  Casimir effect, in a broad interpretation which we adopt here, consists in a
backreaction of a quantum system to adiabatically changing external conditions.
Although the system is usually taken to be a quantum field, we show that this
restriction rather blurs than helps to clarify the statement of the problem. We
discuss the problem from the point of view of algebraic structure of quantum
theory, which is most appropriate in this context. The system in question may
be any quantum system, among others both finite as infinite dimensional
canonical systems are allowed. A simple finite-dimensional model is discussed.
We identify precisely the source of difficulties and infinities in most of
traditional treatments of the problem for infinite dimensional systems (such as
quantum fields), which is incompatibility of algebras of observables or their
representations. We formulate conditions on model idealizations which are
acceptable for the discussion of the adiabatic backreaction problem. In the
case of quantum field models in that class we find that the normal ordered
energy density is a well defined distribution, yielding global energy in the
limit of a unit test function. Although we see the "zero point" expressions as
inappropriate, we show how they can arise in the quantum field theory context
as a result of uncontrollable manipulations.
