Time, Reversal of

Our perceptions of the irreversibility of time seem obvious. We remember the past, we experience the present, and wonder about the future. Organisms are born, live, and die. Entropy, the gradual loss of energy by a body, increases. Nothing in our experience runs backward. There is even a popular phrase for this awareness—the arrow of time. Arthur Stanley Eddington, a physicist, popularized this phrase in the 1920s.

This belief in the forward motion of time is relatively new in our cultural history. Primitive peoples thought time was cyclic. They watched the recurring cycles of time in terms of the movement of the heavens and the seasons and drew a logical, if unstated, conclusion that the past and the future were constantly revolving and repeating. In Western culture, this was true until Judeo-Christian beliefs posited the concept of the irreversibility of time.

However, whether approached from the standpoint of Newtonian physics, Einstein's special theory of relativity, or the quantum mechanics formulated by Heisenberg and Schrödinger, there is a problem with our perception of the arrow of time. Equations from each of these fields work just as well whether time is running forward or backward. Another physicist, Eugene Paul Wigner (1902–1995), formulated the consequences of time reversal invariance for the solutions of the equations of quantum mechanics. Invariance, in mathematics, describes quantities that are unchangeable in mathematical operations. Wigner established the general notion of the time reversal [Page 1315]transformation of quantum states. As it turns out, there is a resolution to this apparent paradox. Statements in quantum terms about the reversibility of time deal with equations relating to motion and not about actual motions that we experience empirically.

When physicists or mathematicians talk about time, they generally use the symbol T to represent the time variable. As such, T is an additive variable; that is, time intervals are physically measurable and can have associated algebraic signs (plus or minus). One can add two intervals together to make a longer one, or subtract intervals to create shorter time intervals. The neutrality of mathematical equations, particularly in physics, would imply that negative T can exist, and this possibility makes it easier to solve some equations as well as to deal with equations formulated in the mid-19th century describing the behavior of electromagnetic waves.

James Clerk Maxwell (1831–1879) was responsible, among other important discoveries, for developing equations that expanded from Michael Faraday's theories about electricity. Maxwell's research ended with four mathematical equations (known as Maxwell's equations) that described how electrical and magnetic fields performed. Maxwell's most important achievement was his extension and mathematical formulation of Michael Faraday's (1791–1867) theories of electricity and magnetic lines of force. In his research, conducted between 1864 and 1873, Maxwell showed that a few relatively simple mathematical equations could express the behavior of electric and magnetic fields and their interrelated nature; that is, an oscillating electric charge produces an electromagnetic field.

Maxwell's equations applied to radio waves imply that these waves travel at the speed of light, yet the equations are invariant regarding the past and future. In other words, the equations work equally well whether radio waves travel into the future or the past.

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