Saturday, 20 July 2013

Dented Space Time


Space Time can be imagined as a rubber sheet in which massive objects create a dent. In a rubber sheet if you place a small ball, there would be a very small dent on the rubber sheet, but if you place a huge ball, you will get a huge dent on the rubber sheet.


This same phenomenon explains Space Time. Sun being very huge in mass w.r.t Earth, so it causes huge distortion in Space Time where as Earth causes a small distortion in Space Time.

Dented Space Time

When a circular object creates distortion in Space time, the distortion is dent shaped. Take a look at the pic. Einstein gave his geometrical definition of Space Time curve. Einstein defined a set of field equations, which represented the way that gravity behaved in response to matter in space-time. These field equations could be used to represent the geometry of space-time that was at the heart of the theory of General Relativity.

The mass of earth creates dent in Space Time.
                        

Mathematics of Space Time

Since mass created a dent in Space Time, it became difficult for astronomers to understand the exact position of celestial bodies as the coordinate geometry to be used to locate a body was not sufficient to locate the body in a dented Space Time coordinate plane.

To overcome such problems, Einstein introduced another principle, the Principle of Covariance. This principle states that the laws of physics must take the same form in all coordinate systems.

In other words, all space-time coordinates are treated the same by the laws of physics — in the form of Einstein’s field equations (You will learn more about Einstein's field equation in the coming chapters). This is similar to the relativity principle, which states that the laws of physics are the same for all observers moving at constant speeds. In fact, after General Relativity was developed, it was clear that the principles of special relativity were a special case.

Einstein’s basic principle was that no matter where you are — Toledo, Mount Everest, Jupiter, or the Andromeda galaxy — the same laws apply. This time, though, the laws were the field equations, and your motion could very definitely impact what solutions came out of the field equations. In simple words Einstein explained that all the laws of mathematics and physics are applicable on the object in a dented Space Time coordinate system.

Take for example at a coordinate plane. It looks the same from the sides and top. Now take a look at the dented coordinate plane, though it appears dented from the sides but it would like like non-dented coordinate plane from the top. Einstein used the same phenomenon to explain the geometry of Space Time.




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