Veni Vidi Vici: Time Travel - Nature and Shape of Time

In order to understand the possibilities of time travel it is important to understand time itself. What is time ? How is it caused ? Which physical phenomenon are responsible for the passage of time.Writer and physicist Paul Davies has called "time" Einstein’s unfinished revolution. Aristotle had speculated that time may be motion. He however added that motion could be slower or faster but not time. Aristotle did not have the privilege of knowing about Einstein’s relativity in which time also becomes amenable to change. Similarly when Einstein was working to develop theory of general relativity and proposed the revolutionary idea that mass curves space he did not know that the universe was expanding.

This discovery by astronomer Edwin Hubble came 13 years after Einstein had published his theory of General Relativity. Had Einstein known of this great discovery he may have incorporated these ideas into his theories. Conceptually it is easier to derive space curvature in an expanding universe as an area of slower expansion under the influence of gravitons. One of the most dramatic aspects of the universe is that it is expanding and the presence of motion, forces and curved space-time happens in the expanding space.

The nature of time is such that it increases in the direction of the expanding universe. Our current understanding of time is based on general relativity. The general relativity when applied to the whole cosmos gives a peculiar shape to time. In order to understand that first consider the notion of a light cone and how it relates to time. To simplify things consider a 2 dimensional space with the observer at a particular point on this plane. Let the time be represented in the 3rd dimension coming out of the plane as shown in the figure below.

Light Cones

The surface of the observer represents the present time. The light rays from the observe propagate in all directions but light has a limited speed so they cannot go beyond the surface of the cone. This conical structure forms a boundary of observable region emanating from the point of the observer. In the future time dimension it represents a cone called the future light cone. Similarly we can also build a past light cone which captures the history of the observer in the past. Now if we extrapolate the past light cone of the observer all the way back to the big bang it will represent the shape of time until the current epoch.

Pear Shape

This actually gives a pear shape to the past light cone. The point of the big bang singularity represents a region of space which had huge matter density. As we know from Einstein's theory of general relativity matter causes light to bend in. Hence at the big bang singularity all the light rays were actually bent inwards.

Thus based on the current understanding of the universe and physics we can conclude that time is pear shaped.