Thiel Owners

The ATC actives use some kind of active phase compensation to align the drivers at the crossover frequencies.  I don't think they go to the trouble Thiel did to keep time alignment throughout.  What big active ATCs have that little else can match is massive dynamics.  I think there is a dynamic linearity as well that makes them very revealing in a way other speakers can't match.  This ability lends a different type of realism that would probably be impossible for first order speakers to achieve.  ATC believes in making the drivers as well as possible so the crossover doesn't have to be complex.  They don't image like Thiels and they don't sound near as lively at low volumes.  I consider my Thiel/ATC systems to be quite complementary.

They describe the active crossover as "380Hz and 3.5kHz, 4th order, critically damped with phase compensation".  They discuss phase response in their literature but don't give specifics.  They're clearly in favor of linear phase response and it's a design goal.  "An ideal speaker system should have phase response linear with frequency, which in simple terms means that all frequencies produced by the driver reach the listener’s ear at the same time. "


http://www.transaudiogroup.com/wp-content/uploads/2015/06/ATC_Engineering_Goals_and_Approaches.pdf

Phase coherence does not guarantee time coherence.
Time coherence does guarantee phase coherence.

would I be right in saying that phase coherence means that the drivers are in phase with each other but not necessarily with the source?  So if two drivers are 50 degrees out of phase with the source signal at a particular frequency we say they're phase coherent but not time coherent?

I would say that there are many ways to produce some of the aspects of coherence. Rather than massaging the various aspects, I find the way to "see" that a transducer is keeping all the temporal information straight is to feed it an impulse. If the graph of that impulse rises immediately from zero to a peak and begins a downhill decline (as no more signal is being fed to it) creating a triangle . . . then and only then is the transducer coherent. A single driver such as a headphone acts this way. When using multiple drivers, they overlap and contribute additively and/or destructively in time and frequency and directionality. When they add to act like a single driver, the term of art is "minimum phase response".

A valid test is to overlay (on an oscilloscope screen etc.) the input impulse and the resultant microphone output from the speaker. The speaker will always degrade the signal in some way due to Murphy's Law of Material Physics. If the waves look subtantively the same, then you have preserved the relevant information.

Otherwise, I would find it difficult to wade through the various claims and side-steps and judgements associated with coherence.

"An ideal speaker system should have phase response linear with frequency, which in simple terms means that all frequencies produced by the driver reach the listener’s ear at the same time. "

This statement seems vague and lacking specifics.  I am not sure what they mean by "reaching the listener's ear at the same time".  May be written by the marketing department. :-)

As Tom said, the only way to prove that a speaker is time-phase coherent is that it can produce a pulse response.  You could come up with a lot of reasons as to why a certain speaker is time-phase coherent, but at the end of the day, it has to be able to produce a proper impulse response.  And I think I've read somewhere that there is a law in which stated that in order to legally advertise your speakers as "time-phase coherent", it has to prove that it can produce a impulse response.
Ideally there would be a single driver that can produce 20Hz - 20kHz but since such a driver does not exist, one has to use electrical filters, and all all filters have phase shift.  Some choose to optimize in frequency domain and some choose to optimize in time domain.
Another things that often overlooked in Thiel design is the geometry of the baffle which I believe was designed as such to reduce the effect of diffraction and I don't think one can underestimate how it helps the speakers disappear.  It definitely adds to manufacture cost and I don't think Thiel did it just for the look.  When I see a lot of high end speakers that basically just have a rectangular and square shape I kind of frown ... I am sure they could do a lot better.
It seems like Thiel products for some reasons produce a lot of polarized opions - you either like it or you hate it - at least that's the sense I got.  I haven't heard all their products, but I appreciate the technologies behind their designs.