Understanding Space-time curvature

According to general relativity mass curves space-time but not just space. It means an object moving in space will go in a straight path for any amount of time but once it approaches any other object it starts to deviate from straight line path and moves in a curved path.

Let us consider a mass A, comparable to the size of mass earth, initially moving alone in space with velocity V from point X in space. Because there is no other mass in its proximity it will follow a straight line path. Let us assume at some point, Y it approaches another mass B, comparable to mass of sun. Once the mass A is in vicinity of mass B, it will no longer follow a straight line but it follow a curved path in space as it approaches mass B.  We can predict three paths for mass A

1.     Mass A spiral around mass B and collide with mass B

2.     Mass A revolve around mass B

3.     Mass A follow a path of curve and fly away(Gravitational lensing)

Depending on the mass of A and B and its velocity it may takes any of the above three paths. But we assumed comparable sizes of earth and sun for mass A and B respectively. So, it will probably take a path of revolving around sun if its velocity is same as that of the earth.

  

The degree of curvature of mass A path depends on strength of gravity between mass A and B but path of mass A is not curved because space is curved. 

Curved Space                                                                             Curved spacetime

 

Common Misconception of Spacetime curvature

Einstein’s theory of General relativity

Einstein came up with a brilliant idea that gravity is not a force but a consequence of curvature of space-time. According to General theory of relativity a mass curves space-time around it and a free-falling objects are moving along locally straight path in curved space-time. Einstein considered time a dimension and related gravity to space & time. This is best explained by a trampoline, though it really is not right example.

When you put a heavy mass on a trampoline we observe the mass pulls down the fiber creating a curvature. If we throw a light mass pointing just away from the mass we observe that it moves in elliptical path just as mercury perihelion effect. This is how a free-falling object rotates. Mass bends space-time around it and so the path of planets is curved and freely falling.

Above explained example of trampoline is best example to understand the path of object moving in space-time but really is not how the space-time is curved. A mass would curve space-time equally in all direction. In trampoline example, gravity pulls lighter mass down and so it decelerates while moving away from larger mass. But in reality space-time is curved same above and below. The net force seems to be equal either up or down. So any mass would follow the curved path initially but would fly away once it reaches other side because there is no force pulling it back. So, the example of trampoline is not quite complete to explain curvature of space-time.

“Curvature of space-time is not a heavier mass curving a space-time around it but a lighter mass following path of curve instead of straight line under influence of gravitation.”

To understand the difference between space and space-time curvature click here