Saturday, 20 July 2013

4th Dimension : Space and Time

When Physics was first discovered, only one dimensional units were used to describe the position of objects. For example The distance of book from Peter is 1m etc. In coordinate physics however we use to (x,y) coordinates to describe the position of object on a two dimensional plane. When two dimensional orbits inside an atom was discovered, the position of electron was given in terms of (x,y) coordinate. However in the later 19th century a need was felt to describe the position of object in a 3D plane using three coordinates (x,y,z). In early 20th century When Einstein postulated his Special theory to describe that Time is relative, it led to development of fourth coordinate of body in a 3D plane which is time. Since Time is relative it was necessary to describe an object's position in a given time.

Space Time

Space Time is a physical quantity that describes Position of a object in a 3D plane with respect to Time, i.e it is a fourth dimensional physical quantity. In this system the seperation between any two events is described by a value called a space time interval. It is an important implication of Special Relativity. When two events happen in different places the space between them is ambigious because it is measured differently in different Frames of reference. This also depends on the velocity of the observer. So Space Time is a mathematical method that can be devised for measuring the seperation of events.

Mathematical derivation of Dimension of Space time

The dimensional formula of Space is [L3] and that of Time is [T1]. Combining these two results the dimensions of Space Time is [L3T2].

Adding up the powers we get 1 + 3 = 4. Taking the modulus of the power sum we get 4. So the dimensions of Space Time is 4, i.e Space Time is fourth dimensional.

Representation of 4th Dimension

A two dimensional figure is a polygon, three dimensional is a polyhedron and four dimensional is a polychoron. The existence of a polychoron seems to be impossible, but Space Time is a polychoron which exists. 4th dimension is could be easily represented by thinking of Space as a two dimensional figure with two axes and Time acts as the third axes, where Time is cone shaped representing Past and Future. This cone shape has been used to explain the boundaries created by the speed of light.

Take a look at this image.

File:World line.svg
Space time in 2D and Time as conical 3D

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