Time, Symmetry of

Although everyday experience leads us to believe that time “flows” in one direction, the equations of both classical and modern physics work equally well in either time direction. Since these equations accurately describe all observations of physical phenomena, from those made with the human eye to those made with the finest scientific instruments, the implication is that time can flow either way.

The arrow of time of human experience results from the fact that macroscopic objects contain many particles and these, to a great extent, move about randomly. The probability for a phenomenon happening in one time direction, such as air escaping from a punctured tire, is often much greater than the probability for the phenomenon happening in the opposite time direction, such as outside air reinflating a punctured tire. The reverse time event is not impossible, just highly unlikely. The arrow of time is defined as the direction of most probable occurrences.

At the level of chemical, nuclear, and elementary particle interactions, however, reactions occur in either time direction. Statistical differences between initial and final states can result in different reaction rates for the two directions, but at the basic interaction level the two directions are equally likely.

One exception occurs in certain elementary particle reactions that are mediated by the weak nuclear force. There a slight asymmetry of 1 part in a 1,000 exists. However, reactions can still proceed in either direction with only a slight difference in probabilities.

In 1949 Richard Feynman showed that an anti-particle, such as the anti-electron or positron, may be viewed as a particle going backward in time. This symmetry is built into the visual aids called Feynman diagrams used by physicists to calculate the rates of various reactions between elementary particles.

Despite the basic time symmetry of physics, most physicists continue to assume directed time in their models. This generally makes no difference, since a particle going backward in time is empiri-cally indistinguishable from its antiparticle going forward in time, where “forward” is defined by everyday experience.

It has been known for decades, however, that quantum mechanics predicts certain phenomena that seem paradoxical. For example, electrons and other particles behave as if they can be in two or more places at the same time. Experiments have been performed that suggest “backward causality,” where the changing of the parameters of a detector [Page 1325]after the particles to be detected are already in flight affects the behavior of those particles, even though they cannot be reached without sending a superluminal signal (signal traveling faster than the speed of light, violating Einstein's theory of special relativity). This is taken as evidence for nonlocality in quantum mechanics, in which two events separated in space are still connected despite the fact that no signal can pass between them without going faster than the speed of light.

Figure I The “Feynman spacetime zigzag”

Source: Illustration courtesy Victor J. Stenger.

Notes: In (a), an electron goes forward in time, scatters off a photon, moves backward in time, scatters again, and goes forward. Note that the electron appears simultaneously in three different places at time B. In (b), the conventional time-directed view is shown in which an electron-positron pair is produced at time A, with the positron annihilating with the other electron at time C. The advantage of view (a) is parsimony, with no need to introduce antiparticles. It also offers an explanation for the indistinguishability of electrons.

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