Resolving the Grandfather Paradox

Many people enjoy science fiction movies and comics exploring time travel, wormholes, and other possible phenomena: all derived from Albert Einstein's theory of general relativity. For centuries, humans have pondered over the possibility of time travel and its consequences. Perhaps one of the most famous consequences is the grandfather paradox posed by science fiction writers Nathaniel Schachner and René Barjavel. 

The grandfather paradox is a classic physics paradox that arises from a hypothetical situation where you go back in time to kill your grandfather. As a result, your parent wouldn’t be born and you wouldn’t be born. However, that would mean you wouldn’t be alive to go back in time to kill your grandfather, creating a paradox. Though many believe that time travel isn’t possible, meaning that this paradox wouldn’t exist in the first place, plausible solutions consistent with the theory of time travel have been developed. 

According to Einstein’s theory of general relativity, gravity is described as the warping of space-time. Think of space-time as a rubber fabric that objects in the universe rest on. Objects curve space-time just as if a soccer ball rolled over and wrinkled an originally flat blanket. Theoretically, objects with an extremely strong gravitational field, or the gravitational force per unit mass exerted on a smaller mass at a certain point, can curve spacetime in a way that spacetime bends back on itself. In other words, a sufficiently massive object could create a large dip in the space-time fabric so that the surrounding space-time curves upwards, resembling a circle. This circle is referred to as a “closed timelike curve” (CTC) loop and provides a path to the past as the two ends of the spacetime fabric (the past and the present) come in contact. Hence, when you travel across the CTC, you can travel back in time and interfere with your past self. 

One possibility is that the grandfather paradox cannot happen in the first place, even if you can successfully travel back in time. In 2010, professor at M.I.T. Seth Lloyd developed a computer simulation that simulated entangled photons being sent along the CTC back in time for a few billionths of a second to terminate their existence—an equivalent situation to the grandfather paradox. Entanglement in quantum mechanics refers to the property of subatomic particles where they are correlated even at large distances. Think of two entangled electrons being separated from each other. Even if they’re on two different planets, they will always have opposite spins of each other. In other words, entangled particles carry a joint unit of information, similar to the entangled photons in the simulation. The entangled photons mimic versions of the same time-traveler in the present, traveling through the CTC loop, or already in the past. The results showed that the closer the photon got to terminating itself back in time, the more frequently the experiment failed, since the photons were unable to terminate their existence while remaining entangled. This suggested the possibility that any journey back in time leading to logical inconsistencies would inevitably fail in the first place, so the grandfather paradox cannot exist. The universe prevents any similar paradox from happening, whether it be the tiniest quantum fluctuation that swerves the bullet away from your grandfather.

Since avoiding the grandfather paradox altogether sparked skepticism among some physicists, others proposed that quantum mechanics can solve the grandfather paradox. Quantum mechanics focuses on the behavior of subatomic particles like electrons and photons. A major pillar of quantum mechanics is the concept of superposition, in which particles can exist in multiple states at once until they are measured or interact with another system—think of Schrödinger’s cat, one who, after being placed in a box with a detonated grenade, can be both dead and alive in a box until it is opened. In quantum mechanics, this applies to the directionality, spin, speed, and location of particles. For example, electrons can exist having both an up and down spin, but when a scientist starts discerning the electron’s properties, the electron is observed to have only either an up or a down spin. Since the electron now has a definite state once it’s being observed, there is a collapse of superposition. 

Superposition happens due to the wave-particle duality of all matter and elementary particles since everything exhibits characteristics of both waves and particles. Most people are acquainted with the particle-like behavior of matter that involves having a definite location at a certain point in time. However, like waves, matter can have multiple states at once. Imagine a ripple propagating through a pond and you observe that the waves created touch multiple points at once. This wave-like property plays a big role in superposition. However, despite measurement showing a discernable collapse of superposition, some physicists avoid the idea of a “collapse” by suggesting that the superposition grows exponentially to envelop the entire universe and then create another world for each individual state. Imagine a chameleon existing in a superposition between being green and being purple. When you look at the chameleon, the universe you exist in tries to maintain the superposition by duplicating itself; in this universe, you observe the chameleon to be green. However, in the alternate universe, you observe the chameleon to be purple. Both observations are happening simultaneously, yet also independently of each other.

In 1991, physicist David Deutsch applied this “Many Worlds Theory” to time travel and proposed that a particle traveling across the CTC loop exists in a superposition of states. Thus, when the particle goes back to some time in the past, a new world is created for that particle. Therefore, in the grandfather paradox, when a time traveler goes back in time to kill their grandfather, they arrive in the past of a separately cloned world where they successfully kill their grandfather while the original world proceeds normally. This way, the time traveler’s grandfather (and consequently the time traveler themself) exists in a superposition of being dead and alive because both events occur simultaneously. Since the two different worlds cannot interact, the grandfather paradox won’t happen, but you can kill your grandfather. In 2014, Tim Ralph and Martin Ringbauer led a computer simulation of Deutsch’s model that sent pairs of polarized photons through the CTC. The simulation imitated the photons going back in time to flip off a switch that would “shut down the photon-making machine.” The polarization of light describes light waves propagating in a single plane. Thus, the CTC was mimicked by polarization since the second photon moving in the same plane as the first made it act as the duplicate of the first photon but in a “parallel world.” After the “duplicate” travels through the CTC and flips off the switch, if its properties still match the properties of the first photon, then self-consistency is preserved—the photon can exist even if its duplicate travels back in time to terminate its creation. In terms of the grandfather paradox, even if you terminate your existence by killing your grandfather in another universe, you are still able to exist in the current universe you’re in and avoid any logical inconsistencies. Interestingly, the experimental result matched this situation because the state of the second photon matched the state of the first photon, demonstrating that the “Many World Theory” is a possible solution to the grandfather paradox.

Ultimately, time travel and the grandfather paradox are currently only theoretical concepts. But with more information to come regarding quantum superposition, other quantum phenomena, the nature of space-time, etc., scientists can more accurately simulate time travel and reach a conclusion about the solution to the grandfather paradox, if the paradox can even exist in the first place.