For Neuhaus (►Bibliography), the term “bridge” corresponds to the locking of the motor apparatus that permits the pianist to transmit the impulse from the shoulder all the way to the bottom of the key. This comparison, even if it is very visual, has a serious inconvenience, because it suggests the stability of a large inert object, where in reality the hand does not remain immobile at the bottom of the key, although it can sometimes rest there, the most often during a fraction of a second.
Simply put, to make a “bridge” means to open the arm and the forearm at the elbow by slight impulses (this is described in detail in chapters How to easily obtain “The Bridge” - basic exercise and Elongated fingers, bridge and crane or inaccuracy in pedagogy). One must also be aware of the order in which the physical events take place: “the bridge”, i.e. the pressure from the shoulder, its contact with the bottom of the key, happens only AFTER the production of sound by the string . The arrival of sound therefore anticipates the “bridge” by several milliseconds. What is the reason for that? Read the point 2 in this chapter.
As for the “crane”, it represents the opposite of the “bridge”, i.e. a state in which the hand is suspended above the keyboard without exerting pressure. Normally while playing, the hand maintains this position from 90 to 95% of the time (this is what we call hovering).
The more rapid the playing, the more the alternation between the bridge and the crane becomes frequent, which, in the most rapid passages, transforms into what one calls shaking the arm, i.e. very frequent impulses initiated by the shoulder - cf. this chapter point 4.3.