We see that, for any fixed l, l_{T (l) increases with increasing T. The integral of IT (l) over all l is, of course, just equal to the quantity IT previously defined. This integral, which is equal to the area under the curves, does increase with the fourth power of T, in agreement with Stefans law. Figure (1) also shows that the spectrum shifts towards shorter wavelength as T increases. A quantitative inspection of the figure will demonstrate the validity of the equation}

where l_max is the l at which I_T (l) has its maximum value for a particular T. This is known as the Wiens displacement law. All these results are in agreement with the everyday experience that bodies emit more heat as their temperature increases, and that with increasing temperature their colour shifts from dull red to blue white (i.e. increasingly more radiant energy is emitted in the region of short wavelength). It may be worth noting that Wiens displacement law allows us to infer the temperature of a body (or a star) once the l_{max is known through the study of the spectrum emitted by it.}

Now consider an object containing a cavity which is connected to the outside by a small hole (Figure 2). Radiation incident upon the hole from the outside enters the cavity and is reflected back and forth by the walls of the cavity, eventually being absorbed on these walls. If the area of the hole is very small compared with the area of the inner surface of the cavity, a negligible amount of the incident radiation will be reflected back to the hole. Then all the radiation incident upon the hole is absorbed. For the hole, absorptivity or the ratio of energy absorbed to the total energy incident per unit area, a = 1 and therefore the hole must have the properties of the surface of a black body.

Fig2:A hole in the wall of a hollow object is an excellent Approximation of a black body

Next assume that the walls of the cavity are uniformly heated to a temperature T. The walls will emit thermal radiation which will fill the cavity. The small fraction of this radiation incident from the inside upon the hole will pass through the hole. Thus the hole will act as an emitter of thermal radiation. Since the hole must have the properties of the surface of a black body, the radiation emitted by the hole must have a black body spectrum. But, as the hole is merely sampling the thermal radiation present inside the cavity, it is clear that the radiation in the cavity must also have a black body spectrum. Wien's Law: We can understand many of the properties of black body radiation from the classical theory of thermodynamics. In 1884 Boltzmann produced a theoretical derivation of the equation giving IT, the total energy emitted per cm2 per second, for a black body radiator (Stefans Law for the case e=1). In this derivation he considered a cavity with reflecting walls in the form of a cylinder with a movable piston and filled with thermal radiation at temperature T. Thermal radiation, in common with all other electromagnetic radiation, can be shown to exert a pressure proportional to its energy density. In this respect it behaves just like a gas. Taking this system through a cycle of expansion and compression, called in thermodynamics a Carnot cycle, Boltzmann obtained a relation between the work done by the pressure of the radiation, and its temperature. This relation leads to the desired result since the pressure can be expressed in terms of the energy density, which can in turn be expressed in terms of IT. In the process of expansion or compression of such a cavity filled with radiation, the wavelength of any spectral component of the radiation will be changed as the result of a Doppler shift upon reflection from the moving piston in the same way the whistle from a railway engine approaching us sounds shrill (i.e. an apparent increase in its frequency) or flat while receding away from us (i.e. an apparent decrease in its frequency). From a detailed consideration of this fact, Wien (1893) was able to derive a general functional form for the spectral distribution of black body radiation known as Wiens law: rT (l) = f (lT) / l5 Fig:3 An experimental verification of Wien's law where f (lT) is some function of the product of the wavelength and the temperature, whose form is not specified by Wiens derivation. rT (l) is the energy density defined such that rT (l) dl is the energy contained in cm3 of the cavity in the wavelength interval l to l+dl. This equation is in excellent agreement with the experimental data, as can be seen from Figure 3. This figure plots l5 times rT (l) as a function of lT, using 1259 K, 1449K, and 1646K data of Lummer and Pringsheim for IT (l) [which is proportional to rT (l)]. We see that all sets of data fall on the same smooth curve, confirming the prediction of Wiens Law that l5rT (l) is equal to a universal function of the variable lT. It is apparent that Wiens law agrees with the empirical fact expressed by equation lmax 1/T.   The Rayleigh-Jeans Theory:   Wiens thermodynamical derivation performed the useful role of allowing all black body spectra measured at different temperatures to be discussed theoretically in terms of the single function f (lT). But the derivation did not evaluate the form of this function. It is typical of a thermodynamical argument to show that certain relations must obtain between the variables which describe some physical system, but not to provide a complete theory of the behaviour of the system. The reason is that such arguments are based on general principles that apply to all physical systems, but do not involve the details of the composition of the particular system in question. A theory which would be able to evaluate the function f (lT) must take into account some of the detailed properties of a black body as well. Max Born                              S.N.Bose                       Chen Ning Yang Consider a cavity with metallic walls at temperature T. The walls emit thermal electromagnetic radiation. In thermal equilibrium this radiation has a black body spectrum characteristic of the temperature T. Furthermore, in the steady state attained at equilibrium the electromagnetic radiation inside the cavity must exist in the form of standing waves with nodes at the metallic surfaces. Rayleigh and Jeans calculated the number of standing waves with nodes at the surfaces of the cavity in the wavelength interval l to l + dl. They then calculated the average energy of these waves. The energy depends on the temperature T and is evaluated form the theory of statistical mechanics. The number of standing waves in the wavelength interval times the average energy of the waves divided by the volume of the cavity is equal to the average energy per cm3 in the wavelength interval l to l + dl, which is just rT (l). From this f (lT) is evaluated by using equation rT (l) = f (lT)/ l5. If we assume a metallic walled cavity filled with electromagnetic radiation in the form of a perfect cube of edge length a, then the number of allowed frequencies N (n) in the frequency interval n to n+dn is given by N (n) dn = 8p a3n3 dn --------- c3   It can be shown that N (n) dn is independent of the assumed shape of the cavity and depends only on its volume a3. The next step in the Rayleigh-Jeans calculation was the evaluation of the average energy contained in each standing wave of frequency n. According to classical physics, the particular energy of some wave can have any value from zero to infinity; the actual value is proportional to the square of its average amplitude. But, if we have a system containing a large number of physical entities of the same kind which are in thermal equilibrium with each other at temperature T, such as the system of standing waves in equilibrium in the black body cavity, the classical theory of statistical mechanics demands that the energies of these entities be distributed according to a definite probability distribution whose form is specified by T. As the average energy is determined by the probability distribution, it must have a definite value that depends on T. It turns out that the average energy per standing wave is given by kT, where k=1.38 x 10-16 erg - deg-1 is Boltzmann constant.   The energy per cm3 in the frequency interval n to n+dn of the black body spectrum of a cavity at temperature T is just the product of the average energy per standing wave (kT) and the number of standing waves in the frequency interval divided by the volume of the cavity. That is, rT (n) dn = 8p n2kT dn                  -----------                 c3   Fig:4 A Coparison of the Rayleigh-jeans spectrum and experiment To make a comparison with our earlier discussion, we must express the energy density in terms of the wavelength l. This can be done by using the relation n = c/l. It now can be easily shown that rT (l) dl = 8pk lT dl /l5   This is the Rayleigh-Jeans spectral distribution of black body radiation. We note that it has the form required by Wiens law since it can be written rT (l) = f (lT)/l5, where f (lT)=8pklT. However, as is seen in Figure (4), the Rayleigh-Jeans spectrum is in complete disagreement with the experimental data; it predicts the wrong form for the function f (lT). In the limit of long wavelength, the Rayleigh-Jeans spectrum approaches the experimental results. But as l0, their theory predicts that rT (l), whereas experiment shows that rT (l) always remains finite and is equal to zero at zero wavelength. The unrealistic behaviour of the Rayleigh-Jeans distribution at short wavelengths is known in physics as the ultraviolet catastrophe. This terminology is suggestive of the importance of the failure of the Rayleigh-Jeans theory. Let us evaluate the total energy per cm3 for the Rayleigh-Jeans spectrum:                                                                                                                                                                                                                                                                                                                            rT(l)dl = 8pkT dl / l4 = 8pkT [lim l0 (1/l3)] / 3 0                                                                                                                                                                                                                                                                              0                                                Tasung Dao Lee                                        Eugene Paul Wigner                       Sin Ltiro Tomonnaga This goes to infinity unless T=0. We have here an even more impressive indication of the complete failure of the Rayleigh-Jeans spectrum. Yet this spectrum is, as we have mentioned earlier, a necessary consequence of the theories of classical physics. Julian Schewinger The "ultraviolet catastrophe" was one of the "minor" details to left to be tidied up in the field of thermodynamics. What the Rayleigh-Jeans formula implies broadly is that the number of frequencies in the high frequency range to be far greater than the number of frequencies in the low frequency range since high frequencies have shorter wave lengths and more could be packed into the black body. So the problem with blackbody radiation is that, if a body radiates all frequencies equally, the number of radiations in the high frequency range should vastly outnumber those in the low frequency range. In fact, almost all the radiation should be high frequency _ that is, at the ultraviolet end of the spectrum. But, that does not happen! And no one could explain why in term of physical theory in the 1890s, although several people had tried hard. Enter Planck: Max Planck wasn't the type to start a revolution. Tall and spare, quiet and dignified _ some said "stuffy and pedantic" _ he was completely devoted to tradition and authority, both in his physics and in his life. His work was competent but promised nothing special. For his doctoral work he chose thermodynamics because he admired Clausius's work in the same field, but there was little in his dissertation to excite anyone's attention; to all outward indications he was headed straight for a largely uninspired and mediocre career. Even after securing a professorial appointment at the University of Berlin in 1889, Planck appeared to be travelling pretty much on the beaten path. Certainly his choice of thermodynamics as his specialty didn't promise much in the way of major achievements. He spent more than six years of his life trying to find a solution to the black body radiation problem. And after he found it, physics would never be the same again. For, in quietly solving the puzzle of blackbody radiation, Max Planck discovered a key principle that, followed up by others, would forever change our understanding of the world. As one science historian put in, "Planck was like a man who, before the discovery of fire, wanted to find the best ways to bore holes, who for months, years, even decades, bored holes in every material he could find in every conceivable fashion and in doing so chanced to discover fire". Based on hunch, in 1900 Planck worked out a simple equation describing the distribution of radiation accurately over the entire stretch of frequency. His basic premise went like this: What if energy is not infinitely indivisible? What if, like matter, energy exists in particles or packets, or quanta, as he called them _ from the Latin interrogative adjective meaning "How much?" Planck also found that the size of these quanta was in direct proportion to the frequency. So radiation at low frequencies is easy _ it requires only small packets or quanta of energy. But for a frequency twice as high, radiation would require twice the amount of energy. Richard P.Feynman The discrepancy between experiment and theory was resolved in 1901 by Planck -- but only at the expense of introducing a postulate which was not only new, but also drastically at variance with certain concepts of classical physics. Murray Gell Mann Planck set out to explain the black body spectrum. He postulated that all solid bodies, and therefore the walls of the cavity, contained little oscillators - he called them resonators - of every imaginable frequency. By resonators Planck meant small electrified particles which wiggled to and fro. It followed that in any range of frequencies, however narrow, there must be resonators having frequencies in that range. Take, for instance, the bright yellow spectrum-line of sodium which is designated by the letter D. We are to imagine, that there are resonators having frequencies within this narrow range. All of them are emitting yellow light into the cavity, and yellow light is coming right back out of the cavity and bathing them and stimulating them to continued oscillation. There is an equilibrium between the energy of the resonators and the energy of the yellow light. So it is with the energy of blue light and the resonators which have the frequency of blue light, and so it is throughout the entire spectrum. If by any valid line of reasoning one could arrive at the energy which the resonators of any frequency have when they are in equilibrium with the light, one would be able to arrive by one simple further step at the energy which the light of any frequency has when it is in equilibrium with the resonators. This would be the answer to Planck's question, for it would give the black body spectrum. Fig;5 Energy Level Diagram for classical simple harmonic Oscillotor and a simple harmonic oscillotor obeying Planck's postulate There was an answer to this question before Planck, but the answer was a disaster, as we shall soon see. This "classical" answer was that all the resonators have the same energy, no matter what their frequency. From this it followed that the quantity of light in the cavity would be infinite, and since the quantity of light in the cavity actually is finite, the theory was sunk. Abdus Salam The flaw in the classical theory lay in one of its assumptions - indeed, a very plausible one - to wit: that any resonator may have any amount of energy; in other words, that it may go continuously up or down the energy-scale through all levels, like a man walking up or down a ramp. Planck replaced the ramp by a ladder, with its rungs, as in any practical ladder, at equal intervals. His assumption was that the resonator must always be on one or another of the rungs, and if it proceeds up or down the ladder, it must proceed by jumping from rung to rung. That is to say, it may absorb or emit energy only in certain discrete units, represented by the equal spacing from rung to rung of the ladder. Planck then affirmed that the spacing between the rungs of the ladder was not the same for all resonators but must be proportional to the frequency of the resonator in each case. He designated the spacing, or energy unit, as hn, and said that h is a universal constant, n being the frequency of the resonator. Sheldon Lee Glashow Planck's substitution of the ladder for the ramp not only avoided the disaster of infinity but yielded the actual from the black body spectrum. Let us see how. The Quantum Postulate Planck's postulate may be stated as follows: Any physical entity whose single "coordinate" executes simple harmonic oscillations (i.e. is a sinusoidal function of time) can posses only total energies e which satisfy the relation e = nhn, n = 0, 1, 2, 3, .. where n is the frequency of the oscillation and h is a universal constant. We may note here that the word "coordinate" is used in its general sense to mean any quantity which describes the instantaneous condition of the entity. Examples are: the length of a coil spring, the angular position of a pendulum bob, the amplitude of a wave. All these examples happen also to be sinusoidal functions of time. An energy level diagram (Figure 5) provides a convenient way of illustrating the behaviour of an entity governed by this postulate, and it is also useful in contrasting this behaviour with what would be predicted by classical physics. In such diagrams we indicate each of the possible energy states of the entity with a horizontal line. The distance from the line to the zero energy line is proportional to the total energy to which it corresponds. Since the entity may have any energy from zero to infinity according to classical physics, the classical energy level diagram consists of a continuum of lines extending from zero up. However, the entity executing simple harmonic oscillations can have only one of the discrete total energies e = nhn, n = 0, 1, 2, 3, , if it obeys Plancks postulate. This is indicated by the discrete set of lines in its energy level diagram. The energy of the entity obeying Plancks postulate is said to be quantized, the allowed energy states are called quantum states, and the integer n is called quantum number. Steven Weinberg Let us recalculate rT (l) under the assumption that Plancks postulate is obeyed by the electromagnetic standing waves whose amplitudes are executing simple harmonic oscillation with frequency n. No modification will be required in the calculation of N (n) dn since at no point in that calculation was it necessary to specify the energy of the standing waves. The calculation of the average energy e however will need to be redone since under Plancks postulate, e can only have the discrete values nhn, where n = 0, 1, 2, 3, , while in classical physics it could assume any value. It turns out that the average energy using Plancks hypothesis is given by hn/(e hn / kT -1) rather than kT as given in classical physics. Evaluating rT (n) dn as in the case of Rayleigh-Jeans theory, we obtain rT (n) dn = 8p n2 hn dn/ c3 ehn/kT1 In terms of the variable l, it would read rT (l) dl = 8phc dl/ l5 e hc/klT 1 Fig:6A comparison of Plank's spectrum and experiment.The dots are experimental and the curve is theroretical T=1646 K This is the black body spectral distribution derived by Planck that marked the beginning of the Quantum Theory. It satisfies Wiens law with f (lT) = (8phc / l5) [1/(e hc/klT 1)]. This function involves the constant h whose numerical value is to be determined by fitting the theoretical spectrum to the experimental data. Such a fit is shown in figure 7. The value providing the best fit to the data is h = 6.63 x 10-27 erg-sec The constant h is known as Planck's constant. Its value must be determined by experiment; it is not prescribed by theory. It has been measured in a variety of ways, and all of the measurements agree. Planck may be characterized as the man who put h into physics. The figure shows that Planck's theoretical spectrum is in extremely good agreement with the experimental spectrum for T=1646K. Since it satisfies Wien's law, we know that it will agree equally well with experiment at any other temperature. Why does Planck's postulate reproduce the black body spectrum? The failure of the Rayleigh-Jeans theory is really due to the rapid increase in N (n) dn as n becomes large. Since the classical law of equipartition of energy requires that e be independent of n, the spectrum itself will also increase rapidly with increasing n (or decreasing l). Plancks postulate has the effect of putting a cut-off into e so that it does not obey the classical law. This keeps the spectrum bounded and, in fact, brings the spectrum to zero as n (or as l 0). It can be shown that for n large enough (l small) so that hn is quite large compared to kT, the average energy for the standing wave is negligible and close to zero, and has the effect of overcoming the ultraviolet catastrophe. On the other hand, for very low frequency standing waves (large l) in which hn is quite small compared to kT, the quantum states are so close together that they behave as if they were continuously distributed as in the classical theory. Thus in the low frequency limit Plancks value of average energy approaches the classical value of average energy, i.e. equal to kT, and the spectrum predicted by Plancks theory and that predicted by Rayleigh-Jeans theory approach the experimental spectrum. Gerardus't Hooft                       Martinus J.G.Veltman Quantum Theory - A Turning Point Planck had solved the blackbody puzzle, but once it was laid out before him with all of its full implications he wasn't happy with the final picture he saw. He didn't want to see classical physics destroyed, and the quantum theory would do that. Still, he knew that he had started something that could not be stopped. The power of the theory was too great, even if its implications were frightening to him. "We have to live with quantum theory", he concluded, "And believe me, it will expand _.. It will go in all fields". Max Planck, though, was not the one who would push it into those fields. For the rest of his life he would be famous for discovering the quantum, but he would spend his working days trying somehow to reconcile his disturbing discovery with his beloved classical physics. It was an attempt bound to fail. "My vain attempts to somehow reconcile the elementary quantum with classical theory continued for many years, and cost me great effort", he wrote near the end of his life, "Many of my colleagues saw almost a tragedy in this, but I saw it differently because the profound clarification of my thoughts I derived from this work had great value to me. Now I know for certain that the quantum of action has a much more fundamental significance than I originally suspected". Sure enough, within five years of Planck's theory of black body radiation, in 1905, Einstein examined the photoelectric effect and proposed a quantum theory of light explaining the phenomenon. The photoelectric effect is the release of electrons from certain metals or semiconductors by the action of light. He realised that Planck's theory made implicit use of the light quantum hypothesis. In 1913, Niels Bohr wrote a revolutionary paper on the hydrogen atom and discovered the major laws of the spectral lines. Arthur Compton derived relativistic kinematics for a scattering of a photon (a light quantum) off an electron at rest in 1923. The year 1924 saw the publication of another fundamental paper. It was written by Satyendranath Bose and rejected by a referee for publication. Bose then sent the manuscript to Einstein who immediately saw the importance of Bose's work and arranged for its publication. Bose proposed different states for the photon. He proposed that there is no conservation of the number of photons. Instead of statistical independence of particles, Bose put particles into cells and talked about statistical independence of cells. Time has shown that Bose was right on all these points. Work was going on at almost the same time as Bose's which was also of fundamental importance. The doctoral thesis of Louis de Broglie was presented which extended the particle wave duality for light to all particles, in particle to electrons. Schrodinger in 1926 published a paper giving his equation for the hydrogen atom and heralded the birth of wave mechanics. Schrodinger introduced operators associated with each dynamical variable. Then came Heisenberg's uncertainty principle. The Theory was now popularly called Quantum Mechanics. The year 1926 saw the complete solution of the derivation of Planck's law after 26 years by P.A.M. Dirac. The quantum theory was finally established on a firm theoretical basis! Then came the applications of quantum mechanics to understand the basic constituents of matter and attempts to unify the different types of forces (or interactions as scientists call them) we come across in nature, say, strong interaction (between the constituents of the nucleus), weak interaction (in radioactivity when an electron is emitted or absorbed by the nucleus), the electromagnetic interaction between charged particles and the gravitational interaction. There has been some success - electromagnetic and the weak interactions have been unified into one interaction called electroweak interaction. There have been attempts also to unify the electroweak force with the strong force into a single gauge theory. However, the theory unifying all the four forces we come across in nature still appears to be a distant dream. In any case, one thing is certain - We have to live with quantum theory! References: Introduction to Modern Physics F.K. Richtmyer, E.H. Kennard and T. Lauritsen McGraw Hill Book Company 1955 A classic reference book for historical development of Modern Physics. Lucidly written. Fundamentals of Modern Physics R.M. Eisberg John Wiley and Sons, Inc., 1961 A standard text book on Modern Physics with emphasis on conceptual development. Concepts of Modern Physics Arthur Beiser McGraw Hill Book Company 1967 Yet another standard text book at elementary level. Beautifully written. The History of Science from 1895-1945 Ray Spangenburg and Diane K. Moser Universities Press (India) Ltd., 1999 Highly readable. A set of five volumes on history of science from the ancient Greeks until 1990s. The Quantum Theory Karl K. Darrow Scientific American, March 1952 An excellent article on Quantum Theory. Quantum Theory: Glossary Important terms used in connection with Quantum Theory are given below. The terms given do not necessarily appear in the present article. Absolute zero : The temperature of -273.16C, or - 459.69F, or 0 K, thought to be the temperature at which molecular motion vanishes and a body would have no heat energy. Absorption coefficient : If a flux through a material decreases with distance x in proportion to e-ax, then a is called the absorption coefficient. Blackbody : An ideal body which would absorb all incident radiation and reflect none. Also known as hohlrarum; ideal radiator. Blackbody radiation : The emission of radiant energy which would take place from a blackbody at a fixed temperature; it takes place at a rate expressed by the Stefan-Boltzmann law, with a spectral energy distribution described by Planck's equation. Bohr-Sommerfeld theory : A modification of the Bohr theory in which elliptical as well as circular orbits are allowed. Bohr theory : A theory of atomic structure postulating an electron moving in one of certain discrete circular orbits about a nucleus with emission or absorption of electromagnetic radiation necessarily accompanied by transitions of the electron between the allowed orbits. Carnot cycle : A hypothetical cycle consisting of four reversible processes in succession: an isothermal expansion and heat addition, an isentropic expansion, an isothermal compression and heat rejection process, and an isentropic compression. Compton effect : The increase in wavelength of electromagnetic radiation in the x-ray and gamma-ray region on being scattered by material objects; the scattering is due to the interaction of the protons with electrons that are effectively free. Also known as Compton-Debye effect. Conservation of parity : The law that, if the wave function describing the initial state of a system has even (odd) parity, the wave function describing the final state has even (odd) parity; it is violated by the weak interactions. Also known as parity conservation. Blackbody radiation : The emission of radiant energy which would take place from a blackbody at a fixed temperature; it takes place at a rate expressed by the Stefan-Boltzmann law, with a spectral energy distribution described by Planck's equation. Bohr-Sommerfeld theory : A modification of the Bohr theory in which elliptical as well as circular orbits are allowed. Bohr theory : A theory of atomic structure postulating an electron moving in one of certain discrete circular orbits about a nucleus with emission or absorption of electromagnetic radiation necessarily accompanied by transitions of the electron between the allowed orbits. Carnot cycle : A hypothetical cycle consisting of four reversible processes in succession: an isothermal expansion and heat addition, an isentropic expansion, an isothermal compression and heat rejection process, and an isentropic compression. Compton effect :The increase in wavelength of electromagnetic radiation in the x-ray and gamma-ray region on being scattered by material objects; the scattering is due to the interaction of the protons with electrons that are effectively free. Also known as Compton-Debye effect. Conservation of parity : The law that, if the wave function describing the initial state of a system has even (odd) parity, the wave function describing the final state has even (odd) parity; it is violated by the weak interactions. Also known as parity conservation. D line : The yellow line that is the first line of the major series of the sodium spectrum; the foublet in the Fraunhofer lines whose almost equal components have wavelengths of 5895.93 and 5889.96 angstroms respectively. Doppler range : A Doppler ranging system that uses phase comparison of three different modulation frequencies on the carrier wave, such as 0.01, 0.1, and 1 megahertz, to obtain missile range data with high accuracy. Electromagnetic wave : A disturbance which propagates outward from any electric charge which oscillates or is accelerated; far from the charge it consists of vibrating electric and magnetic fields which move at the speed of light and are at right angles to each other and to the direction of motion. Electron : A stable elementary particle which is the negatively charged constituent of ordinary matter, having a mass of about 9.11 X 10-28g (equivalent to 0.511 MeV), a charge of about -1.602 X 10-19 coulomb, and a spin of . Also known as negative electron; negatron. Electron diffraction : The phenomenon associated with the interference processes which occur when electrons are scattered by atoms in crystals to form diffraction patterns. Equipartition : The condition in a gas where under equal pressure the molecules of the gas maintain the same average distance between each other. Equipartition law : In a classical ideal gas, the average kinetic energy per molecule associated with any degree of freedom which occurs as a quandratic term in the expression for the mechanical energy, is equal to half of Boltzmann's constant times the absolute temperature. Erg : A unit of energy or work in the centimeter-gram-second system of units, equal to the work done by a force of magnitude of 1 dyne when the point at which the force is applied is displaced 1 centimeter in the direction of the force. Also known as dyne centimeter (dyne-cm). Exclusion principle : The principle that no two fermions of the same kind may simultaneously occupy the same quantum state. Also known as Pauli exclusion principle. Heisenberg picture : A mode of description of a system in which dynamic states are represented by stationary vectors and physical quantities are represented by operators which evolve in the course of time. Also known as Heisenberg representation. Invariance : The property of a physical quantity or physical law of being unchanged by certain transformations or operations, sich as reflection of spatial coordinates, time reversal, charge conjugation, rotations, or Lorentz transformations. Also known as symmetry. Invariance principle : Any principle which states that a physical quantity or physical law possesses invariance under certain transformations. Also known as symmetry law; symmetry principle. In general relativity, the principle that the laws of motion are the same in all frames of reference, whether accelerated or not. Node : A point, line, or surface in a standing-wave system where some characteristic of the wave has essentially zero amplitude. Parity : A physical property of a wave function which specifies its behavior under an inversion, that is, under simultaneous reflection of all three spatial coordinates through the origin; if the wave function is unchanged by inversion, its parity is 1 (or even); if the function is changed only in sign, its parity is -1 (or odd). Parity conservation : The law that, if the wave function describing the initial state of a system has even (odd) parity, the wave function describing the final state has even (odd) parity; it is violated by the weak interactions. Also known as conservation of parity. Photoelectric effect : The liberation of electrons by electromagnetic radiation incident on a electrons by electromagnetic radiation incident on a substance; includes photoemission, photoionization, photoconduction, the photovoltaic effect, and the Auger effect (an internal photoelectric process). Also known as photoelectric effect; phtoelectric process. Planck oscillator : An oscillator which can absorb or emit energy only in amounts which are integral multiples of Planck's constant times the frequency of the oscillator. Also known as radiation oscillator. Planck radiation formula : A formula for the intensity of radiation emitted by a blackbody within a narrow band of frequencies (or wavelengths), as a function of frequency, and of the body's temperature. Also known as Planck distribution law; Planck's law. Planck's constant : A fundamental physical constant, the elementary quantum of action; the ratio of the energy of a photon to its frequency, it is equal to 6.62620 + 0.00005 X 10-34 joule-second. Symbolized h. Planck's law : A fundamental law of quantum theory stating that energy associated with electromagnetic radiation is emitted or absorbed in discrete amounts which are proportional to the frequency of radiation. Quantum : For certain physical quantities, a unit such that the values of the quanitty are restricted to integral multiples of this unit; for example, the quantum of angular momentum is Planck's constant divided by 2p. Quantum electrodynamics : The quantum theory of electromagnetic radiation, synthesizing the wave and corpuscular pictures, and of the interaction of radiation with electrically charged matter, in particular with atoms and their constituent electrons. Also known as quantum theory of light; quantum theory of radiation. Quantum field theory : Quantum theory of physical systems possessing an infinite number of degrees of freedom, such as the electromagnetic field, gravitation field, or wave fields in a medium. Quantum hypothesis : A hypothesis that some physical quantity can assume only a certain discrete set of values; examples are Planck's law, and the condition in the Bohr-Sommerfield theory that the action integral of a system must be an integral multiple of Planck's constant. Also known as quantum postulate. Quantum mechanics : The modern theory of matter, of electromagnetic radiation, and the interaction between matter and radiation; it differs from classical physics, which it generalizes and supersedes, mainly in the realm of atomic and subatomic phenomena. Also known as quantum theory. Quantum number : One of the quantities, usually discrete with integer or half-integer values, needed to characterize a quantum state of a physical system. Quantum statistics : The statistical description of particles or systems of particles whose behaviour must be described by quantum mechanics rather than classical mechanics. Quantum theory of spectra : The contemporary theory of spectra, based on the idea that an atom, molecule, or nucleus can exist only in certain allowed energy states, that it emits or absorbs energy as it changes from one state another, and that the frequency of the associated electromagnetic radiation equals the difference in energies of two states divided by Planck's constant. Quantum-wave equation : A partial differential equation which related the spatial and time dependences of a wave function of a system of one or more atomic or subatomic particles: examples are the Schrdinger equation in nonrelativistic quantum mechanics, and the Klein-Gordon, Dirac, Rarita-Schwinger and Proca equations in relativistic quantum mechanics. Rayleigh-Jeans law : A law giving the intensity of radiation emitted by a blackbody within a narrow band of wavelengths; it states that this intensity is proportional to the temperature divided by the fourth power of the wavelength; it is a good approximation to the experimentally verified Planck radiation formula only at long wavelengths. Relativistic mechanics : Any form of mechanics compatible with either the special or the general theory of relativity. Relativistic quantum theory : The quantum theory of particles which is consistent with the special theory of relativity, and thus can describe particles moving arbitrarily close to the speed of light. Resonator : A device that exhibits resonance at a particular frequency, such as an acoustic resonator or cavity resonator. Schrdinger equation : A partial differential equation governing the Schrdinger wave function y (pronounced psi) of a system of one or more nonrelativistic particles. Schrdinger-Klein-Gordon equation : A wave equation describing a spinless particle which is consistent with the special theory of relativity. Also known as Klein-Gordon equation. Schrdinger picture : A mode of description of a quantum-mechanical system in which dynamical states are represented by vectors which evolve in the course of time, and physical quantities are represented by stationary operators, in contrast to the Heisenberg picture. Schdinger's wave mechanics : The version of nonrelativistic quantum mechanics in which a system is characterized by a wave function y (pronounced psi) which is a function of the coordinates of all the particles of the system and time, and obeys a differential equation, the Schrdinger equation; physical quantities are represented by differential operators which may act on the wave function, and expectation values of measurements are equal to integrals involving the corresponding operator and the wave function. Also known as wave mechanics. Schrdinger wave function : A function of the coordinates of the particles of a system and of time which is a solution of the Schrdinger equation and which determines the average result of every conceivable experiment on the system. Also known as probability amplitude; psi function. Spectroscope : An optical instrument consisting of a slit, collimator lens, prism or grating, and a telescope or objective lens which produces a spectrum for visual observation. Spectroscopy : The branch of physics concerned with the production, measurement, and interpretation of electromagnetic spectra arising from either emission or absorption of radiant energy by various substances. Spectrum : The set of frequencies, wavelengths or related quantities, involved in some process; for example, each element has a characteristic discrete spectrum for emission and absorption of light. Standing wave : A wave in which the ratio of an instantaneous value at one point to that at any other point does not vary with time. Also known as stationary wave. Steady state : The condition of a body or system in which the conditions at each point do not change with time, that is after initial transients or fluctuations have disappeared. Stefan-Boltzmann constant : The energy radiated by a blackbody per unit area per unit time divided by the fourth power of the body's temperature; equal to (5.6696 + 0.0010) X 10-8 (watts)(meter)-2(degrees Kelvin)-4. Stefan-Boltzmann law : The total energy radiated from a blackbody is proportional to the fourth power of the temperature of the body. Also known as fourth-power law; Stefan's law of radiation. Thermal equilibrium : Property of a system all parts of which have attaned a uniform temperature which is the same as that of the system's surroundings. Thermodynamic equilibrium : Property of a system which is in mechanical, chemical, and thermal equilibrium. Thermodynamics : The branch of physics which seeks to derive, from a few basic postulates, relationships between properties of matter, especially those which are affected by changes in temperature, and a description of the conversion of energy from one form to another. Ultraviolet catastrophe : The prediction of the Rayleigh-Jeans law that the energy radiated by a blackbody at extremely short wavelenghts is extremely large, and the total energy radiated is infinite, whereas in reality it must be finite. Uncertainty principle : The precept that the accurate measurement of an observable quantity necessarily produces uncertainties in one's knowledge of the values of other observables. Also known as Heisenberg uncertainty principle; indeterminancy principle. Uncertainty relation : The relation whereby, if one simultaneously measures values of two canonically conjugate variables, such as position and momentum, the product of the uncertainties of their measured values cannot be less than approximately Planck's constant divided by 2p. Also knowns as Heisenberg uncertainty relation. Wave equation : Any of several equations which relate the spatial physical entity which can propagate as a wave, including quantum-wave equation for particles. Wave mechanics : The version of nonrelativistic quantum mechanics in which a system is characterized by a wave y (pronounced psi) function which is a function of the coordinates of all the particles of the system and time, and obeys a differential equation, the Schrdinger equation; physical quantities are represented by differential operators which may act on the wave function, and expectation values of measurements are equal to integrals involving the corresponding operator and the wave function. Also known as Schdinger's wave mechanics . Wien constant : The product of the temperature and wavelength at which the intensity of radiation from a blackbody reaches its maximum; i is equal to approxumetely 2898 micron-degrees. Wien's displacement law : A law for blackbody radiation which states that the wavelength at which the maximum amount of radiation occurs times the temperature is a constant equal to approximately 2898 micron-degrees. Also known as displacement law; Wien's radiation law. Wien's distribution law : A formula for the spectral distribution of radiation from a blackbody, which is a good approximation to the Planck radiation formula at sufficiently low temperatures of wavelengths, for example, in the visible region of the spectrum below 3000K. Also known as Wien's radiation law. Planck's postulate and simple pendulum The success of Planck's postulate in leading to a theoretical black body spectrum which agrees with experiment requires that we tentatively accept its validity, at least until such time as it may be proved to lead to conclusions which disagree with experiment. Apparently, there are physical systems whose behavior seems to be obviously in disagreement with the postulate. For instance, an ordinary pendulum executes simple harmonic oscillations, and yet this system certainly appears to be capable of possessing a continuous range of energies. Before we accept this argument, it would be desirable to make some simple numerical calculations concerning such a system. Consider a pendulum consisting of a 1gm weight suspended from a 10cm string. The oscillation frequency of this pendulum is about 1.6/sec. The energy of the pendulum depends on the amplitude of the oscillations. Assume the amplitude to be such that the string in its extreme position makes an angle of 0.1 radian with the vertical; then the energy E is approximately 50 ergs. If the energy of the pendulum is quantized, any decrease in the energy of the pendulum, due for instance to frictional effects, will take place in discontinuous jumps of magnitude hn = 6.63 x 10-27 x 1.6 ~ 10-26 ergs, whereas E ~ 50 ergs, it is apparent that even the most sensitive experimental equipment would be totally incapable of resolving the discontinuous nature of the energy decrease. No evidence, either positive or negative, concerning the validity of Planck's postulate is to be found from experiments involving a pendulum. The same is true of all other macroscopic mechanical systems. Only when we consider systems in which n is so large and/or E is so small that hn is of the order of E are we in a position to test Planck's postulate. One example is, of course, the high frequency standing waves in black body radiation. Nobel Prizes awarded for work on Quantum Theory and/or its application. The quantum theory brought about a sea change in our conceptual understanding of phenomena observed at atomic level. Here is a list of Nobel Prizes awarded for work on quantum theory and/or its application. 1911 1918 1921 1922   1927 1929 1932   1933   1937 1945   1954   1955   1957     1963     1965   1969 1979     1984   1999 Wilhelm Wien Max Karl Ernst Ludwig Planck Albert Einstein Niels Henrik David Bohr   Arthur Holly Compton Prince Louis-Victor Pierre Raymond de Broglie Werner Karl Heisenberg   Erwin Schrdinger Paul Adrien Maurice Dirac Clinton Joseph Davisson George Paget Thomson Wolfgang Pauli   Max Born   Willis Eugene Lamb Polykarp Kusch Chen Ning Yang   Tsung-Dao Lee Eugene Paul Wigner   Maria Goeppert-Mayer J. Hans D. Jenssen Sin-Itiro Tomonaga Julian Schwinger Richard P. Feynman Murray Gell-Mann Sheldon Lee Glashow Abdus Salam Steven Weinberg Carlo Rubbia Simon van der Meer Gerardus 't Hooft Martinus J.G. Veltman Germany Germany Germany & Switzerland Denmark USA France Germany   Austria   USA Great Britain Austria   Great Britain   USA USA China   China USA   USA Germany Japan USA USA USA USA Pakistan USA Italy the Netherlands the Netherlands the Netherlands in Physics for his discoveries regarding the laws governing the radiation of heat in Physics in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta in Physics for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect in Physics for his services in the investigation of the structure of atoms and of the radiation emanating from them in Physics for his discovery of the effect named after him in Physics for his discovery of the wave nature of electrons in Physics for the creation of quantum mechanics, the application of which has, inter alia, led to the discovery of the allotropic forms of hydrogen in Physics for the discovery of new productive forms of atomic theory -do- in Physics for their experimental discovery of the diffraction of electrons by crystals -do- in Physics for the discovery of the Exclusion Principle, also called the Pauli Principle in Physics for his fundamental research in quantum mechanics, especially for his statistical interpretation of the wavefunction in Physics for his discoveries concerning the fine structure of the hydrogen spectrum in Physics for his precision determination of the magnetic moment of the electron in Physics for their penetrating investigation of the so-called parity laws which has led to important discoveries regarding the elementary particles. -do- in Physics for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles in Physics for their discoveries concerning nuclear shell structure -do- in Physics for their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles -do- -do- in Physics for his contributions and discoveries concerning the classification of elementary particles and their interactions in Physics for their contributions to the theory of the unified weak and electromagnetic interaction between elementary particles, including, inter alia, the prediction of the weak neutral current -do- -do- in Physics for their decisive contributions to the large project, which led to the discovery of the field particles W and Z, communicators of weak interaction -do- in Physics for elucidating the quantum structure of electroweak interactions in physics -do-   A Long Journey Quantum theory has helped us unravel the natural processes at atomic and sub-atomic levels and push the frontiers of our knowledge further and further. Understanding the properties of fundamental particles and the nature of forces in the sub-atomic level could become possible only with the application of quantum mechanics. Let us briefly see where quantum theory has led us to during the last hundred years. Particle physicists zoomed in on the sub-atomic realm with increasingly powerful instruments. Forces were revealed in the sub- atomic level that no one had predicted, the best example being the strong nuclear force that holds the atomic nucleus together. Experiments revealed the existence of hundreds of different and unexpected particles. Eventually patterns emerged and theories were put together and tested. Today, elementary particle physics provides the basis for understanding an astonishing variety of phenomena in terms of just a few "truly" elementary particles and forces between them. The remarkable state of our understanding of elementary particles, embodied in the present theory called the "Standard Model," has taken shape over the last 30 years. The Standard Model provides an organizing framework for the known elementary particles. These consist of "matter particles," which are grouped into "families," and "force particles." The first family includes the electron, two kinds of quarks (called "up" and "down"), and a neutrino, a particle released when atomic nuclei undergo radioactive decay. There are two more families consisting of progressively heavier pairs of quarks and a corresponding lepton and neutrino. All normal, tangible matter is made up only of particles from the first family, since the others live for very short times. Why are there three families? This question is one of the great unsolved mysteries of elementary-particle physics. The matter particles exert forces on one another that are understood as resulting from the exchange of the force-carrying particles, Electric and magnetic forces arise when particles exchange quanta of light or photons (the familiar repulsion or attraction of two magnets results from one of them emitting photons that the other receives). The strong force that holds quarks together to form protons and neutrons comes from the exchange of gluons. The weak forces that cause radioactive decay are created by massive Wand Z particles (the photon and gluon have no mass). These three forces have been successfully described by quantum theories that have remarkably similar structures. Theories have recently been developed that link elementary particles, the very smallest known structures, with one of the grandest questions of all: How did the universe begin? These theories suggest that many of the complexities manifest at lower energies would be greatly simplified under conditions of extremely high energy. For example, under such conditions the different forces between the particles would be seen as unified, different manifestations of a single underlying force. There is nothing artificial about these energies: They are understood to have prevailed at the time of the "big bang" that initiated the expansion of the universe. If these theories are correct, the simplicity long sought by particle physicists is a fact of cosmic history . Although re-creating these energies lies beyond the reach of existing and planned accelerators, experiments at these accelerators could nonetheless reveal evidence for what is called supersymmetry . Supersymmetry, which is really a very profound statement about the structure of space and time, predicts that for every fundamental particle there should exist another related and as yet-undiscovered new particle; conclusive evidence for these additional particles is eagerly sought because supersymmetry shows how the electroweak and strong interactions could be unified. In addition, evidence of supersymmetry would also support another even more comprehensive theory , called string theory. String theory pictures particles as extremely tiny vibrating loops, with details of their vibrations determining their properties and interactions, and leads to a theory that is able to encompass ALL of the forces of nature in a unified and self-consistent manner, including -for the first time - gravity. A long journey indeed since the birth of the quantum!   Explaining the Physical World At some stage of the other, all of us have wondered - how our universe came to be so rich and varied? Often we have wondered how the stars, light, planets, and a hundred different atoms that can be combined into countless molecules. Elementary particle physicists seek answers to these questions by studying sub atomic particles and forces. A century ago, the first elementary particle - the electron - was identified. A revolutionary view of the way matter in the universe is put together was provided by the experimental evidence that electrons were basic constituents of all atoms. Quantum Mechanics explained the paradoxical motion of electrons in the atom and the formation of molecules. Eventually, a vast range of phenomena - the stiffness of steel, the way petrol burns, colours in the surface of the bubble, the ability of X-rays to reveal tumours inside the body - could be accounted for by the quantum mechanical behaviour of the electron. This new perspective, a view of the world on more fundamental scale than the everyday world of our experience, eventually led to a century of spectacular science and technological innovation. Understanding the behaviour of the electron and photon, i.e. the quantum of light, has been critically important to the fields of chemistry, materials science, and biology, as well as to the development of modern computing and communication.