what are the four major problems faced by classical physics at the turn of the twentieth century?

Question

what are the four major problems faced by classical physics at the turn of the twentieth century, how was each problem resolved by "quantization" ?thanks for answering

Answer 1

In 1901, when the first Nobel Prizes were awarded, the classical areas of physics seemed to rest on a firm basis built by great 19th century physicists and chemists. Hamilton had formulated a very general description of the dynamics of rigid bodies as early as the 1830s. Carnot, Joule, Kelvin and Gibbs had developed thermodynamics to a high degree of perfection during the second half of the century.

Maxwell's famous equations had been accepted as a general description of electromagnetic phenomena and had been found to be also applicable to optical radiation and the radio waves recently discovered by Hertz.

Everything, including the wave phenomena, seemed to fit quite well into a picture built on mechanical motion of the constituents of matter manifesting itself in various macroscopic phenomena. Some observers in the late 19th century actually expressed the view that, what remained for physicists to do was only to fill in minor gaps in this seemingly well-established body of knowledge.

However, it would very soon turn out that this satisfaction with the state of physics was built on false premises. The turn of the century became a period of observations of phenomena that were completely unknown up to then, and radically new ideas on the theoretical basis of physics were formulated. It must be regarded as a historical coincidence, probably never foreseen by Alfred Nobel himself, that the Nobel Prize institution happened to be created just in time to enable the prizes to cover many of the outstanding contributions that opened new areas of physics in this period.

One of the unexpected phenomena during the last few years of the 19th century, was the discovery of X-rays by Wilhelm Conrad Röntgen in 1895, which was awarded the first Nobel Prize in Physics (1901). Another was the discovery of radioactivity by Antoine Henri Becquerel in 1896, and the continued study of the nature of this radiation by Marie and Pierre Curie. The origin of the X-rays was not immediately understood at the time, but it was realized that they indicated the existence of a hitherto concealed world of phenomena (although their practical usefulness for medical diagnosis was evident enough from the beginning). The work on radioactivity by Becquerel and the Curies was rewarded in 1903 (with one half to Becqurel and the other half shared by the Curies), and in combination with the additional work by Ernest Rutherford (who got the Chemistry Prize in 1908) it was understood that atoms, previously considered as more or less structureless objects, actually contained a very small but compact nucleus. Some atomic nuclei were found to be unstable and could emit the or radiation observed. This was a revolutionary insight at the time, and it led in the end, through parallel work in other areas of physics, to the creation of the first useful picture of the structure of atoms.

In 1897, Joseph J. Thomson, who worked with rays emanating from the cathode in partly evacuated discharge tubes, identified the carriers of electric charge. He showed that these rays consisted of discrete particles, later called "electrons". He measured a value for the ratio between their mass and (negative) charge, and found that it was only a very small fraction of that expected for singly charged atoms. It was soon realized that these lightweight particles must be the building blocks that, together with the positively charged nuclei, make up all different kinds of atoms. Thomson received his Prize in 1906. By then, Philipp E.A. von Lenard had already been acknowledged the year before (1905) for elucidating other interesting properties of the cathodic rays, such as their ability to penetrate thin metal foils and produce fluorescence. Soon thereafter (in 1912) Robert A. Millikan made the first precision measurement of the electron charge with the oil-drop method, which led to a Physics Prize for him in 1923. Millikan was also rewarded for his works on the photoelectric effect.

In the beginning of the century, Maxwell's equations had already existed for several decades, but many questions remained unanswered: what kind of medium propagated electromagnetic radiation (including light) and what carriers of electric charges were responsible for light emission? Albert A. Michelson had developed an interferometric method, by which distances between objects could be measured as a number of wavelengths of light (or fractions thereof). This made comparison of lengths much more exact than what had been possible before. Many years later, the Bureau International de Poids et Mesures, Paris (BINP) defined the meter unit in terms of the number of wavelengths of a particular radiation instead of the meter prototype. Using such an interferometer, Michelson had also performed a famous experiment, together with E. W. Morley, from which it could be concluded that the velocity of light is independent of the relative motion of the light source and the observer. This fact refuted the earlier assumption of an ether as a medium for light propagation. Michelson received the Physics Prize in 1907.

The mechanisms for emission of light by carriers of electric charge was studied by Hendrik A. Lorentz, who was one of the first to apply Maxwell's equations to electric charges in matter. His theory could also be applied to the radiation caused by vibrations in atoms and it was in this context that it could be put to its first crucial test. As early as 1896 Pieter Zeeman, who was looking for possible effects of electric and magnetic fields on light, made an important discovery namely, that spectral lines from sodium in a flame were split up into several components when a strong magnetic field was applied. This phenomenon could be given a quite detailed interpretation by Lorentz's theory, as applied to vibrations of the recently identified electrons, and Lorentz and Zeeman shared the Physics Prize in 1902, i.e. even before Thomson's discovery was rewarded. Later, Johannes Stark demonstrated the direct effect of electric fields on the emission of light, by exposing beams of atoms ("anodic rays", consisting of atoms or molecules) to strong electric fields. He observed a complicated splitting of spectral lines as well as a Doppler shift depending on the velocities of the emitters. Stark received the 1919 Physics Prize.

With this background, it became possible to build detailed models for the atoms, objects that had existed as concepts ever since antiquity but were considered more or less structureless in classical physics. There existed already, since the middle of the previous century, a rich empirical material in the form of characteristic spectral lines emitted in the visible domain by different kinds of atoms, and to this was added the characteristic X-ray radiation discovered by Charles G. Barkla (Physics Prize in 1917, awarded in 1918), which after the clarification of the wave nature of this radiation and its diffraction by Max von Laue (Physics Prize in 1914), also became an important source of information on the internal structure of atoms.

Barkla's characteristic X-rays were secondary rays, specific for each element exposed to radiation from X-ray tubes (but independent of the chemical form of the samples). Karl Manne G. Siegbahn realized that measuring characteristic X-ray spectra of all the elements would show systematically how successive electron shells are added when going from the light elements to the heavier ones. He designed highly accurate spectrometers for this purpose by which energy differences between different shells, as well as rules for radiative transitions between them, could be established. He received the Physics Prize in 1924 (awarded in 1925). However, it would turn out that a deeper understanding of the atomic structure required a much further departure from the habitual concepts of classical physics than anyone could have imagined.

Classical physics assumes continuity in motion as well as in the gain or loss of energy. Why then, do atoms send out radiations with sharp wavelengths? Here, a parallel line of development, also with its roots in late 19th century physics, had given important clues for interpretation. Wilhelm Wien studied the "black-body" radiation from hot solid bodies (which in contrast to radiation from atoms in gases, has a continuous distribution of frequencies). Using classical electrodynamics, he derived an expression for the frequency distribution of this radiation and the shift of the maximum intensity wavelength, when the temperature of a black body is changed (the Wien displacement law, useful for instance in determining the temperature of the sun). He was awarded the Physics Prize in 1911.

However, Wien could not derive a distribution formula that agreed with experiments for both short and long wavelengths. The problem remained unexplained until Max K.E.L. Planck put forward his radically new idea that the radiated energy could only be emitted in quanta, i.e. portions that had a certain definite value, larger for the short wavelengths than for the long ones (equal to a constant times the frequency for each quantum). This is considered to be the birth of quantum physics. Wien received the Physics Prize in 1911 and Planck some years later, in 1918 (awarded in 1919). Important verifications that light comes in the form of energy quanta came also through Albert Einstein's interpretation of the photoelectric effect (first observed in 1887 by Hertz) which also involved extensions of Planck's theories. Einstein received the Physics Prize for 1921 (awarded in 1922). The prize motivation cited also his other "services to theoretical physics," which will be referred to in another context.

Later experiments by James Franck and Gustav L. Hertz demonstrated the inverse of the photoelectric effect (i.e. that an electron that strikes an atom, must have a specific minimum energy to produce light quanta of a particular energy from it) and showed the general validity of Planck's expressions involving the constant . Franck and Hertz shared the 1925 prize, awarded in 1926. At about the same time, Arthur H. Compton (who received one-half of the Physics Prize for 1927) studied the energy loss in X-ray photon scattering on material particles, and showed that X-ray quanta, whose energies are more than 10,000 times larger than those of light, also obey the same quantum rules. The other half was given to Charles T.R. Wilson (see later), whose device for observing high energy scattering events could be used for verification of Compton's predictions.

With the concept of energy quantization as a background, the stage was set for further ventures into the unknown world of microphysics. Like some other well-known physicists before him, Niels H. D. Bohr worked with a planetary picture of electrons circulating around the nucleus of an atom. He found that the sharp spectral lines emitted by the atoms could only be explained if the electrons were circulating in stationary orbits characterized by a quantized angular momentum (integer units of Planck's constant divided by ) and that the emitted frequencies corresponded to emission of radiation with energy equal to the difference between quantized energy states of the electrons. His suggestion indicated a still more radical departure from classical physics than Planck's hypothesis. Although it could only explain some of the simplest features of optical spectra in its original form, it was soon accepted that Bohr's approach must be a correct starting point, and he received the Physics Prize in 1922.

It turned out that a deeper discussion of the properties of radiation and matter (until then considered as forming two completely different categories), was necessary for further progress in the theoretical description of the microworld. In 1923 Prince Louis-Victor P. R. de Broglie proposed that material particles may also show wave properties, now that electromagnetic radiation had been shown to display particle aspects in the form of photons. He developed mathematical expressions for this dualistic behavior, including what has later been called the "de Broglie wavelength" of a moving particle. Early experiments by Clinton J. Davisson had indicated that electrons could actually show reflection effects similar to that of waves hitting a crystal and these experiments were now repeated, verifying the associated wavelength predicted by de Broglie. Somewhat later, George P. Thomson (son of J. J. Thomson) made much improved experiments on higher energy electrons penetrating thin metal foils which showed very clear diffraction effects. de Broglie was rewarded for his theories in 1929 and Davisson and Thomson later shared the 1937 Physics Prize.

What remained was the formulation of a new, consistent theory that would replace classical mechanics, valid for atomic phenomena and their associated radiations. The years 1924-1926 was a period of intense development in this area. Erwin Schrödinger built further on the ideas of de Broglie and wrote a fundamental paper on "Quantization as an eigenvalue problem" early in 1926. He created what has been called "wave mechanics". But the year before that, Werner K. Heisenberg had already started on a mathematically different approach, called "matrix mechanics", by which he arrived at equivalent results (as was later shown by Schrödinger). Schrödinger's and Heisenberg's new quantum mechanics meant a fundamental departure from the intuitive picture of classical orbits for atomic objects, and implied also that there are natural limitations on the accuracy by which certain quantities can be measured simultaneously (Heisenberg's uncertainty relations).

Heisenberg was rewarded by the Physics Prize for 1932 (awarded 1933) for the development of quantum mechanics, while Schrödinger shared the Prize one year later (1933) with Paul A.M. Dirac. Schrödinger's and Heisenberg's quantum mechanics was valid for the relatively low velocities and energies associated with the "orbital" motion of valence electrons in atoms, but their equations did not satisfy the requirements set by Einstein's rules for fast moving particles (to be mentioned later). Dirac constructed a modified formalism which took into account effects of Einstein's special relativity, and showed that such a theory not only contained terms corresponding to the intrinsic spinning of electrons (and therefore explaining their own intrinsic magnetic moment and the fine structure observed in atomic spectra), but also predicted the existence of a completely new kind of particles, the so-called antiparticles with identical masses but opposite charge. The first antiparticle to be discovered, that of the electron, was observed in 1932 by Carl D. Anderson and was given the name "positron" (one-half of the Physics Prize for 1936).

Other important contributions to the development of quantum theory have been distinguished by Nobel Prizes in later years. Max Born, Heisenberg's supervisor in the early twenties, made important contributions to its mathematical formulation and physical interpretation. He received one-half of the Physics Prize for 1954 for his work on the statistical interpretation of the wave function. Wolfgang Pauli formulated his exclusion principle (which states that there can be only one electron in each quantum state) already on the basis of Bohr's old quantum theory. This principle was later found to be associated with the symmetry of wave functions for particles of half-integer spins in general, distinguishing what is now called fermions from the bosonic particles whose spins are integer multiples of . The exclusion principle has deep consequences in many areas of physics and Pauli received the Nobel Prize in Physics in 1945.

The study of electron spins would continue to open up new horizons in physics. Precision methods for determining the magnetic moments of spinning particles were developed during the thirties and forties for atoms as well as nuclei (by Stern, Rabi, Bloch and Purcell, see later sections) and in 1947 they had reached such a precision, that Polykarp Kusch could state that the magnetic moment of an electron did not have exactly the value predicted by Dirac, but differed from it by a small amount. At about the same time, Willis E. Lamb worked on a similar problem of electron spins interacting with electromagnetic fields, by studying the fine structure of optical radiation from hydrogen with very high resolution radio frequency resonance methods. He found that the fine structure splitting also did not have exactly the Dirac value, but differed from it by a significant amount. These results stimulated a reconsideration of the basic concepts behind the application of quantum theory to electromagnetism, a field that had been started by Dirac, Heisenberg and Pauli but still suffered from several insufficiencies. Kusch and Lamb were each awarded half the the Physics Prize in 1955.

In quantum electrodynamics (QED for short), charged particles interact through the interchange of virtual photons, as described by quantum perturbation theory. The older versions involved only single photon exchange, but Sin-Itiro Tomonaga, Julian Schwinger and Richard P. Feynman realized that the situation is actually much more complicated, since electron-electron scattering may involve several photon exchanges. A "naked" point charge does not exist in their picture; it always produces a cloud of virtual particle-antiparticle pairs around itself, such that its effective magnetic moment is changed and the Coulomb potential is modified at short distances. Calculations starting from this picture have reproduced the experimental data by Kusch and Lamb to an astonishing degree of accuracy and modern QED is now considered to be the most exact theory in existence. Tomonaga, Schwinger and Feynman shared the Physics Prize in 1965.

This progress in QED turned out to be of the greatest importance also for the description of phenomena at higher energies. The notion of pair production from a "vacuum" state of a quantized field (both as a virtual process and as a real materialization of particles), is also a central building block in the modern field theory of strong interactions, quantum chromodynamics (QCD).

Another basic aspect of quantum mechanics and quantum field theory is the symmetries of wave functions and fields. The symmetry properties under exchange of identical particles lie behind Pauli's exclusion principle mentioned above, but symmetries with respect to spatial transformations have turned out to play an equally important role. In 1956, Tsung-Dao Lee and Chen Ning Yang pointed out, that physical interactions may not always be symmetric with respect to reflection in a mirror (that is, they may be different as seen in a left-handed and a right-handed coordinate system). This means that the wave function property called "parity", denoted by the symbol "P", is not conserved when the system is exposed to such an interaction and the mirror reflection property may be changed. Lee's and Yang's work was the starting point for an intense search for such effects and it was shown soon afterwards that the decay and the decay, which are both caused by the so-called "weak interaction" are not parity-conserving (see more below). Lee and Yang were jointly awarded the Physics Prize in 1957.

Other symmetries in quantum mechanics are connected with the replacement of a particle with its antiparticle, called charge conjugation (symbolized by "C"). In the situations discussed by Lee and Yang it was found that although parity was not conserved in the radioactive transformations there was still a symmetry in the sense that particles and antiparticles broke parity in exactly opposite ways and that therefore the combined operation "C"x"P" still gave results which preserved symmetry. But it did not last long before James W. Cronin and Val L. Fitch found a decay mode among the "K mesons" that violated even this principle, although only to a small extent. Cronin and Fitch made their discovery in 1964 and were jointly awarded the Physics Prize in 1980. The consequences of their result (which include questions about the symmetry of natural processes under reversal of time, called "T") are still discussed today and touch some of the deepest foundations of theoretical physics, because the "P"x"C"x"T" symmetry is expected always to hold.

The electromagnetic field is known to have another property, called "gauge symmetry", which means that the field equations keep their form even if the electromagnetic potentials are multiplied with certain quantum mechanical phase factors, or "gauges". It was not self-evident that the "weak" interaction should have this property, but it was a guiding principle in the work by Sheldon L. Glashow, Abdus Salam, and Steven Weinberg in the late 1960s, when they formulated a theory that described the weak and the electromagnetic interaction on the same basis. They were jointly awarded the Physics Prize in 1979 for this unified description and, in particular, for their prediction of a particular kind of weak interaction mediated by "neutral currents", which had been found recently in experiments.

The last Physics Prize (1999) in the 20th century was jointly awarded to Gerhardus 't Hooft and Martinus J. G. Veltman. They showed the way to renormalize the "electro-weak" theory, which was necessary to remove terms that tended to infinity in quantum mechanical calculations (just as QED had earlier solved a similar problem for the Coulomb interaction). Their work allowed detailed calculations of weak interaction contributions to particle interactions in general, proving the utility of theories based on gauge invariance for all kinds of basic physical interactions.

Quantum mechanics and its extensions to quantum field theories is one of the great achievements of the 20th century. This sketch of the route from classical physics to modern quantum physics, has led us a long way toward a fundamental and unified description of the different particles and forces in nature, but much remains to be done and the goal is still far ahead. It still remains, for instance, to "unify" the electro-weak force with the "strong" nuclear force and with gravity. But here, it should also be pointed out that the quantum description of the microworld has another main application: the calculation of chemical properties of molecular systems (sometimes extended to biomolecules) and of the structure of condensed matter, branches that have been distinguished with several prizes, in physics as well as in chemistry.

Answer 2

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