Rock Garden, Ryoan-ji: japan-guide.com
Notes on Time
The following comes from Satosi Watanabes article on Time.  I'll be
studying this article in the next few days.
Reversibility and Retrodictability
It is well-known that all the basic microscopic laws of classical
physics are symmetrical with respect to the two directions of the
time variable. This does not mean that only small-scale physical
phenomena are temporarily symmetrical. It is not a question of
the scale of the system but it is one of the mode of description.
Even large-scale phenomena will show the symmetry if they are
described minutely in every detail. This situation raises
immediately a pair of twin questions. How is it possible that
something essentially symmetric appear asymmetrical, without
being distorted in some sense? Which one of the two equivalent
directions receives the privileged meaning of "past-to-future"?
What precisely do we mean by saying that the microscopic laws are
symmetrical with respect to the two directions of time? We mean
by this what is usually called "reversibility of physical laws. 
In anticipation of what follows, I may mention that in classical
physics reversibility implies retrodictability  but
retrodictability does not necessarily imply reversibility. That is
to say, reversibility is a much more restricted notion.
To explain reversibility, it is probably better to start with the
notions of reversed phenomenon and reversed state. Suppose we take
a motion picture of a physical phenomenon, and run the film backwards
through the projector. The phenomenon one sees on the screen is the
reversed phenomenon, and the state of the system at an instant in
the reversed phenomenon is the reversal of the state of the origin
phenomenon at the corresponding instant. Thus, in a reversed state,
an object will have the same position but it will be moving in the
opposite direction, that is, the velocity changes its sign. In
general, all physical quantities can be classified in two classes,
those which keep the same sign and those which change the sign in the
reverse state. To determine the class of a physical quantity, we
have to agree that the spatial positions of all objects keep the same
sign, and that the basic attributes of objects, such as mass, electric
charge, etc., also keep the same sign.
Now we are prepared to define "reversibility". If a phenomenon and
its reversed phenomenon are both allowed by a theory under
consideration, then the phenomenon is reversible. All the basic
theories (mechanical and electromagnetic) of classical physics from
which all other laws are supposed to be derivable are reversible.
Laws of friction in mechanics, Ohm's Law, Newton's Law of Heat
Conduction, which are secondary macroscopic laws supposedly
derivable in principle from the more basic laws, are not reversible.
All these irreversible laws are in agreement with a general law
called the Second Law of Thermodynamics. This law says that if the
entropy of an (adiabatically) isolated system changes, it can only
This conflict between the basic reversibility and the macroscopic
irreversibility is the classical way of formulating the essential
problem of the direction of time. In this connection, I have to
make two important remarks. First, we have to note, in agreement
with many physicists in the past, that the alleged conflict
originates from the applications of statistical consideration in
the macroscopic description. Second, we want to point out, in a
departure from the accepted view, that the crucial conflict is not
between reversibility and irreversibility, but between
retrodictability and irretrodictability since the direct consequence
of statistical consideration is not irreversibility but
 Aside from considerations of entropy increase, the suggestion
has been made that the expansion of the universe does itself give a
physical phenomenon that defines the direction of time. This
definition would indeed associate time with what appears to be a
universal feature of our universe.
 In quite a different way, Karl R. Popper has argued on the basis
of our lack of definite knowledge of cosmological structure that we
should not give any cosmic significance to entropy decrease, or to
connect that decrease with the arrow of time.
Somehow I got the notion that time is reversible in a quantum
particle if you consider it as a single system. I don't know
if I read it somewhere or I just made it up. Mathematically,
you can predict the propagation of a pure (simple) wave forward or
backward in time. Interacting waves can be superimposed. When
this happens information about the waves before the interaction
are lost if the wave interaction changes the energy states of the
interacting waves. That is, if energy leaves the interacting wave
system. So you cannot make predictions about waves going backwards
in time if their interaction has a net energy change.
Generally, entropy in a system changes whenever energy enters or
leaves the system. It follows then, that the informational content
in a system changes with energy changes in the system. So you can
make predictions about a quantum particle considered as a single system
if it never interacts with another system. Hence this is an idealized
In the quantum world, we observe quantum particles, but not the
manifestion of the medium in which quanta arises from. So we can
make predictions about the exact trajectories of quanta in a magnetic
field for example. But we can't make exact predictions about where
a quantum particle will arise out of a field because we don't have
enough specific information about the "state" of wave fields that
will produce the creation of a quantum. We cannot take enough
measurements about the medium or field from which the quantum
arises from to know enough about the system to make exact predictions.
As observers of the quantum world, we are limited to making
What's important to remember is that everything depends on the states
of the interacting systems. The word "state" is associated with
"information" in the description of interacting systems. The
description of a system as a function of time thus depends on the
changes in its state parameters.
There is a lot of stuff here to figure out. I'm not sure how
correct I am on anything here. But I know this is really fundamental
and important to think about. It's taken me years of thinking about
this to come to this point - surely because of my own limitations.
 Time and the Probabilistic View of the World, Satosi Watanabe,
p. 527, in The Voices of Time, ed. J. T. Fraser., 1966.