• Choose a category
• All
• Classic-Fiction

By Root 400 0

chance of being in leg 2 (T2). The Born interpretation of the wavefunction states that the wave is not a real wave in the sense of the amplitude of an oscillating electromagnetic field. Rather, the wavefunction describes a “probability amplitude wave.” The incorrect interpretation of the wavefunction in terms of photons is that it tells how many photons are in each leg of the apparatus, that is, how many photons are in a region of space. The correct interpretation is that the wavefunction is related to the probability of finding a photon in a region of space. The difference between the incorrect and correct interpretation may not seem like a major difference, but, as shown in detail below, it is a fundamental change in our view of nature. In the classical description of light, the intensity is proportional to the absolute value squared of the amplitude of the electric field, which in turn was given by the amplitude of the wavefunction. In the Born interpretation, the absolute value squared of the wavefunction for a certain region of space gives the probability of finding a particle, in this case a photon, in that region of space.

A PHOTON INTERFERES WITH ITSELF

When the photon meets the beam splitter, two probability amplitude waves are created, one in leg 1 and one in leg 2. The total probability amplitude wave T is the superposition of the probability amplitude waves T1 and T2. After encountering the beam splitter, each and every photon is in a state T1 + T2. Because there are two probability amplitude waves after the beam splitter, they cross in the overlap region. A single photon inside the interferometer has two waves, T1 and T2, associated with it. The interference of these two waves determines the probability of finding a photon near the peak, which is high, and finding a photon near the null, which is low. A photon interferes with itself because it is composed of two waves in the interferometer, and two waves can interfere with each other. Because every single photon is placed in the T1 + T2 superposition state after meeting the beam splitter, there is no problem with turning down the intensity. A single photon entering the apparatus produces two waves, probability amplitude waves, in the interferometer. Therefore, there is always a pair of waves to produce an interference pattern.

A PHOTON CAN BE IN TWO PLACES AT ONCE

The first natural response of a classical thinker to the Born interpretation is “this is nuts.” Are we really to believe that a single photon can be in two places at once? After meeting the beam splitter, the state that is produced is T1 + T2. The state T1 + T2 means that in some sense the photon is simultaneously in both legs of the apparatus. If this is true, why don’t we just make some measurements to see where the photon is? It doesn’t do much good to make the measurement with trillions of photons going into the apparatus. If we put an instrument in leg 1 to see how much light there is, we will find half of the light. However, that doesn’t tell us what we want to know. Maybe half of the photons go in each leg and we see half, or maybe there is a 50% chance that each photon goes into each leg. We will still see half. The correct experiment is to use such low-intensity light so that only one photon is in the apparatus at a time.

Consider the experiment in which we shoot one photon at a time into the interferometer. We use a photodetector that is so sensitive that it can detect a single photon. This is readily doable with the scientific equivalent of a superdigital camera. We place the detector in leg 1 of the interferometer. A photon enters the apparatus, and we detect it. We see an entire photon. We don’t see half a photon. Another photon goes in the apparatus, and we don’t see a photon. Five more photons enter the apparatus. We detect two of them and do not detect the other three. After doing this for a long time, it is found that 50% of the photons are observed by the detector placed in leg 1 of the apparatus. We also find that no interference pattern was produced. In fact, what