The “Arrow of Time”

•Nearly all fundamental laws of Physics are symmetric in time •A process which satisfies these laws can be ‘rewinded’ to give another physically valid process

The “Arrow of Time”

•Nearly all fundamental laws of Physics are symmetric in time •A process which satisfies these laws can be ‘rewinded’ to give another physically valid process •But many macroscopic processes are irreversible, and only valid for a certain time direction

The “Arrow of Time”

•Nearly all fundamental laws of Physics are symmetric in time •A process which satisfies these laws can be ‘rewinded’ to give another physically valid process •But many macroscopic processes are irreversible, and only valid for a certain time direction •This problem hasn’t been solved by the 2nd Law - it is still an active theoretical issue •But there are different views on what exactly needs to be explained

The Arrows

•Psychological flow of time

The Arrows

•Psychological flow of time •2nd Law of TD, Entropy almost never decreases •Electromagnetic radiation from a point source

The Arrows

•Psychological flow of time •2nd Law of TD, Entropy almost never decreases •Electromagnetic radiation from a point source •Collapse of wavefunction under ‘measurement’

The Arrows

•Psychological flow of time •2nd Law of TD, Entropy almost never decreases •Electromagnetic radiation from a point source •Collapse of wavefunction under ‘measurement’ •Cosmological asymmetry, expansion of the universe •Asymmetry of black holes, no “white” holes observed

The Arrows

•Psychological flow of time •2nd Law of TD, Entropy almost never decreases •Electromagnetic radiation from a point source •Collapse of wavefunction under ‘measurement’ •Cosmological asymmetry, expansion of the universe •Asymmetry of black holes, no “white” holes observed •Time asymmetry in particle physics, kaon decay

Time Reversal

What does time reversal symmetry mean?

Time Reversal

What does time reversal symmetry mean?

Time Reversal

What does time reversal symmetry mean?

Time Reversal

What does time reversal symmetry mean?

Big important theorem:

Any local field theory satisfying SR is “CPT” symmetric

Time Reversal Big important theorem:

Any local field theory satisfying SR is “CPT” symmetric •1964 Fitch and Cronin discover neutral Kaon violates CP symmetry •CP symmetry is broken, so Time Reversal must must be violated to maintain CPT symmetry

Time Reversal Big important theorem:

Any local field theory satisfying SR is “CPT” symmetric •1964 Fitch and Cronin discover neutral Kaon violates CP symmetry •CP symmetry is broken, so Time Reversal must must be violated to maintain CPT symmetry •Cosmological asymmetry between matter and antimatter related to arrow of time?

Cosmology and Entropy

•Why does the early universe have such low entropy?

•Fraction of states: 1 in 10^10^30 •statistical fluctuation?

Cosmology and Entropy

•Why does the early universe have such low entropy?

•Fraction of states: 1 in 10^10^30 •statistical fluctuation?

•Thomas Gold: in a contracting universe entropy will begin to decrease with time

Cosmology and Entropy

•Why does the early universe have such low entropy?

•Fraction of states: 1 in 10^10^30 •statistical fluctuation?

•Thomas Gold: in a contracting universe entropy will begin to decrease with time •Can an asymmetric universe be shown to be probable?

•Anthropic Principle?

Thermodynamic Time

•Loschmidt’s Paradox: Any process leading to increase of entropy can be time reversed •Fluctuations of decreasing entropy do occur, but with very small probability

Thermodynamic Time

•Loschmidt’s Paradox: Any process leading to increase of entropy can be time reversed •Fluctuations of decreasing entropy do occur, but with very small probability •Fluctuation Theorem (1993):

Thermodynamic Time

•Loschmidt’s Paradox: Any process leading to increase of entropy can be time reversed •Fluctuations of decreasing entropy do occur, but with very small probability •Fluctuation Theorem (1993): •“Parity of reasoning” -> Low entropy states evolve from high entropy with high probability!

•Why do statistical arguments apply in only one direction?

Thermodynamic Time

•Loschmidt’s Paradox: Any process leading to increase of entropy can be time reversed •Fluctuations of decreasing entropy do occur, but with very small probability •Fluctuation Theorem (1993): •“Parity of reasoning” -> Low entropy states evolve from high entropy with high probability!

•Why do statistical arguments apply in only one direction?

•Interventionism: Random interactions with environment disturb correlated particles •These interactions must be time-asymmetric to begin with

Quantum Measurement

•Evolution of QM state is time symmetric •But under measurement, state “collapses” onto eigenspace

Quantum Measurement

•Evolution of QM state is time symmetric •But under measurement, state “collapses” onto eigenspace •Decoherence: measured state entangled with state of macroscopic system •Interference effects suppressed, as if collapse •Quantum arrow related to ordinary TD 2nd Law

Quantum Measurement

•Evolution of QM state is time symmetric •But under measurement, state “collapses” onto eigenspace •Decoherence: measured state entangled with state of macroscopic system •Interference effects suppressed, as if collapse •Quantum arrow related to ordinary TD 2nd Law •Branched model of spacetime: •Different measurement results correspond to different branches •As present time progresses branches are “trimmed”

Any Questions?

•Savitt, S., ed. 1995.

Time’s Arrows Today

. Cambridge.

•Price, H. 1992.

Cosmology, Time's Arrow, and That Old Double Standard.

UBC.

•Coauthor of Fluctuation Theorem’s website:

http://rsc.anu.edu.au/~evans/