Absolutely Small - Michael D. Fayer [25]
Observation Causes a Nonnegligible Disturbance Causing a Change of State
What is going on? After the photon meets the beam splitter, it is in a superposition state, T1 + T2. However, photons are particles that are small in the absolute sense. The act of making an observation causes a nonnegligible disturbance. When we place the photodetector in leg 1 of the apparatus, we are making an observation of the location of the photon. The act of making the observation causes the system to jump from being in the superposition state T1 + T2 into either a pure state T1 or a pure state T2. The superposition wavefunction has been “collapsed” into one of the pure states that make up the superposition. If the system makes the jump into the state T1, the photon is detected. Of course, once it slams into the photodetector, it does not continue to propagate through the interferometer. If the photon jumps into the state T2, it is not detected with the photodetector that is located in leg 1, and it continues to propagate, eventually reaching the region in which the instrumentation is set up to observe the interference pattern. However, because the photon is in the pure state T2, there is only a single probability amplitude wave. When it reaches the “overlap” region (see the bottom of Figure 5.1), there is no other probability amplitude wave to interfere with. Therefore, no interference pattern is created. A single spot is formed as each photon that traverses the apparatus in the pure T2 state hits a single spot on the detector like a bullet aimed at that spot. The spot has the same size (diameter) as the initial light beam that entered the apparatus, but no spatially oscillatory interference pattern.
BACK TO SCHRÖDINGER’S CATS
Making the observation of the location of the photon with the photodetector in leg 1 of the interferometer causes the photon to jump from the mixed superposition state T1 + T2 into a pure state, either T1 or T2. However, on a single measurement it is not possible to know which state will be produced by the observation. The chance is 50/50 that it is in T1 and 50/50 that it is in T2. After many measurements, we know that the probability of making the jump to T1 is 50%, but it is impossible to say in advance what will happen for any single observation. This is a true physical manifestation of the issues raised with Schrödinger’s Cats in Chapter 1, where we had 1000 boxes with a cat in each one. Each cat was in a superposition state that was 50% alive and 50% dead. In this very nonphysical heuristic scenario, when a box is opened an observation is made as to the health of the cat. Sometimes the cat is perfectly healthy and sometimes the cat is dead. After opening all of the boxes, it was determined that the probability of finding a live cat was 50%, but there is no way of predicting ahead of time when opening a particular box, that is, on making a single observation, whether a live or dead cat will be found. Before opening the box, the cat is in a superposition state that is a 50/50 mixture of live and dead. The act of making the observation makes a nonnegligible disturbance and causes the superposition state to jump into either a pure live state or a pure dead state. As discussed in Chapter 1, a live/dead cat superposition state does not and cannot exist, but the interferometer is a real example of the ideas illustrated by Schrödinger’s Cats.
A photon can easily be placed into a superposition state consisting of a 50/50 mixture of two translations states using the 50% beam splitter. When it is in the superposition state, it is not possible to say whether the photon is in leg 1 or leg 2 of the apparatus. It is only possible to say that if we make a measurement to see where the photon is, the measurement will make a nonnegligible disturbance. The disturbance will cause the state of the system to change from having equal probability of being in the two legs of the interferometer