TIME is a Relative Measure of CHANGE

What is time? This issue has been debated and pondered over since ages. So far the best concept of time has been the intuitive concept; what we all feel by way of our common sense and experience. Still however, there is no unique definition of time. The most common definition may be taken as , ’Time is what we measure by clocks – all sorts of clocks’. But this definition does not throw any light on the fundamental basis or the origin of the notion of time.

For the physical description of natural phenomenon, time (T) is regarded as one of the physical dimensions, just like mass (M) and length (L). However, due to the over bearing dominance of mathematics during the 20^th century, some Mathematicians have started propagating the idea of equivalence of the dimensions of length (L) and time (T). This has shattered the intuitive notion of time and led to a lot of confusion and controversy over the issue. Therefore a critical review of the fundamental basis or the origin of the notion of time has become all the more important now than ever before.

To explore the fundamental basis of the notion of time, let us conduct a thought experiment. Let us take a mental snapshot of the natural phenomenon and store it in memory. Let us take another snapshot of the same natural phenomenon and again store it in memory. Now we compare the two snapshots to see whether they are identical or there are noticeable changes in the second snapshot as compared to the first. Let us imagine we take a series of such mental snapshots and store them in the memory in a systematic order. After examining a large number of such consecutive snapshots, we categorize various types of changes into a few distinguishable sets of changes. Further, let us assume that we concentrate our attention to only those changes, which could be quantified through a measurable parameter.

Let us imagine that type A change is quantified through a measurable parameter ‘a’, type B change is quantified through a measurable parameter ‘b’ and so on. By studying a series of large number of successive snapshots we can analyse the nature of changes in parameters a, b, c etc. While some of these parameters may vary randomly, some others may increase or decrease monotonically over a series of snapshots. Further, let us concentrate our attention to only those changes where the measurable parameters a, d, h etc. continuously vary between specific limits say (a₁, a₂), (d₁, d₂), (h₁, h₂) etc. over a series of snapshots. We designate such changes as cyclic changes. Suppose in a particular series of successive snapshots, parameter ‘a’ goes through N_a cycles of changes, parameter ‘d’ goes through N_d cycles of changes and so on. We can then compare the two sets of changes by saying that while parameter ‘a’ completes one cycle of change, parameter ‘d’ completes (N_d/ N_a) cycles of change. And this comparison between different sets of changes gives rise to the notion of comparatively slow or fast changes and hence to the notion of time.

After a thorough analysis of all such cyclic changes, we may agree to designate the cyclic changes of parameter ‘a’ as a reference scale for comparing all other changes. In particular, we may call one cycle of change in parameter ‘a’ as one unit of change or just one unit of ‘time’. Now when we say that parameter ‘d’ takes 10 units of time to complete its one cycle of change, it implies that in a series of successive snapshots, while parameter ‘d’ completes one cycle of change, parameter ‘a’ completes 10 cycles. Thus the notion of time helps us to compare different sets of change against one reference set.

In Nature, there are a large number of physical processes, which undergo cyclic changes. Depending on the consistency of such cyclic changes and the convenience of their measurement, we may select any one of them as our reference scale for relative measurement of change or the reference scale for time. The angular position of a planet in orbit around the Sun, the angular position of an electron orbiting around the nucleus of an atom, the position of a pendulum oscillating about a mean, the vibrations of many mechanical, electro–mechanical and electro-magnetic systems are all examples of physical processes that undergo cyclic changes. Any such system or process could be adopted as a reference scale for relative measurement of change or measurement of Time. In general, the study of natural phenomenon invariably involves the comparative study of various changes. For this comparative study, we need to use a reference scale for relative measurement of change or for measurement of time. Hence the Time, as a relative measure of change, is an extremely important parameter in the study of an essentially dynamic physical Universe.

Let us consider a very simple example of a particle motion along X–coordinate. This motion can be represented through a distance – time curve or trace on an X–T coordinate plane. The velocity and acceleration of the particle at any point along the X–axis will be represented by the slope and curvature of the trace at that point. Let us now consider a particle moving in a circular orbit in XY plane. The motion of this particle can be represented as a helical trace in a XY–T coordinate space or manifold. The velocity and acceleration characteristics of this particle will be represented by the geometry of helical trace in the XY–T manifold. An important point to be noted here is that the helical trace does not physically exist anywhere at any time; it is just a mathematical or graphical representation of the motion of a particle over a period of time.

Similarly the motion of various particles in three-dimensional physical space XYZ can be represented through suitable traces in a four dimensional XYZ–T space-time manifold. An important point to be noted here too is that four dimensional traces of particles do not physically exist anywhere at any time; these are just mathematical representations of the motion of particles in three dimensional space over a period of time. In the same way, a four-dimensional space–time manifold XYZ–T does not physically exist anywhere at any time; it is just a mathematical notion. However, due to the over bearing dominance of mathematics during 20^th century, the mathematical notion of space–time manifold has been assigned a more sophisticated identity of space–time continuum. In Relativity, the notion of space–time continuum has been treated as a physical entity, which could even be deformed and curved!! Well, that is fundamentally incompatible with the basic notion of Time as discussed above.

Other Important Articles