Quantum_ Einstein, Bohr and the Great Debate About the Nature of Reality - Manjit Kumar [140]
To accommodate uncertainty in the vertical displacement of the first screen, S1, requires an 'averaging' over all of its possible positions. This leads to interference somewhere between the extremes of total constructive and total destructive interference, resulting in a washed-out pattern on the photographic plate. Controlling the transfer of momentum from the particle to the first screen allows the trajectory of the particle through a slit in the second screen to be tracked; however, it destroys the interference pattern, argued Bohr. He concluded that Einstein's 'suggested control of momentum transfer would involve a latitude in the knowledge of the position of the diaphragm [S1] which would exclude the appearance of the interference phenomena in question'.45 Bohr had not only defended the uncertainty principle but also the belief that the wave and particle aspects of a microphysical object cannot both appear in a single experiment, imaginary or not.
Bohr's rebuttal rested on the assumption that controlling and measuring the momentum transferred to S1 accurately enough to determine the particle's direction afterwards results in an uncertainty in the position of S1. The reason for this, Bohr explained, lay in reading the scale on S1. To do so, it has to be illuminated, and that requires the scattering of photons from the screen and results in an uncontrollable transfer of momentum. This impedes the precise measurement of the momentum transferred from the particle to the screen as it passes through the slit. The only way to eliminate the impact of the photon is by not illuminating the scale at all, making it impossible to read. Bohr had resorted to employing the same concept of 'disturbance' that he had earlier criticised Heisenberg for using as an explanation of the origin of uncertainty in the microscope thought experiment.
There was another curious phenomenon associated with the two-slit experiment. If one of the two slits has a shutter that is closed, then the interference pattern disappears. Interference occurs only when both slits are open at the same time. But how was that possible? A particle can go through only one slit. How did the particle 'know' that the other slit was open or closed?
Figure 17: Two-slit experiment (a) with both slits open; (b) with one slit closed
Bohr had a ready answer. There was no such thing as a particle with a well-defined path. It was this lack of a definite trajectory that was behind the appearance of an interference pattern, even though it was particles, one at a time, which had passed through the two-slit set-up, and not waves. This quantum fuzziness enables a particle to 'sample' a variety of possible paths and so it 'knows' if one of the slits is open or closed. Whether it is open or not affects the particle's future path.
If detectors are placed in front of the two slits to sneak a look at which slit a particle is going to pass through, then it seems possible to close the other slit without affecting the particle's trajectory. When such a 'delayed-choice' experiment was later actually conducted, instead of an interference pattern there was an enlarged image of the slit. In trying to measure the position of the particle to establish through which slit it would pass, it is disturbed from its original course and the interference pattern fails to materialise.
The physicist has to choose, says Bohr, between 'either tracing the path of a particle or observing interference effects'.46 If one of the two slits of S2 is closed, then the physicist knows through which slit the particle passed before hitting the photographic plate, but there will be no interference pattern. Bohr argues that this choice allows an 'escape from the paradoxical necessity of concluding that the behaviour of an electron or a photon should depend on the presence of a slit in the diaphragm [S2] through which it could be proved not to pass'.47
The two-slit experiment was for Bohr 'a typical example' of the appearance of complementary phenomena under mutually