I recently (8 months) started Tai Chi with william C C chen, who emphasizes tai chi for fighting and isn't into any mystical kind of anything. He's probably best known for training fighters that win tournaments, both push hands and also san shou (sanda)
his tai chi form is VERY soft, but in his training you separate the ribcage from the abdomen to generate power(in the context of the movement) and each tai chi move has 1--3X of moving, collapsing and raising and twisting the ribcage independently (no bending-without it effecting the rest of your posture, very subtle, you can hardly see it when he's doing the form, but he let me feel his ribs and it was amazing how much movement there was) ...its exhausting and feels like doing situps inside your ribcage... after doing it for a few weeks now I can feel the inside muscles (that I've never used before) becoming stronger... of course that's only one aspect.
the point I'm making is that for master Chen, the internal power is physical, bio-mechanical and not something mystical.
I'm finding it very interesting
here's an interview that he did about 3 years ago at age 75 (though the interviewer doesn't seem to know much about tai chi)
and his latest article: