Interference, recoil, and uncontrollable interaction

When the initial state in a collision involves indeterminate momenta, the conservation law for momentum no longer applies to the individual event with a sharpness beyond the indeterminacy. As a consequence, there are collisions that are recoilless in the sense that the state of one of the quanta is unchanged by the collision while the other quantum emerges in a superposition of momenta. Recoilless collisions that avoid entanglement are basic for experiments studying coherence effects for individual quanta involving interactions of the quantum with reflectors or diaphragms. The idea that in interference experiments there is an inevitable recoil that can be made unobservable by firmly bolting the reflector or diaphragm to a solid support is false since in interference with individual quanta there $\mathit{is}$ no recoil to control. The highly quantal character of the reflector or diaphragm in the interference experiment apparently went unnoticed in the conception of complementarity.

Figure 1

Partial reflector (see Sec. 2a). The source is denoted by $S$, the partial reflector by $A$, and the detection area is at $D$. The partial reflector is free to move and is initially in a wave packet [see (3)].

Figure 2

Diaphragm with aperture (see Sec. 2b). The coordinate axes are indicated, and the horizontal broken line is the $z$ axis $(x=0)$. The source is at large (negative) $z$ values, the diaphragm, which is free to move, is initially in a wave packet [similar to (3)] centered on $x=y=z=0$, and the area of detection is at $z=L$. The width $a$ of the aperture in the $x$ direction is much smaller than the width in the $y$ direction. On the figure the center of the aperture of the diaphragm is displaced to a positive $x$ value as an indication that the position of the diaphragm is indeterminate with indeterminacy $b$. The width $a$ of the aperture can be larger or smaller than $b$. Two secondary waves emerging from the center of the aperture are indicated.