All we can do is use the wave function to calculate the probability that the next electron will be detected here, or there, or way over there.

Where will the next spot appear? We have no way of knowing in advance. Repeating this with more and more electrons will give us a diffraction pattern вЂ“ a pattern possible only with waves вЂ“ made up of a myriad of individual spots, each of which is possible only with particles. If we now allow this electron to impinge on a screen covered with a photographic emulsion, we will find that the electron is detected, leaving a single bright spot at a specific point on the screen. If we push an electron through a narrow aperture, we imagine that it will diffract, spreading out in all directions in the space beyond as a wave (think of what happens to a rolling ocean wave as it squeezes through a gap in a harbour wall).

What we might have previously judged to be physically impossible, quantum mechanics judges to be merely improbable, lending a fungible quality to reality, and challenging the truth of a universe defined by the physics that came before.ДЄnd hereвЂ™s the rub. It underpins a formula that assigns probabilities for any given electron existing in any one place at a particular point in time. It has obvious wave-like properties, but also obvious particle-like properties, such as mass. The wave function accommodates this odd duality. But in different (and mutually exclusive) circumstances, the behaviour can be understood only in terms of electrons moving and spreading out through space as unfamiliar, non-localised waves. Under certain circumstances, this behaviour can be described in terms of electrons as familiar self-contained particles, localised as they move through space. The wave function was introduced in the theory as a way of accounting for the surprising experimental behaviour exhibited by quantum entities such as electrons. At the heart of the debate was the interpretation of the theoryвЂ™s central concept вЂ“ a mathematical object called the wave function. The small community of quantum physicists in continental Europe formed into two distinct camps, and the Austrian-born British philosopher Karl Popper later called this divergence a schism. The debate became polarised around the philosophies of its two principal protagonists: Einstein and the Danish physicist Niels Bohr. Although there had been much discussion about the philosophical interpretation of some concepts that appear in the older theory that preceded it вЂ“ now called classical mechanics вЂ“ the nature and structure of the new quantum mechanics begged all kinds of difficult questions about the very purpose of a scientific theory, if not the purpose of science itself. As they struggled to comprehend what nature was trying to tell them, these pioneers understood only too well what they were getting themselves into. Quantum mechanics was discovered and developed largely by European physicists in the mid- to late 1920s. If you want to figure out how an electron will behave as it moves in time through space, then you need to reach for quantum mechanics. Mechanics is that part of physics concerned with stuff that moves, and quantum mechanics is the theory of the motion of matter and light at the smallest scales: the realm of molecules, atoms, subatomic particles (such as electrons), and photons, the quanta (or вЂatomsвЂ™) of light. These are quantum mechanics and Albert EinsteinвЂ™s theories of relativity. But as they explore the physics of the very fast, or of the very small, or as they ponder the large-scale structure of the Universe, they reach for younger theories that were established only a century ago. These are good enough for most practical purposes. For the most part, physicists are content to make use of foundational theories that have remained broadly unchanged for centuries. At root, physics as a discipline relies on foundational theories of space and time, and of matter and light. We rely on it to provide us with valid conceptions of the nature of the physical world and how it works, conceptions that underpin almost every aspect of our technologically advanced society.

Raspberry pi aeon labs z-stick