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.