What is Quantum Mechanics? 

This week we learn some basics about one of the newest and most interesting fields of physics
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Physics describes the behavior of objects that span an enormous range of sizes, from everyday objects like cars to the tiny components of an atom to the largest galaxies. The physics that is useful to describe one set of objects might be too simplistic or unnecessarily complicated to describe another set of objects. Quantum mechanics is simply the physics used to describe the tiniest objects in our world, and it has some interesting features not found in classical mechanics or relativistic mechanics. Disclaimer: We will be discussing only the most orthodox conceptual understanding of quantum mechanics, termed the Copenhagen interpretation, but there are other interpretations as well.
The most striking aspect of quantum mechanics is that it is a non-deterministic theory, that is, we cannot always calculate exactly what will happen in the future based on the information we know in the present, as we can in classical mechanics. Instead, quantum mechanical calculations deal with probabilities. For example, a particle may have a 50% chance of being in London and a 50% chance of being in Paris. This does not mean that we simply don’t know where the particle is because we lack vital information, but rather that the particle really exists in both London and Paris, a situation termed quantum superposition. When the particle is observed in one location or the other, this observation collapses the superposition, and the particle then truly exists wherever we observed it to be. This non-determinism was incredibly controversial when quantum mechanics was being formulated, and was the inspiration for Schrodinger’s famous thought experiment concerning a cat that is simultaneously alive and dead, as well as Einstein’s supposed insistence that “God does not play dice with the universe”. A related concept is Heisenberg’s Uncertainty Principle, which states a specific relationship between the uncertainties associated with two related variables, like position and momentum. Essentially, the more exactly we know the position of a particle, the less exactly we know its momentum.
Because quantum mechanics is all about probabilities, physicists need a mathematical framework to convey information about all the relevant probabilities for the situation at hand. Wave mechanics is a natural choice, because early experiments showed that things physicists previously thought of as particles, like electrons, sometimes acted like waves, a concept called wave-particle duality. For example, electrons seem to travel through multiple holes in a wall instead of choosing one, and they can interfere with each other as water waves might. Luckily, wave phenomena had been very well studied prior to the advent of quantum mechanics. The most important equation in quantum mechanics, the Schrodinger equation, is based on previously studied wave equations, and describes the environment in which a particle exists. The solutions to this equation are called wave functions, and they describe the particle itself, making it easy to calculate how likely it is that the particle will be located in a particular position, or have a particular energy.
In order for the mathematics behind quantum mechanics to be consistent, there are often certain constraints, called boundary conditions, on these wave functions. Although seemingly a mathematical construct, these boundary conditions have physical consequences, as they result in certain properties of a system being quantized, hence the term “quantum” mechanics. For example, in quantum mechanics, a particle might only be allowed certain values of energy, whereas in classical mechanics a particle can have any energy within a certain range. Another example of quantization concerns the electrons in an atom, which are only located in particular shells and only have particular energies.
The world of sub-atomic particles is surprisingly different from our own, making a lot of familiar concepts like particles and waves useful only as metaphors. However, with the advent of quantum mechanics, physicists are able to describe and study the smallest parts of our world, even without fully visualizing them. Studying quantum mechanics is truly an exercise in humility and creative thinking, and we encourage everyone who is interested to seek out more information.