Physics
The poetry of reality Science 
We must know. We will know. 
A view from the shoulders of giants. 
“”The simplicity of nature is not to be measured by that of our conceptions. Infinitely varied in its effects, nature is simply only in its causes, and its economy consists in producing a great number of phenomena, often very complicated, by means of a small number of general laws.

—PierreSimon de Laplace, Explosition du système du monde.^{[1]} 
Physics is the study of space, time, matter, energy and their interactions with one another. Its scope ranges in size from the smallest subatomic particles to the entire Universe. Physics is therefore the most basic of all natural sciences.^{[2]}^{[3]}
Laws, hypotheses and theories of physics are most often expressed in the language of mathematics. In many cases, breakthroughs in physics are made possible by using already existing mathematical techniques. An example is the application of linear algebra in the matrix formulation of quantum mechanics, or matrix mechanics for short.^{[4]} However, it is worth noting that the development of physics often necessitates that of mathematics. For example, one of the reasons why Newton developed calculus is because he needed it to study classical mechanics and gravitation.
Core developments will be discussed below.
Contents
 1 Early physics
 2 Seventeenth century physics: Warming up
 3 Eighteenth century physics: Age of Newton
 4 Nineteenth century physics: Heat, electricity and magnetism, and chaos
 5 Twentieth century physics: Mainly relativity and quantum mechanics
 6 Twentyfirst century physics: Highenergy physics, gravitation, and condensed matter physics
 7 Astrophysics
 8 See also
 9 External links
 10 Notes
 11 References
Early physics[edit]
Aristotle believed that everything was made up of one of the five elements: earth, fire, air, water, and "quintessence", or the "fifth essence". He also thought the heavenly bodies were perfect and unchanging. His ideas were simply accepted. It is interesting to note that in Eastern philosophy, the Universe is considered to comprise of the five elements: metals, wood, water, fire and earth. There is not much empirical evidence to support either claim. At this stage, research in the natural sciences in general and physics in particular were conducted by philosophers, who could not be bothered to verify their claims with careful observations or experiments.^{[1]} Aristotle in particular made the most casual of observations then drew the most general of conclusions from them. He taught, for example, that an apple falls to the Earth because it has gravity but smoke rises because it has levity.^{[5]}
Things improved dramatically with the arrival of Archimedes of Syracuse. Starting from empirical observations and experiments, he discovered the principle of buoyancy in hydrostatics, the law of the lever and introduced the concept of the center of mass of a body.^{[6]} Archimedes also built a planetarium, which operated on the basis of a heliocentric theory.^{[7]} Observe that the ancient Greeks did in fact entertain the possibility of the Earth and other planets orbiting the Sun. Ultimately, geocentric models proved to be more popular. This was likely due to their fewer observational discrepancies as seen with the naked eye: chiefly, the lack of stellar parallax (it is impossible to state with certainty exactly why heliocentrism was rejected, as no works by heliocentric astronomers or their critics have survived; Aristarchus' heliocentrism is known only because of the reference in Archimedes' The Sand Reckoner). Geocentrism would be held almost unanimously by astronomers until the later 17th century, when Kepler's heliocentric model proved instrumentally superior to the geocentric models (direct observational evidence of Earth's movement, completely shattering the idea that geocentric models were reality, was first done by James Bradley in the early 18th century).
The ancient Greeks made a number of important advances in the study of optics. Euclid of Alexandria, best known for his comprehensive treatise on geometry, published a book on geometric optics. He recognized that light propagated in straight lines, and enunciated the law of reflection, the angle of incidence equals the angle of reflection. He also treated a variety of different mirrors. Hero of Alexandria attempted to explain the behavior of light by assuming that light propagated in such a way that time taken to travel between two points is minimized. During the middle ages, some investigations by scholars working in Baghdad kept the subject alive. But by and large the progress in physics languished. ^{[8]}
Seventeenth century physics: Warming up[edit]
Willebrod Snell experimentally discovered the law of refraction, which now bears his name.^{[8]} Galileo Galilei argued that all bodies fall at the same rate regardless of their masses, if air resistance is negligible. He proved that if air resistance can be ignored, bodies thrown at an angle will fall along a parabolic trajectory. While telescopes were not unheard of at this time, Galileo built superior ones, using which he made observations disproving the Ptolemaic system, discovered the (Galilean) moons of Jupiter, sunspots, that the Moon is full of craters, among other imperfections, all of which contradict Aristotle's teachings. He formulated the law of the pendulum, but failed to design a clock that was usable at sea. Galileo was among the very first scientists as we recognize them today. He fully understood the necessity of experiments and observations and made use of them whenever possible in his investigations. Réne Descartes correctly stated that inertia is the tendency of a massive body to travel in a straight line at constant speed.^{[1]} This later became what we now call Newton's first law of motion. But perhaps his most important contribution was the discovery of coordinate (or Cartesian) geometry, bringing together the powers of symbolic algebra and geometry. The value of this new geometry in both mathematics and physics can hardly be overestimated; it enabled for much more convenient methods of proof and discovery. Furthermore, it paved the way for calculus, which underlies much of physics.^{[9]}
Ole Rømer^{} observed that from Earth, the moons of Jupiter appear to be regularly eclipsed. However, the times between these eclipse are not really constant; in fact they vary according to the position of Earth in its orbit about the Sun. He concluded that the speed of light must therefore be finite. Using the best estimate of the radius of the Earth's orbit available at the time, he calculated the speed of light to be 225,000 km/s. Although this value is not very accurate by modern standards, it was the first time that the speed of light was definitively shown to be finite.^{[1]}
Eighteenth century physics: Age of Newton[edit]
Mechanics and Optics[edit]
Sir Isaac Newton dominated this era. In his masterpiece the Philosophiae Naturalis Principia Mathematica, or Principia for short, he laid down the basics of calculus, the laws of motion and gravitation. Newton gave a theoretical derivation of Kepler's laws of orbital motion, previously obtained from astronomical data provided by Tycho Brahe, and an explanation of tides.^{[1]} While physics has its roots in astronomy and a number of important results have been published before Newton, e.g. Archimedes' principle, it was Newton who constructed physics as a mathematical formalism. It was he who demonstrated that natural phenomena, for all their apparent complexities, arise from a small number of fundamental laws, in a very effective manner. In Opticks, Newton described his famous prism experiment, discussed the laws of optics and articulated his corpuscular theory of light.^{[1]} Christian Huygens and a few others, however, favored a wave theory of light. He also studied the behavior of pendulums, formulating a sophisticated theory of oscillations and inventing a pendulum clock in the process.^{[1]} He suggested that clocks be made using a cycloidal pendulum, which he showed to be isochronous, meaning the period is unaffected by the amplitude of motion. He studied uniform circular motion and obtained the famous formula for the centripetal acceleration.^{[9]}
After Newton's death in 1727, Leonard Euler, Daniel Bernoulli, Jean le Rond d'Alembert, JosephLouis Lagrange, PierreSimon de Laplace, among others, continued the development of calculus and brought classical mechanics to great new heights, as can easily be noted by opening up an advanced textbook on the subject.^{[10]} D'Alembert introduced the principle of virtual work, essentially a reformulation of Newton's laws but one that employs energy, a scalar, rather than forces, which are vectors, or quantities with both magnitudes and direction. This simplifies the analysis of mechanical problems. Euler and Lagrange showed that, equivalently, from the principle of least action, one could, using the machinery of the calculus of variations, which they developed, obtain the equations of motion exactly identical to those derived by a direct application of Newton's laws. Furthermore, the EulerLagrange equations retain the same form regardless of coordinate systems whereas Newton's second law in the familiar form is only valid in Cartesian coordinates. Euler gave a systematic treatment of the dynamics of rigid bodies. Lagrange invented the notion of potentials. Euler and Lagrange studied the threebody problem, such as the SunEarthMoon system, which they solved approximately.^{[note 1]} Lagrange managed to explain lunar libration (apparent oscillations seen from Earth) and why the Moon always shows the same face to the Earth. Lagrange discussed all these amazing developments in mechanics in his masterpiece, Méchanique Analytique.^{[9]}
Near the end of the century in 1791, Giovanni Guglielmini observed the Coriolis Effect by dropping balls down the inside the Tower of Bologna, providing a direct observational detection of the Earth's rotation (the need for such an effect in a rotating Earth was noted by Giovanni Riccioli in the 1650s, and Robert Hooke had previously attempted the experiment, but was not confident in his results).
It was also this period when astronomers completed the shift from geocentrism to heliocentrism (the Vatican didn't acknowledge this change for almost another century, in 1820). Most notably, the Astronomer James Bradley discovered stellar aberration in γ Draconis, which provided a direct demonstration of the motion of the Earth through space, inexplicable by all geocentric systems.
Electricity[edit]
Charles Augustin de Coulomb announced his eponymous inverse square law of electrostatics.^{[11]} It is interesting to note that Sir Henry Cavendish had himself discovered the same thing using similar experimental apparatus, a torsion balance, but did not publish his findings till these were unearthed by Maxwell in the next century. However, Cavendish did publicize his determination of Newton's gravitational constant which appears in his law of universal gravitation to a high degree of accuracy and his discovery that the Earth's core must consist of a very dense material, again using a torsion balance.^{[1]} This is because the mean density of the Earth is five and a half times that of water, which covers much of its surface.^{[9]} Benjamin Franklin performed his kite experiment, which convincingly showed that lightning is an electrical phenomenon. Franklin then invented the lightning rod, which was considered to be heretic by the Vatican, who argued that it interfered with the will of their imaginary friend God. Franklin also put forth the convention of positive and negative charges.^{[11]}
Heat[edit]
Sadi Carnot explored the ability of heat to do work. His rather slim book on a theoretical heat engine, named after him, founded the study of thermodynamics. In fact, Carnot's theorem — there exists no heat engine more efficient than the corresponding Carnot engine — is an early form of the second law of thermodynamics.^{[12]}
Nineteenth century physics: Heat, electricity and magnetism, and chaos[edit]
Mechanics[edit]
Laplace demonstrated the stability of the Solar System, which he modeled as a collection of rigid bodies moving in a vacuum, and expounded upon the nebula hypothesis for its origin.^{[9]} Drawing from his work in analytical probability theory, Laplace showed that almost certainly all bodies the Solar System formed from the same cloud of gas. He also reintroduced the concept of a black hole, previously put forth by John Mitchell, based on the escape velocity formula in Newton's theory of gravity.^{[1]} William Rowan Hamilton, Simeon Denis Poisson, and Carl Gustav Jacobi introduced new mathematical methods for classical mechanics and generalized the subject.^{[9]}^{[10]}
In the final decade of this century, Henri Poincare investigated the threebody problem and came to a surprising conclusion. In general, it has no solutions.^{[note 2]} He also recognized the existence of dynamical systems with extreme sensitivity to small changes to the initial conditions. Any changes to the initial conditions, no matter how small, will in time lead to entirely different behavior. Such systems are called chaotic. Unfortunately, while the discovery that Newton's laws predicted chaos all along is quite remarkable, it was overshadowed by the fanfare associated with what happened right at the start of the next century.^{[10]}
Optics[edit]
Thomas Young considered both the wave and corpuscular models of light and found himself supporting the former.^{[1]} Augustin Jean Fresnel built upon the work on the wave model of light by Huygens and worked out a mathematical description of diffraction. In addition, he successfully accounted for the rectilinear propagation of light in a homogeneous medium, thus dispelling a major obstacle to the wave model.^{[8]} Young performed the doubleslit experiment, which definitively vindicated the wave model. He used Newton's experimental data to calculate the wavelengths of red and violet light to a high degree of accuracy, even by modern standards.^{[note 3]} He also gave a rough estimate of the size of atoms, which remained hypothetical at this time.^{[1]}
Thermodynamics and Statistical Mechanics[edit]
JeanBaptiste Fourier formulated his analytical theory of heat diffusion using experiments and observations. The mathematical technique he discovered during his investigation, Fourier analysis, is of great value in theoretical physics.^{[1]} Fourier predicted the phenomenon of global warming.^{[12]}
Benjamin Thomson (Count Rumford) and James Joule demonstrated by experiment that heat is a form of motion. William Thomson (Lord Kelvin), Rudolf Clausius, Hermann von Helmholtz, and others furthered the work of Carnot and established the laws of thermodynamics. Using these, Lord Kelvin estimated the age of the Earth to between 50 to 500 million years.^{[1]} Their work marked the beginning of the kinetic theory of gases. Now that thermodynamics is established, engineers began designing ever more efficient heat engines and refrigerators.^{[12]}
Maxwell and Ludwig Boltzmann derived the first ever statistical law of physics, the BoltzmannMaxwell distribution of molecular speeds in an ideal gas, from Newton's laws of motion.^{[13]} Boltzmann then spent much of life life developing the kinetic theory of gases and statistical mechanics.^{[1]} Perhaps Boltzmann's greatest contribution is the statistical interpretation of the second law of thermodynamics. A system tends to be in a state of maximal entropy because such a state is the most likely.^{[14]} He also showed that the entropy of a given system is directly proportional to the natural logarithm of its thermodynamic probability; the constant of proportionality is known as Boltzmann's constant in his honor, and is ubiquitous in statistical mechanics.^{[14]}
Gustav Kirchoff, perhaps best known for his laws of circuitry, used the laws of optics and thermodynamics to show that the radiation emitted by a black body is a function only of the temperature of that black body and its wavelength.^{[15]} He then challenged his colleagues to determine such a function. Kirchoff is also noted for his investigations of diffraction. It is interesting to note that even though he employed the elasticsolid model for light propagation, working before the advent of Maxwell's electromagnetic theory, his results are still correct, in the sense that they agree well with experiment.^{[8]} In about the same year, Charles Darwin published his masterpiece, The Origin of Species by Means of Natural Selection. William Strutt (Lord Rayleigh) and Sir James Jeans deduced the RayleighJeans law in response. But it only works for short wavelengths and disturbingly fails for longer ones, predicting that even a mildly heated body is a source an infinite amount radiation. This became known as the ultraviolet catastrophe.^{[12]}
Electricity and Magnetism[edit]
“”When we turn our attention to the general case of electrodynamics… our first impression is surprise at the enormous complexity of the problems to be solved.

—Max Planck.^{[16]} 
Hans Christian Oersted discovered by accident that an electric current induces a magnetic field. Felix Savart and JeanBaptiste Biot established via a series of experiment that such a magnetic field obeys an inverse square law. Lord Kelvin, von Helmholtz, Denis Poisson, and others conducted further mathematical investigations of electricity and magnetism. Drawing upon Oersted's fundamental discovery, AndreMarie Ampere initiated the study of electrodynamics. Michael Faraday showed that a changing magnetic flux induces an electric field and built the first electric motor. Its technological value can hardly be overestimated. Just six decades after Faraday's discovery of electromagnetic induction, electric trains entered service in the United States, Great Britain and Germany.^{[11]}^{[note 4]} James Clerk Maxwell did for electromagnetism what Newton had done for gravitation by building it into a coherent theory, now called Maxwell's equations. Maxwell's equations not only summarize everything there is to know about classical electromagnetism but also predict the existence of electromagnetic waves, propagating at precisely the speed of light c. He could scarcely avoid the conclusion that light is itself an example of an electromagnetic wave. Maxwell's equations imply that the velocity of light does not depend on the velocity of the source or the observer, provided they are not accelerating. This seems to contradict Newtonian mechanics, in which the speed measured depends on the frame of reference. This puzzle would not be resolved till the next century.^{[1]} Shortly after Maxwell's death, Heinrich Hertz conducted a series of experiments in which he generated a lowfrequency electromagnetic wave, now called radio waves. Like light, it can be reflected, refracted, diffracted and polarized. In doing so, he constructed a primitive radio antenna as well as forerunners of satellite dishes. But more importantly, his experiments verified Maxwell's electromagnetic theory of light.^{[11]}
New Physics[edit]
Henri Becquerel discovered a mindboggling natural phenomenon which apparently violated the conservation of energy, later dubbed radioactivity by Marie Curie in an experiment involving a salt of uranium. Energy was given off for no apparent reasons. What is bizarre about this phenomenon is that it is affected neither by temperature nor chemical reactions. Curie and her husband went on to isolate and identify two new elements, polonium and radium, both of which radioactive.^{[1]}
At this point, the basics of classical physics were all established. Using Newton's laws of motion and gravitation, Maxwell's equations of electromagnetism and the laws of thermodynamics, one could explain pretty much everything in the known world. Despite its encouraging success, nineteenthcentury physics encountered a number of major problems that it was unable to explain: (1) the fact that c is independent of the reference frame, (2) the ultraviolet catastrophe, as mentioned above, (3) whether atoms are real or merely theoretical constructs, (4) radioactivity and (5) the photoelectric effect. Solutions to these problems took physicists to places where no one has gone before.
Twentieth century physics: Mainly relativity and quantum mechanics[edit]
Quantum Mechanics[edit]
Max Planck discovered that if he treated light as if it was made up of discrete particles, then he could resolve the ultraviolet catastrophe. During the process, he formulated Planck's law of blackbody radiation.^{[1]} Albert Einstein then entered the stage in the most spectacular manner possible. For his doctoral thesis, Einstein gave a mathematical description of Brownian motion. Brownian motion is the random movements of tiny particles, such as pollen, immersed in a fluid, such as water. In doing so, Einstein gave a convincing argument why atoms real entities rather than theoretical constructs. Using Planck's quantum hypothesis, he explained the photoelectric effect in full detail.
Ernest Rutherford discovered the law of radioactive decay: the rate of decay is directly proportional to the amount present. He identified two kinds of radiation emitted by a radioactive substance, which he dubbed alpha and beta rays. Both of these were found to be deflected by a magnetic field and as such were electrically charged. Further experiments revealed that alpha rays were the nuclei of a helium4 atom and beta rays were electrons (or positrons, not yet known at this time). A third kind of radiation, gamma rays, were later unearthed. Unlike the previous two, gamma rays were unaffected by magnetism and turned out to be electromagnetic waves of very short wavelengths. (See figure above.)
Rutherford realized that radioactive decay enabled him to shoot a stream of particles at a target, observe how they scatter, and study its structure.^{[note 5]} His gold foil experiment revealed that most of the atom is actually empty space and that the electrons are moving about the nucleus much like the way the Earth and other planets orbit the Sun. Unfortunately, his planetary model seems fatally flawed; Maxwell's equations predict that accelerating charged particles emit electromagnetic radiation. If this was true, electrons will continuously lose energy as they spiral towards the nucleus; atoms would collapse in tens of nanoseconds. Niels Bohr saw a way out. His atomic model took into account the quantization of energy. Electrons can only absorb or emit discrete amounts of energy; those at the ground state have no energy to emit and will not collide with the nucleus. Bohr's model successfully reproduces the spectrum of hydrogen and hydrogenlike atoms, those with just one electron, but falters for more complex ones. The cavalry soon arrived. In the 1920s, a group of physicists, perhaps some of the most brilliant in history, developed the modern theory of quantum mechanics. Louis de Broglie and Albert Einstein pointed out the importance of waveparticle duality.^{[note 6]} Werner Heisenberg enunciated the crucial uncertainty principle, which differentiates the quantum world from what we are used to. It states that certain pairs of dynamical variables, such as position and momentum, are such that the more precisely one is measured, the less precisely the other one is known. There is no way around it; uncertainty is built into the fabric of nature. Paul Dirac succeeded in unifying special relativity and quantum mechanics for the first time with his relativistic wave equation for the electron.^{[1]} The prediction of antimatter by Dirac and J. Robert Oppenheimer soon followed. Due to its inherent counterintuitiveness, quantum mechanics has been a favorite target of pseudoscientists. Most professional scientists were simply too happy that this amazing new theory works, and went on to use it in their research. Einstein, however, was deeply troubled about the probabilistic nature of quantum mechanics, which he thought to be incomplete. He tried multiple times to devise a thought experiment that would be able to show the flaw of quantum mechanics. But Bohr managed to defeat him.^{[note 7]} Quantum mechanics survives largely unscathed.
Interrupted by World War II, the development of quantum field theory resumed at full pace in the postwar years. The first major result was quantum electrodynamics, independently developed by SinItiro Tomogana, Julian Schwinger and Richard Feynman. As one of the most accurate theories of physics ever, it is considered to be a crown jewel of science.^{[17]}^{[18]} Building upon this encouraging success, physicists then developed quantum chromodynamics^{[note 8]} to describe the strong nuclear force, and the electroweak theory, which addresses the unification between the electromagnetic and weak nuclear forces, and finally the Standard Model of particle physics, which encompasses all three nongravitational interactions.^{[17]} Superfluidity and superconductivity attracted quite a bit of attention.^{[18]}
Special and General Relativity[edit]
Postulating that the speed of light is the same for all observers and that the laws of physics remain the same in all inertial reference frames, he developed the special theory of relativity, which reduces to classical mechanics if the speeds involved more no more than 10% that of light. Fundamental special relativistic effects are time dilation for moving bodies, length contraction in the direction of motion, and the loss of simultaneity of clocks moving at different speeds. As an afterthought, he derived what is probably the most famous equation in science, , which gives the energy equivalent of a massive body at rest. This impressive creative outburst took place in 1905,^{[1]} a great year for Einstein as well as physics.
As is often the case is science, his success in formulating the special theory of relativity pointed Einstein to the next big problem. While special relativity proclaims that no causal influence can travel faster than the speed of light, Newton's theory of gravity implicitly assumes that gravitational interactions are instantaneous. Einstein realized that (if air resistance is nonexistent or negligible) falling bodies can consider themselves to be at rest and the ground is accelerating towards them; in other words, gravitation and acceleration are equivalent. Einstein considered this to be the happiest moment of his life. His opinion is quite reasonable, since principle of equivalence lies at the core of his theory of gravity, general relativity, nowadays thought to be his magnum opus. Moreover, it is a crucial insight in to the nature of the Universe. Special relativity stipulates that all inertial frames are equivalent, as far as the laws of physics are concerned. With the principle of equivalence, the basic laws of physics hold in all frames of reference, inertial or not. Einstein quickly recognized that in his new framework, spacetime itself is curved, which means the conventional Euclidean geometry cannot be used. Fortunately, the necessary mathematics, differential geometry, has already been introduced six decades before by Bernhard Riemann. After ten years of hard work, Einstein finally published his field equations for gravity in 1916. John Wheeler eloquently summarized them thus, "Mass [and energy] tells space [strictly, spacetime] how to curve. Space tells mass how to move."^{[17]}According to general relativity, the influence of gravity travels at exactly the speed of light. Indeed, a jiggling massive body emits gravitational waves, or radiation. Unfortunately, since gravity is so feeble, detecting gravitational waves is a Herculean task.^{[19]} Just a few months later, Karl Schwarzschild obtained the first nontrivial exact solution^{[note 9]} to Einstein's field equations.^{[20]} Schwarzschild's solution describes a spherically symmetric body so compact that not even light on it surface can escape its gravitational pull. Wheeler later gave this object the name "black hole". Einstein showed that general relativity correctly accounts for the perihelion of Mercury, something Newton's theory of gravity cannot explain. Since spacetime is curved, the path of light near a massive body must be also curved. Sir Arthur Eddington verified this prediction by astronomical observations in 1919.^{[17]} Subrahmanyan Chandrasekhar, J. Robert Oppenheimer and others set the stage for future developments in relativistic astrophysics. Unfortunately, most pure research came to halt when Germany invaded Poland in 1939.^{[21]} Interest in general relativity returned in the postwar era and important results concerning cosmic expansions and black holes were built upon. Indeed, the period from the 1960s to the mid1970s was the golden age of general relativity.^{[21]}
Classical Mechanics[edit]
In the 1960s, physicists rediscovered Poincare's results in chaos theory via computer simulations. Since then, this latest branch of classical mechanics has received considerable attention, not least because of its relevance to weather forecasting. Since the behavior of a weather system depends sensitively on its initial condition, which cannot be measured with absolute accuracy, longterm forecasting is all but impossible.^{[10]}
New Physics[edit]
As they currently stand, the Standard Model and general relativity contain almost everything physicists know for certain (within the limits of experimental uncertainty, pun intended) about how the Universe works. However, contemporary physics has very little to say about the behavior and characteristics of neutrinos, dark matter, and dark energy; cosmological observations suggest the latter two comprise the overwhelming majority of our Universe.^{[17]} So do expect some groundbreaking results in the twentyfirst century.
Twentyfirst century physics: Highenergy physics, gravitation, and condensed matter physics[edit]
Highenergy Physics[edit]
On the Fourth of July, 2012, the European Center for Nuclear Research (CERN in French) announced it has observed a particle whose behavior is consistent with what theorists call the God particle Higgs boson to a very high degree of statistical significance.^{[22]}^{[note 10]} The Higgs boson, first predicted by Peter Higgs and others, is of fundamental importance in quantum field theory. In interacts with some of the other particles in such a way that it gives them mass.
In May 2018, physicists at the Fermi Accelerator National Laboratory (Fermilab), the most powerful particle accelerator in the U.S., found some evidence for the hypothetical fourth flavor of neutrinos, the sterile neutrino, not part of the Standard Model. Sterile neutrinos do not interact via the the weak nuclear force, unlike its cousins. However, this result contradicts other experiments and needs further research.^{[23]}
Gravitation[edit]
In February 2016, about one hundred years after Einstein completed of his general theory of relativity, physicists at the Laser Interferometer Gravitational Observatory (LIGO) revealed after painstaking data analysis they have indeed detected signatures of gravitational waves, predicted by Einstein himself.^{[24]} This detection event actually took place on September 14, 2015, but the researchers wanted to be absolutely certain before publicizing this landmark discovery. The signal they detected came from two merging black holes about 30 times the mass of our Sun. This has opened up an entirely new possibility. Astronomers have traditionally observed celestial bodies using the electromagnetic radiation emitted at different wavelengths. Now, they can do so via gravitational waves.^{[note 11]} In the foreseeable future, we can expect more detection of gravitational waves coming from not just other pairs of black holes but also pairs of neutron stars, a neutron starblack hole system, and even supernovae, if they are close enough. As a matter of fact, LIGO announced in June, 2016, their second detection, recorded on December 26, 2015. This time, the signal came from another pair of black holes, but with fourteen and eight solar masses. Calculations indicate that the chances of LIGO being fooled by a random vibration of the same appearance as a gravitational wave signal is negligible, one in twenty billion. When LIGO's sister project in Italy, VIRGO^{[note 12]} finally comes online, physicists and astronomers will be able to locate the source of the signals with greater confidence.^{[25]} Indeed, in September, 2017, teams at LIGO and VIRGO announced the fourth detection of gravitational waves, this time of two colliding black holes of similar masses two billion light years away. Not only did they triangulate the source, they also measured its polarization, or the direction of vibration.^{[26]} One month later, the LIGOVIRGO collaboration announced the first detection of gravitational waves emitted by two neutron stars spiraling towards each other. Observation by telescopes operating at the entire electromagnetic spectrum followed, and a wealth of data was collected. This detection helps explain the origins of heavy elements of the periodic table, such as gold, silver and platinum, and lends some evidence to the hypothesis that collisions of neutron stars are responsible for at least some of the gammaray bursts we observe.^{[27]} Previously, it was thought that heavier elements were manufactured by nuclear reactions taking place in the interior of a large star in its final moments. Subsequent calculations suggested this was not enough. Debris ejected from a collision of neutron stars, observations show, provides the missing amounts.^{[28]}
In 2018, physicists announced that general relativity passed yet further stringent tests, on gravitational lensing and other strong field effects.^{[29]}^{[30]}^{[note 13]}
Cosmological measurements suggest that the overwhelming majority of the Universe consists of dark matter and dark energy, thus named because they do not interact electromagnetically. The properties of dark matter and dark energy remain largely unknown at this point.
Another active research topic is how gravity works at the quantum level. For decades, physicists' attempts to unify general relativity with quantum mechanics have been in vain, as these two immensely successful theories as we know them are fundamentally incompatible with each other. A calculation involving both yields nonsensical answers, such as infinities. Unfortunately, nobody has yet figured out how to circumvent this obstacle completely. A variety of approaches have been pursued, such as quantum field theory in curved spacetime, HawkingHartle gravity, twister theory, loop quantum gravity, among others. Besides theories, physicists have devised and conducted a number of experiments intended to probe the quantummechanical nature of gravity; they have yet been successful.^{[31]}
Another potential way out that has captured much attention is string theory. It essentially "tames" the infinities by spreading out interactions in spacetime. An appealing aspect of string theory is that it also accounts for the other three fundamental forces of nature. It is thus called a "theory of everything" because it says that all four of the known fundamental forces (gravitational, weak nuclear, strong nuclear, and electromagnetic) are manifestations of one underlying mechanism. The problem with string theory is, however, that there is neither empirical evidence for nor against it. Therefore, it should be strictly speaking called the "string hypothesis" until it gives some empirically verifiable predictions and be able to explain phenomena on which other theories are either silent or give incorrect results. In the meantime, one has every right to remain skeptical. Recent research suggests that dark matter is incompatible with string theory. This means either cosmology is very different from what we think, or that string theory is wrong.^{[32]}
Condensedmatter Physics[edit]
Perhaps due to the influence of popular books, people outside of the physics community tend to think that all current research in physics consists of just the fields mentioned above, namely astrophysics and cosmology on one hand and particle physics on the other. However, the largest and most active field of physics is actually condensed matter physics.^{[33]} As a matter of fact, about one in four physicists wrote their doctoral dissertation on a topic in this branch of physics. Meanwhile, specialists in (general) relativity are on what Chandrasekhar would call the "lonely byways of science".^{[34]}^{[35]}^{[note 14]} Condensed matter physics explores the properties of large numbers of interacting particles in the liquid or gaseous states. More specifically, a condensedmatter physicist studies the electric, magnetic, optical, thermal and tensile properties of a material. Therefore, insulators, conductors, semiconductors, and superconductors are all topics of this branch of physics. Of great interest is crystalline materials, whose regular atomic arrangement makes them amenable to quantummechanical treatment. ^{[36]}
Astrophysics[edit]
Astrophysics is simply the physics of astronomy. Astrophysicists use spectroscopy on light to determine the composition of stars, nebulae, and other matter in the universe. They observe radiation such as microwaves emitted from pulsars, red shifted light from the big bang, and the energy emitted by black holes. They develop and utilize theories of relativity, string cosmology, dark matter, and dark energy. This scientific field utilizes other fields of physics such as thermodynamics and is related to cosmology, which deals with properties of immense bodies.
The field of astrophysics was formed when Isaac Newton coupled Galileo Galilei's hypothesis of the dynamics of planetary orbits, itself based on Nicolaus Copernicus' notion of heliocentrism, with Johannes Kepler's empirical laws of planetary motion, thereby demonstrating that gravity works the same on celestial bodies as it does on Earth. Newton's Law of Universal Gravitation is included in his work Philosophiæ Naturalis Principia Mathematica.
See also[edit]
External links[edit]
 What Makes The Hardest Equations in Physics So Difficult? Surprisingly, the most notoriously hardtosolve equations in physics actually model phenomena familiar to daily life, namely fluid flow.
 What You Never Learned about Mass. This is a crucial insight that led Einstein to the general theory of relativity.
Notes[edit]
 ↑ This led him to what we now call the five Lagrange points, L_{1} to L_{5}, the first three unstable while the last two stable. In nature, debris tend to collect in the vicinity of Lagrange points and many artificial satellites have been made to orbit these locations.
 ↑ Special cases have been solved (approximately) by Euler, Lagrange and others.
 ↑ This tells us how skilled an experimental Newton was and how insightful a theorist Young was.
 ↑ The London Underground opened in 1863 and became electrified in 1890, making it the first metro system that uses electricpropulsion.
 ↑ In order for you to see an object, your eyes must be able to pick up photons emitted by, say, a candle, bouncing off that object. The same principle is at play here.
 ↑ Richard Feynman stated very simply that the waveparticle duality was the mystery of quantum mechanics and nothing could be said about it other than it had to be taken by faith. Of course, it has been verified experimentally for a gazillion times but we don't have anything by way of explanation. If a reactionary Christian reads this, (s)he will probably salivate: "See, the physicists base something on faith!" But it is a very different kind of faith, especially regarding the numerous experiments.
 ↑ See the BohrEinstein debates
 ↑ It has nothing to do with color in the everyday sense of the word.
 ↑ Of course, a vacuum is an obvious solution; spacetime is perfectly flat.
 ↑ Note the ironic date. This could easily have been a U.S. discovery in light of the fact that the Superconducting Super Collider is designed to smash subatomic particles at 20 GeV while the Large Hadron Collider could only do so at 16 GeV after its most recent upgrade. Alas, the Super Collider was cancelled in the 1990s by "budget hawks".
 ↑ Gravitational waves are a kind of radiation. In physics, radiation is a mechanism that transports energy and momentum. Thus, sound is another example of radiation. And so is wind, but unlike the previous examples, this matter is also transported in this special case.
 ↑ Nothing superstitious here. Move along, folks!
 ↑ Artist's impression of lighting bending around the black hole at the center of the Milky Way.
 ↑ To give this some context, Subrahmanyan Chandrasekhar made this morose remark some time during the late 1970s and the 1980s, after the Golden Age of General Relativity has ended, leaving him on his own personal and final quest to clarify what was known and to tie up some loose ends, which resulted in the epic monograph The Mathematical Theory of Black Holes (1983), and to study the collisions of gravitational plane waves.
References[edit]
 ↑ ^{1.00} ^{1.01} ^{1.02} ^{1.03} ^{1.04} ^{1.05} ^{1.06} ^{1.07} ^{1.08} ^{1.09} ^{1.10} ^{1.11} ^{1.12} ^{1.13} ^{1.14} ^{1.15} ^{1.16} ^{1.17} ^{1.18} Gribbin J. Science, A History, 15432001. London: Allen Lane; 2002. ISBN 0713995033.
 ↑ Physics. MerriamWebster Online Dictionary.
 ↑ Giancoli D. Physics: Principles with Applications. 6th ed. Upper Saddle River, NJ: Pearson Education; 2005. ISBN 0130606200.
 ↑ Kakalios J. The Physics of Superheroes. New York: Gotham Books; 2005. ISBN 0715635492.
 ↑ BBC Documentary: Isaac Newton, the Last Magician. (Daily Motion link)
 ↑ Archimedes, Heath T.L (trans. and ed.). The Works of Archimedes, Edited in Modern Notation with Introductory Chapters. Mineola, NY: Dover Publications, Inc.; 1897. ISBN 0486420841.
 ↑ Geymonat M. The Great Archimedes. Waco, Tex.: Baylor University Press; 2010. ISBN 9781602583115.
 ↑ ^{8.0} ^{8.1} ^{8.2} ^{8.3} Hecht, Eugene. “Chapter 1  A Brief History.” Optics. Hecht, 5th ed., AddisonWesley, 2017. ISBN 9780133977226.
 ↑ ^{9.0} ^{9.1} ^{9.2} ^{9.3} ^{9.4} ^{9.5} Ball, W. W. Rouse. A Short Account of the History of Mathematics. 4th ed., Dover Publications, Inc., 1908. ISBN 0486206300.
 ↑ ^{10.0} ^{10.1} ^{10.2} ^{10.3} Hand L, Finch J. Analytical Mechanics. Cambridge: Cambridge University Press; 1998. ISBN 0521575729 paperback.
 ↑ ^{11.0} ^{11.1} ^{11.2} ^{11.3} Baigrie B. Electricity and Magnetism: A Historical Perspective. Westport, Conn. [u.a.]: Greenwood Press; 2007. ISBN 0313333580.
 ↑ ^{12.0} ^{12.1} ^{12.2} ^{12.3} Lewis J. Heat and Thermodynamics: A Historical Perspective. Westport, CT: Greenwood Press; 2007. ISBN 9780313333323.
 ↑ Gribbin J. In Search of Schrödinger's Cat: Quantum Physics and Reality. Toronto: Bantam Books; 1984.
 ↑ ^{14.0} ^{14.1} Schroeder D. An Introduction to Thermal Physics. San Francisco, CA: Addison Wesley; 2000. ISBN 0201380277.
 ↑ Planck M, Masius M (trans). The Theory of Heat Radiation. New York: Dover Publications, Inc.; 1959
 ↑ Modern Electrodynamics by Andrew Zangwill. ISBN 9780521896979. Reviewed by James S. Russ. American Journal of Physics. June 22, 2015.
 ↑ ^{17.0} ^{17.1} ^{17.2} ^{17.3} ^{17.4} Greene B. The elegant universe : superstrings, hidden dimensions, and the quest for the ultimate theory. New York, NY: W. W. Norton and Company, Inc.; 1999. ISBN 0375708111.
 ↑ ^{18.0} ^{18.1} Gribbin, John R., and Mary Gribbin. Richard Feynman: a Life in Science. New York, NY, Penguin, 1997. ISBN 052594124X.
 ↑ Gribbin J, Gribbin M. The Universe: A Biography. London: Penguin books; 2006.
 ↑ McEvoy, J. P, et al. Stephen Hawking for Beginners. Icon, 1995. ISBN 1874166250.
 ↑ ^{21.0} ^{21.1} Thorne K. Black Holes and Time Warps: Einstein's Outrageous Legacy. W. W. Norton and Company; 1994. ISBN 0393035050.
 ↑ Physicists See Best Proof Yet of 'The God Particle' (ABC News)
 ↑ Has US physics lab found a new particle?. BBC News. June 6^{th}, 2018
 ↑ Scientists Make First Direct Detection of Gravitational Waves. MIT News. February 11, 2016.
 ↑ PBS Space Time: The Future of Gravitational Waves (YouTube link).
 ↑ Gravitational Wave Hunters Bag Fourth Detection. BBC News. September 17, 2017.
 ↑ Einstein's waves detected in star smash. BBC News. October 16, 2017.
 ↑ In a First, Gravitational Waves Linked to Neutron Star Crash. National Geographic. December 20, 2017.
 ↑ Milky Way's Black Hole Provides LongSought Test of Einstein's General Relativity. The Scientific American. July 26^{th}, 2018.
 ↑ Laura Otto, University WisconsinMilwaukee. Einstein's theory of gravity holds – even in extreme conditions. Phys.org. July 4^{th}, 2018.
 ↑ Is Gravity Quantum?. Scientific American. August 14, 2018.
 ↑ Dark Energy May Be Incompatible With String Theory. Quanta Magazine. August 9, 2018.
 ↑ History of Condensed Matter Physics. American Physical Society.
 ↑ Wali, Kameshwar C. Chandra: A Biography of. S. Chandrasekhar. The University of Chicago Press, 1992. ISBN 0226870545.
 ↑ Trends in Physics PhDs. American Physical Society.
 ↑ Condensedmatter physics. Encyclopedia Britannica. Accessed February 11, 2018.
Mathematics Articles on RationalWiki  

 Conservapedian mathematics  Fermat's last theorem  Fibonacci sequence  Golden Ratio  Gödel's incompleteness theorems  Hypatia of Alexandria  Information  Mathematics  Metric system  Metric system  Phli (fun)  Pyramid  Rene Descartes  Sophie Germain  Statistics  wikiFactor  Zero  