In physics, the term "time distance" is not a commonly used or well-defined concept. However, based on the context you provided, I assume you are referring to the concept of spacetime intervals in the theory of special relativity.
In special relativity, the notion of spacetime combines three dimensions of space with one dimension of time into a four-dimensional continuum. Spacetime intervals are used to describe the distance between two events in this four-dimensional spacetime.
There are two types of spacetime intervals: space-like intervals and time-like intervals.
Space-like Interval: A space-like interval refers to the distance between two events that are not causally connected, meaning that no information or signal can travel from one event to the other within the limitations of the speed of light. In a space-like interval, the temporal component of the interval is imaginary, and the spatial components contribute to the overall magnitude. The square of the space-like interval is negative: Δs² = -Δt² + Δx² + Δy² + Δz², where Δs represents the spacetime interval, Δt is the difference in time coordinates, and Δx, Δy, and Δz are the differences in spatial coordinates.
Time-like Interval: A time-like interval refers to the distance between two events that are causally connected, meaning that information or signals can travel from one event to the other. In a time-like interval, the temporal component of the interval is real and contributes to the overall magnitude. The square of the time-like interval is positive: Δs² = Δt² - Δx² - Δy² - Δz².
In both cases, the spacetime interval Δs provides a measure of the separation between events in spacetime. However, it is important to note that the term "time distance" itself is not a standard term used in physics, and the concept of spacetime intervals is generally used to describe the relationship between time and space in the theory of special relativity.