 | Annus Mirabilis Papers: Encyclopedia II - Annus Mirabilis Papers - Papers
Annus Mirabilis Papers - Papers
Three of those papers (on Brownian motion, the photoelectric effect, and special relativity) deserved Nobel Prizes according to some physicists. Only the paper on the photoelectric effect would win one. What makes these papers remarkable is that, in each case, Einstein boldly took an idea from theoretical physics to its logical consequences and managed to explain experimental results that had baffled scientists for decades.
Annus Mirabilis Papers - Background
When Einstein wrote the papers, he was without much scientific literature to which he could refer or many scientific colleagues with whom he could discuss his theories. During the time he wrote these papers, Einstein was an examiner at the Patent Office in Bern, Switzerland. This provided him information on various efforts and devices via inventors' patent applications. In addition to his job, Einstein's wife, Mileva Marić, may have had some influence on Einstein's work but how much is a debated question [1][2].
Annus Mirabilis Papers - Photoelectric effect
The first paper, named "On a Heuristic Viewpoint Concerning the Production and Transformation of Light", ("Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt") proposed the idea of energy quanta. The idea of energy quanta was motivated by Max Planck's earlier derivation of the law of black-body radiation by assuming that luminous energy could only be absorbed or emitted in discrete amounts, called quanta. Einstein stated,
Energy during the propagation of a ray of light is not continuously distributed over steadily increasing spaces, but it consists of a finite number of energy quanta localised at points in space, moving without dividing and capable of being absorbed or generated only as entities.
Einstein showed that, by assuming that energy actually consisted of discrete packets, he could explain the Hertz effect.
The idea of light quanta contradicted the wave theory of light that followed naturally from James Clerk Maxwell's equations for electromagnetic behavior and, more generally, the assumption of infinite divisibility of energy in physical systems. Einstein stated,
A profound formal difference exists between the theoretical concepts that physicists have formed about gases and other ponderable bodies, and Maxwell's theory of electromagnetic processes in so-called empty space. While we consider the state of a body to be completely determined by the positions and velocities of an indeed very large yet finite number of atoms and electrons, we make use of continuous spatial functions to determine the electromagnetic state of a volume of space, so that a finite number of quantities cannot be considered as sufficient for the complete determination of the electromagnetic state of space.
[... this] leads to contradictions when applied to the phenomena of emission and transformation of light.
According to the view that the incident light consists of energy quanta [...], the production of cathode rays by light can be conceived in the following way. The body's surface layer is penetrated by energy quanta whose energy is converted at least partially into kinetic energy of the electrons. The simplest conception is that a light quantum transfers its entire energy to a single electron [...]
Even after experiments showed that Einstein's equations for the photoelectric effect were accurate, his explanation was not universally accepted. Niels Bohr, in his 1922 Nobel address, refused to accept Einstein's theory. Bohr stated, "The hypothesis of light-quanta is not able to throw light on the nature of radiation".
By 1921, when Einstein was awarded the Nobel Prize and his work on photoelectricity was mentioned by name in the award citation, some physicists accepted that the equation (hf = Φ + Ek) was correct and light quanta were possible. In 1923, Arthur Compton's X-ray scattering experiment (Compton scattering) helped convert many more scientists still questioning the theory to the position that the theory was correct. The theory of light quanta was a strong indication of wave-particle duality; that concept, used as a fundamental principle by the creators of quantum mechanics, states that physical systems can display both wave-like and particle-like properties. A complete picture of the photoelectric effect was only obtained after the maturity of quantum mechanics.
Annus Mirabilis Papers - Brownian motion
His second article in 1905, named "On the Motion Required by the Molecular Kinetic Theory of Heat of Small Particles Suspended in a Stationary Liquid", ("Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen") delineated a stochastic model of Brownian motion. Einstein stated,
In this paper it will be shown that, according to the molecular kinetic theory of heat, bodies of a microscopically visible size suspended in liquids must, as a result of thermal molecular motions, perform motions of such magnitudes that they can be easily observed with a microscope. It is possible that the motions to be discussed here are identical with so-called Brownian molecular motion; however, the data available to me on the latter are so imprecise that I could not form a judgment on the question ...
Brownian motion generates expressions for the root mean square displacement of particles. Using the then-controversial kinetic theory of fluids, it established that the phenomenon, which still lacked a satisfactory explanation decades after it was first observed, provided empirical evidence for the reality of atoms. It also lent credence to statistical mechanics, which was also controversial at the time. Before this paper, atoms were recognized as a useful concept, but physicists and chemists hotly debated whether atoms were real entities. Einstein's statistical discussion of atomic behavior gave experimentalists a way to count atoms by looking through an ordinary microscope. Wilhelm Ostwald, one of the leaders of the anti-atom school, later told Arnold Sommerfeld that he had been converted to a belief in atoms by Einstein's complete explanation of Brownian motion.
Annus Mirabilis Papers - Special relativity
Einstein's third paper that year was called "On the Electrodynamics of Moving Bodies" ("Zur Elektrodynamik bewegter Körper", published on June 30, 1905). In this paper, Einstein was able to reconcile 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.
The content of the paper is highly self-contained work, making only a single reference to other works that may have led to its development. While developing this paper, Einstein wrote to Mileva about "our work on relative motion", and this has led some to ask whether Mileva played a part in its development (as well as the other papers). This paper introduced a theory of time, distance, mass and energy that was consistent with electromagnetism, but omitted the force of gravity.
At the time, it was known that Maxwell's equations, when applied to moving bodies, led to asymmetries, and that it had not been possible to discover any motion of the Earth relative to the 'light medium'. Einstein put forward two postulates to explain these observations. First, he applied the classic principle of relativity, which stated that the laws of physics remained the same for any frame of reference, to the laws of electrodynamics and optics as well as mechanics. In the second postulate, Einstein proposed that the speed of light remained constant in all inertial frames of reference, independent of the state of motion of the emitting body.
Special relativity avoided the problem in science that was present since the Michelson-Morley experiment, which had not detected a medium of conductance (or aether) for light waves unlike other known waves that require a medium (such as water or air). Einstein stated,
... the unsuccessful attempts to discover any motion of the earth relatively to the "light medium," suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest.
The speed of light was thus fixed, and not relative to the movement of the observer. This was impossible under Newtonian classical mechanics. Einstein stated,
... the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the "Principle of Relativity") to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell's theory for stationary bodies. The introduction of a "luminiferous ether" will prove to be superfluous inasmuch as the view here to be developed will not require an "absolutely stationary space" provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place.
The theory [...] is based - like all electrodynamics - on the kinematics of the rigid body, since the assertions of any such theory have to do with the relationships between rigid bodies (systems of co-ordinates), clocks, and electromagnetic processes. Insufficient consideration of this circumstance lies at the root of the difficulties which the electrodynamics of moving bodies at present encounters.
It had already been conjectured by George Fitzgerald in 1894 that the Michelson-Morley result could be accounted for if moving bodies were contracted in the direction of their motion. Indeed, some of the paper's core equations, the Lorentz transforms, had been introduced in 1903 by Dutch physicist Hendrik Lorentz, giving mathematical form to Fitzgerald's conjecture. But Einstein revealed the underlying reasons for this geometrical oddity.
His explanation arose from two axioms. First was Galileo's old idea that the laws of nature should be the same for all observers that move with constant speed relative to each other. Einstein stated,
The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion.
The second was the rule that the speed of light is the same for every observer. Einstein stated,
Any ray of light moves in the "stationary" system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body.
Special relativity has several striking consequences, because the absolute concepts of time and distance are rejected. The theory came to be called the "special theory of relativity" to distinguish it from his later general theory of relativity, which considers all observers to be equivalent. Special relativity at first met with disdain and even ridicule from some quarters since it abounds with apparent paradoxes, and violates "common sense". However, the self-consistency of special relativity was proven in 1908 by Hermann Minkowski, and it has been supported by an ever-increasing body of confirmatory experimental evidence. As a result the correctness of special relativity has come, over time, to be largely taken for granted in the scientific community.
Annus Mirabilis Papers - Matter and energy equivalence
A fourth paper, "Does the Inertia of a Body Depend Upon Its Energy Content?", ("Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?") was published on September 27 in Annalen der Physik, containing one of the most famous equations in the field of Physics: E=mc². Einstein considered the equivalency equation to be of paramount importance because it showed that a massive particle possesses an energy, the "rest energy", distinct from its classical kinetic and potential energies. Nevertheless, most scientists simply regarded the finding as a curiosity until the 1930s.
The paper was based on James Clerk Maxwell's and Heinrich Rudolf Hertz's investigations and, in addition, the axioms of relativity, as Einstein stated,
The results of the previous investigation lead to a very interesting conclusion, which is here to be deduced.
[The previous investigation was based] on the Maxwell-Hertz equations for empty space, together with the Maxwellian expression for the electromagnetic energy of space ...
The laws by which the states of physical systems alter are independent of the alternative, to which of two systems of coordinates, in uniform motion of parallel translation relatively to each other, these alterations of state are referred (principle of relativity).
The equation set forth was that energy of a body at rest (E) equals its mass (m) times the speed of light (c) squared, or E = mc². Einstein stated,
If a body gives off the energy L in the form of radiation, its mass diminishes by L/c². The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference, so that we are led to the more general conclusion that
The mass of a body is a measure of its energy-content; if the energy changes by L, the mass changes in the same sense by L/9 × 1020, the energy being measured in ergs, and the mass in grammes.
[...]
If the theory corresponds to the facts, radiation conveys inertia between the emitting and absorbing bodies.
The mass-energy relation can be used to predict how much energy will be released or consumed by chemical and nuclear reactions; one simply measures the mass of all constituents and products and multiplies the difference by c2. The result shows how much energy will be released or consumed, usually in the form of light or heat. If applied to certain nuclear reactions, the equation shows that an extraordinarily large amount of energy will be released, much larger than in the combustion of chemical explosives, where the mass difference is hardly measurable at all. This explains why nuclear weapons produce such phenomenal amounts of energy, as they release binding energy during nuclear fission and nuclear fusion.
According to Umberto Bartocci (University of Perugia historian of mathematics), the famous equation was first published two years earlier by Olinto De Pretto, an industrialist from Vicenza, Italy, though this is not generally regarded as true or important by mainstream historians. Even if De Pretto introduced the formula, it was Einstein who connected it with the theory of relativity.
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