The proof that there are three time dimensions is based on showing that a temporal position is a vector, that is, it has magnitude and direction. That may be shown by considering three orthogonal movements of an object. Let the position of the object be represented by a point (as on a corner) relative to an origin point.

Consider the travel times of three separate orthogonal movements from their distances traveled divided by their average speeds, times their unit vectors (**e _{1}**,

**e**, and

_{2}**e**):

_{3}(s_{1}* / v _{1}*)

**e**, then (

_{1}*s*)

_{2}/ v_{2}**e**, then (

_{2}*s*)

_{3}/ v_{3}**e**.

_{3}The resultant duration vector **t** is found by adding each of the three orthogonal vectors together by vector addition:

**t** = (*s _{1} / v_{1}*)

**e**+ (

_{1}*s*)

_{2}/ v_{2}**e**+ (

_{2}*s*)

_{3}/ v_{3}**e**.

_{3}That is, the resultant duration vector **t** has three components:

**t** *= t _{1} *

**e**+

_{1}*t*

_{2}**e**+

_{2}*t*

_{3}**e**.

_{3}Since *t _{1}, t_{2}*, and

*t*can be different, they represent three different components of the vector

_{3}**t.**That is,

*t*, and

_{1}, t_{2}*t*are orthogonal components of a temporal vector

_{3}**t**:

**t** *= (t _{1},*

*t*

_{2},*t*).

_{3}Thus we have demonstrated three dimensions of time.

These three dimensions are based on the same directions as displacement (spatial), velocity, force, and other physical vectors.