Time travel is one of the most intriguing fantasy concepts. But it raises many questions - both for physicists and philosophers - and can also lead to various paradoxes. The “murdered grandfather paradox” is one of them.
The concept of time travel is used in full swing in literature and cinema, regardless of genre. Often in the center of all such stories are the changes made by the traveler to the events of the past, which lead to real disasters in the future. It is worth remembering at least the story of Ray Bradbury "And Thunder Rocked".
This dilemma, also known as the murdered grandfather paradox, represents the main objection of physicists and philosophers to time travel: a possible violation of causality. And while time travel is still speculation, the likely outcomes of violating causality and how nature might prevent them are hotly debated among scientists such as Stephen Hawking and Kip Thorne.
What is the "murdered grandfather paradox"
The Murdered Grandfather Paradox presents a hypothetical situation in which a time traveler travels back in time and does something that causes him to never exist (usually the accidental death of the traveler's grandfather is considered) or an event that makes his travel impossible … The paradox is due to the fact that this person was never born. And since he never existed, how could he go back in time and kill grandfather? Thus, the very idea of time travel leads to a possible violation of causality - the rule that a cause always precedes an effect.
According to Special Relativity, the past (cause) always precedes the future (effect) / Helen Klus.
Let's imagine a scenario in which a talented young inventor - let's call him Eugene - creates a time machine in 2018. Since Eugene never knew his grandfather, he decides to travel back in time to meet him. After careful research, he finds out exactly where his grandfather was - still young and single - at 15:43 on November 22, 1960. He gets into the time machine and begins his journey.
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Unfortunately, Zhenya takes everything literally, and when he found out where his grandfather would be, he went to that very place. He "lands" right where his grandfather should be at that moment … with a very predictable result. After a quick DNA test, he realizes that it really was his father's father, gets back into the car and waits for his disappearance.
What to do next
Physicists and philosophers have proposed several solutions to the paradox. The Novikov self-consistency principle, developed in the 1970s by the Russian physicist Igor Dmitrievich Novikov (Evolution of the Universe, 1979), suggests using geodesic lines to describe the curvature of time (roughly how the curvature of space is described in Einstein's General Theory of Relativity). These closed, time-like curves will not break any causal relationships that are on the same curve. The principle also assumes that time travel will only be possible in areas where these closed curves are present - for example, in the presence of wormholes, as described by Kip Thorne and colleagues in their 1988 paper Wormholes, Time Machines, and the Weak Energy Condition (Wormholes, Time Machines, and the Weak Energy Condition). In this case, events would be cyclical and self-consistent. This, in turn, implies that time travelers would not be able to change the past - whether through some kind of physical barriers or the lack of the ability to make such a choice. So no matter how hard Eugene tried, he would not have been able to land his car at that very point, even if he suddenly decided to kill his grandfather.
Igor Dmitrievich Novikov / Photo archive of the GAISh MSU.
This idea was later expanded upon by Caltech students Fernando Esheverria and Gunnar Klinghammer in collaboration with Kip Thorn. In their article, they presented a billiard ball thrown into the past through a wormhole along a trajectory that would eventually prevent him from entering it. They argued that the physical properties of the wormhole would change the trajectory of the ball in such a way that it could not interfere with itself, or that the ball could not enter the wormhole due to actual interference from the outside.
Thus, if you follow Novikov's theory, any actions taken by the time traveler become a fait accompli, and observers cannot see these events on the Cauchy horizon.
Upon returning to 2018, our Evgeny discovers that his family's house has disappeared, as well as other traces of its existence. After reading about Novikov's theory and billiard balls from Caltech scientists, he curses the Universe for inaction. And at this moment he realizes that maybe the Universe did not intervene, since this required some corrective action. He runs back to the time machine to change his own actions and save his future.
Esheverria and Klinkhammer solution / Wikipedia.
Novikov's solution may look somewhat far-fetched, since it definitely requires many mechanisms that are still unknown to physics. It is for this reason that the scientific community rejects this solution of the “murdered grandfather paradox”.
Could there be a more economical solution to the paradox, built on already existing aspects of physics introduced by other theories? It turns out that a hypothesis like the many-worlds interpretation of quantum mechanics can provide it.
The many-worlds interpretation of quantum mechanics rushes to the rescue
The many-worlds interpretation of quantum mechanics was proposed by Hugh Everett III in the 1950s as a solution to the wave function collapse problem observed in Young's famous two-slit experiment.
As it travels through the slit, an electron can be described by a wave function with a finite probability of passing either slit 1 or slit 2. When an electron appears on the screen, it looks like a blurry wave. And in other cases, it manifests itself as a particle. This is called wave function collapse. In other words, the wave seems to disappear, and a particle remains in its place. This, in turn, is a key factor in the Copenhagen interpretation of quantum mechanics. But scientists did not understand why the wave function collapsed.
Everett asked another question: does the wave function collapse at all?
He presented a situation in which the wave function continues to grow exponentially without collapsing. As a result, the entire Universe acquires one of two possible states: the "world" in which the particle passed through slot No. 1, and the "world" in which the particle passed through slot No. 2. Everett argued that the same "division" of states occurs in all quantum events, multiple outcomes of which exist in different worlds in a state of superposition. The wave function to us looks like it is collapsing, since we live in one of these worlds that are not able to interact with each other.
Diagram of the division of worlds according to the many-worlds interpretation of quantum mechanics / Wikipedia.
Hence, when Eugene arrives in 1960, the universe is divided. He is no longer in the world from which he came (let it be World No. 1). Instead, he created and occupied a new world. When he travels to the future, he moves along with the chronology of this world. He never existed in it and, in fact, never killed his grandfather. His grandfather continues to exist in good health in World No. 1.
Summarize
Of course, none of the proposed solutions and hypotheses makes time travel a reality. Einstein's special theory of relativity and the limitations on the speed of a mass object pose serious barriers to this. However, they provide interesting solutions to the puzzle. Ironically, the most plausible solution to the "murdered grandfather paradox" comes from a single physical hypothesis that has spawned even more fantastic stories than many other ideas and hypotheses put forward by scientists over the past century.
Curiously, the many-worlds interpretation may also answer another conundrum associated with time travel. If such technology is ever going to be anything more than fantasy, where are all the time travelers? Why haven't they come to us to tell us about their discovery?
The likely answer is that we live in a primordial world in which time machines are destined to be created. And inventors and their fellow travelers simply end up in other worlds, which they themselves generate. If this is true, then the invention of the time machine will lead our world to the fact that many physicists and inventors will disappear from it.
Vladimir Guillen
