Keith Dysart wrote:
How coherent do the two signals have to be for interference to
occur?

Instead of spending hours typing the answer, I will point
you to "Optics", by Hecht, 4th edition, Chapter 12, Basics
of Coherence Theory.

In my example, the one source is an ideal single frequency
source. Thus all signals existing within the system are
completely coherent, by definition. Your questions are
irrelevant to the example provided.

You say that when the sources are coherent, interference occurs
but when the frequency differs by 30% it does not.

In between "completely coherent" signals and "completely incoherent"
signals is a very large gray area. Please read the reference.

What happens if one of the sources has just a bit of phase noise,
or the frequency wanders just a bit, or is just offset a bit?

Please read the reference. In my example, the source is ideal
so that problem doesn't exist.

How much of a difference does there have to be for interference
to stop? What is the threshold? Phase noise? Wander? Offset?

Please read the reference. In my example, the source is ideal
so those problems don't exist.

And is it the mechanism that creates interference that stops working
once the threshold is crossed?
Or does the mechanism still work, but we just no longer call the
result interference? Why do we stop calling it interference once
the threshold is crossed?

In "Optics", by Hecht, Chapter 7 is on superposition and
Chapter 9 is on interference.

Quoting "Optics", by Hecht, Chapter 12. "Thus far in our
discussion of phenomena involving the superposition of waves,
we've restricted the treatment to that of either completely
coherent or completely incoherent disturbances. ... There is
a middle ground between these antithetic poles, which is of
considerable contemporary concern - the domain of
*partial coherence*.

What is the mechanism that creates the effect we call interference?

"Interference", in this context, is not defined in the IEEE
Dictionary. The closest I can come to a definition is from
"Optics", by Hecht: "... optical [EM] interference corresponds
to the interaction of two or more lightwaves yielding a resultant
irradiance [average power density] that deviates from the sum of
the component irradiances [average power densities]."
--
73, Cecil http://www.w5dxp.com