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In or around 1665, when Isaac Newton derived the motion of objects falling under gravity, the first clear formulation for mathematical physics of a treatment of time began: linear time, conceived as a universal clock.
1824 - Sadi Carnot scientifically analyzed the steam engines
1st law of thermodynamics - the law of conservation of energy
2nd law of thermodynamics - the law of entropy
Somewhere between 1831 and 1879, James Clerk Maxwell developed a combined theory of electricity and magnetism. These vector calculus equations which use the del operator () are known as Maxwell's equations for electromagnetism, when a vacumm is assumed, they are as follows:
See special relativity, general relativity.
In 1875, Hendrik Lorentz discovered the Lorentz transformation, upon which Einstein's theory of relativity, published in 1915, is based. The Lorentz transformation states that the speed of light is constant in all inertial frames.
Einstein's theory of relativity uses Riemannian geometry, employing the metric tensor which describes Minkowski space: , to develop a geometric solution to Lorentz's transformation that preserves Maxwell's equations.
Einstein's theory was motivated by the assumption that no point in the universe can be a 'center', and that correspondingly, physics must act the same in all inertial frames. His simple and elegant theory shows that time is relative to the inertial frame, i.e. that there is no 'universal clock'. Each inertial frame has it's own local geometry.
See dynamical systems and chaos theory, dissipative structures
One could say that time is a parameterization of a dynamical system that allows the geometry of the system to be manifested and operated on. It has been asserted that time is an implicit consquence of chaos (i.e. nonlinearity/irreversibility): the characteristic time, of a system. Mandelbrot introduces intrinsic time in his book Multifractals and 1/f noise.
Newtonian physics and linear time
Thermodynamics and the paradox of irreversibility
Electromagnetism and the speed of light
where c is a constant that represents the speed of light in vacuum, E is the electric field, and B is the magnetic field.Einsteinian physics and time
E = energy, m = mass, p = momentum, c = the speed of lightQuantum physics and time
Dynamical systems
Further Reading