# Quantum mechanics

Quantum mechanics is the theory of what happens at very small dimensions, on the order of 10-30 meters or less! It is therefore the theory which must be used in order to understand atoms and elementary particles.

According to quantum mechanics, what is “out there” is a vast amount of space – not an empty backdrop, but actually something. This space is filled with particles so small that the distance between them is huge compared to their own sizes. Not only that, but they are waves, or something else which acts sometimes like waves and sometimes like particles. The modern interpretation of this is in terms of fields, things which have a value (and perhaps a direction) at every point in space. “Every particle and every wave in the Universe is simply an excitation of a quantum field that is defined over all space and time.1Blundell, 1.

Nobody can actually measure simultaneously where a particle is and how fast it is moving (or how much energy it possesses and when). This effect is referred to as indeterminacy, or the Uncertainty Principle, one of the more uncomfortable and, simultaneously, fruitful results of the theory.

As a result of this indeterminacy, energy need not be conserved, regardless of thermodynamics, for very short periods of time, giving rise to all sorts of unexpected phenomena, such as radiation from black holes. But that is another subject.

Time-dependant non-relativistic Schrödinger equation from Wikipedia

QM is explained by a mathematical formalism based on an equation, generally referred to as the Schrödinger equation, although it exists in several forms (differential, matrix, bra-ket, tensor). The solution to this equation is called the wave function, represented by the Greek letter ψ. The wave function serves to predict the probability that the system under study be in a given state. It gives only a probability for the state. (In fact, the probability is not the wave function itself, but its complex square.) This knowledge only of probabilities really irks some people and nobody really understands what it means (dixit Richard Feynman, one of the greatest of quantum theorists). But the mathematics works.

According to QM, some parameters of a system, such as energy or wavelength, can only take on certain values; any values in between are not allowed. Such allowed values are called eigenvalues. The eigenvalues are separated by minimal “distances” called quanta and the system is said to be quantized. We will see a good example of them when we look at atomic structure.

An important result of QM is that certain particles known as fermions are constrained so that two of them can never occupy the same QM state. This phenomenon, called the Exclusion Principle, is at the root of solid-state physics and therefore of the existence of transistors and all the technologies dependent thereupon – portable computers, mobile telephones, space exploration and the Internet, just as to mention a few examples. So QM has indeed revolutionized modern life, for the better and for the worse.

The exclusion principle is also responsible for the fact that electrons in a collapsing super-dense star cannot all be in the same state, so there is a pressure effectively keeping them from being compressed any further. We will read more about that in the cosmology chapter. Closer to home, fermions constitute matter, including us.

An important subject of study and discussion in current theoretical physics is the interpretation of QM, such as in the many-worlds hypothesis, but that subject is beyond the scope of this article.

Go on to read about relativity, because it’s probably not what you thought it was.

Notes

↑1 Blundell, 1.