Time as Curled Dimension

        Today we understand that time is a necessary dimension in our universe to define the state of an object completely. Unlike the 3 other dimensions, time cannot be visualised as an axis.(Note: The graph we plot against time axis is only a form of representation to study variation of other quantities with time. Time is never an axis.) Then where is the time dimension? It might seem absurd if it is proposed that time is a dimension curled with other 3 dimensions, but it can be proved.


        Let us analyse this situation. Let there be a particle of mass 'm' (take any value for mass here, as it would not affect our analysis). Whenever we encounter an equation describing the motion of a particle, it is generally of the form s=ax+by+cz but not of the form s=ax+by+cz+dt (here dt is not a differential, d is a constant). Rather it is of the form s=axt+byt+czt+dzt. Suppose a particle moves in space such that its coordinates change from P(x1,y1,z1) at t1 time to Q(x2,y2,z2) at t2 time. If we do not associate time dimension with x,y and z then we would surely describe the equation to be s=ax+by+cz+dt1, but how do we visualise the fourth term? Moreover, we can see that the particle has moved in all dimensions. The movement of the particle in space is x,y,z but in space-time continuum it is xt,yt,zt. Lets say that at t1 the position of particle is s1=x+y+z+t1 and at t2 it is s2=x+y+z+t2 (Taking the constants a=b=c=d=1 for sake of simplicity). Analysing this we find that the positions are separated in time but not it space, implying that the position of the particle has not changed even though we have considered the particle to be motion. This is actually not possible. Since the particle has moved in space and in time with time being  a parameter to measure the position in every dimension it is concluded that the time is a curled dimension.

Space Time Continuum

A general misunderstanding of common people is that we live in a world that has significantly only three dimensions- length, breadth and height. For a longer time the physicists thought that the universe is in three dimension (3D). It was Einstein who proved that our universe has one more dimension- time. The fourth cannot be represented as an axis on a paper (for better understanding only, in many areas time is represented as an axis). He suggested that our universe is a space time continuum. The dimensions originated for the purpose of defining the state of an object at any instant of time completely.

To understand it in a better way, lets try out a simple exercise. Let us assume that time is not the fourth dimension. Now with three dimensions we will try to define the state of an object at a certain difference of time. Consider a person A who is at point P(x1,y1,z1) at a time say t1. Say at this instant your friend makes a phone call. Now the person moves from point P and reaches point Q(x2,y2,z2) at time say t2. Now if your friend asks you "Where is A ?", you answer him Point Q. Alternatively if he asks "Where was A when I made a phone call ?". The answer will be point P. This shows that if we do not use time as the fourth dimension, the sense of 'when' i.e. the time of occurrence is lost and we would be unable to define the state of an object completely.