Have you ever wondered what time is? If you have, you are certainly not alone: Quite a few people have scratched their heads about this topic, among them many natural scientists. Although we think we understand a bit, the physical concept is still somewhat mysterious and many open problems remain. In this and in future posts I will present my view on the topic, which is a bit special given my educational background.
In this first post, we cover the idea of Newtonian time. This concept of time appears in the physical theory of relatively large objects, called classical mechanics, and is named after Isaac Newton, one of the founders of the theory. The problems for which classical mechanics is used are close to our daily experience and hence the theory is rather intuitive, but its applicability is limited. In particular, if we take a look in the microscopic world of elementary particles, atoms and molecules, we find that classical mechanics cannot predict what is observe. Hence, starting in the early 20th century, scientists developed a better theory, called “quantum mechanics”, which describes the microscopic world well and which effectively turns into classical mechanics for macroscopic systems. We will talk about how time appears in quantum mechanics in other posts, but for now we stay the realm of classical mechanics where everything is still relatively simple.
Superficially, the concept of time seems straightforward. If you have ever been exposed to classical mechanics (or if you trust your intuition), you have learned that time is a parameter that orders the “evolution” of a physical system like the frames of a movie. What we mean by that is best explained with a figure. In figure 1, snapshots of balls on a billiard table are ordered with a time parameter \(t\). Based on the snapshots, we can come up with the following story: At \(t=t_1\), the cue hits the white ball. At \(t=t_2\), the white ball hits the blue ball, and at \(t=t_3\) the blue ball hits the wall. Our natural ordering of the snapshots is \(t_1 < t_2 < t_3\), although we don’t really know — much might have happened in between these snapshots and in principle, other orders are also possible.12 We assume this time order based on the snapshots and based on our experience of cause-effect relationships that give us an intuition about how billiard balls ought to behave.
Classical mechanics can be used to describe the motion of the balls. In the theory of classical mechanics, the balls are assumed to be points with a position in a two-dimensional space (the billiard table) defined by coordinates \(x\) and \(y\). For example, the position of the white ball can be described by a set of two numbers \((x_{\rm w}, y_{\rm w})\) corresponding to the \((x,y)\)-coordinates of that ball, as depicted in figure 2. When we determine the motion of the balls using the tools of classical mechanics, we find that these two numbers change continuously when \(t\) changes continuously from \(t_1\) to \(t_2\) to \(t_3\).3 The values of \(x_{\rm w}\) and \(y_{\rm w}\) are functions of \(t\), which we can indicate as \((x_{\rm w}(t),y_{\rm w}(t))\). In this way we can trace the position of the balls, make snapshots of their positions also at other values of \(t\) than just \(t_1\), \(t_2\), \(t_3\), and combine them to a movie that corresponds to our experience of how billiard balls move.
The time which appears in this picture is called “Newtonian time”. A Newtonian time is something external to the system that we are looking at, some “divine” ordering parameter that continuously and uniformly changes without any underlying reason — it flows. We seemingly measure that flow with better and better clocks which seem to give us better and better access to the time parameter. In some sense, our use of time as one of the fundamental SI units reflects the view of time being something fundamental, and this view is supported by our ability to measure a duration with astonishing precision using atomic clocks. Notwithstanding, there are problems with the concept of Newtonian time which show that time can (fortunately) not be like that.
We will talk about problems of Newtonian time in the next posts where we talk about quantum mechanics, and there are even more problems when we try to take the general theory of relativity into account. For now, we just note that the idea that time is something “external” is not satisfying. In particular, if we (for whatever reason) want a theory of the whole universe, we don’t want something external that is not contained in the theory, but we want it to contain everything by construction. This is also true if we want to describe so-called closed systems, which are idealized physical systems that effectively have no interaction with the rest of the universe. Without something external, how can we understand the notion of time? By making time a part of the system, which we can achieve by explicitly considering the clock.
To summarize, we found that time in classical mechanics
- labels how the positions (and velocities) of a system of particles change,
- is usually treated as Newtonian time, that is, as an external parameter that is just “there” and changes continuously without any underlying reason, and thus
- is problematic because if we want to describe “everything”, an unknown external parameter does not make sense.
Footnotes:
- For example, the balls could all be moving chaotically around the table, e.g. due to people hitting the table while enjoying a bar fight. Then any order of the snapshots is possible.
- Actually, in classical mechanics we do not only know the position but also the velocity of the object. This, however, does not change the situation describe here.
- A continuous change means that if we change \(t\) only a little, the coordinates can also only change a little.