Popper's Experiment - Popper's Proposed Experiment

Popper's Proposed Experiment

Popper first proposed an experiment that would test indeterminacy in Quantum Mechanics in two works of 1934. However, Einstein wrote a letter to Popper about the experiment in which he raised some crucial objections, causing Popper to admit that his initial idea was "based on a mistake". In the 1950s he returned to the subject and formulated this later experiment, which was finally published in 1982.

Popper wrote:

I wish to suggest a crucial experiment to test whether knowledge alone is sufficient to create 'uncertainty' and, with it, scatter (as is contended under the Copenhagen interpretation), or whether it is the physical situation that is responsible for the scatter.

Popper's proposed experiment consists of a low-intensity source of particles that can generate pairs of particles traveling to the left and to the right along the x-axis. The beam's low intensity is "so that the probability is high that two particles recorded at the same time on the left and on the right are those which have actually interacted before emission."

There are two slits, one each in the paths of the two particles. Behind the slits are semicircular arrays of counters which can detect the particles after they pass through the slits (see Fig. 1). "These counters are coincident counters that they only detect particles that have passed at the same time through A and B."

Popper argued that because the slits localize the particles to a narrow region along the y-axis, from the uncertainty principle they experience large uncertainties in the y-components of their momenta. This larger spread in the momentum will show up as particles being detected even at positions that lie outside the regions where particles would normally reach based on their initial momentum spread.

Popper suggests that we count the particles in coincidence, i.e., we count only those particles behind slit B, whose partner has gone through slit A. Particles which are not able to pass through slit A are ignored.

The Heisenberg scatter for both the beams of particles going to the right and to the left, is tested "by making the two slits A and B wider or narrower. If the slits are narrower, then counters should come into play which are higher up and lower down, seen from the slits. The coming into play of these counters is indicative of the wider scattering angles which go with a narrower slit, according to the Heisenberg relations."

Now the slit at A is made very small and the slit at B very wide. Popper wrote that, according to the EPR argument, we have measured position "y" for both particles (the one passing through A and the one passing through B) with the precision, and not just for particle passing through slit A. This is because from the initial entangled EPR state we can calculate the position of the particle 2, once the position of particle 1 is known, with approximately the same precision. We can do this, argues Popper, even though slit B is wide open.

Therefore, Popper states that "fairly precise "knowledge"" about the y position of particle 2 is made; its y position is measured indirectly. And since it is, according to the Copenhagen interpretation, our knowledge which is described by the theory – and especially by the Heisenberg relations — it should be expected that the momentum of particle 2 scatters as much as that of particle 1, even though the slit A is much narrower than the widely opened slit at B.

Now the scatter can, in principle, be tested with the help of the counters. If the Copenhagen interpretation is correct, then such counters on the far side of B that are indicative of a wide scatter (and of a narrow slit) should now count coincidences: counters that did not count any particles before the slit A was narrowed.

To sum up: if the Copenhagen interpretation is correct, then any increase in the precision in the measurement of our mere knowledge of the particles going through slit B should increase their scatter.

Popper was inclined to believe that the test would decide against the Copenhagen interpretation, as it is applied to Heisenberg's uncertainty principle. If the test decided in favor of the Copenhagen interpretation, Popper argued, it could be interpreted as indicative of action at a distance.