Mappings, functions

In this book, the term architecture refers to a non-mathematical description of the sequence of events which collectively describes an experiment.

Continuous time (CT) classical mechanics (CM) is based on some explicit and implicit assumptions that generate architectures radically different from those describing quantum processes. In the following list, which is not complete by any means, most of these assumptions may appear obvious and overstated, but one or two are subtle and should be brought to light, since they have an enormous impact on the theories which are based on them. Our comments are in square brackets at the end of each item in the list.

1. At any given time, a system under observation (SUO) exists in a unique physical state with absolute properties independent of any observer [a standard classical metaphysical assumption].

2. The physical state of an SUO at any given time t may be represented by a single element Ψ(t) called a state of some fixed state space U (or universe) [a reasonable mathematical assumption].

3. The state Ψ(t') of an SUO at any time t' later than t is also an element of U, not necessarily the same state Ψ(t) at the earlier time [a reasonable classical mathematical assumption].

4. Observers are exophysical, meaning that they stand outside of U [a nearly universal metaphysical assumption; observers are not discussed in detail in CM or QM simply because there is no comprehensive theory of what constitutes an observer].