*In order
to deal quantitatively with clocks synchronization it is customary to use a
formalism developed by Hans Reichenbach in 1928. In the following picture the
typical synchronization scene is depicted. *

*When
clock A reads time t _{A}=t_{1}
a light signal is sent towards clock B, which is reached at time t_{B}=t_{2}.
The light signal is instantly reflected towards A which, in turn, is reached at t_{A}=t_{3}.
Using Einstein’s convention we are entitled to define t_{2}
as:*

This
definition seems quite natural. After all, the velocity of light is constant and
the time it takes to go from A to B equals the time taken for the reverse
journey. But we have seen that a one-way velocity is in principle non-measurable
unless a synchronization procedure is first selected. Thus, another valid choice
for time *t _{2} is the following:
*

, (1.1)

ε being a real number between 0 and 1 (0<ε<1). Each numerical value assumed by ε corresponds to a specific synchronization or, equivalently, to a specific value for the one-way velocity of light. When ε=1/2 formula (1.1) becomes Einstein’s synchronization.

Let us,
now, find an expression for the one-way velocity of light from A to B, indicated
as *c _{ε+}*, as function of the two-way velocity of light,

(1.2)

To
measure one-way velocities we use two synchronized clocks positioned at A and B.
Then *c _{ε+}* is defined as follows:

From
(1.1) we know that *t _{2}-t_{1}=ε(t_{3}-t_{1})*,
then the above expression is transformed into the following one:

Using
formula (1.2), *t _{3}-t_{1}* can be expressed as

(1.3)

Formula
(1.3) clearly shows how assigning a given synchronization (i.e. a particular
value of ε) is equivalent to defining a particular one-way velocity of
light. This makes sense because, according to the arguments previously
introduced, one-way velocities contain a non-eliminable element of
conventionality. Incidentally, if we use Einstein’s synchronization, *ε=1/2*,
in formula (1.3), obtain *c _{ε+}=c*; this is in agreement with
Einstein’s postulate that the one-way velocity of light equals

The
velocity of light is not the only velocity affected by a synchronization choice.
Indeed all one-way velocities will strongly depend upon the particular way
distant clocks are synchronized. An expression for any one-way velocity, *v _{ε+}*,
can be obtained with the procedure described hereafter. Consider, again, clock A
and clock B in the following picture.

At
*t _{A}=0* both a light signal and a point-like body leave A and
travel towards B. Light will, eventually, reach B at

*c _{ε+}*
can be replaced using formula (1.3). After some algebraic manipulation the above
equation yields the following expression for

(1.4)

Equation (1.4) leaves no doubt on the dependency of any one-way velocity from the synchronization parameter. When Einstein’s synchronization is adopted,