature dependent?

EntropyEntropy

• Entropy can be thought of as Entropy can be thought of as waste heat generated in any waste heat generated in any

realistic processrealistic process

• ““Disorder” in a systemDisorder” in a system

Second Law:Second Law:Entropy of a system always Entropy of a system always

increases under realistic increases under realistic (“irreversible”) process(“irreversible”) process

Only law of nature that Only law of nature that exhibits direction of time!exhibits direction of time!

““Thermodynamic system”:Thermodynamic system”:System with lots of particlesSystem with lots of particles

(Gas)(Gas)Obeys second lawObeys second law

But individual particles obeyBut individual particles obey

Newtonian physicsNewtonian physics

Central Paradox:Central Paradox:Gas is a thermodynamic system;Gas is a thermodynamic system;

obeys second law.obeys second law.

But if gas particles individually But if gas particles individually obey time-symmetric Newtonian obey time-symmetric Newtonian

physics, how canphysics, how canarrow of time arise?arrow of time arise?

Boltzmann attempts to deriveBoltzmann attempts to deriveincrease of entropy increase of entropy

from from Newtonian PhysicsNewtonian Physics

H-TheoremH-Theorem

Loschmidt Strikes Back

Boltzmann goes to probabilistic Boltzmann goes to probabilistic theorytheory

An ordered deck of cardsAn ordered deck of cards

becomes disordered on shufflingbecomes disordered on shuffling

Gibbs strikes back

Another Problem: Another Problem:

Entropy should not alwaysEntropy should not alwaysbe equated with disorderbe equated with disorder

Prigogine’s Solution:Prigogine’s Solution:

Second Law is fundamental.Second Law is fundamental.

Can’t derive.Can’t derive.

Chaotic systems manifest irreversibleChaotic systems manifest irreversible

Behavior.Behavior.

Entropy increase tied up with chaosEntropy increase tied up with chaos

Objection:Objection:

Chaotic systems are time-symmetric.Chaotic systems are time-symmetric.

If a system is chaotic into the future, it is If a system is chaotic into the future, it is

also chaotic into the pastalso chaotic into the past

ConclusionConclusion::

To date no satisfactory To date no satisfactory explanation for direction of explanation for direction of

timetime