Quantum theory is the crown jewel of modern science. It is the basis of much of modern technology, such as the semiconductor p-n junction, of which digital computers are the most important result. Quantum theory also led to the development of nuclear reactors (and nuclear weapons), lasers, and magnetic resonance imaging (MRI). In basic science, quantum theory is the foundation for the study of fundamental particles, nuclei, atoms, molecules, solids, light, and the interaction of these systems. The chemistry of simple molecules can be quantitatively predicted using quantum theory, and the behavior of more complicated systems, consisting of hundreds of atoms, can be understood qualitatively by applying the theory. Quantum theory explains many observations for which classical physics (physics as it existed before relativity theory and quantum theory) is an utter failure at providing either qualitative or quantitative explanations.
In the early 20th century, quantum theory began humbly as a somewhat contrived way of explaining the colors of light emitted by heated materials. In the span of thirty years or so (see George Gamow's book, Thirty Years That Shook Physics), the theory was made mathematically rigorous and achieved the enormous successes stated above. And yet, even in the 21st century, many who have studied it in-depth, are disturbed by this eminently successful theory of the way the world works at its very roots. There is indeed something very strange and troubling about what the quantum theory appears to imply. To cut to the heart of the problem, quantum theory seems to say that the physical properties which we can measure for the basic particles, of which everything is made, don't really exist. That is, a given property of an electron, such as its position, velocity, energy, etc. is not physically real until that property is measured. For example, an electron does not have a position until we ask it, by performing a measurement, to tell us its position. The electron then obliges and gives us its position through the reading of our instrument. Quantum theory can tell us, under a carefully prepared experiment, what the probabilities are for different results. By applying the theory, we can predict the probability that the electron will tell us, through the instrument, that it is located in a particular region in space. But, in general, it can tell us nothing more than these probabilities. Quantum theory cannot tell us exactly what result we would obtain for our measurement! Quantum theory predicts probabilities of outcomes for measurements, not the actual results! It is this distinction with classical physics that sowed the seeds of the physicists' angst.
Prior to John Bell and his famous theorem of 1964, most physicists
would have dismissed the following question: