The verdict is in, and has been for a while now: time travel is possible... at least hypothetically. In keeping with Einstein's theory of general relativity, there are a number of theoretical ways that travel backward through time might be achieved. However, none of these seem to have practical applications that would allow for a functional time machine to be built.
With or without arguments against its practicality, time travel has seen plenty of other contests over the years. Namely, these come in the form of paradoxes that seem to contradict it; a classic among them involves the so-called "Grandfather Paradox." While familiar to most time travel enthusiasts (especially since, thanks to the prevalence of time travel in popular culture, the concept is almost a household term), the rough idea goes something like this: you travel back in time, and either by choice or by accident, you assassinate your own grandfather earlier in his life. In doing so, you prevent the birth of your parents, and thereby your own birth as well; hence, if you were never born, then who killed your ancestors?
The example outlined above is the most popular iteration of the paradox, although it applied more broadly to virtually any conceivable set of conditions where the past is altered by a prospective time traveler, and hence the future is changed. Resolutions to the paradox have appeared as well; one, taking theories of a multiverse into consideration, contends that an individual who travels back in time and alters history actually does so on a timeline separate to the one from which they arrived. Whatever the case, all such theories pertaining to time travel, while mathematically demonstrable in some instances, are purely speculative.
Despite the popularity of the Grandfather Paradox in such discussions, there are other more challenging paradoxes that exist, which do more than simply argue against time travel.
Consider, for instance, the following scenario: let's say a professor of mathematics gains access to a time machine, and he travels forward in time to a future date where reads a mathematical equation from a textbook. He returns to the past, and discusses what he read with one of his students, who becomes inspired by the idea, and decides to work out the equation for himself. After a bit of labor, he manages to produce a working variation of the mathematical equation his professor described seeing, and then publishes a book about it... which becomes the very book that the professor read about during his visit to the future.
The idea seems simple enough thus far... so where's the paradox? Here's the catch: conceptually, the idea for the newly discovered equation didn’t come from the professor, nor did it come from the student; each of them learned about it second hand from the other, as a result of the professor's journey into the future... and yet, it came to exist nonetheless. So where, in truth, did the idea come from?
Another version the same principle, known as the Ontological Paradox, was featured in October 2015 on the BBC's Doctor Who in series nine, episode four, entitled "Before the Flood." The clip appears below, conveyed brilliantly by actor Peter Capaldi in his role as the Twelfth Doctor:
The paradox, referred to here by Capaldi as the "Bootstrap Paradox" (a reference to the nonsensical expression of "pulling oneself over a fence by one’s bootstraps") does more than twist our mind in circles as we try to understand where equations and classical compositions might have come from when time travelers get involved in the mix. In fact, what is most unique about this thought experiment is that it seems to suggest the idea that information can enter the universe from nowhere. But can it?
For physicists, this is indeed a disturbing proposition, because it contradicts the orderly nature of things expressed by the known laws of thermodynamics. Herein we find a close relationship between entropy and information in our universe, and thus, the idea that information could simply appear “from nowhere” is akin to breaking thermodynamic laws. Since this is impossible according to what we know about the laws that govern our physical universe, one might ask, does this also disprove the notion of time travel as being viable at all?
As we've already expressed, time travel (at least backward in time) is a hypothetical possibility and could be achieved in a variety of ways that are in keeping with general relativity. However, if it were ever to become a functional reality, and information could indeed be passed from one temporal state to an earlier one in history, the outcome may be so strange and unforeseen that perhaps we would indeed be forced to ask ourselves things like, "who really did write Beethoven's Fifth?"