Robert Hooke and Christiaan Huygens begun working on a wave theory of light in the 1670s, this was reliant on the idea that light waves must propagate through a medium and so the void between the Sun and the Earth must be filled with an aether. In 1704 Newton suggested a corpuscular (particle) theory of light and presented experimental results proving his theory. Newton's corpuscular theory suggested that light would travel faster in a denser medium, something which was denied by the wave theory of light and so it was possible to experimentally verify Newton's result. It was not possible to do these experiments until 1850 and Foucault's results proved Newton wrong. Thomas Young and Augustin-Jean Fresnel had already provided experimental evidence in favour of the wave theory of light at the turn of the 19th century. Their famous double-slit experiments showed that light produced interference patterns which are expected from waves and Young went on to explain Newton's results in terms of his wave theory.
Towards the end of the 1800s Maxwell proposed that light could be understood as the propagation of electromagnetic waves; at any point on a beam of light there is an electric and a magnetic force moving perpendicularly to each other in the direction of the beams propagation. These force fields oscillate periodically and are therefore detected as waves. Maxwell showed this by verifying a set of four equations which describe the interrelationship between electric field, magnetic field, electric charge, and electric current.
Max Planck first introduced the concept of quanta in 1900, this reintroduced a corpuscular theory of light. Planck was looking at the relationship between the amount of radiation a blackbody emits and its temperature and he found that the experimental data only made sense if it was assumed that energy radiates in discrete 'quanta', or photons, each containing a packet of energy proportional to the frequency with which they radiate. This proportionality constant is known as Planck's constant.
Einstein applied the idea of Planck's constant to the problem of the photoelectric effect in 1905. The photoelectric effect shows that electrons can be released from certain metals by interacting with light, and that the amount of electrons that released depended not upon the intensity of the light, as Maxwell's theory suggested, but on the lights frequency. Einstein showed that this could be explained with a quantum theory of light whereby electrons are released only when particular frequencies are reached, corresponding to multiples of Planck's constant.
The double slit experiment can be performed on one photon at a time by letting sufficiently weak light travel through the slits. It was expected that no interference pattern would form as the photon must travel through either one slit or the other and would have nothing to interfere with. Yet this experiment has been performed numerous times and after letting a stream of photons through one at a time, what looked like random distribution soon turned into an interference pattern. This implies that the photon split when going through the two slits and reformed to be detected as a single photon on the other side. In order to see if this is what happened a photon detector was placed at each slit and the experiment was repeated. Yet no matter how many times this was done an interference pattern was never formed. The same results were found even when the detectors were placed on the other side of the slits, implying that the photon somehow knew that the detector would be there. It was found that photons behave as a particle when equipment is used to test for a particle and as a wave when a wave is being tested for.
In 1913 Bohr used the idea of quantised energy to explain how electrons orbit a nucleus by relating the angular momentum of electrons to Planck's constant. He deduced that electrons orbit with energy and momenta that are quantised to multiples of Planck's constant. All other values are not accessible to the electron, including certain spatial regions, and so when traveling between orbits the electrons seem to disappear and simultaneously appear somewhere else. This is why electrons do not loose energy as they orbit the nucleus but do so when 'jumping' between states. Just over a decade after Bohr extended the quantum theory to electrons, de Broglie proposed that all matter behaves this way.
In 1926 Schrodinger showed that quantum states can be represented not as waves or particles but by a complex function which evolves according to a second-order differential wave equation. Schrodinger's wave equation shows that a quantum state has a unitary evolution, with quanta existing in all physically possible states at once, this is known as a superposition. Schrodinger saw that if two quantum objects influence each other and are then parted they will be in a state of entanglement, such that interacting with one will change the state of another. If a pair of electrons are emitted from a common origin in an entangled state, and travel in different directions, then we can measure the spin of the electron in one plane and know the result of the other because they are always anti-correlated. Schrodinger showed that there is no equation for the state of a single entangled electron, they cannot really be said to possess individual spin states.
Around the same time as Schrodinger produced the wave equation Niels Bohr and his assistant at Copenhagen, Werner Heisenberg, used a matrix theory to interpret quantum mechanics, leading to the formulation of Heisenberg's uncertainty principle. Bohr and Heisenberg showed that properties corresponding to more than one physical possibility cannot be measured simultaneously for an object in a superpositional state, these properties are said to be non-commuting. The wave and particle properties of light are non-commuting and so by detecting a photon with a particle detector we remove our ability to measure any of its wavelike properties.
Energy and time are also non-commuting properties. The lowest energy state for waves is always right at the peak, if you imagine a pendulum swung on a string, it is stationary for just a second as it passes through the point between swinging from one side to the other. Here gravitational potential energy converts to kinetic energy, the position and momentum would be zero and so if we apply this logic to quantum mechanics we would assume that a quantum state would have zero energy at this point. The analogy is flawed however because quantum systems cannot have their position and momentum measured simultaneously, they can not both be zero and so they must have a non-zero minimum energy. In fact, quanta can have extremely high energies for very short periods of time. When a stream of quanta are fired at an impenetrable wall some will gain enough energy to tunnel through and appear on the other side.
These fluctuations are occurring everywhere and so if we look closely Einstein's smooth spacetime is in fact 'foaming' with quantum energy, this energy can create objects like electrons or photons which are continuously coming into existence for extremely short periods of time. The energy from these quantum fluctuations adds up to an enormous amount and since Einstein discovered that energy is interchangeable with mass this huge amount of energy would be so heavy that it should bend space, curving it up into a small ball. Later that year Max Born proposed a statistical interpretation of Schrodinger's wave function, with the square of the wavefunction interpreted as a probability amplitude. The mathematical interpretation of quantum mechanics was completed when the matrix mechanics used in Heisenberg's theories and the wave mechanics used in the Schrodinger equation were made compatible. This problem was tackled most notably by John von Neumann and Paul Dirac. In the standard von Neumann theory a quantum system is thought of as a point in Hilbert space. Hilbert space is analogous to the dimensional phase space of classical mechanics but includes an infinite amount of dimensions, representing the infinite amount of linear combinations of vectors corresponding to all of the possible states. Measurable properties, are represented as linear Hermitian operators on Hilbert spaces and the uncertainty principle can be explained by the fact that the two operators are non-commutating. A different approach came in 1926 when Pascual Jordan provided an independent unification of matrix and wave mechanics known as transformation theory.
Einstein was amongst many who believed that the theory of quantum mechanics must be incomplete because of the appearance of action at a distance. Einstein proposed a hidden variable theory with the motion of the quantum objects guided by the electromagnetic field. This was similar to the de Broglie-Bohm pilot-wave model of the wavefunction. In 1964 John Stewart Bell devised a way to theoretically test whether a hidden variable theory could be correct. In 1972 the experiments were conducted and they showed that Einstein was wrong and the Aspect experiments, performed in 1982, showed that this is true even if the distance between the entangled objects was such that any 'message' would have to travel faster than the speed of light. The Bell experiments strongly imply that entangled quantum systems can instantaneously influence each other even when separated across vast regions. The idea of action at a distance could be seen as analogous to Newtonian action at a distance but it differs in two respects. Firstly, quantum action at a distance does not have the symmetry that gravitational force has because in quantum mechanics the first measurement always determines the outcome of the other, they are not of mutual influence. Secondly in quantum mechanics the effects are irrespective of distance, whereas in the Newtonian model the force decreases proportionally to the square of the distance between objects. A better interpretation may be quantum holism. Holism refers to the idea that aspects of a state are not determined by its constituent parts but of the state as a whole.
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