  In classical information theory, a causal relationship between two variables
is typically modelled by assuming that, for every possible state of one of the
variables, there exists a particular distribution of states of the second
variable. Let us call these two variables the causal and caused variables,
respectively. We shall assume that both variables are continuous and
one-dimensional. In this work we consider a procedure to transform each
variable, using transformations that are differentiable and strictly
increasing. We call these increasing transformations. Any causal relationship
(as defined here) is associated with a channel capacity, which is the maximum
rate that information could be sent if the causal relationship was used as a
signalling system. Channel capacity is unaffected when the two variables are
changed by use of increasing transformations. For any causal relationship we
show that there is always a way to transform the caused variable such that the
entropy associated with the caused variable is independent of the value of the
causal variable. Furthermore, the resulting universal entropy has an absolute
value that is equal to the channel capacity associated with the causal
relationship. This observation may be useful in statistical applications. Also,
for any causal relationship, it implies that there is a 'natural' way to
transform a continuous caused variable. We also show that, with additional
constraints on the causal relationship, a natural increasing transformation of
both variables leads to a transformed causal relationship that has properties
that might be expected from a well-engineered measuring device.
