This post is a companion with the post “Is space one-dimensional?“. As we can compare the alleged one-dimensionality of time with how we think about space, so we can compare the three-dimensionality of space with how we think about time. In both cases the comparison is instructional. Space and time are parallel in both cases but in the latter case which we are examining here, the answer to the question is Yes.
A world line is the path of an object through spacetime. It has both spatial and temporal components, so its simplest representation is with one dimension of space and one dimension of time on a two-dimensional surface as a graph. But then we say that space has two other dimensions which are not represented in such a case.
These two other dimensions of space are movements in different directions, so there are components of distance in a total of three dimensions. Does it take time for an object to traverse these components of distance in the other two dimensions? Yes, it takes time to move in each dimension, that is, an object has a measurable component of duration in each of the dimensions.
So there are three components of distance in three dimensions, and there are three components of duration in three dimensions. Since we speak of these three dimensions as space (because of the three components of distance), should we not also speak of time as having three dimensions (because of the three components of duration)? Yes, we should.
Why haven’t we seen the three dimensions of time? Time has been associated with movement and space with stasis. But the movement of an object involves change in both space and time. The movement of an object is measured by its distance and its duration. For example, speed is a ratio of change in spatial position (distance) over change in temporal position (duration).
The conception of spacetime that comes from relativity theory is ready-made for this recognition of the three-dimensions of time. Space and time are parallel and intertwined and so might be considered together, as a six-dimensional spacetime.