The Bootstrap Paradox is a theoretical paradox of time travel that occurs when an object or piece of information sent back in time becomes trapped within an infinite cause-effect loop in which the item no longer has a discernible point of origin, and is said to be “uncaused” or “self-created”. It is also known as an Ontological Paradox, in reference to ontology, a branch of metaphysics dealing with the study of being and existence.

Etymology of Bootstrap Paradox

The term Bootstrap Paradox is derived from the expression to “pull oneself over a fence by one’s bootstraps”, which indicates performing an impossible or ludicrous task. In this instance, by pulling yourself over a fence by holding onto your bootlaces and tugging upwards. The first reference to such an absurdly impossible action is widely believed to originate from an 18th century literary classic, The Surprising Adventures of Baron Munchhausen, in which the eponymous hero is stuck in a swamp, and manages to escape by pulling upwards on his own hair.

The term “bootstrap paradox” was subsequently popularized by science fiction writer Robert A. Heinlein, whose book, By His Bootstraps (1941), tells the story of Bob Wilson, and the time travel paradoxes he encounters after using a time portal. One such example involves Wilson traveling to the future and being give a notebook by his future self, before then traveling to an earlier point in the future and using the book’s useful information to set himself up as a benevolent dictator. After the notebook becomes worn, Wilson copies the information into a new notebook and disposes of the original. He later muses that there never were two notebooks, and that the newly created one is actually the one given to him in the far future. So who wrote the book, and where did its information actually originate?

Bootstrap Paradox Examples

– Information: An example of a bootstrap paradox involving information would be if a time traveler went back in time and taught Einstein the theory of relativity, before returning to his own time. Einstein claims it’s his own work, and over the following decades the theory is published countless times until a copy of it eventually ends up in the hands of the original time traveler who then takes it back to Einstein, begging the question “where did the theory originate”. We cannot say that it came from the time traveler as he learned it from Einstein, but we also cannot say that it is from Einstein, since he was taught it by the time traveler. Who, then, discovered the theory of relativity?

In fiction, the Doctor Who episode ‘Blink’ contains an information paradox in which a video message forms an endless loop spanning thirty-eight years. Likewise, the two-part Doctor Who episodes ‘Under the Lake’, and ‘Before the Flood’ also features a nifty paradox anecdote involving Beethoven’s music. The 2014 film ‘Time Lapse‘ provides a further example of a story rich in bootstrap paradoxes, with the main characters responding daily to photos they receive from 24 hours into their future.

– Object: Somewhere in Time (1980) provides an example of a bootstrap paradox involving an object, in this case a pocket watch. In 1972, Christopher Reeve is given a watch by an old woman, which it turns out was given to her younger self by Reeve after traveling back to 1912. The young woman then completes the infinite loop by giving the watch to Reeve in 1972 when she’s older. An inconsistency that subsequently arises is how the pocket watch survives countless time cycles while remaining “unaged” and unaffected by time. The problem is no less true for information trapped inside a bootstrap paradox. Both seem to violate the second-law of Thermodynamics, which states that entropy (gradual decline into disorder) will always increase over time.

In the Terminator movies, Skynet is an example of a bootstrap paradox involving an object. Skynet, the conscious AI system and mankind’s nemesis, could not have been invented without the leftover components of the T-800 cybernetic organism it sent back in time to stop John Connor. The technology was analyzed and Skynet and cyborgs were subsequently created through reverse engineering.

– Person: The most extreme example of a bootstrap paradox involving a person can be found in the Robert A. Heinlein’s short story “All You Zombies” (1959), which inspired the 2014 movie “Predestination“. Here the main character, an intersex male born a female, is tricked into going back in time and impregnating his pre-gender reassigned female self, who subsequently gives birth to himself/herself. As a result he becomes a self-created entity who is both his own mother and father. This naturally presents a real mind bending chicken-and-egg conundrum. Once again, however, the story appears to be self-consistent, with no changes taking place each time through the loop. Nevertheless, Heinlein doesn’t attempt to answer the role “free will” plays in this imaginative scenario.

The Futurama episode ‘Roswell That Ends Well’ where Fry becomes his own grandfather provides another good example of a person centric bootstrap paradox in fiction. As does the Terminator movies, once more, with a future John Connor sending Kyle Reese to the past to impregnate Sarah Connor, who then gives birth to John Connor.

Self-Consistent with Timeline

Consistency Paradoxes, such as the Grandfather Paradox, The Hitler paradox, and Polchinski’s Paradox, result in a ‘self-inconsistent’ solution with the timeline’s history. After all, if a time traveler killed his own grandfather then he would never have been born, and so would not have been able to travel back through time and murder his grandfather. This would be a paradox.

The Predestination Paradox and the Bootstrap Paradox, on the other hand, are examples of closed loops in time in which ’cause and effect’ repeat in a circular pattern, resulting in a self-created entity with no point of origin. Despite being an oddity and apparently conspiring against our understanding of causality, this ‘self-caused’ event, like the Big Bang, does not appear to be an impossibility. Nor does it imply any inconsistency with the timeline’s history. In fact, all the events in the time loop are “fixed” and take place on a single unchangeable timeline.

Problems

Einstein’s Theory of General Relativity tells us that we have got almost complete freedom of movement into the future. Time travel to the past, on the other hand, throws up a number of paradoxes. That’s despite his equations maintaining that four-dimensional space-time can be twisted into any shape, and that loops in space-time are possible. Any time travel paradoxes which do arise are therefore of particular concern to theoretical physicists. Their line of reasoning has subsequently lead many of them to conclude that time travel to the past must be impossible. Some of those fundamental breeches in the laws of physics include the following examples:

– Law of Causality: While a bootstrap paradox may produce a consistent account of the timeline’s history, one problem associated with this ontological conundrum is an apparent violation of the Law of Causality. As a result, scientists are presented with an obvious problem in that they are no longer able to say that a past ’cause’ leads to a future ‘event’. After all, the event may equally have been created in the future before leading to its cause in the past. This suggests that instead of time moving from a dead past to an undetermined future, the past, present and future are, in fact, all equally real at the same time. In the process, rendering the task of defining the “origin” of anything, a term usually associated with the past, now meaningless.







– Law of Entropy: Another problem associated with a bootstrap paradox is an apparent violation of the second law of thermodynamics, which states that systems always flow from a state of order to a state of disorder. This would suggest that an object or information trapped within a time loop would continue to age and eventually disintegrate. We touched upon this earlier with the pocket watch in Somewhere In Time, which one would have expected to get older as it progressed through the cycle. In which case, the item cannot be the same as the one sent back in time, which creates a contradiction and raises the prospect of Theseus’ paradox, and the question of identity. Furthermore, the watch ultimately wearing out would also indicate a discontinuity in the story, as Jane Seymour could then have never have received it as a young woman and the time loop could never have started.

Possible Solutions

Working on the assumption of an “immutable” timeline in which the circle of events are identical every time, the ‘Somewhere In Time’ example raises the problem of an increasingly aging pocket watch. One solution may be to assume that entropy is somehow reversed by time travel, although this may also suggest that the matter which comprised Reeve himself would also have subsequently been restored to its 1912 state when he returned to the past, which needless to say would not be in the form of Reeve.

Well, perhaps not, according to Russian professor Novikov, as the second law of thermodynamics is thought to be a statistical law, and not an absolute one, making spontaneous entropy reversals or failure to increase improbable, but not impossible. Furthermore, the second law of thermodynamics applies only to a system isolated from the external world, and as Novikov argues:

“.. in the case of macroscopic objects like the watch whose worldlines form closed loops, the outside world can expend energy to repair wear/entropy that the object acquires over the course of its history, so that it will be back in its original condition when it closes the loop. (wiki)”

Otherwise, it would be intriguing to consider the possibility that the time traveling watch might have to obey the ‘timeline protection hypothesis’ which states that any attempt to create a paradox would fail due to a probability distortion being created. Imagine a young Jane Seymour becoming angry, for instance, and throwing the watch at the wall. The wall may be damaged slightly but the watch must remain in the same state. Probability would bend to prevent any damage occurring to the watch, which could result in some pretty incredible outcomes. Nevertheless, the universe must favor an improbable event happening, in order to prevent an impossible one.

A final possibility involves a chrononaut finding himself in a parallel universe or multiverse each time he travels to the past, thereby changing nothing of his original timeline.