Class content I > The Main Question: Motion > Kinematics
3.1.3
Prerequisites
The other half of talking about motion (after figuring out "where") is specifying "when". For this we need to quantify time -- create a mathematical model of it.
There are lots of regularly occurring events in our experience -- our heartbeat, day and night, phases of the moon, seasons, etc. -- and they give us a personal sense of time and time passing. We've quantified that by creating clocks, but our everyday description turns out to be inconvenient for doing science because of the messy units -- years, months, weeks, days, hours, seconds, etc. In order to be able to do math with time, we want to map physical time (the time in the real world) into a mathematical structure that carries with it all the nice properties of arithmetic that match our sense of time: ordering, adding, and subtracting.
To create a mathematical model of time for use in science, we map time onto the real number line. Just as with space, we have to make a number of choices.
While this idea of mapping time onto the real number line seems quite reasonable, it turns out to be tricky to use. Each point on the number line of time corresponds to a particular "fixed instant" of time. Thinking about such a fixed instant is "stopping time". It's like we are watching a movie and a particular time corresponds to specifying a particular frame of the movie. Typically we tend to think about what's happening as a continuous and related set of events. "Stopping time" and thinking about what is happening at a particular instant (while time continues to run in our heads!) can be more challenging than you expect.
Follow-ons
Joe Redish 7/25/11