What is the nature of time? In our contemporary culture, this is considered a question for physics to answer. In Einstein’s general relativity, time (as well as space) are relative and dynamic, depending on gravity and mass. Time is part of the nature of the physical world. In the Timaeus, Plato also expresses a view in which the time is created along with the physical world as an image of a deeper eternal unity:

Wherefore he resolved to have a moving image of eternity, and when he set in order the heaven, he made this image eternal but moving according to number, while eternity itself rests in unity; and this image we call time. For there were no days and nights and months and years before the heaven was created, but when he constructed the heaven he created them also. They are all parts of time, and the past and future are created species of time, which we unconsciously but wrongly transfer to the eternal essence.

In other words, time is not fundamental but a derivative image. And the movement of this image is mathematical. The manifest multiplicity in time is the mathematical movement of an underlying eternal unity. This Platonic vision is remarkably similar to the notion of symmetry. Put simply, a symmetry is an imagined change that produces no change. Where there is an invariant amidst variation, there is a symmetry. For example, a rotation of a circle by 90 degrees changes the circle but leaves it unchanged in a deeper, more fundamental sense. The symmetry transformation is a moving image of the eternal invariant structure. And in modern physics, fundamental constants of motion (conserved quantities) are directly related to symmetries through Noether’s theorem. Mathematical symmetry expresses the relationship of time and eternity, the sense in which time is a moving image of eternity, change within the unchanging, variation within an invariant.

A physical law itself is also an invariant that expresses the variations in the physical world. A law of physics provides a mathematical form that describes the invariant relationships between variable quantities. For example, F=ma is (within classical physics) a universal formula that is invariant across all times and places. While the values for m, a, and F can change, their relationship expressed by this equation is an invariant amidst this change. Thus, physical law itself is a symmetry that reveals the physical world as a moving image of eternity.

A paradox of sorts emerges at this point. On the one hand, the very notion of symmetry, of invariance within variation, presupposes a very basic form of change and time. On the other hand, physical time itself is part of the physical world that manifests as a moving image of eternity. Thus, time seems to be at once both cause and effect of manifestation. It is here that we are prompted to distinguish between layers of time. The most basic “proto-time,” the bare possibility of imagined change of the unchanging, is without any elaborate structure. Physical time, on the other hand, is rich with structure. It is entangled with space in a four-dimensional curved space-time whose dynamics depend on gravity and mass. The nature of physical time is part of the solution to equations of physics. But these equations themselves presuppose a more basic proto-time that is embedded in the very notion of law itself. The origin of this proto-time is presupposed by physical law, and is therefore not within the domain of physics per se. It is beyond or outside of physics. One might say it is part of meta-physics. Deeply understanding the foundations of physics necessarily takes one into this realm beyond physics, just as studying the foundations of a building takes one into the Earth. Structural engineering ultimately opens up to geology.

*Philosophy, Science*

Posted on 24 November 20080