Beam splitters can be classified according to the mechanism used to split the incident light beam. As shown in Figure 127a, some beam splitters are made by depositing reflective elements over a transparent substrate. The reflective elements could be fully reflective mirrors arranged in a polka-dot pattern or fine metallic particles dispersed in a random manner. In these beam splitters, at least in theory, a photon hitting the exact same point on the beam splitter will always do the same thing (either be transmitted or reflected).
Figure 127 There are two basic techniques used in beam splitters to divide an incident beam. (a) Reflective elements are dispersed over a transparent surface, separating photons based on their location within the incident beam. (b) True quantum beamsplitting through a purely statistical process.
On the other hand, cube beam splitters cause photons to be transmitted or reflected completely at random. Even if the same exact spot is hit every time, the photons will randomly transmit or reflect. This begs the question: what is the mechanism that randomizes the direction that the photons will take when they encounter the beam splitter?
As we discussed before, Einstein, de Broglie, and Schrödinger absolutely abhorred the idea that randomness would still be expected with enough information about the system. So, who is flipping the coin when a photon hits the beam splitter?
One theory that Einstein and de Broglie had proposed to resolve this type of problem is that the photon would somehow be born “preprogrammed” on how to behave when it encounters a beam splitter. The “program” would be completely hidden from our view, so this idea falls within the category of hidden-variables theory, about which we will talk widely.
To explore why a simple beam splitter is such an interesting component to physicists, set up three beam splitters as shown in Figure 128. Here, photons are split by a first beam splitter and then again by two other beam splitters, forming four possible paths: TT (transmitted and transmitted again), TR (transmitted and then reflected), RT (reflected and then transmitted), and RR (reflected and reflected again). Now, let’s suppose that we follow Einstein’s thought and assume that the photons are preprogrammed when they are “born” within the laser to either always transmit or always reflect when encountering a beam splitter. In that case, a T photon coming out of beam splitter 1 would always be transmitted when encountering a beam splitter, so it would exit through TT from beam splitter 2. On the other hand, an R photon coming out of beam splitter 1 would be preprogrammed to always reflect at a beam splitter, so it would have to come out of RR when encountering beam splitter 3. There would never be any photons coming out of TR or RT.
Figure 128 Setting up three beam splitters as shown in this figure defines four possible paths for the photons. T photons exiting beam splitter 1 are split again by beam splitter 2 into TT (transmitted and then transmitted) photons and TR (transmitted and then reflected) photons. R photons exiting beam splitter 1 are also split again by beam splitter 2 into RT and RR photons. If the photons were preprogrammed to always reflect or always transmit when encountering a beam splitter, then we would see photons exiting only at RR and TT but not at RT nor at TR.
Go ahead—run the experiment by looking at the intensity of the four exit beams. You should find that they are all approximately the same, demonstrating that photons are not preprogrammed at birth—at least as far as behavior when encountering a beam splitter. You should find that a photon has a 25% probability of exiting at any given output: 25% for TT, 25% for TR, 25% for RT, and 25% for RR. This simple experiment does not support a hidden-variables theory, and indicates that the “coin flipping” takes place somewhere else within the system to randomize the direction a photon will take when going through a cube beam splitter.
This is a very simple experiment, and you may think it trivial. However, as we will discuss the question of the existence of hidden variables is at the core of one of the most intriguing properties of quantum mechanics.
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