• Choose a category
• All
• Classic-Fiction

Einstein reduced the intensity of a beam until only one particle at a time passed through the slit in the first screen, S1, and one of the two slits of the second screen, S2, before hitting the photographic plate. As each particle left an indelible mark where it hit the plate, something remarkable would happen. What initially appeared to be a random sprinkling of specks was slowly transformed, as more and more particles left their imprint, by the laws of statistics into the characteristic interference pattern of light and dark bands. While each particle was responsible for only a single mark, it nevertheless contributed decisively through some statistical imperative to the overall interference pattern.

By controlling and measuring the transfer of momentum between the particle and the first screen it was possible, said Einstein, to determine if the particle was deflected towards the upper or lower slit in the second screen. From where it hit the photographic plate and the movement of the first screen, it was possible to trace through which of the two slits the particle had passed. It appeared that Einstein had devised an experiment in which it was possible to simultaneously determine the position and momentum of a particle with a greater precision than the uncertainty principle allowed. In the process he also seemed to have contradicted another fundamental tenet of the Copenhagen interpretation. Bohr's framework of complementarity posited that either particle-like or wave-like properties of an electron or a photon could be manifest in any given experiment.

There had to be a flaw in Einstein's argument, and Bohr set out to find it by sketching the sort of equipment needed to conduct the experiment. The apparatus he focused on was the first screen. Bohr realised that the control and measurement of the transfer of momentum between the particle and screen hinged on the screen's ability to move vertically. It is the observation of the screen moving either up or down as the particle passes through the slit that allows the determination of whether it passes through either the upper or lower slit in the second screen, after it strikes the photographic plate.

Einstein, despite his years at the Swiss Patent Office, had not considered the details of the experiment. Bohr knew that the quantum devil lay in the details. He replaced the first screen with one hanging by a pair of springs fixed to a supporting frame so that its vertical motion due to the transfer of momentum from a particle passing through the slit could be measured. The measuring device was simple: a pointer attached to the supporting frame and a scale engraved on the screen itself. It was crude, but sensitive enough to allow the observation of any individual interaction between screen and particle in an imaginary experiment.

Figure 16: Bohr's design of a moveable first screen

Bohr argued that if the screen was already moving with an unknown velocity greater than any due to an interaction with a particle as it passed through the slit, then it would be impossible to ascertain the degree of momentum transfer and with it the trajectory of the particle. On the other hand, if it was possible to control and measure the transfer of momentum from particle to screen, the uncertainty principle implied a simultaneous uncertainty in the position of the screen and slit. However precise the measurement of the screen's vertical momentum, it was strictly matched, in accordance with the uncertainty principle, by a corresponding imprecision in the measurement of its vertical position.

Bohr went on to argue that the uncertainty in the position of the first screen destroys the interference pattern. For example, D on the photographic plate is a point of destructive interference, a dark spot in the interference pattern. A vertical displacement of the first screen would result in a change in the length of the two paths ABD and ACD. If the new lengths differed by half a wavelength, then instead of destructive interference there would be