|The poetry of reality|
|Extraordinary claims with extraordinary evidence|
|Hot from the giants' shoulders|
The languages of most physical theories and laws use higher mathematics such as calculus and analysis, and especially differential equations, e.g Newton's second law. Most breakthroughs in physics have necessitated the use of already existing mathematical techniques. Examples include matrix mechanics for quantum interpretation. However, in some cases, such as classical mechanics, the relevant mathematical methods - calculus - had to be invented. It is worth noting that the need for physical applications can motivate the development of mathematics.
The four principal breakthroughs in the history of physics have been:
- Sir Isaac Newton's laws of motion and his contemporaries' work on such things as planetary motion, fluid flow, wave propagation and the classical kinetic theory of gasses.
- James Clerk Maxwell's formulation of the laws of electromagnetism, crucial to the next level of understanding of matter after gravity.
- Albert Einstein's seminal work on relativity and his famous mass-energy equivalence.
- Quantum physics and its counter-intuitive explorations of atomic, molecular and subatomic physics.
 Early physics
Aristotle believed that everything was made up of one of the five states of matter: earth, fire, air, water, or magic: the "quintessence", or "fifth essence". There wasn't much research to build on back then. 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. Again, there is not much empirical evidence to support this claim.
 Seventeenth century physics
Galileo Galilei[wp] demonstrates that bodies fall at the same speed regardless of mass.
Ole Rømer[wp] measured the speed of light for the first time. His value for this was not accurate, but this was the first time that the speed of light was shown to be finite.
 Eighteenth century physics
Newton did a pretty good job of mathing up some stuff. In his masterpiece the Principia, he laid down the laws of motion and gravitation and investigated some of their consequences, including, but not limited to, Kepler's laws of orbital motion and the conservation of linear and angular momentum. He is also credited with the invention of calculus, alongside Gottfried Wilhelm von Leibniz. While physics has its roots in astronomy and a number of important results have been published before Newton, e.g. Archimedes' principle, it was he who constructed physics as a mathematical formalism.
Later in the century, Leonard Euler, Joseph-Louis Lagrange, Pierre-Simon de Laplace, among others, continued the development of calculus, variational calculus, and classical mechanics while others still, like Charles Coulomb and Andre-Marie Ampere explored electrodynamics.
Some other people pitched in with more details.
 Nineteenth century physics
James Joule, William Thomson (Lord Kelvin), Rudolf Clausius, Hermann von Helmholtz, and others studied and established the laws of thermodynamics.
James Clerk Maxwell did for electromagnetism what Newton had done for mass and gravity by building it into a coherent theory, now called Maxwell's equations. One little 'problem' was that the equations said that the velocity of light (etc) didn't depend on the velocity of the source or the observer, provided they are not accelerating. That is, to put it poetically, the speed of light remains the same in all inertial reference frames. Cue much scrabbling around to work out why this wasn't bonkers.
With Ludwig Boltzmann, Maxwell 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. Boltzmann then went on to develop statistical mechanics and thermodynamics.
Gustav Kirchoff, perhaps best known for his laws of circuitry, showed that the radiation emitted by a black body is a function only of the temperature of that black body and its wavelength. He then challenged his colleagues to formulate such a function. Jozef Stefan, on empirical grounds, and Bolzmann, on theoretical grounds, proposed the Stefan-Boltzmann law in response. But this 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.
Despite its rising success, nineteenth-century physics encountered a number of major problems that it was unable to explain: (1) the constancy of c in all inertial frames and (2) the ultraviolet catastrophe, as mentioned above and (3) whether atoms are real or merely theoretical constructs. Solutions to these problems took physicists to places where no one has gone before.
 Twentieth century physics
Max Planck straddled the centuries. He presented his findings about energy quanta on 14. Dec. 1900 to the German Physical Society but published them in early 1901.
Ernest Rutherford made great contributions to nuclear physics. To him: "All science is either physics or stamp collecting." Then he was awarded the Nobel Prize in chemistry (1908).
Einstein had a go at what would happen if Maxwell's constancy of light velocity wasn't bonkers. His "Special Relativity" refined Newton's laws of motion for object at high relative velocities; gives lots of fun to web-loony watchers (Whaddya mean, time and distances are relative? You an atheist or summin'?); and spawned a bazillion misstatements about what the 'paradox' in the Twins paradox is supposed to be.
He also had a bit of a think about why an object's inertial mass (resistance to acceleration) is always the same as its gravitational mass (strength of attraction to other masses). Hey, what if acceleration and gravity are just two names for the same thing? Bingo! General Relativity. Mass bends space. Stars bend light. More refining Newton. More loony websites.
Quantum mechanics then made some very strange predictions about how the universe works at a very small scale. Due to the inherent "spookiness" of quantum mechanics, it has been a favorite target of pseudoscientists (to be fair, even Einstein wasn't too chuffed about its use of probabilities). The disagreements over the 'real' interpretation of quantum mechanics, and the lack of an underlying theory linking quantum mechanics and general relativity is a fertile area for people who like to point out that because science cannot answer everything, all science is wrong and therefore [insert orbiting teapot equivalent here] must be true. Einstein and Niels Bohr had one of the most famous exchanges of letters in science history, the Bohr-Einstein debates[wp]. Einstein would propose a thought experiment to demonstrate a weakness in quantum mechanics, and Bohr would explain where Einstein was mistaken. Bohr won that exchange hands down. Bohr was especially pleased when he was able to use Einstein's Theory of Relativity to make a point.
Later in the century, especially in the years after World War II, physicists began developing quantum field theory in earnest. The result was quantum electrodynamics (there was such a fine man), one of the most accurate theories of physics ever and a crown jewel of science; quantum chromodynamics (it has nothing to do with color!); electroweak theory; and finally the Standard Model of particle physics. Interest in general relativity returned, and important results concerning cosmic expansions and black holes were built upon. Also of great interest are superfluidity and superconductivity (and the unborn Superconducting Supercollider). 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.
 Twenty-first century physics
One of the more popular of today's physics topics is the attempt to unify the theory of general relativity (GR) with quantum mechanics. When one tries to combine GR and quantum field theory, one encounters a problem of infinities. No one has figured out how to get around this. One of the many proposals is string theory. It essentially "tames" the infinities by spreading out interactions in spacetime. String theory also accounts for the other three interactions of nature. It is thus called a "theory of everything" because it says that all four of the known fundamental forces (gravity, weak nuclear, strong nuclear, and electromagnetic) are a manifestation of one underlying mechanism. The problem with string theory is, however, that while there is no evidence against it, neither is there any strong evidence for it - more or less all evidence which is consistent with string theory is also consistent with numerous other theories.
- ↑ Classical mechanics are equivalent to Newtonian mechanics, obviously, since they are subject to the same physical laws. Lagrange formulated his version, then Hamilton expanded that and this formulation, the Hamiltonian, eventually became a basic mainstay of quantum mechanics. Things have a way of working out like that in physics and mathematics.
- ↑ Hint: The traveling twin has to accelerate to be able to return. Special Relativity does not account for acceleration.
- ↑ Incredible but true!
- ↑ To expand a bit about Feynman. He 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.
- ↑ Leonard to Sheldon (according to memory): "You have to invent 11 dimensions to make the math work!".