Time

As previously discussed, in Physics – particularly Classical Mechanics – we study the motion of an object. As, as we defined, motion is the change of position of an object. However, that raises an important question: what is time?

If we were to “define” time, it would be very complicated and would not serve our purpose of studying Physics that efficiently. It is more of a matter of Metaphysics in Philosophy. So, I shall use a simple definition of time: a parameter by which we can compare the object to itself to observe what changed accordingly.

So, why does time need to be here? Let us return to the main mission of every science: find the “cause” of the “what”. That is, we need to find why the consequences result in the results. But, according to one of the central assumptions in science (and even in life for many people), the Causation Principle, consequences must happen before the results. Basically, without this assumption, we are essentially looking for nothing in science: what are we going study, if our main objective is to find the cause, but the cause does not exist? Now, for our study to be meaningful, we must assume Causation Principle. However, the Causation Principle already implied the existence of time (or, at least, the idea of it applied in our model): things happen in order. That is, as time evolves, things will evolve in orderly states. Now, we can see that ever since we assumed the Causation Principle for our study to be meaningful, we already accepted the existence of time.

For the purpose of simplicity, we shall assume one thing (that is also true in Physics, as far as I know): time itself does not change anything in the Physics system we study. That is, changes in time do not change the system itself. For visualization, we can picture this: the system exists as a thing itself, and it does not know what “time” is. Similarly, time is also a thing itself, but does not know who space is. However, they still exist independently. Now, this is an important assumption (it is not to be forgotten that all assumptions, or axioms, are important): it justifies our simple definition of “time” as a parameter previously. It does not change the system itself. That is, when we examine the system at a specific point in time, time does not play a role and is a constant. It is not to be confused with the idea of the “value” of properties. For example, you can write the position as a function of time, but position does not change because time changes. Mathematically, it means the system does not explicitly depends on time. It might be a bit vague to discuss time like this, so let us imagine this: we are drinking a cup of water, and a clock is ticking on a table nearby. Do we drink as time evolves (as the clock ticks)? Yes, we are. But, are we drinking because the clock is ticking? Probably not. The same idea goes for our mechanical system: it changes as time evolves, but it does not mean time makes the system changes. However, let us not forget that even though time is not what makes the state of the mechanical system change, we can still, Mathematically, express the function that describes the mechanical state of the system as a function of time.