Science in Science-Fiction: Time Travel & Temporal Paradoxes

Posted on Wednesday, May 1st, 2013 at 02:30
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My novel Trilogy ‘Paradox War’ is a genre-mash hard science-fiction/fantasy story with pop culture and history elements (along with some of the paranoid fiction and mind-bending sub-genres tricks and a bucket of Forteana). The broad scope of the science-fiction side is based on those classic tropes of sci-fi: Time-Travel and Multiple Dimensions.

Science has a big problem with Time travel – the paradoxes. In my books at least one of the sides of the war (as a consequence of their Time-travel) weaponize temporal paradoxes, deliberately altering history to influence the course of the war. The Eusaiveans (the guys who abduct Desi in the books) also instigate “Project Bootstrap” a plan that seeds technology back in time, allowing them to accelerate technological development as they extrapolate the next technology from the now historical previous version, and hopefully grant themselves a head-start on the “Rebels”. Which seems to be an incredibly large source of paradoxes, although as it turns out, this is nothing compared with the climax of the series, where the space-time continua of multiple dimensions are knotted together, and finally resolved with an Alexandrian solution to end all paradoxes. So here’s a not so quick primer on Time travel Paradoxes of the sorts that drive physicists to declare time travel (and any sort of time space continuum travel) must be impossible and how various writers (including me) have written their way around this. Whilst there are many, many subtypes of paradox that time-travel can cause there are really only two major classes or types of chronological paradox.

The Grandfather Paradox

XKCD.com - Time Machine

The Grandfather Paradox in four stickman panels. (xkcd.com)

This is the basic time travel paradox, called by some ‘The Granny Paradox’ and by others ‘The Killing Hitler Paradox’: The time traveller goes back into the past and alters the time-line, making a past that means the time-traveller cannot (or won’t want to) travel back in time, which means they can’t alter the time-line… so the original events should occur which allows the time-traveller to travel and alter the past… — you see how that works? In the classic grandfather paradox (as described by René Barjavel) the time traveller kills their own grandparent so that their own parent and themselves aren’t born. Of course there are many variants on the time-travelling assassin (or should that be time-traveling assassin there are as many linguistic debates as scientific ones you know) – killing yourself as a baby (auto-infanticide), killing yourself just before you step through the time portal, going back and modifying the time machine so it won’t work, saving the dinosaurs so that humanity never evolved, killing Hitler to prevent World War Two, and then not knowing that you have to go back and kill Hitler, etc.

Scene from Back To The Future

An interesting take on the Grandfather Paradox. Your Grandfather knocks you out as you are saving your father from being run over… Hilarity ensues.

This is the entire premise of several time-travel stories, and a variant is actually referred to as “McFly Syndrome” due to its plot pivotal role in the ‘Back To The Future’ trilogy. The real paradox is of course: if the time-traveller doesn’t exist, who killed their grandparent? Although often waved as a self-evident proof that time-travel is both a logical and actual impossibility the Grandfather Paradox may not actually be a paradox at all. It is a generally accepted model within Quantum Mechanics that there is not a single causative universe, but rather that we live in a multi-verse of divergent time-streams, alternate timelines, multiple dimensions or (as they are normally called in sci-fi) ‘parallel universes’. This is the “Everett many-worlds interpretation” as opposed to the probabilistic model or ‘Copenhagen interpretation’ of Quantum Mechanics – early on the probabilistic model held sway, these days fewer and fewer physicists completely subscribe to it. That said, many real Physicists still find it hard to accept that these parallel universes are actually real, they prefer to think of them as more of a virtual existence that makes the maths easier, although those who actually work deep in the field seem reasonably confident of the reality of these Quantum alternates.

Infinite Earths explode

Multiple Earths could be separated by the thickness of a thought.

In the multiverse model there is no reason why someone from time-line 1 cannot nip back in time, immediately spawning a divergent time-line (2) where they can act with impunity, before returning to the future, depending upon the nature of the time-machine they will then either return to their original future (1), with history intact – as though they had imagined the entire incident – or they will travel forward on time-line 2 discovering a future where all the changes they made, including their own non-existence, are fully integrated into history. The parallel universe may then decide (to get anthropomorphic for a moment) that since the time-traveller did not exist their atoms should now return to their equivalent locations in time-line 2, so the time-traveller literally fades away. There is another way around this apparent temporal paradox that is called the Novikov self-consistency principle which basically states that our would be Chrononaut killer will/would discover that events are fixed. They are/will be unable to alter the past, even though they take part in the events then. The traveller may venture back and find a man who looks like a younger version of his Grandfather at the address his grandparents lived at and kill him, only to discover that when he gets back nothing has changed, when quizzed his grandmother admits that her first husband, was killed, and then she married his twin brother. However, while the Novikov self-consistency principle does allow time-travel without apparent causal paradoxes it does not actually directly solve the Grandfather Paradox. Even the more narratively satisfying work by Seth Lloyd at MIT (which supposes that events will get increasingly improbable in an effort to stop the impossible, so perhaps the gun misfires allowing the time-traveller to believe they shot their grandfather, when in fact, they did not) but is not actually a solution to the Paradox in the same way as the branching history solution. Neither is Huggins displacement theory, which allows you to travel in time, but insists that you will be displaced in space as well so that even light you emit will not be able to interfere with anything that occurred in your own past. Which neatly bypasses any ability to create a Grandfather Paradox. However, the Huggins Theory is of limited use to a science-fiction writer, and presupposes that there is no possible method of super-luminary travel that would allow the time-traveller to jump aboard an FTL-cruiser and head back to Earth to have a meddle. It is also of limited use to Quantum Mechanics, who know that the entire universe will reorder its electron energy states to incorporate the matter of the time-traveller, thereby potentially allowing even a distant traveller to influence events near home (see spooky action at a distance, entanglement and the Pauli exclusion principle in any good physics textbook or website – I might cover this in another post later).

Bootstrap Paradox

Also known as a causality loop, Boot lace paradox, the ontological paradox, or a predestination paradox. The Bootstrap Paradox is the time paradox where a temporal-travelling entity (be they being, object or just information) exists only in a closed loop of time. Some people separate the predestination paradox where only a time-traveller’s knowledge loops in time, but both involve closed loops in time, which certainly seem impossible.

The Bootstrap Paradox is named after the idea that you can pull yourself upward by grabbing hold of you bootlaces (or straps) and tugging with more force than your own weight, a real impossibility when you are applying the opposite force to your boots from the inside.

In its simplest form the Ontological Paradox (which means a paradox of existence-studies which is a terrible name and hence why I prefer Bootstrap, which sounds piratical) goes as follows: a scientist is told how to build a time-machine by a mysterious old man, and after having finally completed the time-machine, which takes many years, he goes back and tells himself how to build a time machine. The actual design of the time-machine is never originated, but exists only because of the loop in time that creates it, or for those of you searching because of the Doctor Who episode “Before The Flood”; the information is Beethoven’s music.

If you consider that this knowledge loops in time then you can see that a object might loop in time in a similar way, perhaps in the form of notebook. This notebook (like the knowledge itself) would seem to exist in breach of the Second Law of Thermodynamics, as its entropy must increase and yet the earlier notebook is identical to the later one. Entropy is a measure of ‘disorderedness’ and within a closed system must increase with time. As time goes on any system that doesn’t have interference from outside will grow more disordered. Gas released into a closed vessel will initially be quite ordered, hanging about on the side of the chamber where it was introduced, however quite quickly it spreads, increasing its entropy as it fills the chamber.

Astounding Stories Cover for 'By His Bootstraps'

Heinlein’s By His Bootstraps investigates the Bootstrap Paradox in some depth (wikicommons)

Robert Heinlein solved some of this paradox in his short ‘By His Bootstraps’ by having the time-traveller copy the notebook from the old battered copy he had received from the future into a new notebook which he gives to his younger self, which follows the strict second law for the physical book — entropy has its effects upon the pages — but fails to explain the origin of the contents of the notebook. In The Doctor’s example he explains that he copies out Beethoven’s sheet music, but the music itself is never composed.

Physicists are pretty convinced that Entropy must affect information as well, so they rule out this Bootstrap paradox as impossible. It is often assumed within science-fiction that if a causality loop is closed into a consistent causal loop like this then the system becomes stable, which (if time-travel is possible) would probably not be the case. Objects that only exist in a closed loop of time will exist in breach of the second (and possibly first) laws of thermodynamics.

Somewhere in time collectors edition.

Christopher Reeve travels in time, without a red cape in this 1980s Romantic Sci-Fi movie.

The 1980 Christopher Reeve movie ‘Somewhere in Time‘ suffers from an extreme version of this lack of entropy. Reeve is given a pocket watch by an old woman, which it turns out he gave to her in the first place. The watch circles in time (and represents the only real proof that Reeves actually time-travelled, and isn’t just a nut-job), and should progressively get more scratched and battered as it loops, and yet it is exactly the same at either end of the loop. Clearly,  it exists in breach of the second-law of Thermodynamics, and this is no less true for any information that might also be circling in time.

Instead, the closed temporal loop should only appear so to the casual observer, with additional information being inserted into the system, perhaps in the form of a friend who guesses a smudged word in the copying process and so (in the inevitable iterations across multiple universes) the friend deduces the entire book one word at a time, computer software, or a chain of  holographic fake ghost, deaf lip-reader, sign language interpreter, school teacher can be substituted, if you like.

Miles Dyson in Terminator 2: Judgement Day

Miles Dyson ponders the Bootstrap Paradox of creating Terminator technology by examining Terminator technology in Terminator 2: Judgement Day (from the terminator wiki)

This is the approach used in the Terminator series, where the work of Miles Dyson fills in the gaps in the chips that were passed back in time.

Although, the Terminator franchise never seems to set any two movies in the same time-line (and the original movie states the time machine was destroyed— yeah, right), each movie seems to come from a later iteration of the future, with both sides of that temporal conflict having access to improved technology that has been fed back in time. Which is perfectly consistent with multiple universes, each one feeding back onto the next parallel iteration that Skynet creates. Which is the reason the Terminators from the later movies have much more impressive weaponry and technology, while the original “Cyberdyne Systems Model 101” or T-101 continues to stomp about and talk in an Austrian accent, despite being re-designated as “Cyberdyne Systems Series 800 model 101” by the second iterative future and later as a T-850 (the previously “new” T-800/101 endoskeleton was now being made by humans before Judgement day).

In the ‘Paradox War‘ the Eusaiveans perform missions into the past to accomplish goals and leave evidence of events that they know they must perform from the historical record. Such as the events in Roswell in 1947 and so on, this is a specific form of the ontological paradox known as a Predestination Paradox or self-fulfilling prophecy. The time-travellers have certain specific goals that they must perform in the past to create the present/future they are from, or are predestined to do something because they encounter a future version of themselves that tells them what the future holds.

Bill & Ted's Excellent Adventure

Possibly the most extreme version of the Predestination Paradox. The Entire movie is one big example, with many sub-iterations.

The most excellent example of the predestination paradox is probably the movie Bill & Ted’s Excellent Adventure which has the two titular, but hapless, idiots encounter themselves near the beginning of the movie and pretty much explain the whole plot to themselves. Leading the boys to play out all the events exactly as they explained to themselves. They then loop back through the conversation commenting that ‘it made much more sense this time’, and go on to come up with increasingly more convoluted examples of predestination paradoxes throughout the movie and its sequel (and the cartoon show too).

Yes, this does mean that technically the Temporal paradox in “Before The Flood” is actually a Predestination Paradox, as Future Doctor speaks to Past Doctor through the Cass, Lunn, Clara chain, but since the Predestination Paradox is a subset of the Bootstrap / Ontological Paradox  or Causal Loop, we can probably let Toby Whithouse have that one.

Now if time-travelling occurs into a parallel universe (or creates a parallel universe each temporal jump) then the predestination paradox is not a paradox of any sort, as even having the information will not guarantee that events play out as predicted at all. If the predestination paradox takes place within a single time-line then it is often used by writers to examine concepts of fate, destiny, free will and other metaphysical questions that science prefers to swerve on the whole. The universe of Doctor Who has stated that the laws of Time are not actually physical laws, but were enforced by the Time Lords (and possibly the Shadow Proclamation), and the Whoniverse behaves like a wounded animal around Paradoxes rather than them being impossible. So in these cases the Bootstrap Paradox is not a real* paradox at all.

*by which I mean its not a physical impossibility that negates the possibility of time-travel.

Paradoxes that aren’t

There are a number of apparent paradoxes that are bandied around about time-travel that are often used to try and disprove the possibility of time-travel. However a lot of them are not actually any form of physical paradox at all, or are simply logical or linguistic paradoxes that reality wouldn’t touch with a catastrophic universe ending time-line collapse.

The Self-visitation paradox

Spock meets Spock in the Star Trek reboot

Having explained that if Spock meets Spock the universe could end, Star Trek proves that Zach Quinto and Leonard Nimoy are not the same person.

This is a bit of a silly one, and simply put states that if you sit down on Monday and on Tuesday travel back to Monday then on Monday you were simultaneously stood and sat which is impossible. Of course it’s not impossible at all, its a bit like saying that because you sat on Monday you must be sat on Tuesday. It is simply the case that you could be sat in one time-space location and stood in a different time-space location, when phrased like this (or in the mathematics involved) the “self-visitation paradox” evaporates.

Even so there are a lot of science-fiction writers who will play with this, stating things like the time-traveller cannot meet themselves, matter cannot exist in two places at once and other nonsense. Actually matter not only can exist in two places at once, small pieces of matter actually seem to not exist in only one place, so there is no reason (energy calculations aside) why a macroscopic object, like a time-traveller cannot exist in two places at the same time.

The Super-luminary paradox

This is one of those really annoying paradoxes that isn’t a paradox at all, and certainly isn’t a temporal paradox. You’ll often see it cited on physics forums whenever the discussions turn to time-travel. Simply put the paradox goes like this: Time-travel is impossible because its impossible to accelerate a mass to the speed of light. Well, the first problem with this statement is that matter falling into a black-hole does accelerate to the speed of light, because space is bent by the singularity (although one might argue that it ceases to be matter because of it). Accelerating to light-speed either does not therefore actually require an infinite energy – as the matter will evaporate into massless photons as we approach lightspeed (called ‘c’ for celeritas), or if it does we all have infinite potential gravitational energy relative to every blackhole in the universe, which seems unlikely given the first law of thermodynamics. Yes, I know that this is because the mass of the accelerating object increases and therefore the force of gravity increases toward infinity also, but still the fact remains that accelerating to lightspeed is possible when you manipulate the space-time continuum to create motion (usually with gravity).

A piccy of a spaceship in a strange sky

An FTL ship jumps out of a temporal wormhole and heads away.

The second problem with this “paradox” is that it assumes that the only way to travel backwards in time is to travel faster than light, which is almost certainly not true. Closed time-like loops, cosmic strings and Kerr’s spinning ring singularities all create areas of space-time that seem capable of creating tunnels in the space-time continuum (or wormholes if you prefer) that can have ends in different time-space locales, and that means one end of the wormhole can be in the past and one in the future. There are even time-travel like effects that occur within Quantum Mechanics, where particles seem to be ‘aware’ of imminent collisions and interactions, before they happen. In short the super-luminary paradox is not a temporal paradox, it is – at best – a logical paradox that makes physical time-travel non-trivial (a physics term meaning difficult, requiring enormous amount of energy or exotic forms of energy and matter that, perhaps, only exist in the imaginations of theoretical physicists).

The Causality Paradox

This is a tricky one to get your head around, which is probably why people pull it out as a Temporal paradox from time to time. Basically in classical Physics any event must be preceded by its cause. To put this in a Newtonian model, if you have a mass travelling along, it cannot change direction until after a force has started acting upon it. Now the extrapolation of that is that there can be no way that an object jumps back in time, as the force that puts it back in time starts happening after the objects arrival. The “Cause” follows the “Effect” – which is nonsensical.

Diagram of a wormhole

Closed time-like curves, wormholes and extra-dimensional blue boxes may all be ways of travelling in space-time, to paraphrase New Scientist.

Now whilst this may seem once again to be an unassailable problem, yet again it is not really a paradox at all. There is a basic assumption within the classical models that time is universal, later relativistic models of space-time still require effect to follow cause, but only for inertial observers. This means that if our observer follows a time-like curve back in time, then what they observe conforms to cause followed by effect. In other words, as far as the time-traveller is concerned the exit in the past takes place after the activation of the time-machine. For him (or her – although there is a dearth of female time-travellers who aren’t “companions” of a two-hearted Gallifreyan, a wild-haired scientist or a Victorian adventurer) moving in the same space-time inertial frame as the time-machine, the effect follows the cause and all is right with the universe. So the Causality paradox only appears so to an observer who is not following the machine through time. Any physicist that tries to use a causality paradox to deny time-travel either doesn’t believe Einstein made his point well enough or has suffered from a severe failure of imagination.

The Presentist Paradox

Presentism is a concept that there is no such thing as the past or the future, only the present truly exists. Now, according to presentism, since the past doesn’t exist, you can’t travel to it. Even ignoring the huge problems that Presentism represents about the concepts of history, cause and effect, memory, relativistic time dilation (as experienced by all astronauts and cosmonauts) and so on, there is a problem with declaring that Presentism proves time-travel impossible, and that is simply that a time-machine would be able to rewrite the present to represent an exact duplicate of some moment from the past. In short, if we live only in the ‘now’ and the ‘now’ is made to look like the past, only with the time-traveller inserted into it, then there would be no difference as far as the time-traveller would be concerned between the past he remembered and the ‘new/past now’ he is experiencing. He will have travelled in time. Now going back to Presentism for a moment. We don’t live in the present at all. Everything that we see, hear and even think is not happening now. Which might be a problem for Presentists to accept, but is true. The events that cause the sun to shine take place at least eight minutes before receptors in our eyes respond to them, even then our brain takes time to process the signals from the receptors and presents it as vision to the rest of the brain. We actually live entirely in the past, even our thoughts are the looped back on themselves, the output of the brain feeding back into itself is now believed to be the cause of consciousness. It could perhaps be argued (ignoring all of Einstein’s work on the Space-Time continuum) that time is actually a process not a dimension, although such process time theories are very far from mainstream physics and would probably require luminiferous ether to exist to complete the model.

The Fermi Paradox (temporal redux)

The Fermi Paradox was something Enrico Fermi the Physicist said about aliens. He said if Aliens were as common as scientists had predicted (with the Drake equation – which is now predicting even more aliens than ever before thanks to exoplanet astronomy) and FTL drives are possible (or even sub-light speed generational starships) then we should be observing aliens visiting the Earth. This apparent paradox (which of course ignores all that ancient astronaut and UFOlogical ‘evidence’ on the grounds that we haven’t been conquered or asked to join any celestial commonwealths yet, and UFOs are not required to build pyramids) can also be extended to time-travel. If at some point in the future time-machines are invented then where are all the time-travellers?

XKCD The Search

Maybe we just don’t know how to look properly…

Well actually Fermi’s Paradox does seem to suggest that not only is time-travel impossible, so is interstellar travel, which is pretty terrible for science fiction writers. There is some hope in that some physicists seem to think that time-travel may be possible, but only within the life-time of the time-machine (you can only go back to when the time machine was first turned on), which is a little like the ‘Quantum Leap’ TV show where Sam could only travel within his own life-time (oh and his grandfather if I remember right), perhaps implying that the creator of the time-machine is in some way the time-machine itself in that show’s physics (deities that pretend to be diner owners aside), but there is another option, perhaps the time-travellers (and those aliens) are among us, but they don’t want us to know… yet.

Actually, this is the seed paradox that lead me to think about the ‘Paradox War’ trilogy itself. I realised that there was plenty of evidence lurking about the history books that could be interpreted as time-travellers, if you were so inclined, admittedly ‘Occam’s Razor’ would suggest other solutions to some, but for a science-fiction author there is enough ambiguity to hang a story off. So, while I won’t be posting any spoilers, the Fermi Paradox is a defining Paradox in the Paradox War, why not read the time-travel / mind-bending subgenre trilogy (An0ma1y, Cu1ture B0mb & Chronoclysm) available on Amazon or other ebook retailers and find out how? Next Month: Interplanetary Spacecraft part 1: launch  

 
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