Thermodynamic fluctuations and statistical physics
Albert Einstein's first paper[86] submitted in 1900 to Annalen der Physik was on capillary attraction. It was published in 1901 with the title "Folgerungen aus den Kapillarität Erscheinungen," which translates as "Conclusions from the capillarity phenomena". Two papers he published in 1902–1903 (thermodynamics) attempted to interpret atomic phenomena from a statistical point of view. These papers were the foundation for the 1905 paper on Brownian motion, which showed that Brownian movement can be construed as firm evidence that molecules exist. His research in 1903 and 1904 was mainly concerned with the effect of finite atomic size on diffusion phenomena.[86]General principles
He articulated the principle of relativity. This was understood by Hermann Minkowski to be a generalization of rotational invariance from space to space-time. Other principles postulated by Einstein and later vindicated are the principle of equivalence and the principle of adiabatic invariance of the quantum number.Theory of relativity and E = mc²
Main article: History of special relativity
Einstein's "Zur Elektrodynamik bewegter Körper" ("On the
Electrodynamics of Moving Bodies") was received on 30 June 1905 and
published 26 September of that same year. It reconciles Maxwell's equations for electricity and magnetism with the laws of mechanics, by introducing major changes to mechanics close to the speed of light. This later became known as Einstein's special theory of relativity.Consequences of this include the time-space frame of a moving body appearing to slow down and contract (in the direction of motion) when measured in the frame of the observer. This paper also argued that the idea of a luminiferous aether – one of the leading theoretical entities in physics at the time – was superfluous.[87]
In his paper on mass–energy equivalence Einstein produced E = mc2 from his special relativity equations.[88] Einstein's 1905 work on relativity remained controversial for many years, but was accepted by leading physicists, starting with Max Planck.[89][90]
Photons and energy quanta
In a 1905 paper,[91] Einstein postulated that light itself consists of localized particles (quanta). Einstein's light quanta were nearly universally rejected by all physicists, including Max Planck and Niels Bohr. This idea only became universally accepted in 1919, with Robert Millikan's detailed experiments on the photoelectric effect, and with the measurement of Compton scattering.Einstein concluded that each wave of frequency f is associated with a collection of photons with energy hf each, where h is Planck's constant. He does not say much more, because he is not sure how the particles are related to the wave. But he does suggest that this idea would explain certain experimental results, notably the photoelectric effect.[92]
Quantized atomic vibrations
Main article: Einstein solid
In 1907 Einstein proposed a model of matter where each atom in a
lattice structure is an independent harmonic oscillator. In the Einstein
model, each atom oscillates independently – a series of equally spaced
quantized states for each oscillator. Einstein was aware that getting
the frequency of the actual oscillations would be different, but he
nevertheless proposed this theory because it was a particularly clear
demonstration that quantum mechanics could solve the specific heat
problem in classical mechanics. Peter Debye refined this model.[93]Adiabatic principle and action-angle variables
Main article: Old quantum theory
Throughout the 1910s, quantum mechanics expanded in scope to cover many different systems. After Ernest Rutherford
discovered the nucleus and proposed that electrons orbit like planets,
Niels Bohr was able to show that the same quantum mechanical postulates
introduced by Planck and developed by Einstein would explain the
discrete motion of electrons in atoms, and the periodic table of the elements.Einstein contributed to these developments by linking them with the 1898 arguments Wilhelm Wien had made. Wien had shown that the hypothesis of adiabatic invariance of a thermal equilibrium state allows all the blackbody curves at different temperature to be derived from one another by a simple shifting process. Einstein noted in 1911 that the same adiabatic principle shows that the quantity which is quantized in any mechanical motion must be an adiabatic invariant. Arnold Sommerfeld identified this adiabatic invariant as the action variable of classical mechanics. The law that the action variable is quantized was a basic principle of the quantum theory as it was known between 1900 and 1925.[citation needed]
Wave–particle duality
Main article: Wave–particle duality
Although the patent office promoted Einstein to Technical Examiner
Second Class in 1906, he had not given up on academia. In 1908, he
became a privatdozent at the University of Bern.[94] In "über die Entwicklung unserer Anschauungen über das Wesen und die Konstitution der Strahlung" ("The Development of Our Views on the Composition and Essence of Radiation"), on the quantization of light, and in an earlier 1909 paper, Einstein showed that Max Planck's energy quanta must have well-defined momenta and act in some respects as independent, point-like particles. This paper introduced the photon concept (although the name photon was introduced later by Gilbert N. Lewis in 1926) and inspired the notion of wave–particle duality in quantum mechanics.Theory of critical opalescence
Main article: Critical opalescence
Einstein returned to the problem of thermodynamic fluctuations,
giving a treatment of the density variations in a fluid at its critical
point. Ordinarily the density fluctuations are controlled by the second
derivative of the free energy with respect to the density. At the
critical point, this derivative is zero, leading to large fluctuations.
The effect of density fluctuations is that light of all wavelengths is
scattered, making the fluid look milky white. Einstein relates this to Raleigh scattering, which is what happens when the fluctuation size is much smaller than the wavelength, and which explains why the sky is blue.[95]
Einstein quantitatively derived critical opalescence from a treatment
of density fluctuations, and demonstrated how both the effect and
Rayleigh scattering originate from the atomistic constitution of matter.Zero-point energy
Main article: Zero-point energy
Einstein's physical intuition led him to note that Planck's
oscillator energies had an incorrect zero point. He modified Planck's
hypothesis by stating that the lowest energy state of an oscillator is
equal to 1⁄2hf, to half the energy spacing between levels. This argument, which was made in 1913 in collaboration with Otto Stern, was based on the thermodynamics of a diatomic molecule which can split apart into two free atoms.General relativity and the Equivalence Principle
Main article: History of general relativity
As Albert Einstein later said, the reason for the development of general relativity was that the preference of inertial motions within special relativity was unsatisfactory, while a theory which from the outset prefers no state of motion (even accelerated ones) should appear more satisfactory.[96] So in 1908 he published an article on acceleration under special relativity. In that article, he argued that free fall is really inertial motion, and that for a freefalling observer the rules of special relativity must apply. This argument is called the Equivalence principle. In the same article, Einstein also predicted the phenomenon of gravitational time dilation. In 1911, Einstein published another article expanding on the 1907 article, in which additional effects such as the deflection of light by massive bodies were predicted.
Hole argument and Entwurf theory
Main article: Hole argument
While developing general relativity, Einstein became confused about the gauge invariance
in the theory. He formulated an argument that led him to conclude that a
general relativistic field theory is impossible. He gave up looking for
fully generally covariant tensor equations, and searched for equations
that would be invariant under general linear transformations only.In June 1913 the Entwurf ("draft") theory was the result of these investigations. As its name suggests, it was a sketch of a theory, with the equations of motion supplemented by additional gauge fixing conditions. Simultaneously less elegant and more difficult than general relativity, after more than two years of intensive work Einstein abandoned the theory in November 1915 after realizing that the hole argument was mistaken.[97]
Cosmology
Main article: Cosmology
In 1917, Einstein applied the General theory of relativity to model
the structure of the universe as a whole. He wanted the universe to be
eternal and unchanging, but this type of universe is not consistent with
relativity. To fix this, Einstein modified the general theory by
introducing a new notion, the cosmological constant. With a positive cosmological constant, the universe could be an eternal static sphere.[98]
Modern quantum theory
Main article: Schrödinger equation
Einstein was displeased with quantum theory and mechanics, despite
its acceptance by other physicists, stating "God doesn't play with
dice." As Einstein passed away at the age of 76 he still would not
accept quantum theory.[99] In 1917, at the height of his work on relativity, Einstein published an article in Physikalische Zeitschrift that proposed the possibility of stimulated emission, the physical process that makes possible the maser and the laser.[100]
This article showed that the statistics of absorption and emission of
light would only be consistent with Planck's distribution law if the
emission of light into a mode with n photons would be enhanced
statistically compared to the emission of light into an empty mode. This
paper was enormously influential in the later development of quantum
mechanics, because it was the first paper to show that the statistics of
atomic transitions had simple laws. Einstein discovered Louis de Broglie's
work, and supported his ideas, which were received skeptically at
first. In another major paper from this era, Einstein gave a wave
equation for de Broglie waves, which Einstein suggested was the Hamilton–Jacobi equation of mechanics. This paper would inspire Schrödinger's work of 1926.Bose–Einstein statistics
Main article: Bose–Einstein condensation
In 1924, Einstein received a description of a statistical model from Indian physicist Satyendra Nath Bose,
based on a counting method that assumed that light could be understood
as a gas of indistinguishable particles. Einstein noted that Bose's
statistics applied to some atoms as well as to the proposed light
particles, and submitted his translation of Bose's paper to the Zeitschrift für Physik. Einstein also published his own articles describing the model and its implications, among them the Bose–Einstein condensate phenomenon that some particulates should appear at very low temperatures.[101] It was not until 1995 that the first such condensate was produced experimentally by Eric Allin Cornell and Carl Wieman using ultra-cooling equipment built at the NIST–JILA laboratory at the University of Colorado at Boulder.[102] Bose–Einstein statistics are now used to describe the behaviors of any assembly of bosons. Einstein's sketches for this project may be seen in the Einstein Archive in the library of the Leiden University.[81]Energy momentum pseudotensor
Main article: Stress-energy-momentum pseudotensor
General relativity includes a dynamical spacetime, so it is difficult to see how to identify the conserved energy and momentum. Noether's theorem allows these quantities to be determined from a Lagrangian with translation invariance, but general covariance makes translation invariance into something of a gauge symmetry.
The energy and momentum derived within general relativity by Noether's
presecriptions do not make a real tensor for this reason.Einstein argued that this is true for fundamental reasons, because the gravitational field could be made to vanish by a choice of coordinates. He maintained that the non-covariant energy momentum pseudotensor was in fact the best description of the energy momentum distribution in a gravitational field. This approach has been echoed by Lev Landau and Evgeny Lifshitz, and others, and has become standard.
The use of non-covariant objects like pseudotensors was heavily criticized in 1917 by Erwin Schrödinger and others.
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