Opinion Science & Technology

Escaping the Grandfather Paradox

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Time-travel has long been a staple of genre films, novels and television shows serving as everything from a backdrop to teen-comedy hi-jinks in ‘Back to Future’ to thoughtful contemplation in Ray Bradbury’s short story ‘A Sound of Thunder’. Often these tales centre around one particular aspect of time-travel, the possible consequences of a traveller in time changing past events in resulting in a nightmarish scenario playing out upon their return to the future, impacting on their ability to have travelled back to the past at all. This dilemma, known as the ‘grandfather paradox’ outlines both philosopher’s and physicist’s main objection to time-travel, the possible violation of causality. Whilst time-travel itself remains in the realm of pure speculation, the possible results of the violation of the principle of causality and how nature may prevent them, are hotly debated topics beyond the realms of pulp-fiction with philosophers and physicists such as Stephen Hawking and Kip Thorne speculating on possible solutions. Is it possible that the ‘many-worlds’ interpretation of quantum mechanics can rescue a hapless (and clumsy) time-traveller? 

What is the ‘grandfather paradox’ and why is it so concerning?


The grandfather paradox lays out a hypothetical situation in which a time-traveller ventures back into the past only to inadvertently cause an event that results in the time-traveller never having existed at all (usually the accidental death of the titular grandfather) or some other event which makes their journey an impossibility. The paradox arises because if the time-traveller never existed, how can they possibly have travelled back in time to commit grand-patricide? Thus the very idea of time-travel seems to raise the possibility of the violation of causality, the rule that a cause must always precede its effect

Fry, the bumbling main character of Matt Groening’s Futurama had a rather unfortunate encounter with both his grandfather and his grandmother in the award-winning episode ‘Roswell that ends well.’ (21st Century Fox, 1999)

To consider this let’s picture a scenario in which a gifted young inventor, Marty, creates a time-machine in the year 2018. As Marty never knew his grandfather, he decides to undertake a trip to the past to meet his patriarch. After careful research, Marty discovers exactly where his grandfather, still a young man and childless at this point, will be located on November 23rd, 1963. He enters his machine and begins his trip to the past.

A sketch of Marty’s journey if we allow only one world line to exist

Unfortunately, Marty is an extremely literal chap, and when we said he discovered exactly where his grandfather would be, this was no exaggeration. Marty lands in the exact spot his grandfather would be, with predictable results. After a quick DNA test to ensure this is, indeed his grandfather, Marty patiently awaits his disappearance…..

A solution to Marty’s dilemma?

Physicists and philosophers have speculated on several solutions to the paradox. The Novikov self-consistency principle, also known as Niven’s Law of the conservation of history, developed by Russian physicist Igor Dmitriyevich Novikov in the late 1970s (Evolyutsiya Vselennoĭ(1979)) suggested the use of geodesics (similar to those used to describe the curvature of space in Einstein’s theory of general relativity) to describe the curvature of time. These closed time-like curves (CTCs) would prevent the violation of any causally linked events that lie on the same curve. It also suggests that time-travel would only be possible in areas where these CTCs exist, such as in the presence of wormholes as speculated by Kip Thorne and colleagues in the 1988 paper “Wormholes, Time Machines, and the Weak Energy Condition”. The events would cyclical and self-consistent. This strongly implies that time-travellers would not be able to change the past, whether this means they are physically prevented or whether they actually lack the ability to chose to do so. So no matter how hard Marty tries, he could not land his machine at that exact spot, even if he actively intended to kill his grandfather.

This idea was expanded upon by Caltech students Fernando Echeverria and Gunnar Klinkhammer together with physicist Kip Thorne in a paper which imagined throwing a billiard ball into the past via a wormhole in a trajectory that would interfere with the ball entering the wormhole. They argued that the physical properties of the wormhole would alter the ball’s trajectory in such a way that it could not interfere with itself or the actual interference is what causes the ball to enter the wormhole in the first place.

A visual representation of the Echeverria and Klinkhammer’s resolution. (Brightroundircle)

So, by Novikov’s theory, any actions that are undertaken by a time-traveller simply become part of pre-existing history and observers are forbidden from seeing these events by what is known as a Cauchy-horizon.

Upon returning to 2018, our hero Marty discovers that his family home is gone as is all trace of his existence. Reading about Novikov’s theory and intersecting billard balls he curses the universe’s lack of action. It’s at this point he realises that maybe the universe didn’t interfere as there was some other rectifying action required to occur. Inspired by talk of colliding billiard balls, he races to his time-machine determined to use it to knock his earlier self off course and save his own future…..

Novikov’s solution may seem somewhat arbitrary to you as it certainly requires the existence of multiple mechanisms currently unknown to physics, enough to permanently blunt Occam’s razor. It is for this reason, it is a solution to the grandfather paradox that is generally rejected by the scientific community at large. Physicist Matt Visser, a researcher in the field of general relativity suggests that the Novikov self-consistency principle is far too “ad-hoc” to be accepted as a rescue of causality.

Is there a more parsimonious solution to the grandfather paradox that is built on pre-existing aspects of physics introduced by other theories or disciplines?

It just so happens that one such solution may be provided by a well-known facet of quantum physics: the ‘many worlds’ interpretation of quantum mechanics.

The many-worlds interpretation of quantum mechanics to the rescue…. kind of.

The ‘many worlds’ interpretation of quantum mechanics was first suggested by Hugh Everett III in the 1950s as a solution to the problem of wave-function collapse demonstrated in Young’s infamous double slit experiment. 

A basic diagram of the double-slit experiment. Electrons can pass through one of two slits

electrons fired through individually begin to build a distinctive interference pattern on a screen beyond the two slits

As the electron is travelling it can be described as a wavefunction with a finite probability of passing through either slit S1 or slit S2. When the electron appears on the screen it isn’t smeared across it as a wave would be. It’s resolved as a particle-like point. We call this the collapse of the wavefunction as wave-like behaviour has disappeared, and it’s a key factor of the so-called Copenhagen interpretation of quantum mechanics. But the question remained, why does the wavefunction collapse?

Everett asked a different question. Does the wavefunction collapse at all?

He imagined a situation in which instead of the wavefunction collapsing it continues to grow exponentially. So much so that eventually the entire universe is compassed as just one of two possible states. A ‘world’ in which the particle passed through S1, and a world where the particle passed through S2. Everett also stated the same ‘splitting’ of states would occur for all quantum events, with different outcomes existing in different worlds in a superposition of states. The wavefunction simply looks like it has collapsed to us because we occupy one of these worlds which are forbidden from interacting.

So this means that when Marty arrives back in 1963, a split. He is no longer in the world he came from, let’s call it World 1. Instead, he has created and occupies a new world. When he travels forward in time he travels along the timeline of this world. He never exists in this world and in truth he hasn’t actually killed his grandfather. His grandfather exists safe and sound back in 1963 of World 1.

A sketch of Marty’s journey if the ‘many-worlds’ interpretation of quantum mechanics is applied. An attempt to travel backwards causes a downward ‘hop’ of world lines

So what happens when Marty travels back to the past in an attempt to rescue his world he inadvertently creates another state, a World 3. This world may resemble World 1 in almost every conceivable way, but according to the application of the interpretation, it is not the same due to one event. The collision of two time-machines on November 23rd, 1963.

If Marty attempts to travel back to 1963 again to correct the initial interference he simply creates another state. World 3

The truth is if this is the correct solution of the grandfather paradox then Marty can never return to World 1. It’s intrinsic to the ‘many-worlds’ interpretation that superposed worlds cannot interact with each other. Marty can move ‘down’ because it’s his presence at a particular moment that creates the world. Non-interaction means no matter what measures he takes, every time he travels back into the past he creates a new state and hops ‘down’ to that state and can then only move forward in time on that line. Somewhere in his world, World 1, Marty, that inventive young man simply disappeared one day never to return.

Conclusion.

Of course, none of this makes time-travel anymore possible, or likely. Einstein’s theory of special relativity and the restrictions on the speed an object with mass severely limit the possibility. But it provides an interesting out to a logical conundrum. It’s ironic that the most plausible solution to the grandfather paradox comes from perhaps the only concept in physics that has created even more fantastical stories and adventures, the concept of multiple universes, even if in this case said universes are co-existing in a non-interacting supposition of states.

The ‘many worlds’ interpretation suggests an almost infinite amount of possible worlds…. even one where you decided to grow a beard and become evil (eviler). (Paramount Pictures, 1967)

Interestingly, this application also answers another conundrum often posed about time-travel. If such technology does ever move from wild speculation to reality, where are the time-travellers? Why haven’t they visited us to discuss their wonderous discovery?

The answer could be we exist in a primary world in which the time machines are destined to be built. The inventors and passengers of such simply disappearing to other worlds of their own creation. To us, the invention of time machines will simply be marked by a chain of disappearing physicists.

Turns out Marty had it easy.

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About

Robert is a member of the Association of British Science Writers, qualified in Physics, Mathematics and Contemporary science. As well as contributing articles on topics as diverse as quantum physics, cosmology, medical science and the environment at Scisco media, he also writes the Null Hypothesis blog which examines pseudoscience and poor science reporting in the news media.

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