FOUNDATIONS OF QUANTUM MECHANICS

94 CHAPTER IV. THE COPENHAGEN INTERPRETATION
Using an interferometer with three upstanding teeth, a monochromatic beam of neutrons with
a de Broglie wavelength of approximately 1 Å now hits the first tooth of this crystal. The crystal
lattice acts like a grid and lets the beam pass in very sharply defined directions. Under suitable
conditions there are exactly two emanating beams, one transmitted (T) and one reflected (R), as
shown in figure IV. 5 a.
At the second tooth this process is repeated, and both beams are again split up. Two of them are
now outside the interferometer where they are screened, no longer participating. The remaining two
beams are bent towards each other and meet at the third tooth. Here, both beams are split up again,
and now the straightforward going beam of one path is superimposed on the reflected beam of the
other path. Neutron detectors are placed in both emanating beams.
T
T
2
R
A
R
1
R
B
T
a) A sketch of the setup b) The experimental results
(Rauch and Werner 2000 )
Figure IV. 5: The interference pattern in the neutron interferometer is acquired by measuring the
intensity in the detectors at a variable optical path length difference.
If the incoming beam comes from below, and the beams are not manipulated, all neutrons turn out
to end up in the upper beam at detector A, undergoing constructive interference, while the neutrons
in the lower beam extinguish each other. For this phenomenon it is essential that the interferometer
consists of only one crystal, for in that case the waves remain coherent even though, along the way,
the beams have been separated by ‘macroscopic distances’, approximately 5 cm or ≃ 10 9 λ. When a
neutron has arrived in a detector it can have traveled along one of both paths.
Upon introducing a phase difference between the two paths by sliding a small piece of aluminium
of variable thickness in one of the paths, the intensity shifts from the upper to the lower detector. This
intensity is a periodic function of the thickness of the piece of aluminium, see figure IV. 5 b. This is
the interference pattern.
Now the question is if we can, in some way, uncover along which path the particle has traveled.
Following Bohr’s line of thought this should be possible by sawing off one of the teeth and measuring
the recoil it receives of the neutron. Such an experiment can, however, not be carried out with the
required experimental exactitude.
Another option is to make use of the fact that the neutron is a spin 1/2 particle and therefore has
an internal degree of freedom. We can carry out such an experiment with a polarized beam, where