The Rise and fall of Theoretical Physics- Abhas Mitra

In the first part of this article, I shall briefly describe the birth and rise of ``Theoretical Physics, from a somewhat historical perspective. It is warned at the outset that this description will be extremely sketchy and far from comprehensive. Further, the emphasis here will be on ``Theoretical Physics rather than ``Mathematical Physics.

Physics as a subject concerns observation, understanding and prediction about the physical world. It is different from mere philosophical or spiritual or religious understanding. In a sense, it is an evolved and more analytical form of Natural Sciences studied in the pre-Newtonian era. And ``Theoretical Physics is the basic framework for understanding and predicting physical phenomena in terms of well defined premises, laws in analytical form. Thus although ``Theoretical Physics may involve various mathematical formulae or tools, it is not mathematics in itself. On the contrary, ``Theoretical Physics originates from observations and experimentations of physical phenomena, and it could even be able to predict unknown physical effects. The success of ``Theoretical Physics (TP) lies in the verifiability of its predictions.

Indeed the birth of TP may be related to the improved facility for observations or technological developments. It might be seen that, there was hardly any TP, say 400 years ago. Following this vacuum, even without using telescopes, Tycho Brahe (15461601) made accurate observations of planetary motions and many other astronomical phenomena like Supernova Explosion. Based on such observations Johannes Kepler (1571-1630) published his laws on planetary motion during 1609-19. Such laws, in conjunction with Galileo Galileis (1564-1642) telescope based

observations overthrew the classic philosophy based Aristotlean world views to herald modern physics. For instance, Aristotle had argued that the orbits of heavenly bodies must be circular because circle has a perfect symmetry. But observations showed that such orbits in general are elliptical. To be more precise, Isaac Newton (16421727), guided by Keplers laws of planetary motion, predicted an universal law of gravitation. He was also influenced by Galileos experiments, and probably, ``Theoretical Physics as a matured subject was born on July 5, 1687 when Newton published

"Mathematical Principles of Natural Philosophy", often referred to simply as the Principia.

While formulating his physical theories, Newton developed and used Calculus. However, one hardly needs to emphasize the fact that calculus itself is no physics or science. Neither any mathematics nor any geometry by itself is physics even though they may provide the language for

formulating TP. Once Galileo and Newton formulated the classical physics, it grew with inputs from many greats. In classical physics, the important law of elasticity, that the restoring force is proportional to displacement,

was given by Robert Hooke(16351703) in 1960. However, while Newton considered light as a collection of point particles even at the classical level, it was Christian Huygens (1629-1695) who correctly predicted the wave nature of the same in 1678. Also, it was Huygen who first got the laws of motion for an oscillating pendulum. Later, William Rowan Hamilton (1805-1865) reformulated

Robert Hooke

classical mechanics in 1833 by the Principle of Least Action, a method known as Lagrangian Mechanics. This was based on Analytical Mechanics and variational calculus developed earlier by Joseph Louis Lagrange (1736- 1813). The concept of ``Lagrangian and ``Hamiltonian proved to be important milestones not only classical mechanics but also for entire TP whether it is quantum physics or relativistic physics. The variational principle used in the Lagrangian and Hamiltonian formulations were originally due to Pierre de Fermat (1601 -1665) and Pierre Louis Maupertuis (1698-1759). In particular Fermat had postulated that light travels between two given points along the path of shortest time. It is interesting to note that the Snells Law of refraction of light rays, obtained by Willebrord Snellius (15801626), follows from the principle of least action/time.

Amalie Emmy Noether (1882-1935) introduced by her name in 1931. The Noether a theorems Theorem explains the fundamental connection between symmetry and conservation laws in all realms of TP. Note, Emmy is probably the best known female theoretical physicist and mathematician in the history.

The basic structure of massive self-gravitating astrophysical objects, such as stars and galaxies, is described by the so called Lane-Embden equation which was independently obtained by Jonathan Homer Lane(1819 -1880) in 1870 and Jacob Robert Emden(1862 1940) in 1907. The NavierStokes equations of fluid motion, important for many areas of physics too, was developed by Claude-Louis Navier(1785-1836) in 1822 and George Gabriel Stokes (1819- 1903) in 1850.

The phenomenon of static magnetism and electricity have been studied since antiquity. And based on such observations and not from just intellectual speculation, Charles Coulomb (1736-1806) published the inverse square law of static electricity, known by his name, in 1785. Of course whether it is Newtons or Coulmobs law, they all have been verified by various observations and experimentations. Few decades before it, in 1752, Benjamin Franklins (1707-1790) observations had already opened up the subject of electric currents. There were observations suggesting intimate connection between of electric and magnetic phenomena, and the experiments of Hans Christian rsted(1777-1851) and Andr-Marie Ampre (1775-1836) gave birth to the subject of electromagnetism during 1819-1820. Following this, Michael Faraday (1791 -1867) not only invented the electric motor in 1821 but also developed the concept of an electromagnetic field. The ultimate unification of ``electricity and ``magnetism as well as the realization that light was a form of electromagnetic wave can be ascribed to James Clerk Maxwell (1831-1879). His laws formally got announced in 1865. This was the culmination of the classical phase of the modern physics, and much of the fruits of this epoch making discoveries were put to use for the benefit of human kind by the researches of the great technologist Nikola Tesla (1856-1943). Maxwells equations were however ignored by many peers for a long time; one of the reasons for this was that Lord Kelvin (1824- 1907), one of the most influential British physicists of those days, was a staunch believer in the existence of ``aether and was rather conservative about new physics and technologies.

After Newton, Johann Carl Friedrich Gauss (1777-1855) is the best example of how mathematicians of the highest order can contribute to the pioneering development of

Amalie Emmy Noether

Theoretical Physics which are testable by experiments unlike present day mathematical physics, say in the field of Quantum Gravity, which rarely make any verifiable prediction. In 1835, Gauss formulated ``Gauss's law relating the distribution of electric charge to the resulting electric field. This however got published only in 1865 as one of the ingredients of the Maxwells Equations of electromagnetism.

A very important parallel development of classical physics and TP had also been in progress. Thomas Newcomen (1664-1729) had developed a commercially successful model of Steam Engine in 1712. And James Watt (1736 1819) invented a qualitatively superior version of the same during 1762- 1775. This and other associated technological big leaps gave rise to Industrial Revolution (1750-1850) in Europe. As the scientists wanted to understand the functioning of new machines and improve their efficiencies ``Thermodynamics got developed as a subject. The concept of Carnot Cycle came in 1824 following the experiments by Nicolas Lonard Sadi Carnot(1796 -1832), and then Rudholp Clausius (1822-1888) formulated the 1st and 2nd

laws of thermodynamics in 1850. And it is he who introduced the concept of entropy in 1865. Further in 1870, he found ``Virial Theorem which connects the potential and kinetic energies of a fluid. A crucial aspect of 1st law is the concept of ``mechanical equivalence of heat was developed by Julius von Mayer (1801-1869) and James Joules (1818-1889) during 1840-1843 through a series of experiments. Such experiments and the development of thermodynamics led Hermann von Helmholtz (1821-1894) to formulate the Principle of Conservation of Energy. In 1871, Helmholtz also announced that the velocity of the propagation of electromagnetic induction was about 314,000 meters per second! As to the 3rd

law of thermodynamics, Lord Kelvin first spoke

about an absolute zero of temperature. By armed with the laws of conservation of energy and Newtonian gravitation, Helmholtz and Kelvin independently developed one of the fundamental aspects of Theoretical Astrophysics in the nineteenth century:

A self-gravitating fluid, during its contraction, not only becomes hotter but also must radiate out part of the released gravitational potential energy (H-K Process).

The birth of Statistical Mechanics can be largely attributed to the physical intuition of Ludwig Boltzman (1844-1906). By 1988, he was a very well known physicist and even became a Fellow of the Swedish Royal Academy of Sciences. It is after this period that he developed atomic theory of heat. He along with James Maxwell gave the Maxwell- Boltzman distribution formula of speeds of atoms in a gas. However most of his peers wanted to see ``heat only as a form of energy and were not ready to attribute microscopic molecular motions to it. This was one of the reasons which drove Boltzman to mental depression, and he leapt to his death into the Adriatic sea at Trieste on Sept. 05,1906. His tombstone bears the inscription: S=k ln W! Ironically, the spot where he committed suicide is adjacent to the International Centre for Theoretical Physics (ICTP).

The spectrum of a black body radiation, being studied experimentally since 1850, could not be

explained by a single theoretical formula. In 1900, Max Planck (1858-1947) offered the much needed theoretical platform by introducing the revolutionary concept that radiation can be seen as sum of discrete quanta whose energies are Max Planck

proportional to the frequency of the radiation. However, historically, Boltzman had suggested in 1877 that, in a physical system, energy can appear in discrete values. Formally the concept of a ``photon as the quanta of radiation was further developed by Einstein in 1905 while explaining the phenomenon of ``Photo-electricity discovered in Philipp Lenard 1902. Formally, the term "photons", was however introduced by Gilbert N. Lewis (1875-1956) in 1926. The old form of Quantum Mechanics (QM) came into being in 1913 as Niels Bohr (1885-1962) offered a model of atoms where electrons revolve the central nucleus in orbits having quantized energies. The Bohr model was a quantum improvement of the model of atomic nucleus offered by Ernest Rutherford (1871-1937) just two years earlier. Bohrs research is a very important in TP contribution because it correctly explained the spectral lines of the hydrogen atom. Accordingly, Bohr won the Nobel prize for this successful model/theory in 1925.

To see the close relationship of TP with observations and experimentations, we may recall the MichelsonMorley experiment performed in 1887 by Albert Michelson (1852-1931) and Edward Morley (1838-1923). It was designed to detect the relative speed of Earth with respect to the aether. The null/negative result of this experiment suggested that the speed of light in the vacuum is constant and vacuum is actually not filled with any mythical fluid, aether through which light waves were supposed to propagate. This result challenged the Galilean Relativity, and in order to explain this null result, in 1895, Hendrick Lorenz (1853-1928) proposed that moving bodies contract in the direction of motion. Such a Length contraction was already postulated by George Francis FitzGerald (1851-1901) in 1889. Actually, Maxwells equations of electromagnetism obtained in 1965 are not invariant under Galilean Transformation, and thus new laws of coordinate

transformations were already due irrespective of Michelson Morley null results. And this was probably first realized by Jules Henri Poincar (1854 1912). He elevated the proposal of ``Lorentz Fitzerald Contraction into a revolutionary new complete coordinate/velocity transformation law, i.e., ``Lorentz Transformations. As he showed that Maxwells equations are invariant under the new transformation law, pre-natal phase of Special Theory of Relativity (STR) was born. Incidentally, it was called ``special because the relevant transformations were thought to be applicable only for inertial frames. The fact that physical laws must be invariant under appropriate coordinate transformations, in other words, the principle of relativity was laid down by Poincare. He made such presentations to the Academy of Sciences in Paris on 5 June 1905. In fact the most famous equation of physics E=Mc2 first appeared in Poincares manuscript.

Further Emil Georg Cohn (1854 1944) also published two papers in 1904 whose title contained the phrase ``electrodynamics of moving bodies, and derived most of STR. However, Cohn thought that Lorentz Transformations had validity only for optical phenomena.

Yet, STR, as a fundamental and complete physical theory, was developed by Albert Einstein. His paper ``On the Electrodynamics of Moving Bodies, submitted on June 30, 1905 and published on September 26, 1905, is the true thesis on STR. To Einstein, the phenomenon of constancy of the speed of light was not just a result of Michelson Morley experiment, nor just a consequence of Maxwells electromagnetism, but on the other hand, a fundamental law of the Physical World. Accordingly, he independently considered ``Principle of Relativity a fundamental all encompassing fact of Physics. By basing on these two fundamental postulates, he arrived at the Lorentz Transformation formulae. While the

E=Mc2 formula found by Poincare was only in the context of electromagnetic waves, the same for Einstein was a fundamental equivalence of ``Mass and ``Energy. Einsteins paper announcing STR did not cite a single reference, an act, which would be castigated by all modern science journals!

While Poincar too questioned the concept of universality, but contrary to Einstein, he continued to use the concept of aether in his papers. His contention was that the clocks in the ether show the "true" time, and moving clocks show the local time. In effect, Poincar tried to keep the relativity principle in accordance with classical concepts, while Einstein developed a mathematically equivalent kinematics based on the new physical concepts of the relativity of space and time. Thus, Einstein was the real founder of STR.

It became soon clear that Newtonian gravitation was inconsistent with STR, and after a long struggle and several false starts, and also help from various quarters, in particular from the mathematician Marcel Grossmann (1878 -1936), Einstein arrived at the correct form of General Theory of Relativity (GTR) in 1916. This was now called ``general theory because it was applicable to all frames. The central equation of GTR, called, Einstein Equation, proposed that the geometry of the 4-D space-time continuum (tensor) is directly generated by Matter Energy Momentum (tensor). As far as the mathematical derivation of Einstein Equation is concerned, the mathematician David Hilbert (1982-1943) derived it by elegant variational principle almost simultaneously. In other words, gravitation is the manifestation of space-time structure. Some of these experimental verifications of GTR have been based on the solution for the space-time structure around a neutral ``point mass (massenpunkt) by Karl Schwarzschild (1873 -1916) and David Hilbert (1862-1943) which differ by the choice of the origin of the radial parameter. While modern

relativistic astrophysics correctly use the geometrically significant ``Hilbert solution, somehow, by some historical mistake, it is referred to as the ``Schwarzschild Solution! The gravitational mass of a star or galaxy, appearing in this solution must indeed be positive and finite. However, in 2009, it was shown (A. Mitra, Journal of Mathematical Physics, Volume 50, pp. 042502: http://arxiv.org/abs/0904.4754) that, for genuine point mass (and not for a finite object), the gravitational mass would shrink to zero due to loss of mass-energy during prior shrinking of say, a star. Nonetheless, the ``Black Hole Paradigm is based by ignoring this fact, and instead by adopting the Newtonian notion that even a point particle can have arbitrary high mass. It is now widely acknowledged that GTR is the most self-consistent and beautiful physical theory humankind has ever formed. Esthetics apart, GTR has passed most of the experimental tests carried out so far to cross-check it, and definitely scores well above several other relativistic gravity theories proposed from time to time. Such alternative theories often have additional/ ad-hoc assumptions and lack the beauty and simplicity of GTR. The only ad-hoc element added to GTR is the so-called ``Cosmological Constant introduced in 1917. However, ``Cosmological Constant is badly needed only by the presently popular (1998-2012), ``Concordance Cosmology which could very well be incorrect. And it is well known that, in his later years, Einstein himself wanted to do away with this ad-hoc constant.

Talking about Poincar, it must be mentioned that he was also the first scientist to discover a chaotic deterministic system and which would be the foundations of modern chaos theory, applicable for most of the physical systems having multiple degrees of freedom and in particular for complex systems. Though this article is about TP, I cannot resist here telling the fact that Poincare is

the founder of the mathematical subject ``Topology, and that proposer of the ``Poincare Conjecture of mathematics.

The concept of quantum mechanics took a new and interesting turn in 1924 with the postulation of wave-particle duality by Louis de Broglie in his Ph.D. thesis; and in the same year, the phrase "quantum mechanics"was first used by Max Born (1882-1970) in his paper"Zur Quantenmechanik". Modern QM however was born, so to say, in 1925 when Werner Heisenberg (1901-1976), Max Born and Pascual Jordan(1902 -1980) presented its Matrix Formulation. In the following year, Erwin Schrodinger (1887-1961) revolutionized physics by publishing the wave equation for a quantum system. In the same year, Enrico Fermi (1901 -1954) and Paul Dirac (1902-1984) independently gave ``FermiDirac statistics applicable for identical particles with half-odd-integer spin in a system in thermal equilibrium. On the other hand, in 1924, Satyendra Nath Bose (1894-1974), in collaboration with Einstein gave BoseEinstein statistics, applicable for integer spin particles. And this discovery paved the way for the theory of the BoseEinstein condensate. By 1925, Wolfgang Pauli (1900 -1958) suggested the Exclusion Principle, known by his name, by which two

Fermions are prohibited to occupy an exactly same quantum state. A natural consequence of the wave particle duality was perhaps fuzziness for the precise location of a

particle. And this was highlighted by the ``Uncertainty Principle by Heisenberg in 1927.

A truly path breaking application of the Pauli exclusion principle was made in 1926, when Ralph H. Fowler (1989-1944) showed that the compact White Dwarf stars could be supported by degenerate Fermi-Dirac electron gas. Also Arnold

Sommerfeld (1868 -951) was one of the pioneers of atomic physics by using the Fermi-Dirac statistics and gave the concept of a Fine Structure Constant.

Relativistic Quantum Field Theory, the theory that unified STR and QM, got developed with the publication of theory of electrons (spin half particles) by Paul Dirac in 1928. This theory also first gave the idea of anti-matter/positrons. Immediately before this, in the same year, Pauli had introduced the 2 2 Pauli matrices as a basis of spin operators, thus solving the non-relativistic theory of spins. In contrast Diracs theory involved 4X4 matrices. Before this, in 1926 Oskar Klein (1894-1977) and Walter Gordon (1893-1939) had (unsuccessfully) purported to offer a relativistic theory of electrons. Klein Gordon equation was however the correct relativistic form of Schrodinger equation and describes the motion of a quantum scalar or psedo scalar field, a field whose quanta are spin-less particles.

Pauli also postulated the existence of neutrinos by studying beta-decay in 1930. The idea of neutrinos got consolidated with the discovery of neutrons by James Chadwick (1891 -1974) in 1932.

In 1934, Meghnad Saha(1893 - 1956) presented the ionization equation known by his name. This equation was crucial for the interpretation of stellar spectra.

In 1935 Hideki Yukawa (1907-1981) published his theory of mesons, which explained the interaction between protons and neutrons.

During 935-1938, Hans Albrecht Bethe (1906-2005) developed the theory of nucleo-synthesis, in particular, carbon-oxygen-nitrogen cycle , in the core of Sun like stars. The traditional H-K process is not sufficient to generate luminosities for main-sequence-stars for so long.

R.H. Fowler

The development of Quantum Electrodynamics (QED) was completed by Richard Feynman (1918- 1988), Julian Seymour Schwinger (1918 -1994), Freeman Dyson (1923) and Sin-Itiro Tomonaga (1906 -1979) in the 1940s. QED is a successful theory not because of any mathematical novelty but because it was successful in giving correct values of Lamb shift, a small difference in energy between two energy

levels and of hydrogen atom, and magnetic moment of the electron. The QED calculations for the Lamb Shift were carried out by Victor Frederick Weisskopf (1908 -2002).

As was noted earlier, self-gravitating objects like stars during their contraction must emit radiation. After the formulation of GTR in 1916, Prahalad Chunnilal Vaidya (1918 2010), first gave the expression for space-time structure around a radiating and contracting star in 1951. Physical applicability of his work was straight forward and transparent unlike many other exact solutions of GTR.

In 1956, Shivaramakrishnan Pancharatnam(19341969) discovered a type of geometric phase sometimes known for polarized beams of particles passing through crystals. Much later, this was rediscovered by Michael Berry (1941) in 1984.

In a landmark paper published in Reviews of Modern Physics in 1957 (B2FH paper), Margaret Burbidge (1919) , Geoffrey Burbidge (1925-2010), William Fowler (1911-1995) and Fred Hoyle (1915-2001), gave the complete theory of synthesis of various elements at the core of massive stars by extending the initial work of Bethe.

In 1954, Chen Yang(1922) and Robert Mills (1927 -1999) formulated the first Quantum Field Theory for Strong Interaction by invoking SU(3) (Special Unitary Group of Rank 3, referring to some

geometrical symmetry of the interaction) symmetry group. This Yang-Mills theory laid the foundation for the Quantum Chromodynamics (QCD). The so-called Higgs Mechanism by which elementary particles are supposed to acquire their mass was first proposed by Philip Warren Anderson (1923) in 1962. Its relativistic version got developed in 1964 by many including Peter Higgs (1929). In 1961, Jeffrey Goldstone (1933) considered the possibility of spontaneously broken continuous symmetry of interaction of quantum fields and attendant spontaneous generation of bosons.

Building on the pioneering work by Schwinger, Higgs and Goldstone, Sheldon Glashow (1932), Steven Weinberg (1933) and Abdus Salam (1926 -1996) independently showed how the weak nuclear force and quantum electrodynamics could be merged into a single electroweak force. And they jointly won the 1979 Nobel Prize in Physics.

However as far as pure weak interaction is concerned , its theory was first proposed by George Sudarshan (1938) & Robert Marshak (1916 -1992) in a conference paper in 1957. This theory of was in terms of ``Vector minus Axial Vector (V-A) Lagrangian and crucial for the theory of weak interactions. Six months later, Feynman and Murray Gell-Mann (1939) published similar idea in a journal. As claimed by Sudarshan, Gell-Mann got this idea from him. In fact Feynman admitted in 1963 that "The V-A theory that was discovered by Sudarshan and Marshak, publicized by Feynman and Gell-Mann. However both Marshak and Sudarshans contributions were ignored while awarding the 1979 Nobel Prize in Physics.

In 1963, Sudarshan also developed the of way of writing down the state of any type of light using the coherent states as a basis. Afterwards, in the same year, Roy J. Glabauer (1925) presented

almost the same theory and won the Nobel in physics in 2005, while Surdarshan was again denied due recognition!

The idea that hadrons (heavy particles) like neutrons and protons are made of Quarks were independently proposed by physicists Murray Gell-Mann (1929) and George Zweig(1937) in 1964. The concept of asymptotic freedom, i.e., the bonds between quarks become asymptotically weaker as energy increases and distances decrease was predicted by 1970s by David Politzer (1949), by Frank Wilczek(1951) and David Gross (1941). Gerard 't Hooft (1949) had also independently found asymptotic freedom even earlier (but did not publish).

QCD is a successful theory because the Positron-Electron Tandem Ring Accelerator found evidences for gluons and 1979. Later, perturbative QCD also got verified up to a certain degree in Large ElectronPositron Collider at CERN.

Not only classical theories, but quantum field theories too suffered from the problem of occurrences of infinities as interaction distances would tend to zero. In classical electron theory, renormalization, an ansatz for removing such unphysical infinities, were introduced by Lorentz and Max Abraham (1875 -1922). In the context of QED, Kenneth Geddes Wilson(1936) suggested methods of renormalization in 1970s. In the context of QCD, one of the most popular renormalization ansatz is due to Hooft and Martinus J.G.Veltman (1931). Renormalization schemes would often be motivated by condensed matter theories where the discrete structure of atoms provide natural short distance scales. On the other hand, for quantum field theories, in contrast, Plank Length (~10-33 cm), should provide such spatial cut off. Indeed, all such renormalization schemes have ad-hoc aspects and

many leading physicists such as Dyson, Dirac and Feynman were critical about such attempts.

The task of physics is to explain not only microscopic phenomena and fundamental interactions but also all macroscopic phenomena too. In the world at large, physical entities like clouds, leaves, mountains, coastlines do not have well defined geometrical shapes. Neither can one endeavour to understand climate, rainfall, storm, in terms of conventional basic physics. In other words, when large number of degrees of freedoms are at play, there are complex systems which require new broad physics. Even a nucleus with many nucleons may behave as complex systems. Though natural philosophers have been studying such complexities from antiquity, such studies got a big leap as Benot B. Mandelbrot (19242010) coined the term Fractal in 1975 and gave the modern framework for studying complex systems.

CONCLUDING REMARKS:

I feel that, as of now, theoretical physics may have peaked with the formulation of the Standard Model encompassing electromagnetic, weak and strong (nuclear) interactions in the 1970s. This is so even though it is far from a fully self-constant and complete theory. In fact, the evidence for a tiny yet finite neutrino mass creeping up since 2002, is in contradiction with the predictions of SM. Yet, I think that, as of now, SM was the best bet, because (i) It does not invoke fictitious extra spatial dimensions, (ii) It does not require ad-hoc and unverified additional baggage like ``Super Symmetry and most importantly. And most importantly many of the important predictions of the SM have been verified: e.g., , (i) the neutral weak currents caused by Z boson exchange in 1973, (ii) Bottom quark discovered in 1977 (iii) W and Z bosons discovered in 1981, (iv) Top quark discovered in 1995, and (v) Tau neutrino