Grandfather Paradox

The grandfather paradox expresses a logical contradiction arising from a theoretical thought experiment involving time travel to the past. In this thought experiment, a contradiction arises if a person travels to the past and kills their own grandfather before the person’s parent is born. If the person carries out this act, they would never have been born and therefore could not have traveled back in time to kill their grandfather. This situation raises the question of whether time travel contradicts the principle of causality and is particularly debated in philosophy and theoretical physics.

The paradox is based on the question of whether a time traveler can perform an action that eliminates their own existence. Fundamentally, if time travel is possible, a time traveler may possess a certain ability under specific circumstances while simultaneously lacking that same ability; this constitutes a contradiction and thus suggests that time travel is impossible.

Content of the Grandfather Paradox

The paradox is commonly explained through the following story: A person named A harbors hatred toward their grandfather B due to actions B took long before marrying and having children. A builds a time machine and travels back to 1921 to prevent B from performing those actions. A finds B asleep and prepares to strangle him. However, A does not kill B, allowing B to live and have children, including A’s mother.

The central question here is: When A decides not to kill B, did A have the ability to kill B, or was that ability beyond their power?

A visual representing the grandfather paradox. (Generated by artificial intelligence.)

• Argument for Lack of Ability: It is clear that A lacked the ability to kill B. Because if A had killed B that night, B would not have had children and A would never have been born, and therefore would not have existed. In this case, if A could have killed B, A could have erased their own existence. Yet by killing B, A would both have to exist (to carry out the killing) and never have existed. No one can consistently affirm a contradiction.
• Argument for Possession of Ability: Yet it is equally clear that A had the ability to kill B. Imagine a room similar to the one where A and B are located, but instead of A, a person named C who is not a time traveler stands beside D, who resembles B. C could strangle D. C and A are so similar that they must possess the same abilities. In fact, they could be identical at the molecular level.

This situation can be formulated as a three-premise argument against the possibility of time travel:

• Possibility: If time travel is possible, then a time traveler (call them A) can travel to the past, locate their grandfather (call him X), and approach him within arm’s reach.
• Ability: If A travels to the past, locates X, and approaches him within arm’s reach, then A would have the ability to kill X.
• Lack of Ability: If A travels to the past, locates X, and approaches him within arm’s reach, then A would lack the ability to kill X.
• Conclusion: Therefore, time travel is impossible.

This paradox is based on the idea that it conflicts with claims about the time traveler’s free will.

Variants of the Paradox

There are several variants of the grandfather paradox, each asserting that a time traveler both has and lacks a certain ability, though the nature of that ability varies across versions.

• Easy Versions: For example, one variant involves a time traveler X who attempts not to kill their grandfather but their grandfather’s brother (their great-uncle) Y. X ultimately fails to kill Y, losing courage at the last moment. The concern regarding A’s ability to kill B arises because if A had killed B, A would never have existed. But this concern does not apply to X: if X had killed Y, there would be no reason why X would not exist.
• Harder Versions: More challenging versions focus on time travelers who attempt to kill their own infant selves. For instance, a character named Z, who despises their younger self, uses a time machine to travel back to when they were one year old and intends to kill them. But upon arriving, Z changes their mind and merely strokes the younger self’s head. Here too, a contradiction looms: if Z had used this ability, Z would never have existed.

New Perspectives and Proposed Solutions

For centuries, time was accepted as an absolute entity. After Einstein introduced his theory of relativity in 1905, the scientific community began to question the absolute nature of time. The possibility of time travel, a consequence of relativity, became an attractive topic for physicists and philosophers, prompting various attempts to resolve time-travel-related paradoxes. Several approaches have been developed to address the paradox:

• David Lewis’s Contextual Solution: David Lewis argues that the phrase “A can do S” expresses different relations in different contexts. Thus, in one context it may be true that A has the ability to kill B, while in another context it is true that A lacks that ability. This does not result in a contradiction because the meaning of “can” shifts between contexts.
• Denial of Ability: Some thinkers argue that A lacks the ability to kill B. This view holds that even if A attempts to kill B, they will inevitably fail.
• Argument Against a “Protective Force”: According to this approach, the time traveler’s failures are explained not by an external force preventing the act, but by the simple impossibility of the event occurring.
• Non-Hausdorff Spacetime Model: Visser proposes a Non-Hausdorff spacetime model to prevent time-travel paradoxes. This topological space presents a branching structure in which any event may have multiple pasts or futures. This model is also related to the multiverse concept in quantum mechanics.
• World Splitting: Sharlow argues that when a person travels to the past and kills their grandfather, the world splits at that moment into two branches: World A, where the time traveler never existed, and World B, where the grandfather was not killed.
• Hawking’s View on Closed Timelike Curves (CTCs): Stephen Hawking stated that the laws of physics prevent the formation of closed timelike curves — hypothetical paths allowing travel to the past.
• The “Already There” Idea: Some experts suggest that if a time traveler could go to the past, they must have already been there. If a person intends to kill their grandfather, this implies that the person was already present in the past under those circumstances.
• Branching Spacetime Model and Multiverse: This model is based on the quantum mechanics concept of the multiverse and proposes that the universe repeatedly splits into multiple future branches at any given time. Thus, even if a time traveler kills their grandfather, the act occurs in a different historical branch and does not threaten their own existence. Cassidy similarly argues that the time traveler journeys to a parallel world where they kill their grandfather without violating the laws of causality.
• Quantum Gravity Perspective: Quantum gravity calculations suggest that quantum fluctuations at extremely short distances may reach ultimate high energies, potentially forming microscopic black holes and disrupting the homogeneity of spacetime. This mechanism could prevent or make extremely improbable the passage of a macroscopic particle through a wormhole.
• Kupervasser’s Solution: Kupervasser offers a solution based on both quantum and non-quantum gravity theories. According to him, macroscopic objects will disintegrate due to the alignment of thermodynamic arrows of time, while for microscopic objects, the collapse of the wormhole is the primary solution. In both cases, he argues that the time traveler cannot succeed in killing their grandfather.

Mohammad Nazemi’s paper titled “Grandfather paradox from a new perspective” presents a novel viewpoint by arguing that the paradox should be denied rather than solved. According to Nazemi, certain paradoxes like twin paradox arise from an absurdity in the definition of speed and are not genuine paradoxes. However, the grandfather paradox is widely accepted as the fundamental paradox of backward time travel.

A visual representing the grandfather paradox. (Generated by artificial intelligence.)

Nazemi’s Argument Against the Grandfather Paradox

Nazemi points out that an important aspect is overlooked in discussions of this paradox: when a time traveler journeys to the past, all their cells, molecules, atoms, and even the elements, molecules, and atoms of their spaceship and equipment begin traveling backward in time from the very start. By the time the traveler reaches the era of their grandfather, they are no longer an adult with the intention to kill their grandfather; instead, they are a collection of billions of scattered atoms. In an ideal scenario, if the traveler goes back further than the stage of conception, they would become two cells — one in their mother’s body and one in their father’s body. The question arises: how could these atoms carry out an act of killing?

Nazemi illustrates this with a simple example: Even if a time traveler journeys to the past with a gun and equipment, these objects, having surpassed their historical production dates, would rapidly disintegrate and vanish. The gun would become a tree branch, an iron ore, and a handful of gunpowder in a distant mountain. The traveler would gradually grow younger, then become a fetus, then two cells in two bodies, and eventually disperse into several atoms in different locations. In short, traveling to the past requires that all conditions and the environment be compatible with the past. Thus, when the traveler arrives in the grandfather’s era, they would have neither a gun nor a brain or tissue capable of making decisions or taking action.

Nazemi argues that the grandfather paradox remains meaningless unless a spaceship can preserve travelers and their equipment in their current state during backward time travel. Even if such a technology (an anti-time reverse transition capsule) were developed one day, Nazemi maintains that the paradox would still be rejected. Because in such a capsule, the time traveler cannot interact with the past; they can only be an observer. Just as a cinema audience cannot kill an actor on screen, the traveler cannot kill their grandfather. In this scenario, the time traveler’s timeline (preserved within the capsule) and the grandfather’s timeline would coexist in the same time and space. Thus, history cannot be rewound or altered; the time traveler can only visit the past.