# General Relativity

## General Relativity

### Matter tells Space-Time how to curve :- ### Space-Time tells Matter how to move :- ## The Equivalence Principle

### The above statement means that an experiment performed from a stationary position within a Uniform Gravitational field will give the same results as an experiment performed in the absence of a Gravitational field inside an accelerating region ( i.e. a spacecraft ) :- ### The Equivalence Principle can be demonstrated by the two Spacecraft above. In a windowless Spacecraft, it is impossible to distinguish between a Spacecraft accelerating at 9.8 ms-2 and a Spacecraft stationary at the Earth's Surface. The Reaction Force experienced within the accelerating Craft mimics the Gravitational Force on the Earth's surface exactly. ## Gravitational Lensing

### A consequence of Curved Space-Time is that Starlight passing the Sun will follow a curved path, and as such will appear in a different position within the Sky :- ### Identical effects can be seen on the Scale of Galaxies, except in this case, its not a single Star that is distorted, but the emitted light of a whole Galaxy :- ### Depending on the relative sizes and position of the two Galaxies, an Optical Effect known as an Einstein Ring can occur. An Einstein Ring is a two-dimensional consequence of Gravitational Lensing and can be seen in the image below :- ## Gravitational Redshift

### Einstein's Theory of General Relativity can also be used to explain the concept of Gravitational Redshift. The Diagram below shows the visual effect on a Ray of ( Initially ) Blue Light emitted by a Massive Object :- ### As the Photon moves away from the Mass, Work must be done to escape the Gravity Well. As was seen in the Higher Physics course, the Energy of a Photon is related to Frequency by :- ## Gravitational Time Dilation

### The above Observation of Gravitational Redshift can also be explained through the concept of Gravitational Time Dilation. If the vibrations of a Wave are used to measure time, as the Wave experiences Redshift the period of the Wave increases. This implies that as the Gravitational Field increases, the slower Time Passes. The diagram below shows an example of this, with the dotted line representing the Schwarzschild Radius of the Mass. ## What is Space-Time ?

### Space-Time, but so far in this section it hasn't been explicitly defined. Space-Time is a 4-dimensional coordinate system which takes into account that an event will occur at a location with a set 3-dimensional position ( x,y,z ) and time ( t ) . This can be represented graphically using the following four-quadrant graph :- ### The Diagram below shows a graphical representation of three objects in Space-Time, relative to the x-direction :- ### However, as shown in other sections of the Physics course, the Speed of Light places an upper limit on velocity, and as such there are velocities which are not allowed :- ### However, World Lines can cross from right to left. In this case, the crossing point denotes when an Event is Observable. The diagram below shows an example of this :- ### The diagram below shows a 2-dimensional representation the Space-Time Graph showing an Event occurring at the Origin :- 