Just like the division of calendar era into BC and AD, the Physics era should be divided as Before Einstein and After Einstein. Before him Time was defined but never understood properly and Gravity was understood but never defined properly. His theories changed the way we observe the Universe and opened the door to new studies.
Generally curvature of space due to gravity is explained by placing balls or heavy objects on a Trampoline or rubber sheets. These objects make the sheet as a curved surface by creating a depression where they were placed as shown in the picture below
In this article we will take a similar approach using a sheet of paper. We will also analyse the consequences of the curvature along the way
We will start by placing a sheet of paper on the floor. Let’s assume this sheet of paper represents a two dimensional space with only length and width and not having any height. Now if we start applying inward force on the edges of the paper it starts to curve into a concave shape. As a result of the curvature created by the force the two dimensional paper can now exist in three dimensions. The curvature gives the paper access to an higher dimension(height). The more the curvature the more access to a higher dimension
But the beings living in the two dimensional paper space cannot perceive this, as they don’t understand the higher dimensions. Suppose we have two ants in the two dimensional space started walking parallel to each other in straight lines, since the surface is curved the ants will start drifting apart, since they can’t perceive the curvature they feel some invisible force is pulling them apart. The force which doesn’t exist but a phenomenon created by the curved surface which we call gravity in our three dimensional Universe
The point of the article is to discuss curvature, we will explore gravity in the future articles. Just like the above two dimensional paper, a one dimensional thread which has only length will curve and gets access to width (new dimension) by any force applied to it sideways.
If we try to apply the above analogy to a three dimensional space, the curvature of space created by the mass gives access to a fourth dimension which is time. Time is a dimension and the three dimensional space got access to time by the curvature created by the mass present in the Universe. Just like you get access to more height with more curvature in the two dimensional paper scenario, you get more curvature with more more mass and hence access to more time. This extra access to time given by a heavier masses (due to more curvature) makes any system to change slowly compared to the lighter masses which have lesser access to time dimension (due to small curvatures) and hence the time dilation
To better understand time dilation we will first explore height dilation in the two dimensional paper space. Imagine each ant on two different papers with same dimensions but different curvatures. Place a point in the diagonal intersection of the paper. For both the ants the point appears equal distance in their dimensions (length and breadth of paper) if they are starting at the same edge. This is because they don’t understand the third dimension (height). From both the ants view if they start walking towards the point they will reach the point at the same time but the ant on the paper with higher curvatures has access to more height and hence reaches the point late. This is height dilation created by the curvature in a two dimensional world
Now replace the process of ants reaching the mid point of paper with the process of reaching to certain age (let’s say 50) in the three dimensional world. You and your cousin were born at the same time and at the age of 10 your cousin moved to another planet which revolves around a black hole. Since the space around black hole is more curved than here around the earth your cousin will have access to more time (4th dimension) and hence will reach 50 slower than you, though you may both see reaching 50 as equal rate from 10
The mere existence of mass curves the space and gives access to time. Without mass there is no curvature and hence no access to time. Physicists believe that space and time came into existence after big bang. Space and time might have existed even before big bang but the curvature of space might came into existence with the big bang and hence the beginning of time with the curvature
The only criteria for the curvature to happen in all the above cases whether it is a rubber sheet, a paper or a thread is to have a restricted boundary condition. The space in the above dimensions should have a restricted boundary condition for curvature to happen in the presence of force. Maybe our Universe also has a boundary condition.
We will explore black holes in two dimensional worlds in the future articles