3.4  Quantum Mechanics

The foundations of Quantum Mechanics were established during the first half of the 20th century by many scientists, including: Max Planck (1858-1947), Niels Bohr (1885-1962), Werner Heisenberg (1901-1976), Louis de Broglie (1892-1987), Arthur Compton (1892-1962), Albert Einstein (1879-1955), Erwin Schroedinger (1887-1961), Max Born (1882-1970), John von Neumann (1903-1957), Paul Dirac (1902-1984), Enrico Fermi (1901-1954), Wolfgang Pauli (1900-1958), Max von Laue (1879-1960), Freeman Dyson (b. 1923), David Hilbert (1862-1943), Wilhelm Wien (1864-1928), Satyendra Nath Bose (1894-1974), Arnold Sommerfeld (1868-1951), and others.

Based on various experimental observations in the 17th and 18th centuries, scientists such as Robert Hooke (1635-1703), Christiaan Huygens (1629-1695) and Leonhard Euler (1707-1783) proposed the wave theory of light. This theory became widely accepted after the famous double-slit experiment by Thomas Young (1773-1829) in 1803. After the black-body radiation problem reported by Gustav Kirchhoff (1824-1887) in 1859, Ludwig Boltzmann (1844-1906) suggested in 1877 that the energy states of a physical system can be discrete. In 1896, Wien empirically determined a distribution law of black-body radiation, and Boltzmann independently arrived at this result by considerations of Maxwell’s equations. However, this law was valid only at high frequencies while greatly underestimated the radiance at low frequencies. This was known as the ultraviolet catastrophe which eventually led to the quantum hypothesis by Planck in 1900, in which he suggested that energy is radiated and absorbed in discrete quanta or energy packets, that precisely matched the observed patterns of black-body radiation.

According to Planck, each energy elementis proportional to its frequency, expressed in the famous simple relation:

The constantis called Planck’s constant, which plays an essential role in quantum physics, and it is equal to.

Planck first considered that his quantum hypothesis is only a mathematical trick to get the right answer, and had nothing to do with the physical reality of the radiation itself.

However, in 1905, Einstein offered a theory to explain the photoelectric effect, which was reported in 1887 by Heinrich Hertz (1857-1894) who observed that when light with sufficient frequency hits a metallic surface, it emits electrons whose energy was later found to be related only to the frequency of light, and not to its intensity. Even strong beams of light toward the red end of the spectrum might produce no electrical potential at all, while weak beams toward the violet end would produce higher voltages. This observation could not be explained according to classical electromagnetism, which predicts that the electron’s energy should be proportional to the intensity of the radiation. Einstein explained this observation by postulating that a beam of light is a stream of particles, which were later called photons, whose energy is proportional to the frequency of the incident light beam, then each photon has a discrete energy packet, and since an electron is likely to be struck only by a single photon, the intensity of the beam has no effect and only its frequency determines the maximum energy that can be imparted to the electron. In 1921, Einstein was awarded the Nobel Prize in Physics for this work, rather than Relativity.

As a result of all this and other related scientific research, by 1910, the atomic theory of matter and the corpuscular theory of light became widely accepted as scientific facts. In 1911, the nuclear model of the atom was discovered experimentally by Rutherford, and based on it, in the same year, Bohr developed his theory of the atomic structure, which was later confirmed by the experiments of Henry Moseley (1887-1915).

Einstein’s description of light, as being composed of particles, extended Planck’s notion of quantized energy, but although the photon is a particle, it is still described as a wave with frequency. This eventually led to the wave-particle duality that will be discussed further in section 4.4.1.

On the other hand, according to Bohr model and its later amendments, electrons are arranged around the nucleus in discrete energy levels, or quantized orbits, and when the atom emits or absorbs energy, the electron did not move in a continuous trajectory from one orbit around the nucleus to another, as might be expected classically. Instead, the electron would jump instantaneously from one orbit to another, giving off the emitted light in the form of a photon. The possible energies of photons given off by each element were determined by the differences in energy levels of the different orbits, and so the emission spectrum for each element would contain a certain number of lines that could be calculated and compared with experimental observations.

In 1925, Heisenberg derived a mathematical theory that incorporated directly the empirical data, such as the wavelengths of spectral lines, and in the same year, de Broglie argued that material particles, such as electrons, could act as waves with a wavelength given by, whereis the particle’s mass andis its velocity. This was confirmed very soon by producing a diffraction pattern by scattering electrons from the Nickel crystals. In 1926, the particles of light were called photons, after Bohr and Heisenberg published their results that defended the particle behavior in certain processes and measurements. It was found therefore, that both photons and subatomic particles have certain properties of particles and waves at the same time. This originated the concept of wave-particle duality, as we shall discuss in section 4.4.1. The new field of quantum physics was met with wider acceptance at the famous Solvay Conference in Brussels in 1927.

By 1930, Quantum Mechanics had been further unified and formalized by the work of Hilbert, Dirac and von Neumann with greater emphasis on measurement, the statistical nature of our knowledge of reality, and philosophical speculation about the ‘observer’. Many new related disciplines emerged after that, including quantum chemistry, quantum electronics, quantum optics, and quantum information science.

Quantum Field Theory also emerged after combining the various conceptions in classical fields, Special Relativity, and Quantum Mechanics, as we shall discuss in section 5. Additionally, the distinctive success of Quantum Field Theory in explaining the fundamental interactions, apart from gravity, led to the Standard Model of Elementary Particles, that will be discussed in 5.18, and its failure to include gravity, or General Relativity, also led to various speculative theories such as Strings theory and Loop Quantum Gravity, to be discussed in sections 7 and 8, respectively.

Quantum Mechanics is essential to understanding the behavior of microscopic systems, because Classical Mechanics can not explain the atomic structure and how electrons could orbit the nucleus without emitting radiation, and eventually colliding with the nucleus due to this loss of energy. Instead of the classical view of defined orbits, electrons remain in an uncertain, smeared, probabilistic wave-particle orbital about the nucleus, which collapses only at the time of observation. It must be noted, however, that although Quantum Mechanics has held up to rigorous and thorough experimental testing, many of these experiments are open to many different interpretations, none of them could fully explains many of the weird quantum phenomena, as we shall discuss in section 4.3. In this regard, the Duality of Time provides a distinctive reasoning that could explain the wave-particle duality, and other related essential observations and quantum mechanical concepts, such as uncertainty, the measurement problem or the effect of observers and consciousness, as well as the reality of wave-function and its collapse. We shall introduce this new interpretation and some related consequences in section 4.5.16.

Quantum Mechanics is exceptionally successful in explaining many phenomena in physics and cosmology. It has strongly influenced String theories and other candidates for a Theory of Everything, because it explains the behavior of the subatomic particles that make up all forms of matter. Moreover, Quantum Mechanics has many applications in modern technology, including electronics, cryptography, and quantum computing.