In mathematics, a four-dimensional space refers to a space that has four dimensions, typically denoted as (x, y, z, w) or (x₁, x₂, x₃, x₄), where each dimension represents a different degree of freedom. It is an extension of our familiar three-dimensional space, which is commonly described using Cartesian coordinates (x, y, z).
In a four-dimensional space, you can think of an additional coordinate, often referred to as the "w" coordinate, that is orthogonal to the three spatial dimensions. However, it's important to note that this is purely a mathematical concept and not something that is directly observable or experienced in our everyday lives.
The physical reality we perceive is commonly described as three-dimensional space, with time being considered as the fourth dimension in a four-dimensional spacetime. This concept arises from Einstein's theory of general relativity, which treats spacetime as a unified entity. According to this theory, spacetime is curved by mass and energy, and objects move through this curved spacetime along paths called geodesics.
While the theory of general relativity describes our universe as a four-dimensional spacetime, the extra spatial dimension beyond the three we experience is not directly observable or evident in our daily lives. Various hypotheses and theories in physics, such as string theory, suggest the existence of extra dimensions beyond our familiar three, but there is currently no experimental evidence to support their existence.
In summary, a four-dimensional space is a mathematical concept with an additional spatial dimension beyond our familiar three dimensions. Our universe, as described by the theory of general relativity, is considered to be a four-dimensional spacetime, with three spatial dimensions and one time dimension, but the extra spatial dimension is not directly perceivable in our everyday experiences.