Special and General Relativity
Einstein developed two theories of Relativity :-
1. Special Relativity - Explains relative uniform motion between two reference frames.
2. General Relativity - Explains relative non-uniform motion ( taking accelerations due to Gravity into account ) between two reference frames.
Special Relativity has been extensively discussed within the Higher Physics course ( see Special Relativity ) and as such, the Advanced Higher course focuses on General Relativity.
General Relativity is Einstein's explanation as to "How Gravity works". It is based upon the concept that Mass distorts the space around it (more specifically the Space-Time around it), and that Gravity is a consequence of this curvature of space. The diagram below sums up General Relativity in its simplest terms as described by John Archibald Wheeler :-
"Matter tells Space-Time how to curve; Space-Time tells Matter how to move"
Matter tells Space-Time how to curve :-
Space-Time tells Matter how to move :-
Note - The above diagrams demonstrate the curvature of Space-Time using the rubber-sheet analogy. This shows a 2-dimensional representation (a flat Sheet) of the 4-dimensional Space-Time.
The explanation of movement within Space-Time explains why the path of a ray of light is distorted by passing near a Mass. A ray of light (and any other object) will follow the shortest possible path (known as a Geodesic) through curved Space-Time. This causes the ray of light to follow a curved path and from the point of view of an external observer, the path of the light bends.
The Equivalence Principle
In the National 5 course the acceleration due to Gravity (g) was given two different units, either ms-2 or Nkg-1 . The first Unit (ms-2) states that the Object is accelerating, whilst the second Unit (Nkg-1) states that the object is experiencing a Gravitational Force. Throughout the National 5 course, these two concepts were seen as interchangeable (and they are) , but no reason as to why was given. The two units (and therefore concepts) are interchangeable due to the understanding of Einstein's Equivalence Principle.
The Equivalence Principle states that :-
"No experiment can differentiate between the effect of a Uniform Gravitational field and an accelerating reference frame."
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.
The Equivalence Principle can also be demonstrated with a Projectile thrown horizontally within the two Spacecraft. In both cases, the Projectile will follow a curved path, in the Spacecraft's Reference Frame.
Diagram One - the Projectile ( once thrown ) does not experience the acceleration of the Craft, and travels in a Straight Line ( in the projectile's reference frame ) , but due to the relative acceleration of the Craft, the path is Curved ( in the Craft's reference frame ).
Diagram Two - The Projectile experiences an acceleration vertically due to the Gravitational Field, and as such the path is Curved.
The same effect is also seen with Light. The Path of Light in an Accelerating Reference Frame is Curved due to the Relative acceleration, and therefore in a Gravitational Field the path of a beam of Light Curves.
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 :-
This apparent shift in Stellar Position was used to "prove" Einstein's Theory of General Relativity. In 1919, Sir Arthur Eddington observed the shift in Position of Stars in the Constellation Taurus during a Solar Eclipse to match exactly the predictions of General Relativity.
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 :-
In the above image, the central yellow region is a nearby Elliptical Galaxy. The ring around is the Einstein Ring, the Optical distortion of a more distant Galaxy.
Note - Gravitational Lensing is being used to identify regions of high Dark Matter density. Dark Matter causes light to experience Gravitational Lensing, and in the absence of a visible Object to cause the effect, Dark Matter can be located.
The video below shows a summary of Gravitational Lensing :-
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 :-