A graphical notion of the expansion of the universe. There is an arrow of time pointing in the direction away from a singularity. Image source: NASA via Wikimedia Commons

A graphical notion of the expansion of the universe. The arrow of time points in the direction away from a singularity. Image source: NASA via Wikimedia Commons

The nature of time is a hard thing to define because one perceives it as an inescapable fact: tomorrow always comes. But will there ever be a day in which tomorrow does not come? What is the nature of the end of time? In addition, could there be people who live in “backwards” time? Can one talk to them? Professor Lawrence S. Schulman of Clarkson University discussed these topics at the Dartmouth Physics Department on October 18.

Traditionally, time is defined in two different contexts: the expansion of the universe and entropy. Entropy measures how many different arrangements of a system are possible. Given a room full of boxes and a handful of balls, how many different ways could one put the balls in the boxes? It is obvious that having all of the balls in one box is relatively unlikely, compared to having the balls scattered among all the boxes. This is the essence of the 2nd Law of Thermodynamics: entropy tends to increase over time because there are many more ways for a disordered state to occur than the single-box state.

One may also compare this to the cosmological definition of time, in the sense of the expanding universe. As far as mankind knows, the universe started from an infinitely small point and expanded to what we see today. So in a sense, time proceeds in the direction of the expanding universe and not towards the direction of the original singularity.

These very different definitions of time were not connected until the 20th century cosmologist Thomas Gold conjectured that the expansion of the universe enabled continued progression of entropic disordering without reaching thermal equilibrium. He did not definitively reconcile the definitions, but brought up a good point that these notions of time should be connected in some way.

During his talk, Schulman uses a fairly simple system to model time. He takes a set of a points in a square and makes them go to a new point relative to their positions. He then repeats this process a set number of times. The set of points is filtered to contain only points that start within a narrow region and end in another narrow region, representing a universe that starts and ends in tiny states. Then, he measures the entropy associated with the system as a function of the number of simulation steps taken.

Interestingly, if Schulman introduces a perturbation mapping— a transformation that is not part of the normal transition— the effects of the perturbation always tend towards the middle of the time-steps. This occurs even if the perturbation action was performed after the time the position represents in the iterated simulation. This is important because it would be impossible to find out if someone were traveling “forward” or “backwards” in time without comparing two opposite systems.

Schulman’s contrived system provides some insight on what should happen if the universe ends. Comparing mappings with different end times, we see an interesting pattern. If the universe ends, then we would not be able to realize this fact until at least half of its total age has passed, as it otherwise behaves identically to an infinite universe. Perturbation experiments provide a method to distinguish the possibilities by calculating how long it takes a system to return to equilibrium. In an experiment with timescales that are comparable to the life of the universe, noticeable deviations indicate that the universe has a finite lifespan.

A philosophical problem can also be considered. Isaac Asimov, the famed science fiction writer, theorized about talking with backwards-time people. In his scenario, communication in the form of messages might be possible, but never meaningful conversation. The nature of time is interesting, not merely on a scientific level, but also at the philosophical level Asimov’s theory represents. After all, the vantage point from which we perceive time, at different points in Schulman’s model or from various disciplines of analysis, affects our conclusions about time’s nature.