The quantum is the fundamental building block of physical reality, the basis of all physical existence. Everything is made of quanta. The quantum is a very peculiar thing which is what makes quantum theory so famously weird. Whenever physicists perform an experiment to measure exactly where a quantum is, it is found to be in a specific location, just as we would expect. But unobserved a quantum is nonetheless not in a specific position. It exists in a different form, as a spread-out wave; and the wave defining a single quantum, such as an electron, may be spread over inches, miles or even light-years. This is what we have discovered. This is the fundamental definition of physical reality.
The mathematical definition of the quantum is the ‘wave function’. This picture illustrates the wave function of a single quantum, passing through two very narrow slits in the black wall at the top of the image. The quantum could be a quantum of energy, such as a photon of light, or even a quantum of matter, such as an electron.
The wave function defines every possible position where the quantum could be found to be, if the position is measured. The wave is a wave of probability: the bigger the wave at any position, the greater the probability of the quantum being found to be there, if one looks. This wave is mathematically defined by the Schrödinger wave equation, discovered by Erwin Schrödinger in 1925. This is the foundation of quantum mechanics: the operational mechanics of the quantum. Reality is defined by probabilities.
This aspect of quantum theory is no longer theoretical. We know for sure that reality is indeed of this nature. It has been tested to greater degrees of accuracy than any other theory in scientific history, with 100% success. Experiments such as the well-known double-slit experiment, which is what is illustrated in the picture, are conclusive. Waves of probability of this nature are the basis of all physical reality. Strangely, therefore, as has often been noted, the fundamental stuff of reality is really non-stuff. So said Werner Heisenberg, who won the Nobel Prize in 1932 for the creation of quantum mechanics. He stated clearly that the elementary particles themselves, the quanta, are not real things in the same way as the phenomena of everyday life:
… they form a world of potentialities or possibilities rather than one of things or facts. (1962, 128)
Not just energy, but even the solid matter of reality behaves as a spread-out wave of this kind, except when observed. That is the first, thoroughly weird, bit of quantum theory. But then, the moment it is observed, the quantum is found to be a specific actuality, a ‘point particle’: a tiny particle of matter at a specific position. This is the second, equally weird part of quantum theory. It seems as if the spread-out wave of probabilities collapses to a tiny, specific actuality when an observation is made. The question of how this happens, why this happens, and even whether or not it does in fact happen, has been the subject of heated debate ever since the discovery of quantum theory nearly a hundred years ago. This is the measurement problem.
At first, the discovery of the collapse of the wave function was taken at face value. This formed the basis of the Copenhagen interpretation, developed by Niels Bohr with his team at Copenhagen University. Unobserved, reality is just waves of probability; but whenever the state of reality is measured, simply making an observation, the wave of probabilities collapses to a specific state of being. Thus reality is determinate, meaning defined as specific physical entities in specific states, when, and only when, one looks at it. As Bohr tartly commented:
Anyone who is not shocked by quantum theory has not understood it. (Gribbin, 1984, 5)
This explanation was not universally adopted because of the enormous absurdity of imagining that just by looking at something, one could possibly alter its physical state. How can just looking at reality cause the spread-out, amorphous nature of the wave function to suddenly collapse, and turn into the determinate state of a specific tiny physical entity, a point particle? So although this seemed to be what was happening, for many physicists this was not an acceptable concept. But no one could discover an alternative explanation that worked. The whole fundamental issue remained in limbo for decades. Then in 1957, Hugh Everett came up with the perfect solution, the many worlds interpretation. As explained in Many Worlds, his theory has been incomprehensible, but in the light of Logical Types it all makes perfect sense.