In order to understand anything we need to have good definitions. Otherwise the words we use will lead us astray — which is what has happened with the word “time”.
I have a copy of the McGraw Hill Dictionary of Physics, Third Edition. Here is its definition of time:
- The dimension of the physical universe which, at a given place, orders the sequence of events.
- A designated timepoint in this sequence, as the time of day. Also known as epoch
What’s wrong with this definition? Events can be ordered in various ways, and that’s the gospel truth (compare the differences among the four gospels). Events can also be ordered by their correspondence to space; here’s an example:
“When did you get to the race?” “We didn’t arrive until they’d gone a quarter of the way.”
So time is not an ordering, though it has an ordering. It’s interesting that this dictionary doesn’t define space at all, though it refers to “ordinary space” as if it’s obvious what that is.
Time is not the dimension of ordering; it’s not a dimension at all. Would we call space a dimension? No, we say space has dimensions. It’s the same for time: time has dimensions. What are dimensions? Dimension is a concept that comes to us from geometry, where it is defined as the minimum number of coordinates needed to specify a point on (or in) it.
If time is neither an ordering nor a dimension, what is it? Both time and space should be defined in terms of movement because that’s how we measure them.
Measuring a movement requires comparing it with a parallel movement. There are two basic movements which can be standardized for systematic use in science and other disciplines. One is angular movement and the other is linear movement. Comparison with constant angular movement results in a temporal measurement, a point in time or a length of time. Comparison with constant linear movement results in a spatial measurement, a point in space or a length of space.
This leads to the following parallel definitions of time and space:
- Time (space) is what is measured by a standardized angular (linear) movement that begins and ends. In everyday terms, time (space) is what is measured by a stopwatch (surveyor’s wheel) or its equivalent.
- A point in time (space) is the beginning or ending of something, an object or event.
- A length of time (space) is the difference between the beginning and ending of something, an object or event. Also known as a duration (length).
- A dimension of time (space) is a coordinate for specifying a point in time (space) relative to an origin, a standard reference point. Both angular and linear coordinates are possible.
- A position vector of time (space) is an ordered pair of numbers for a point in time (space): the first is the magnitude of the length of time (space) from the origin in time (space) and the second is the direction from the origin in time (space).
- As a matter of observation and fact, there are three dimensions of time (space).
Does this mean there are six dimensions in all? Perhaps. Both time and space have three dimensions, and their dimensions might be combined, as Minkowski combined four dimensions.