How the word "interference" causes confusion

It is good to check on whether some terms used in physics are "well posed" and do their jobs right. I believe one of the unfortunate, sloppy semantic habits in physics is use of "interference." The word came from observation of light and dark fringes in e.g. double-slit experiments. This can be explained by superposition (amplitudes add linearly) and squaring of summed amplitudes to get intensity. The classic experiments reveal a vivid depiction of this principle, but led to careless semantics that were wrongly tied down to the original context and to superficial demands of visible manifestation. For example, if the phases between waves changes around for various reasons, or they can't match up in a well-ordered or stable way (different frequency or polarization etc.) people loosely say "the waves don't interfere anymore." But of course the waves still superpose everywhere, the result just isn't a stable or evident pattern over time and space.

And as for polarization: yes, x and y polarized light do "interfere" in the genuine technical sense, properly enlarged to mean vector addition and not just "amplitude" as a scalar. Add x and y light in phase: we get a definite 45 degree wave. If added at pi out of phase, they make a 135 degree wave; or circular etc. in other phases. We can even get a pattern of varying polarization type on a screen from little x and y sources acting like slits, but it all has the same amplitude. Should we call them "state-fringes" or "type-fringes"? (And yet, we could pull back a bit and choose to pick out the x or y with filters. That seems to offer 'which way' information in a contradictory way, reminiscent of issues raised by the Afshar experiment.) But since that isn't the historically conditioned intensity fringes, this led to careless and misleading talk that "orthogonal polarized states don't interfere."

This confusion about "interference" plays a major role in the fallacious claims that "decoherence" resolves the puzzle (to whatever extent) of collapse of the wave function by in some sense converting superpositions into mixtures. There are many faults with that interpretation. Briefly, it is a circular argument since it introduces at the outset what it is trying to explain: collapse is required as unacknowledged "selector" to introduce quantum statistics into the density matrix along with the classical statistics. Then such a hybrid DM is used to seem to explain the collapse it already incorporated.

DI proponents often say that "decohered states don't interfere anymore." That harks back to old, careless classical talk of vividly evident fringes, which are equivalent to the orderly statistics of ensembles with consistent phase relations. First, REM that classical interference wasn't about "statistics" at all, but amplitudes and their squares per se. The conceptual models of QM say the superpositions always exist together until "collapse" somehow both concentrates and isolates a given state, allowing for statistical outcomes. Second, it is misleading to talk of "interference" when comparing waves to each other that occur in different instances in an ensemble of trials. Superposition is about waves existing and adding together here and now, not a collective. Third, once we understand the universality of superposition, we realize that claim of non-interference is actually false. Instead, decohered states do "interfere" in the technically correct sense of following the superposition principle. If the phase difference is phi1 one time and phi2 another time, so what. The states still would superpose accordingly each time. That is regardless of whether the overall patterns made either by their squared sums in any one case, or by the statistics from collapse applied to ensembles of such superpositions was coherent and orderly; versus whether the patterns (merely) simulated the behavior of genuine mixtures.