Final answer:
The 4th dimension refers to time, integrated with three spatial dimensions into a concept called spacetime, essential for the theory of special relativity. Lorentz transformations are mathematical tools used to describe the relative observations of time and space for objects in motion. Spacetime can be distorted by mass and is analogous to representing a 3D city on a 2D map.
Step-by-step explanation:
Understanding the 4th dimension is best achieved by learning how spacetime coordinates lend themselves to the description of events in our universe. The fourth dimension integrates the element of time with the familiar three spatial dimensions. This framework is essential in the theory of special relativity, which introduced the need for Lorentz transformations as a way to reconcile observations concerning time and space when objects are moving at significant fractions of the speed of light.
Lorentz transformations are more complex than simple Galilean transformations, primarily because they include time as a dimension and account for the finite speed of light. These transformations allow for the conversion of coordinates between two observers moving relative to each other at constant velocity. In essence, a Lorentz transformation corresponds to a rotation of the space-time axes, which contrasts with traditional rotations in three-dimensional space, as they involve both the spatial dimensions and time.
When mass is present in the universe, it causes a distortion of spacetime, an effect which is often illustrated through analogies. For instance, one could consider the condensed representation of a three-dimensional city like New York on a two-dimensional map. In similar ways, the events and intervals in four-dimensional spacetime can be represented in diagrams that capture both spatial and temporal dimensions.