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.

If you have trouble getting around this, you are not the only one. You can always try the simpler version. But this one is better.

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. As if that were not bad enough, it is impossible to measure simultaneously where they are and how fast they are moving (or how much energy they possess and when). This last 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 conserved1)In spite of the first law 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

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 is not deterministic, 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 those allowed values are not allowed. Such allowed values are called quanta and 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 in such a way that no two of them can 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.

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. In spite of the first law of thermodynamics.

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