Interference and macroscopic objects

We have stressed that a wavefunction which contains a sum of
several terms (a pure state) is genuinely different from a wavefunction
which is either one term or another (a mixed state).
The reason for the difference is that, in principle, it is possible
to arrange that two terms in a sum interfere when a particular probability is calculated, and this interference can be observed.
Indeed, as we have seen, e.g. in $2.5, there are many experiments
where this interference has been measured and found to agree
perfectly with the predictions of quantum theory. However, in
practice, in many situations, and in all cases where macroscopic
apparatus is involved, it is not possible to design a suitable experiment
to observe the interference, so the two wavefunctions are
effectively indistinguishable.
To understand why this is so, let us suppose we want to check
that the wavefunction for the barrier-plus-two-detectors experiment
really does contain the sum of two pieces, e.g. as in figure
15(b). To this end we would like to arrange that the two pieces are
allowed to interfere. Thus, in effect, we need to do both the potential
barrier experiments of Chapter One in the same experiment.
However, even when the waves corresponding to the reflected and
transmitted particles are brought together by mirrors they will not
interfere because, unlike the situation in 01.4, they now contain
different states of the detectors (ON/OFF or OFF/ON respectively). In
order to have interference it is necessary that the detectors be
brought to the same state. At first sight this might appear to be
easy; they can be switched to the OFF position, say. However, in
order to have interference the states must be identical, and for
macroscopic objects that is not possible. To reverse exactly the
process whereby one of the detectors was switched to ON is, by
many orders of magnitude, outside the range of any conceivable
experimental technique; there is, for example, no conceivable
mechanical interaction between macroscopic objects that does not
remove a few atoms, slightly change the temperature of the object,
alter its shape, etc. This is the reason why interference between
macroscopic objects cannot be experimentally verified.
For a proper treatment of this topic we would need to use the
mathematical formalism of quantum mechanics. Some of the ideas
are discussed further in Appendix 6. Here we shall be content with
the above rather sketchy outline of the argument. The key to it, to
which we shall return, is the inherently irreversible nature of
macroscopic changes.
It is clear that there is a continuum of scales ranging from the
micro- to the macroscopic, so we naturally ask how far towards the
latter we can go with interference experiments. At present, it seems
as though the answer is not very far: all experiments so far performed deal with ‘elementary’ particles, or, more precisely, with
systems that, for the purpose of the experiment considered, can be
regarded as having very few degrees of freedom. Some ideas for
doing interference experiments with larger systems are being
explored at the present time