The Wikipedia article on ‘Time‘ states: “defining it in a manner applicable to all fields without circularity has consistently eluded scholars.” In other words, most definitions of time in some way end up including it. Examples, from the same article, are: “Time is a dimension in which events can be ordered from the past through the present into the future, and also the measure of durations of events and the intervals between them.” What is the past? (Earlier time?) What are durations and intervals? (other than time itself?).
Is it impossible to define time without circularity? Interestingly, ancient cultures often referred to time itself as a circle – “the circle of time”, the “kalachakra” in Sanskrit, in which time through vast eons repeats itself, each cycle lasting for what would amount to millions of years.
Another aspect of time which is equally difficult to objectify and define is its direction. Unlike the dimensions of space in which we, and other objects we see, are free to move back and forth, time resolutely follows the arrow from ‘past’ to ‘future’. What defines this direction? Is is subjective or objective? Cosmic, thermodynamic or subatomic?
A strange twist to our understanding of time came with Einstein’s theories of relativity which showed that in different inertial - as well as accelerating or gravitational – frames of reference, the rate and concurrence of events vary – shattering the concept of ‘absolute’ time. This leads to the conclusion that Time, like Space is a dimension of reality which is closely inter-wined with matter and energy and cannot be studied or defined in isolation.
Defining time in relation to matter and energy brings us to the issue of change. Unless there is a change in the observable properties of a system, there is no way to measure or detect the passage of time. The property could be location in space, physical composition, or any other parameter like charge or temperature - a discharging battery is a good example. Right to the subatomic level, ‘Time‘ is that which separates ‘events’ – which are nothing but changes in the physical properties of matter and energy. In an empty universe without matter and energy, time simply cannot exist. Thus, the ‘Big Bang’ is not only the beginning of matter and energy but also of space and time as well – as the Universe expands, it creates the space and time it needs to expand into.
Thus, change happens and the dimension in which change happens is time. Without time, there can be no change and without change, there can be no time.
But what about the direction of time? Many changes are simply not reversible. This irreversibility can be used to define the direction of time. Consider a perfectly reversible system like an oscillating pendulum. In this system, the direction of time would be meaningless. Irreversible change gives a direction to time – be it is cosmic, thermodynamic or subatomic.
The cosmic arrow of time is defined by the irreversible expansion of the universe. The thermodynamic arrow of time derives from the famous second law of thermodynamics which states that ‘entropy’ – the physical measure of disorder or chaos of a system – must increase with time. This irreversible increase in entropy defines the thermodynamic arrow. Interestingly, they both point in the same direction, perhaps pointing to an underlying fundamental connection between the expansion of the universe and entropy. (There is a third arrow of time – the one in our mind, the psychological arrow of time, which is likely influenced by the irreversible changes we observe around us, like growth and decay, birth and death. The irreversibility of these phenomena are all, arguably, related to the thermodynamic arrow.)
Finally, time has both objective and subjective aspects. Change happening without an observer would also require time, but once the change is observed, the time becomes subjective.