Bronze-level articlePhysics

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The poetry of reality


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Extraordinary claims with
extraordinary evidence
Hot from the
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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.
—Pierre-Simon de Laplace[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.


[edit] Early physics

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.[5] 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.[6]

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.[7] Archimedes also built a planetarium, which operated on the basis of a heliocentric theory.[8] 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).

[edit] Seventeenth century physics: Warming up

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 introduced coordinate geometry, of fundamental importance is both physics as well as mathematics, and correctly stated that inertia is the tendency of a massive body to travel in a straight line at constant speed.[5] This later became what we now call Newton's first law of motion.

Ole RømerWikipedia's W.svg 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 225,000km/s. Although this value is not very accurate, it was the first time that the speed of light was definitively shown to be finite.[5]

[edit] Eighteenth century physics: Age of Newton

A prism disperses light such that incident white light is turned into a rainbow.

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.[5] 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[5]. 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 oscillatory motion and inventing a pendulum clock in the process.[5]

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.

Later in the century, Leonard Euler, Daniel Bernoulli, Jean le Rond d'Alembert, Joseph-Louis Lagrange, Pierre-Simon de Laplace, William Rowan Hamilton, among others, continued the development of calculus and brought classical mechanics to great new heights.[9] Charles Augustin de Coulomb announced his eponymous inverse square law of electrostatics.[10] 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 to a high degree of accuracy and his discovery that the Earth's core must consist of a very dense material.[5] 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.[10] 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).

Sadi Carnot explored the ability of heat to do work. His rather slim book on a theoretical heat engine founded the study of thermodynamics.[11]

[edit] Nineteenth century physics: Heat, electricity and magnetism, and chaos

Laplace demonstrated the stability of the Solar System and expounded upon the nebula hypothesis for its origin. Drawing from his work is probability calculus, Laplace showed that it almost certainly, all bodies the Solar System formed from the same cloud of gas. He also reintroduced the concept of a black hole, based on the escape velocity formula in Newton's theory of gravity.[5]

Thomas Young considered both the wave and corpuscular models of light and found himself supporting the former. Young performed the double-slit 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. He also gave a rough estimate of the size of atoms, which remained hypothetical at this time[5]. Jean-Baptiste 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.[5] Fourier also predicted the phenomenon of global warming.[11]

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.[5] Now that thermodynamics is established, engineers began designing ever more efficient heat engines and refrigerators.[11]

A diagram of the electromagnetic spectrum comparing different wavelengths to other physical objects. Note that names are merely labels for electromagnetic radiation at different wavelength orders of magnitude.

Hans Christian Oersted discovered by accident that an electric current induces a magnetic field. Felix Savart and Jean-Baptiste 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, Andre-Marie 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.[10] 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.[5] Shortly after Maxwell's death, Heinrich Hertz conducted a series of experiments in which he generated a low-frequency 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.[10]

Maxwell and Ludwig Boltzmann derived the first ever statistical law of physics, the Boltzmann-Maxwell distribution of molecular speeds in an ideal gas, from Newton's laws of motion.[12] Boltzmann then spent much of life life developing the kinetic theory of gases and statistical mechanics.[5] 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.[13] 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.[13]

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.[14] He then challenged his colleagues to determine such a function. William Strutt (Lord Rayleigh) and Sir James Jeans deduced the Rayleigh-Jeans 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.[11]

Henri Becquerel discovered a mind-boggling natural phenomenon which apparently violated the conservation of energy, later dubbed radioactivity by Marie Currie in an experiment involving a salt of uranium. Curie and her husband went on to isolate and identify two new elements, polonium and radium, both of which radioactive.[5]

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, nineteenth-century 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.

In the final decade of this century, Henri Poincare investigated the three-body problem and came to a surprising conclusion. In general, it has no solutions.[note 1] 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 been overshadowed by the fanfare associated with what happened right at the start of the next century.[15]

[edit] Twentieth century physics: Mainly relativity and quantum mechanics

The double-slit experiment for electrons.

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.[5] 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. 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, E = mc^2 , which gives the energy equivalent of a massive body at rest. This impressive creative outburst took place in 1905,[5] a great year for Einstein as well as physics. Ernest Rutherford discovered the law of radioactive decay: the rate of decay is directly proportional to the amount present. 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 hydrogen-like 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 wave-particle duality.[note 2] 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.[5] The prediction of antimatter by Dirac and J. Robert Oppenheimer soon followed. Due to its inherent counter-intuitiveness, 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 3] Quantum mechanics survives largely unscathed.

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 non-existent 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."[16]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.[17] Just a few months later, Karl Schwarzschild obtained the first non-trivial exact solution[note 4] to Einstein's field equations.[18] 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.[16]

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 Sin-Itiro Tomogana, Julian Schwinger and Richard Feynman. It is one of the most accurate theories of physics ever and a crown jewel of science. Physicists then developed quantum chromodynamics[note 5] 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 non-gravitational interactions. Interest in general relativity returned, and important results concerning cosmic expansions and black holes were built upon. Superfluidity and superconductivity attracted quite a bit of attention. 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. Not too surprisingly, contemporary physics has very little to say about the behavior and characteristics of neutrinos, dark matter, and dark energy; the latter two comprise the overwhelming majority of our Universe. So do expect some ground-breaking results in the twenty-first century.

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, long-term forecasting is all but impossible.[15]

[edit] Twenty-first century physics

A computer animation showing gravitational waves being generated as two black holes or neutron stars spiral around each other before they coalesce.

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. [19][note 6] The Higgs boson, first predicted by Peter Higgs and others, is of fundamental importance and quantum field theory. In interacts with some of the other particles in such a way that it gives them mass. 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.[20] 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. 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 star-black hole system, and even supernovae, if the 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 Europe, Virgo[note 7] finally comes online, physicists and astronomers will be able to locate the source of the signals with greater confidence.[21]

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 have tried to do this by unifying general relativity with quantum mechanics 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 figured out how to circumvent this obstacle. One potential way out 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 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.

[edit] Notes

  1. Special cases have been solved (approximately) by Euler, Lagrange and others.
  2. Richard Feynman stated very simply that the wave-particle 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.
  3. See the Bohr-Einstein debates
  4. Of course, a vacuum is an obvious solution; spacetime is perfectly flat.
  5. It has nothing to do with color in the everyday sense of the word.
  6. Note the ironic date. This could easily have been a US discovery in light of the fact that the Superconducting Supercollider is designed to smash subatomic particles at 20GeV while the Large Hadron Collider could only do so at 16GeV after its most recent and final upgrade.
  7. Nothing superstitious here. Move along, folks!

[edit] References

  1. Explosition du système du monde, as quoted in Gribbin J. Science, A History, 1543-2001. London: Allen Lane; 2002.
  3. Giancoli D. Physics: Principles with Applications. 6th ed. Upper Saddle River, NJ: Pearson Education; 2005.
  4. Kakalios J. The Physics of Superheroes. New York: Gotham Books; 2005.
  5. 5.00 5.01 5.02 5.03 5.04 5.05 5.06 5.07 5.08 5.09 5.10 5.11 5.12 5.13 5.14 5.15 5.16 Gribbin J. Science, A History, 1543-2001. London: Allen Lane; 2002.
  6. BBC Documentary: Isaac Newton, the Last Magician. (Daily Motion link)
  7. Archimedes, Heath T.L (trans. and ed.). The Works of Archimedes, Edited in Modern Notation with Introductory Chapters. Mineola, NY: Dover Publications, Inc.; 1897.
  8. Geymonat M. The Great Archimedes. Waco, Tex.: Baylor University Press; 2010.
  9. Hand L, Finch J. Analytical Mechanics. Cambridge: Cambridge University Press; 1998. Just look inside a textbook on mechanics and you will see.
  10. 10.0 10.1 10.2 10.3 Baigrie B. Electricity and Magnetism: A Historical Perspective. Westport, Conn. [u.a.]: Greenwood Press; 2007.
  11. 11.0 11.1 11.2 11.3 Lewis J. Heat and Thermodynamics: A Historical Perspective. Westport, CT: Greenwood Press; 2007
  12. Gribbin J. In Search of Schrödinger's Cat: Quantum Physics and Reality. Toronto: Bantam Books; 1984.
  13. 13.0 13.1 Schroeder D. An Introduction to Thermal Physics. San Francisco, CA: Addison Wesley; 2000.
  14. Planck M, Masius M (trans). The Theory of Heat Radiation. New York: Dover Publications, Inc.; 1959
  15. 15.0 15.1 Hand L, Finch J. Analytical Mechanics. Cambridge: Cambridge University Press; 1998.
  16. 16.0 16.1 Greene B. The Elegant Universe. New York, NY: W. W. Norton and Company, Inc.; 1999.
  17. Gribbin J, Gribbin M. The Universe: A Biography. London: Penguin books; 2006.
  18. McEvoy J, Zarate O, Appignanesi R. Introducing Stephen Hawking.
  19. Physicists See Best Proof Yet of 'The God Particle' (ABC News)
  20. Scientists Make First Direct Detection of Gravitational Waves (MIT News)
  21. PBS Space Time: The Future of Gravitational Waves (YouTube link).
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