General Relativity

This topic is contained in pages $75-86$ of the textbook.

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Special relativity deals with motion in inertial (non-accelerating) frames of reference and general relativity deals with motion in non-inertial (accelerating) frames of reference.

→ Special relativity relates to inertial frames of reference — frames of reference that are not accelerating with respect to each other. General relativity relates to non-inertial frames of reference — frames of reference that are accelerating with respect to the other.

The equivalence principle states that it is not possible to distinguish between the effects on an observer of a uniform gravitational field and of a constant acceleration — the effects of gravity in one direction are equivalent to acceleration in the opposite direction.

→ To an external observer, time runs slower in stronger gravitational fields; this is known as gravitational time dilation. The reverse is also true, where the force of gravity is weaker, time passes more quickly (to an external observer).

→ The effective gravitational field can be ascertained by taking into account the acceleration of an object (and any real gravitational field effects).

Spacetime can be considered as a unified representation of three dimensions of space and one dimension of time.

→ General relativity leads to the interpretation that mass curves spacetime, and that gravity arises from the curvature of spacetime.

→ Small masses can be pulled into the ‘dips’ of larger masses. However, the greater their acceleration, the larger the ‘dip’ must be to pull them in.

Light or a freely moving object follows a geodesic path in spacetime — the path with the shortest distance between two points.

A geodesic is path can also be called a world line. World lines can be represented using diagrams which show both the movement of an object in physical space but also with respect to a time axis.

→ Four dimensions cannot be shown on paper, so one or more of the spatial dimensions are collapsed to allow time to be drawn as well.

→ Stationary objects are represented by straight, vertical lines like $D$, objects moving with constant speed are represented by straight, sloped lines like $A$ and $B$, and objects which are accelerating are represented by curved lines like $C$.