This article is an overview of the
subject. For a more technical discussion
and for information related to current
research, see Entropy.
The Arrow of Time, or Time's Arrow, is a
concept developed in 1927 by the British
astronomer Arthur Eddington involving
the "one-way direction" or "asymmetry"
of time. This direction, according to
Eddington, can be determined by studying
the organization of atoms, molecules,
and bodies, might be drawn upon a
four-dimensional relativistic map of the
world.
Physical processes at the microscopic
level are believed to be either entirely
or mostly time-symmetric: if the
direction of time were to reverse, the
theoretical statements that describe
them would remain true. Yet at the
macroscopic level it often appears that
this is not the case: there is an
obvious direction of time.
Eddington 
In the 1928 book The Nature of the
Physical World, which helped to
popularize the concept, Eddington
stated:
Let us draw an arrow arbitrarily. If as
we follow the arrow we find more and
more of the random element in the state
of the world, then the arrow is pointing
towards the future; if the random
element decreases the arrow points
towards the past. That is the only
distinction known to physics. This
follows at once if our fundamental
contention is admitted that the
introduction of randomness is the only
thing which cannot be undone. I shall
use the phrase ‘time's arrow’ to express
this one-way property of time which has
no analogue in space.
Eddington then gives three points to
note about this arrow:
It is vividly recognized by
consciousness.
It is equally insisted on by our
reasoning faculty, which tells us that a
reversal of the arrow would render the
external world nonsensical.
It makes no appearance in physical
science except in the study of
organization of a number of individuals.
According to Eddington the arrow
indicates the direction of progressive
increase of the random element.
Following a lengthy argument upon the
nature of thermodynamics he concludes
that, so far as physics is concerned,
time's arrow is a property of entropy
alone.
Overview 
The symmetry of time can be understood
by a simple analogy: if time were
perfectly symmetrical a video of real
events would seem realistic whether
played forwards or backwards. An obvious
objection to this notion is gravity:
things fall down, not up. Yet a ball
that is tossed up, slows to a stop and
falls into the hand is a case where
recordings would look equally realistic
forwards and backwards. The system is
T-symmetrical but while going "forward"
kinetic energy is dissipated and entropy
is increased. Entropy may be one of the
few processes that is not
time-reversible. According to the
statistical notion of increasing entropy
the "arrow" of time is identified with a
decrease of free energy.
If we record somebody dropping a ball
that falls for a meter and stops, in
reverse we will notice an unrealistic
discrepancy: a ball falling upward! But
when the ball lands its kinetic energy
is dispersed into sound, shock-waves and
heat. In reverse those sound waves,
ground vibrations and heat will rush
back into the ball, imparting enough
energy to propel it upward one meter
into the person's hand. The only
unrealism lies in the statistical
unlikelihood that such forces could
coincide to propel a ball upward into a
waiting hand.
Arrows 
= The thermodynamic arrow of time =
The arrow of time is the "one-way
direction" or "asymmetry" of time. The
thermodynamic arrow of time is provided
by the Second Law of Thermodynamics,
which says that in an isolated system,
entropy tends to increase with time.
Entropy can be thought of as a measure
of microscopic disorder; thus the Second
Law implies that time is asymmetrical
with respect to the amount of order in
an isolated system: as a system advances
through time, it will statistically
become more disordered. This asymmetry
can be used empirically to distinguish
between future and past though measuring
entropy does not accurately measure
time. Also in an open system entropy can
decrease with time.
British physicist Sir Alfred Brian
Pippard wrote, "There is thus no
justification for the view, often glibly
repeated, that the Second Law of
Thermodynamics is only statistically
true, in the sense that microscopic
violations repeatedly occur, but never
violations of any serious magnitude. On
the contrary, no evidence has ever been
presented that the Second Law breaks
down under any circumstances." However,
there are a number of paradoxes
regarding violation of the Second Law of
Thermodynamics, one of them due to the
Poincaré recurrence theorem.
This arrow of time seems to be related
to all other arrows of time and arguably
underlies some of them, with the
exception of the weak arrow of time.
Harold Blum's 1951 book Time's Arrow and
Evolution "explored the relationship
between time's arrow and organic
evolution." This influential text
explores "irreversibility and direction
in evolution and order, negentropy, and
evolution." Blum argues that evolution
followed specific patterns predetermined
by the inorganic nature of the earth and
its thermodynamic processes.
= The cosmological arrow of time =
The cosmological arrow of time points in
the direction of the universe's
expansion. It may be linked to the
thermodynamic arrow, with the universe
heading towards a heat death as the
amount of usable energy becomes
negligible. Alternatively, it may be an
artifact of our place in the universe's
evolution, with this arrow reversing as
gravity pulls everything back into a Big
Crunch.
If this arrow of time is related to the
other arrows of time, then the future is
by definition the direction towards
which the universe becomes bigger. Thus,
the universe expands - rather than
shrinks - by definition.
The thermodynamic arrow of time and the
Second law of thermodynamics are thought
to be a consequence of the initial
conditions in the early universe.
Therefore they ultimately result from
the cosmological set-up.
= The radiative arrow of time =
Waves, from radio waves to sound waves
to those on a pond from throwing a
stone, expand outward from their source,
even though the wave equations allow for
solutions of convergent waves as well as
radiative ones. This arrow has been
reversed in carefully worked experiments
which have created convergent waves, so
this arrow probably follows from the
thermodynamic arrow in that meeting the
conditions to produce a convergent wave
requires more order than the conditions
for a radiative wave. Put differently,
the probability for initial conditions
that produce a convergent wave is much
lower than the probability for initial
conditions that produce a radiative
wave. In fact, normally a radiative wave
increases entropy, while a convergent
wave decreases it, making the latter
contradictory to the Second Law of
Thermodynamics in usual circumstances.
= The causal arrow of time =
A cause precedes its effect: the causal
event occurs before the event it
affects. Birth, for example, follows a
successful conception and not vice
versa. Thus causality is intimately
bound up with time's arrow.
An epistemological problem with using
causality as an arrow of time is that,
as David Hume maintained, the causal
relation per se cannot be perceived; one
only perceives sequences of events.
Furthermore, it is surprisingly
difficult to provide a clear explanation
of what the terms cause and effect
really mean, or to define the events to
which they refer. However, it does seem
evident that dropping a cup of water is
a cause while the cup subsequently
shattering and spilling the water is the
effect.
Physically speaking, the perception of
cause and effect in the dropped cup
example is a phenomenon of the
thermodynamic arrow of time, a
consequence of the second law of
thermodynamics. Controlling the future,
or causing something to happen, creates
correlations between the doer and the
effect, and these can only be created as
we move forwards in time, not backwards.
= The particle physics arrow of time =
Certain subatomic interactions involving
the weak nuclear force violate the
conservation of both parity and charge
conjugation, but only very rarely. An
example is the kaon decay [1]. According
to the CPT Theorem, this means they
should also be time irreversible, and so
establish an arrow of time. Such
processes should be responsible for
matter creation in the early universe.
That the combination of parity and
charge conjugation is broken so rarely
means that this arrow only "barely"
points in one direction, setting it
apart from the other arrows whose
direction is much more obvious. This
arrow is not linked to any other arrow
by any proposed mechanism.
= The quantum arrow of time =
According to the Copenhagen
interpretation of quantum mechanics,
quantum evolution is governed by the
Schrödinger equation, which is
time-symmetric, and by wave function
collapse, which is time irreversible. As
the mechanism of wave function collapse
is philosophically obscure, it is not
completely clear how this arrow links to
the others. Despite the post-measurement
state being entirely stochastic in
formulations of quantum mechanics, a
link to the thermodynamic arrow has been
proposed, noting that the second law of
thermodynamics amounts to an observation
that nature shows a bias for collapsing
wave functions into higher entropy
states versus lower ones, and the claim
that this is merely due to more possible
states being high entropy runs afoul of
Loschmidt's paradox. According to one
physical view of wave function collapse,
the theory of quantum decoherence, the
quantum arrow of time is a consequence
of the thermodynamic arrow of time.
= The quantum source of time =
Physicists say that quantum uncertainty
gives rise to entanglement, the putative
source of the arrow of time. The idea
that entanglement might explain the
arrow of time was by Seth Lloyd in
1980s, when he was a 23-year-old
philosophy student working towards an MA
at Cambridge University after having
received an AB in Physics from Harvard.
Lloyd realized that quantum uncertainty,
and the way it spreads as particles
become increasingly entangled, could
replace human uncertainty in the old
classical proofs as the true source of
the arrow of time. According to Lloyd;
“The arrow of time is an arrow of
increasing correlations.”
= The psychological/perceptual arrow of
time =
A related mental arrow arises because
one has the sense that one's perception
is a continuous movement from the known
to the unknown. Anticipating the unknown
forms the psychological future which
always seems to be something one is
moving towards, but, like a projection
in a mirror, it makes what is actually
already a part of memory, such as
desires, dreams, and hopes, seem ahead
of the observer. The association of
"behind ⇔ past" and "ahead ⇔ future" is
itself culturally determined. For
example, the Aymara language associates
"ahead ⇔ past" and "behind ⇔ future".
Similarly, the Chinese term for "the day
after tomorrow" literally means "behind
day", whereas "the day before yesterday"
is referred to as "front day."
The words yesterday and tomorrow both
translate to the same word in Hindi: कल,
meaning "the day remote from today."
The other side of the psychological
passage of time is in the realm of
volition and action. We plan and often
execute actions intended to affect the
course of events in the future. Hardly
anyone tries to change past events.
Indeed, in the Rubaiyat it is written:
- Omar Khayyám.
See also 
Anthropic bias
Causality
Ilya Prigogine
Loschmidt's paradox
Maxwell's demon
Philosophy of space and time
Royal Institution Christmas Lectures
1999
Time evolution
Time reversal signal processing
Wheeler–Feynman absorber theory
References 
Further reading 
Time's arrow and Boltzmann's entropy
Joel L. Lebowitz Scholarpedia,
3(4):3448. doi:10.4249/scholarpedia.3448
Boltzmann, Ludwig. Lectures On Gas
Theory. University Of California Press. 
Translated from the original German by
Stephen G. Brush. Originally published
1896/1898.
Carroll, Sean. From Eternity to Here:
The Quest for the Ultimate Theory of
Time. Dutton.  Website
Coveney, Peter; Highfield, Roger, The
Arrow of Time: A voyage through science
to solve time's greatest mystery,
London: W.H. Allen, ISBN
978-1-85227-197-8 
Feynman, Richard. The Character of
Physical Law. BBC Publications.  Chapter
5.
Halliwell, J.J.; et al.. Physical
Origins of Time Asymmetry. Cambridge.
ISBN 0-521-56837-4. .
Mersini-Houghton, L., Vaas, R. The
Arrows of Time. A Debate in Cosmology.
Springer. ISBN 978-3642232589. .
Peierls, R. Surprises in Theoretical
Physics. Princeton.  Section 3.8.
Penrose, Roger. The Emperor's New Mind.
Oxford University Press. ISBN
0-19-851973-7.  Chapter 7.
Penrose, Roger. The Road to Reality.
Jonathan Cape. ISBN 0-224-04447-8. 
Chapter 27.
Price, Huw. Time's Arrow and Archimedes'
Point. ISBN 0-19-510095-6.  Website
Zeh, H. D. The Physical Basis of The
Direction of Time. ISBN 3-540-42081-9. 
Official website for the book
"BaBar Experiment Confirms Time
Asymmetry". 
External links 
The Ritz-Einstein Agreement to Disagree,
a review of historical perspectives of
the subject, prior to the evolvement of
quantum field theory.
The Thermodynamic Arrow: Puzzles and
Pseudo-Puzzles Huw Price on Time's Arrow
Arrow of time in a discrete toy model
The Arrow of Time
