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The double-slit experiment with particles The double-slit experiment with waves
The planetary model of the atom was suggested by New Zealand physicist Ernest Rutherford that same year when his experiments showed that the atom is mostly composed of empty space (Rutherford, pp.669-688). The idea that electrons orbit the nucleus was refuted by the fact that they are electrically charged. This means that they should lose energy and eventually spiral into the nucleus causing the atom to collapse. This problem was solved by Danish physicist Niels Bohr in 1913 (Bohr, pp.10-31). Bohr realised that electrons orbit with an energy that is quantised to multiples of Planck's constant. Electrons can only travel a complete wavelength and so must have a non zero minimum energy which stabilises their orbit.
In 1916, Einstein suggested that the momentum of light is also quantised (Einstein, 1916) and this was proven in 1922, when American physicist Arthur Compton measured this effect in x-rays scattered from the electrons in aluminium foil (Compton, pp.483-502). Compton was the first to suggest that magnetisation depends upon an intrinsic property of the electron. This concept, known as spin, was demonstrated that same year by German physicists Otto Stern and Walther Gerlach (Gerlach and Stern, pp.349).
Stern and Gerlach devised an experiment which placed a flat beam of silver atoms through a magnetic field and onto a photographic plate. They saw that the magnetic field separated the atoms into two streams. In 1925, Austrian physicist Wolfgang Pauli devised the Pauli exclusion principle which shows that pairs of electrons within each energy shell of an atom, are orientated so that they have opposite spins. The single electron on the outer shell of the silver atom does not have a partner to counterbalance it and so roughly half were attracted to the magnetic field and half were repelled by it.
Image credit: Think Quest
It was suggested that the electrons must be rotating in order to provoke a magnetic response. Pauli criticised this idea, arguing that the electron would have to be moving faster than the speed of light in order for it to rotate quickly enough to produce the necessary angular momentum, violating Einstein's theory of special relativity. In 1924, French physicist Louis de Broglie suggested that all matter could be described using wave equations and Pauli resolved the problem of spin in 1927 following the work of German physicist Werner Heisenberg and Austrian physicist Erwin Schrodinger (Atmanspacher and Primas, pp.53).
In 1926, Bohr and Heisenberg, his assistant at The University of Copenhagen, used a mathematical method called matrix theory to interpret quantum mechanics, leading to the formulation of Heisenberg's uncertainty principle. Bohr and Heisenberg showed that if an object is small enough to be described in terms of quanta, then it is in a 'quantum state' and properties corresponding to more than one physical possibility cannot be measured simultaneously. These properties are said to be non-commuting. Heisenberg found that a measurement of one non-commuting property widens the uncertainty of the other in proportion to Planck's constant. 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. Within a few months, Schrodinger came to the same conclusions using wave mechanics (Schrodinger, pp.1049-1070).
Schrodinger showed that quantum states can be represented, not as waves or particles, but by a complex wavefunction which evolves in accordance with a second-order differential wave equation. Schrodinger's wave equation replaces classical concepts of position, momentum and energy with operators. It shows that a wavefunction has a unitary evolution, with quanta existing in all physically possible states at once, this state is known as a superposition. The interference patterns exhibited by single photons in the double slit experiment are caused by the superposition of all the possible paths the photon could take.
In special relativity, energy bears the same relation to time as momentum does to space and so it was assumed that the uncertainty principle would also apply to energy and time. Although energy and time must be able to commute in order for an object to evolve, there is enough uncertainty over an objects energy that large amounts can exist for short periods of time. The uncertainty relationship between energy and time means that if a stream of quanta are fired at an impenetrable wall, some will have enough energy to tunnel through and appear on the other side. This effect is known as quantum tunnelling.
Many electrical devises depend on quantum tunnelling to work and the effect has been used to build microscopes which can demonstrate electron waves. They do this by moving single atoms into a sphere and creating what are known as quantum corrals. This effect was first achieved in 1993 by Mike Crommie, Chris Lutz and Don Eigler whilst working for IBM in California (Crommie et al., 1993). Quantum tunnelling also accounts for alpha decay and nuclear fusion.
Quantum corrals
The collapse approach to quantum mechanics was first suggested by Bohr and Heisenberg after German physicist Max Born proposed a statistical interpretation of Schrodinger's wave equation in 1926 (Born, 1954). Born interpreted the square of the complex wavefunction as a probability amplitude. This can be used to calculate the probability of every possible event which could occur when the system is measured. Bohr and Heisenberg interpreted the process of measurement as invoking a 'collapse' of the wavefunction, from a superpositional state into a state which can be described classically, in accordance with Born's rule. After a measurement has been made, the object will continue in the same state no matter how many more measurements are made.
The collapse approach suggests that the universe must be objectively indeterminate because you can only ever know the probability of a quantum event. This implies that you could not know the future of the universe even if you knew all of the physical laws and everything about its current state.
The mathematical interpretation of quantum mechanics was completed when the matrix mechanics used in Bohr and Heisenberg's theories were made compatible with the wave mechanics used in the Schrodinger equation. American mathematician John von Neumann did this in 1926 by invoking the concept of Hilbert space, a mathematical concept discovered by German mathematician David Hilbert. Hilbert space is analogous to the dimensional phase space of classical mechanics but includes an infinite amount of dimensions, which von Neumann used to represent the infinite amount of quantum possibilities. Within a year, English physicist Paul Dirac proposed another way of combining the two mathematical systems, known as transformation theory (Dirac, pp.243).
References
Atmanspacher,H. and Primas, H., 2008, 'Recasting Reality: Wolfgang Pauli's Philosophical Ideas and Contemporary Science', Springer-Verlag, Berlin
Bohr, N., 1913, 'On the theory of the decrease of velocity of moving electrified particles on passing through matter', Philosophical Magazine, Vol.25
Born, M., 1954, 'The statistical interpretation of quantum mechanics', Nobel Lecture, December 11, 1954
Compton, A.H., 1923, 'A Quantum Theory of the Scattering of X-rays by Light Elements', Physical Review, Vol.21
Crommie, M.F., Lutz, C.P., and Eigler, D.M., 1993, 'Imaging standing waves in a two-dimensional electron gas', Nature, Vol.363, pp.524-527 and Crommie, M.F., Lutz, C.P., and Eigler, D.M., 1993, 'Confinement of electrons to quantum corrals on a metal surface', Science, Vol.262, pp.218-220
See also STM Image Gallery
Dirac, P., 1927, 'The Quantum Theory of the Emission and Absorption of Radiation', Proceedings of the Royal Society of London, Series A, Containing papers of a Mathematical and Physical Character, Vol.1
Einstein, A., 1916, 'Zur Quantentheorie der Strahlung', Phys. Gesellschaft, Zuich, Mittenihungen, Vol.16
Gerlach, W. and Stern, O., 1922, 'Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld', Zeitschrift für Physik A Hadrons and Nuclei, Vol.9
Klein, M.J., 1961, 'Max Planck and the beginnings of the quantum theory', Archive for History of Exact Sciences, Vol.1
Rutherford, E., 1911, 'The Scattering of alpha and beta Particles by Matter and the Structure of the Atom', Philosophical Magazine, Vol.21
Schrodinger, E., 1926, 'An Undulatory Theory of the Mechanics of Atoms and Molecules', The Physical Review, Vol.28
Taylor, G.I., 1910, 'The Conditions Necessary for Discontinuous Motion in Gases', Proceedings of the Royal Society of London, Series A, Containing papers of a Mathematical and Physical Character, Vol.8
Quantum Mechanics (1900-1927)
In 1900, German physicists Heinrich Rubens and Ferdinand Kurlbaum showed that Wien's law, which states that the peak wavelength of a blackbody is only dependent upon its temperature, does not apply to infrared light. This problem was solved by English physicists John William Strutt, better known as Lord Rayleigh, and Sir James Hopwood Jeans. Rayleigh and Jeans did this by treating light as if it was made of waves, however their theory did not work for ultraviolet light.
Ultraviolet light has a smaller wavelength than optical light. This means that it has a higher frequency because more waves can travel across the same distance if they have shorter wavelengths. By the end of the year, Wien's colleague, fellow German physicist Max Planck had solved the problem by showing that blackbodies emit light that has 'quantised' energies. This means that if the lowest possible energy is E, other possible energies are 2E, 3E, 4E etc. they cannot be 2/3E, 3/4E or ?E etc. Each quanta, or photon, contains a 'packet' of energy proportional to the lights frequency (Klein, pp.459). This proportionality constant is known as Planck's constant. At high frequencies, light has higher energies and a blackbody is less likely to absorb and emit these energies.
In 1905, Einstein extended this idea by showing that all light is quantised. This explained the photoelectric effect which shows that electrons can be released from certain metals during interactions with light. Einstein showed that the amount of electrons released does not depend upon the lights intensity, as Maxwell's theory suggests, but upon its frequency. Electrons are only released when particular frequencies, corresponding to multiples of Planck's constant, are reached. Light is like particles because it is quantised but it is also like waves because it has a frequency.
Four years later, English physicist Geoffrey Ingram Taylor decided to settle the matter by repeating Thomas Young's double slit experiment on a succession of single quanta, or photons as they would come to be known (Taylor, pp.371). An interference pattern was not expected to form as the photons must travel through either one slit or the other and would have nothing to interfere with. But this was not the case, what looked like a 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 particle 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 never formed. Photons behave as particles when equipment is used to detect particles and as waves when a wave is being tested for. 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.