Gaining any level of understanding of quantum mechanics is one of the great intellectual challenges in science. In a quantum world of indeterminism and probability, uncertainty and fuzziness, phenomena completely unseen in our everyday lives are the norm for atoms and particles.
At the center of the strangeness is particle-wave duality, the notion that particles can at times act like ‘solid’ balls, but in different circumstances can behave like a wave. Likewise, something we normally think of as a wave, such as light, can certainly act like a wave under certain conditions, but in quantum mechanics light can also behave like particles we refer to as photons. In fact, a favorite question I pose to students is, ‘When light is traveling from a light bulb to your eye, is it a particle or wave?’ Ultimately, someone will offer the answer, ‘It is both!’ That is an acceptable answer; but what does this mean? How can an ‘object’ be two things simultaneously, which is what the answer ‘both’ implies.
No one is comfortable with this answer, and yet it fits in with the foundational principles of quantum mechanics. The reason is, in the mathematics of quantum mechanics, objects are described with a wave function. This is a mathematical function that encompasses possible states the object can take. So a photon that is moving through space can be thought of as a combination of two states, something like Photon = [particle state] + [wave state]. More specifically, this function can be used to determine the probability of finding the photon in a particle or wave state.
But I think most of us still come back to the same questions: How do we interpret this mathematical nonsense? What does this mean for the object? This is where an analogy comes in handy, that will perhaps put this probabilistic concept into a more understandable context.
If I am talking about this in a class, I ask students to look around at each other and identify the personality snapshot of each of their classmates. This means to identify who is happy, sad, confused, angry, sarcastic, sleepy, bored, or anything else. So while there are numerous possible ‘personality states’ any person can have, while observing a person we can select one personality state at that time because we are interacting with them. However, what do we do when the bell rings and everyone goes on their way? If I ask someone to identify which personality state a specific person is in when they are no longer available for observation or interaction, what is the answer? The best we can do is to effectively guess…but to do this mathematically, we would acknowledge that at any given moment when a person is not being observed in any way, we cannot be certain about the personality state and can only try to identify the probability of that person being in each state. Perhaps there is a 20% chance she is happy, and 25% chance of being sad, and so on for each possible personality state.
This is the way we think about particles and waves when those entities are not being observed. When we do observe the entity, the act of observing selects out the personality from the mix of possible personalities. Another way of saying it is the experiment we do selects out a single observable state that we then identify. For a person, maybe it is the ‘happy’ state that becomes crystallized out of the ‘personality state’ function that includes all the possible personality states. For an electron, if we put it through a diffraction grating the wave personality is selected, whereas if we shoot it at an atom and it is deflected, the particle personality was selected instead.
Thinking this way is not necessarily normal, obvious or instinctive, but it is something we can try to understand the way the quantum world works. Of course, in real quantum mechanical problems, the mathematics becomes very hard very fast, but trying to find more concrete ways of thinking about the consequences of probabilistic concepts can only help the student to whom this is all new.