Towards the end of the nineteenth century it began to become increasingly evident that classical physics (a system based on deterministic Newtonian mechanics) could not explain a diverse range of experimental observations which were beginning to be made on very small objects (including atoms and their constituent "fundamental" particle components).
The work of Max Planck, Erwin Schrodinger, Werner Heisenberg, Neils Bohr, Paul Dirac and Enrico Fermi amongst others in the 1920s and the 1930s led to the development of a new and revolutionary theory which became known as "Quantum Mechanics".
The new theory was completely successful in that it was able to account for existing observations - as well as predict new phenomenon - with remarkable accuracy. However, with bizarre new concepts being involved (e.g. Heisenberg's Uncertainty Principle - which states that it is physically impossible in principle to obtain complete information about the position and momentum of a given particle at the same time) many philosophical questions were raised by quantum mechanics - which appears to completely overturn the basic notions of mechanistic determinism and "cause and effect" as "built in" to the previously established classical physics and our intuitive understanding of the everyday world.
Many older physicists were reluctant to believe that quantum mechanics was in fact a correct description of nature, and even intellectual giants such as Albert Einstein (whose Nobel prize winning explanation of the photoelectric effect in 1905 ironically gave significant impetus to the development of the new theory) found the ideas involved very difficult to accept.
Theoretical arguments called "thought experiments" were thus devised to show up the apparant contradictions in the theory: These included the infamous "Schrodinger's Cat" scenario (a situation in which quantum mechanics decrees that a cat in an unopened box can be considered to be both dead and alive at the same time), and the "EPR [Einstein -Podolsky - Rosen] Paradox" (in which a process known as "entanglement" highlights a contradiction with relativity, invoking the notion of what Einstein called "spooky action at a distance"). However, despite such determined attempts by some of the greatest thinkers of our time, no arguments have yet proved powerful enough to falsify the so far incontravertable body of evidence which shows that when applied to objects at the subatomic level the theory of quantum mechanics works perfectly and has been extensively tested by experiment in situations where the predictions of classical physics fail!
Furthermore, it should be realised that the laws of classical physics can actually be derived from quantum mechanics by considering how the theory works at a larger scale (the so called "correspondence principle"). In view of this it seems likely that our problems in "understanding" quantum mechanics actually stem from our own cognitive prejudices (in that all our experiences are based on observations of the macroscopic and apparantly deterministic world where "common sense" classical physics approximates, rather than the underlying microscopic quantum mechanical world from which it is all composed).
In otherwords, things really are a lot stranger than we could ever imagine them to be!
Despite obvious philosophical difficulties with the interpretation of the theory, practical application of quantum mechanics is directly responsible for many of the innovations on which our modern world has been built (e.g. semiconductors, microelectronics and microcomputers, lasers and superconductors etc). Furthermore, through the work of Richard Feynman and others, quantum mechanics has been used to develop detailed "quantum field theories" (including quantum electrodynamics [QED] and quantum chromodynamics [QCD] - which describe the electromagnetic and strong force interactions respectively). QED in particular has been experimentally tested to incredible precision, and along with other components of a so-called "Standard Model" has been instrumental in developing our understanding how the fundamental forces of nature work, leading to important progress in the subject of high energy particle physics and towards mooted "Grand Unified Theories" and a (hoped for) final "Theory of Everything"..
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