Is Time Travel Logically Possible?

(This is an extended version of the essay for an online introductory course on philosophy I took in Coursera.)

Introduction

In H. G. Wells' The Time Machine, the protagonist travels both backward and forward in time. The Doraemon animation series which was created in Japan in the 60s features a robotic cat who travels 2 centuries backward. In Hollywood, we have Terminator series which is predominantly based on the theme of travel. A web-search on 'mythology' and 'time travel' would bring up many resources. But human's fascination with time-travel is not new. Einstein's special theory of relativity (1905) and then General theory (1915) gave a hint that time is not a physical absolute that keeps all universe chained to one single point which moves at its own personally chosen pace. Different objects experience different personal times depending on how close their relative speeds are to the speed of light. It's over a 100 years since then. Design of time machine hasn't been achieved yet. That prompts us look at the phenomenon of time-travel with some more scepticism; to investigate what would logically entail when the external and personal times of an object start diverging.

Here I present my thoughts on time travel. In this essay, I present three arguments: Unique existence, impossibility of passive existence and causal loops. My analysis makes me believe that time travel may not be a logically well-founded notion, at least not in the form we popularly perceive it in.

The Issue of Unique Existence

This argument rests on an assumption that, given any point and time in all space -- the (x, y, z, t) co-ordinates -- there can be only one particle occupying it. Suppose I (means, the collection of all particles in me) am occupying a particular space at a given point in time. What happens if an object or person travelling through time pops out this very moment -- apparently from nowhere -- to occupy the same space that I occupy. What would happen to the particles in me? Would they be displayed here and there? Would they just disappear giving place to the newly arrived object? At any rate, two particles occupying the same coordinates in the space is incomprehensible.

Impossibility of Passive Existence

The phenomenon of objects popping out of thin air has yet another issue. Each such event is bound to create counterfactual changes. Even if an object pops out at a point previously occupied by nothing else (i.e. vacuum), it's sure to change the course of history of the universe. If it's a charged particle, it will set an electric field around itself. A radiating object will change the illumination of the place. If not anything else, the very fact of an object having a mass immediately causes it to interact with all other particles of the universe through the force of gravity. The fact of something's existence is fundamentally determined by its ability to interact with the universe surrounding it in someway. Even a passive spectator of events around it must be stimulated by physical stimuli (e.g. light, sound waves etc.) to sense them. Absorbtion of physical signals results in changes in the surrounding that wouldn't have happened if the signals hadn't been absorbed. In other words, an absolutely passive existence sounds like a vacuous idea. May be, invoking Descartes' idea of substance dualism may succeed in modelling such a 'ghost' existence. But, in my mind, I am unable to do so.

Causal Loops

The most serious difficulty in the notion of time-travel, according to me, comes from the notion of causality. If we write out all the events in the universe, and for every pair of events A and B, we draw an arrow from A and B if A directly causes B This exercise (of drawing arrows between events) would give us a directed acyclic graph (DAG) of causality. As per this idea, all events in the history of the universe can be tracked back to a set of events, which in turn, aren't caused by any other event. There can exist no cycles of causality in this graph. Put another way, no event can directly or indirectly cause itself.

However, time travel can create cycles in this causality graph. Several examples are present in the Terminator series of movies. For example, a soldier named Reese is sent back in time by John himself from the Terminator. John is born out of the love between Reese and his mother Sarah. Does this mean that John caused his own existence? In fact, it would have been possible for John to father himself, had the storyteller decided to tighten the loop of causality a bit further! Even more interesting is the advent of the Skynet -- the AI network which wages a war on humans. Skynet develops out of the remains of the first Terminator, the one which had travelled to 1984 from 2029 to assassinate Sarah. And its Skynet which creates Terminator. The question is: wherefrom comes the idea Skynet or Terminator. They seem to have begotten each other! The trouble here is more serious than that a machine invents a machine. We may imagine, at least in theory, that AI machines sophisticated enough may even invent other machines. But the acyclicity of causality is an even more important requirement in the case of ideas and thoughts than in the case of physical events like birth of people.

Conclusion

We have presented three arguments which speak against the logical possibility of time travel. The first objects to time travel based on the incomprehensibility of two particles occupying the same co-ordinates in space at any given instance of time. The second rests on the notion that existence of a physical object can't be passive in true sense; it must interact with the outside world. And therefore, it must have a role in the course of history. The third objection rests on the assumption that causation is acyclic: Time travel makes it possible for events to cause themselves.

There are other difficulties which are physical. For instance, how would time travel as we understand it, fit in with laws of conservation of mass and energy?

It also appears to me that the objections raised above, more than proving a fundamental impossibility of time-travel, brings forth a certain incomprehensibility of the reality that would result from it. To prevent time-travel from creating an anomalous universe, one must imagine a concept of time travel very different from the one popularly held.