In physics, the treatment of time is a central issue. It has been treated as a question of geometry. (See: philosophy of physics.)

Contents

1 Newtonian physics and linear time 2 Thermodynamics and the paradox of irreversibility 3 Electromagnetism and the speed of light 4 Einsteinian physics and time 5 Quantum physics and time 6 Dynamical systems 1 Further reading 2 See also

Newtonian physics and linear time

See classical physics

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.

Thermodynamics and the paradox of irreversibility

1824 - Sadi Carnot scientifically analyzed the steam engines

1st law of thermodynamics - the law of co- the law of entropy

<math>E =\, \cdots<math> (thermal energy)

<math>ds =\, \cdots<math>

<math>\frac{\partial ^2T}{\partial t^2} =\frac{\partial T}{\partial x}<math>

Electromagnetism and the speed of light

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 (<math>\nabla<math>) are known as Maxwell's equations for electromagnetism, when a vacuum is assumed, they are as follows:

<math>\nabla \times \mathbf{E} = - \frac{1}{c} \frac{\partial \mathbf{B}}{\partial t}<math>

<math>\nabla \times \mathbf{B} = \frac{1}{c} \frac{\partial \mathbf{E}}{\partial t}<math>

<math>\nabla \cdot \mathbf{E} = 0<math>

<math>\nabla \cdot \mathbf{B} = 0<math>

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

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:

<math>\left[(dx^1)^2+(dx^1)^2+(dx^2)^2+(dx^3)^2-c(dt)^2)\right],<math>

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 its own local geometry.

<math>E^2 = m^2c^4+p^2c^2 \ <math> (atomic energy)

E = energy, m = mass, p = momentum, c = the speed of light

Quantum physics and time

See quantum mechanics

Dynamical systems

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.

Further reading

• Boorstein, Daniel J., "The Discoverers". Vintage. February 12, 1985. ISBN 0394726251
• Prigogine, Ilya, "Order out of Chaos". ISBN 0394542045
• Stengers, Isabelle, and Ilya Prigogine, "Theory Out of Bounds". University of Minnesota Press. November 1997. ISBN 0816625174
• Mandelbrot, Benoit, "Multifractals and 1/f noise". Springer Verlag. February 1999. ISBN 0387985395
• Serres, Michel, et al., "Conversations on Science, Culture, and Time (Studies in Literature and Science)". March, 1995. ISBN 0472065483
• Kuhn, Thomas S., "The Structure of Scientific Revolutions". ISBN 0226458083

See also

• Time domain
• Arrow of time