ON THE DOUBLE SLIT EXPERIMENT

ON THE DOUBLE SLIT EXPERIMENT

In this paper we give an account of the double slit experiment in the light of the views presented under the paper "A New Interpretation of Quantum Mechanics". The position and the momentum of a particle constitute the best known example of two conjugate modes. If a particle is observable in the position mode then it is not so in the momentum mode though that mode also "exists". In the Copenhagen interpretation if the position of a particle has been measured then the observer has a knowledge of the position but not of the momentum. When the momentum is measured, as far as the observer is concerned, the knowledge of the position is "washed out". In the new interpretation, it is not the knowledge of the "existence" of the position observable that is washed out, but the knowledge of the particular value of the position that had been measured.

According to the new interpretation the operation of making the photon passing through the slits is not an observation, and no "value" is given to the position of the photon, though we have a knowledge of the photon passing through both slits. However, when the photon is made to strike a screen, the new operation amounts to an observation (measurement). The photon is now "observed" at a particular point on the screen, represented in the position mode by an eigenvector of the position operator, it having interacted with the material on the screen. The photon strikes a position of the screen with a certain probability, and thousands of photons striking the screen would give rise to an interference pattern. When the photon strikes the screen, it is not the momentum of the photon that is measured but its position. The operation of making the photon to pass through two slits, and making it to strike the screen, are operations with respect to the momentum mode and position mode respectively, and are carried out one after the other changing the state of the photon.

The recent experiment by Shahirar S. Afshar as reported in the New Scientist of 24th July 2004, does not give us a knowledge of the slit through which the photon passed on its way to the detector. What is detected by any one of the detectors is a photon that has passed through both slits, with or without the wire mesh. The photon does not interact with the wire mesh as the probability of finding the photon at the points where the mesh happens to be is zero, and the placing of the mesh does not change the outcome of the experiment. After the photon passes through the two slits its position mode is represented as a linear combination of two eigenvectors and the situation is not changed as it passes the wire mesh. However, the photon interacts with the lens, and at the lens the position of the photon is detected. What is detected is the position of the photon at the detector, after the photon has passed through the slits, the wire mesh and interacted with the lens, and not the path of the photon. The experiment does not give us any knowledge of the particular slit through which the photon passed, as it has passed through both slits. However it could be detected at only one of the detectors and it is predicted that if the experiment is done with a single photon, then it would be detected only at one of the detectors and not at both detectors.

Instead of the wire mesh and the lens, if we have a single slit and then a screen, after the photon has passed through the two slits we predict that the photon would pass through the single slit with the same probability as that of finding the photon at the point where the slit is kept. If the slit is kept at a point where the probability of finding the photon is zero, the photon would not pass through the slit to strike the screen. Thus the photon would not be recorded on the screen. On the other hand, if the slit is kept at any other point there is a non zero probability that the photon would pass through the slit, and it would strike the screen. This implies that if a stream of photons is passed through the two slits, and then the single, to strike the screen, depending on the position of the single slit the intensity with which the photons strike the screen would change.

Suraj Chandana.

Department of Physics, University of Kelaniya, Kelaniya, Sri Lanka.

and

Nalin de Silva.

Department of Mathematics, University of Kelaniya, Kelaniya, Sri Lanka.