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Extending the Special Theory to All Observers
The special theory of relativity is based on the idea that the laws of physics must be the same for all inertial observers.
Mach suggested that it should be possible to reformulate the laws so that they were the same even for observers in accelerated (non-inertial) frames of reference.  
Einstein attempted to prove that this assumption is valid and the result of his work is the general theory of relativity (published in 1915).  
   
The general theory of relativity gave a new way of looking at gravity.  
It is rather complicated, mathematically, but a few basic ideas associated with this theory can be introduced here.  
   
The Principle of Equivalence  
Consider the three situations shown below  
 
   
1 No acceleration.
  Rocket (and mobile laboratory) very far from earth (or any other similar body).
  Apple released by space-person stays near the hand that released it.
  This situation shows the inertia of the apple. It is an inertial frame of reference.
   
2 Rocket and laboratory accelerating at 9.8ms-2.
  We are now in a non-inertial frame.
  Now, if the apple is released it will accelerate towards the floor.
  The bigger (heavier, more massive) apple will do exactly the same thing.
   
3 Go back to earth and repeat the observations. 
  What do you find?
  The earthís gravitational field produces exactly the same effect as the acceleration of the rocket.
 
   
Einsteinís conclusion was that an accelerated frame of reference must be considered to be equivalent to a reference frame at rest in a gravitational field.  
   
The Equivalence of Gravitational and Inertial Mass  
 Newton's second law of motion can be rearranged to give a definition of inertial mass, mi  
 
The inertial mass is a measure of how much force is needed to change the state of the motion of a body.  
Newton's law of universal gravitation also involved the concept of mass.   
Let's call this mass, gravitational mass, mg (for obvious reasons!)  
The law leads to the following equation  
 
In formulating these laws, Newton assumed that the two masses, mi and mg were equivalent quantities.  
The fact that all bodies fall with the same acceleration supports this assumption.  
Einsteinís principle of equivalence explains why it is reasonable to consider that mi and mg are the same by stating that acceleration (related to the idea of inertia) and gravitational field (related to gravitational mass) are exactly equivalent.  
See also here for more on this.  
   
Gravity in General Relativity  
In reformulating the laws of physics in accordance with Machís principle, Einstein arrived at a new theory of gravity.  
He suggested that the presence of a massive body causes a curvature of space-time.  
The distortion of space-time can be considered to have two effects:  
1. space is curved near a massive body  
2. time runs more slowly near a massive body*  
 
These two effects modify the paths of moving objects (and of electro-magnetic radiations) near massive bodies and together they form what we call a gravitational field.  
   
* Donít confuse this effect with the time-dilation effect. If you are moving relative to me, I will see your clock as running slowly and you will see my clock as running slowly..
 Considering this new effect: if I am very near the earth and you are far away from the earth, you will measure my clock to be running slowly and I will measure your clock to be running fast
 
   
Black Holes  
When a star has "used up" all its nuclear fuel, it can collapse under the influence of gravity.  
This is thought only to happen to very massive stars (much more massive than the sun).  
After the collapse, the star becomes very dense.  
This very dense object is predicted to have a gravitational field which is so strong that nothing can escape it, not even light.  
   
The boundary across which nothing can pass is called the event horizon and its radius was calculated by Karl Schwarzschild.  
The Schwarzschild radius is thus a measure of the size of the black hole.  
It is given by the (perhaps) surprisingly simple formula  
 
where M is the mass of the star, c is the speed of light and G is the universal constant of gravitation.  
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