Double slit experiments and the root of quantum weirdness
You are probably familiar with the legendary double slit experiment. It is a simple, straight-forward experiment that introduces the wave-particle duality and the weirdness that is at the foundation of quantum mechanics. Many people read or hear about the generic double slit experiment and assume that it is the end of the story. Worse, many intrinsically curious people erroneously assume that this phenomenon is understood. Or, they believe that they have a benign explanation for a particular experimental result. Hence, they don’t dig deeper into the challenge and excitement that can be found in the quantum world. Digging through the layers of experimental results helps ensure we are questioning the implications of our hypothesis, and testing whether it remains consistent and valid.
In the typical double slit experiment, a beam of light is directed at a pair of slits in a wall. The resultant interference pattern is then observed on a screen or some other sort of detector. You can see a five-minute introduction to the double slit experiment by Dr. Quantum: “Double Slit Experiment”. Photons are typically used, although according to de Broglie and confirmed by Davisson and Germer, electrons or any other particle will work. Using photons greatly simplifies the technical difficulties and cost of the experiment.
The experimental apparatus consists of a coherent light source, a wall with two narrow slits (the width and separation of the slits are comparable to the wavelength of the light), and a detection screen behind the wall. A narrow beam of light strikes the pair of slits. The pattern on the detection screen is an interference pattern. So what, light is a wave. Or, at least it acts that way sometimes. We can easily calculate the details of the interference pattern using the dimensions of the experimental setup and the frequency of the light. The two different paths, (source – slit A – screen; or source – slit B – screen), have different path lengths. Hence, the two interfering waves have different phases and can add constructively or destructively.
Doubling the dosage of quantum weirdness
The rub comes in when you dial down the intensity of the beam of light so that only one photon at a time is passing through the slits. One photon can’t pass through both slits, right? It can’t interfere with itself, right? Well, the interference pattern is still there. Quantum mechanics tells us that the photon is in a superposition of states. See Feynman’s QED: The Strange Theory of Light and Matter (Princeton Science Library) or Cox and Forshaw’s The Quantum Universe: (And Why Anything That Can Happen, Does)for excellent conceptual descriptions of how to visualize what the particle is up to.
I can contemplate how a single “particle” can act like a wave sometimes, a particle other times, or some combination thereof. I can do that without feeling like I am losing my grip on reality. But, here is where things start to get really weird. If you modify the above experiment so that you can tell which slit the photon traveled through, the interference pattern goes away. It is as if each photon realizes they are being watched and stops their shenanigans. But how do they “know” they are being watched? How do they know that it is time for “wave function collapse”? In wave function collapse, the photon discards the superposition of states and selects a specific value or path (a specific eigenstate).
The quantum measurement problem
This is the crux of the “quantum measurement problem”: Why are there two different processes describing the evolution of a particle’s wave function? These two processes are (1) the continuous evolution described by Schrödinger’s equation, and (2) the spontaneous collapse into a specific eigenstate. What triggers the collapse? Why can’t we observe a superposition or the collapse process? How can a wave function that is spread out over arbitrary distances collapse seemingly instantaneously? Some scientists have argued that wave function collapse is triggered by an interaction between the observer and the photon, or between the measurement apparatus and the photon. For example, the momentum that is imparted to the photon by the act of measurement may break the superposition. The problem with this argument, however, is that clever experimentalists have already devised and carried out experiments using interaction-free measurements.
Now for some truly bizarre quantum weirdness
If you have followed the discussion so far, it is still not safe to unfasten your seatbelt and start walking about the cabin. This is the point where I start to feel my grip on reality slipping away. Particles are doing something we completely do not understand, in apparent response to some trigger we completely do not understand. Consider “delayed choice” experiments and “quantum eraser” experiments. In delayed choice experiments, the decision to determine which path the photon used is made well after the photon has passed the slits*. Yet, the results seem to indicate that the photon has retroactively collapsed its wave function and chosen a single path. If you mark through which slit each photon went, the interference pattern is destroyed. This happens even if you mark the path without disturbing the photons movement. In quantum eraser experiments, photons are tagged based on which path they took. By itself, that tagging destroys the interference pattern. However, when this path information is discarded (erased), the interference pattern is restored.
This begs the following questions: What happens to the discarded part of the wave function when wave function collapse occurs? Some people argue that the wave function is not real, it just encodes our knowledge of the situation. But when the tagging is erased, how does the quantum system “know” what superposition to re-enter?
“Delayed choice quantum eraser” experiments combine all of the absurdities of the above experiments. This experiment is arranged to identify which one of the paths the photon uses. And, this information can be erased after the fact. See the adjacent figure from Wikipedia. Photons are emitted one at a time from the lower-left and then subjected to a 50% beam splitter. After the beam splitter (green block), photons travel along two possible paths, the red or blue lines. Reminds me of a Tokyo subway map. In the top diagram, the trajectory of each photon is known. If a photon emerges at the top of the apparatus, it appears to have come by the blue path. If it emerges at the side of the apparatus, it appears to have come by the red path. As shown in the bottom diagram, a second beam splitter is introduced at the top right. This can direct either beam towards either path, erasing the which-path information. So, the decision whether or not to remove the path information is made after-the-fact. If you remove the path information, the interference pattern is restored. The photon appears to recover its superposition properties.
Mind-blowing quantum paradoxes
Indeed, quantum physics is rich with paradoxes and non-intuitive behaviors. While contemplating a certain experiment, it is important to ensure you have a complete picture of what the theorists and experimentalists are trying to tell us. By merely considering one particular experiment, it is possible to convince yourself that you understand what is happening. But, other experiments may contradict or invalidate your conceptual line of reasoning. It seems to me that there is some deep, underlying concept or unifying principle that we are missing. Some key piece of the puzzle that will show us that superposition and entanglement are fundamental, and apparently not constrained by space and time. There must be some (comprehensible) reason for why matter behaves like this.* Many experiments use alternative path-separation devices, such as mirrors or beam splitters. Additionally, different techniques have been used to “tag” specific paths or to detect the photons. The math and the concepts are the same in these various setups. Different arrangements help to clarify the results and resolve concerns over subtle technical issues.
"The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them." - Albert Einstein