Time Travel & the Grandfather Paradox Explained

The Grandfather Paradox Explained

The Grandfather Paradox arises when something traveling back in time creates inconsistencies that contradict the timeline’s history. The most common cited example of this time travel paradox involves a person traveling to the past and killing their own grandfather, thereby making their own birth impossible.

The term Grandfather Paradox does not apply to just the above example involving a person’s grandparent, though. There have been many intriguing examples of grandfather paradoxes imagined by physicists and philosophers over the years. For instance, the “Hitler paradox” points out that a person traveling back in time and killing a young Hitler would erase any knowledge of Hitler from history, and thus remove their reason for wanting to kill him in the first place.

Another grandfather paradox involves an electronic circuit sending a signal back in time to shut itself off, thus receiving the signal before it had even sent it. Or there’s Polchinski’s Paradox, which imagines a billiard ball entering a wormhole and emerging in the past, before knocking its younger version off course, therefore preventing itself from entering the wormhole.

What are Paradoxes?

Paradoxes can be described as statements or situations that may be true, but appears to be impossible or difficult to resolve or understand because the statement or situation is constructed of two opposite facts, conditions, or characteristics. In most instances, the opposing facts or situations that are presented as being paradoxical seem to be mutually exclusive in the sense that if one fact (or situation) is true, the other cannot possibly be true.

What is the Grandfather Paradox, exactly?

Despite its name, the grandfather paradox is a common expression of the great many other paradoxes that all deal with inconsistencies in logic and/or history that arise when a time traveler commits any action that changes not only the time traveler’s past, but also the pasts and possibly the futures of anybody that is in any way connected to the changed event.

Essentially, the specifics of the Grandfather Paradox hold that it is possible to prevent one’s own birth by traveling far enough backwards in time to arrive at a time that allows one an opportunity to kill one’s own grandfather. Leaving all moral and ethical considerations aside for the moment, the paradoxical situation the act of killing one’s grandfather creates is this: Killing one’s own grandfather prevents the birth of one’s parents (or at least one parent), which logically prevents one’s own birth.

This scenario was first suggested in short stories published in the US science fiction magazine Amazing Stories as early as 1929/1930 in various levels of detail, and with various motivations for people wanting to kill their own grandfathers. Nonetheless, while the premise of the Grandfather Paradox is not particularly obtuse or difficult to understand, its potential to disrupt the relationship between cause and effect makes it both particularly interesting, and extremely resistant to a resolution from scientific, if not philosophical perspectives, which begs this question can it be resolved?

Can the Grandfather Paradox be Resolved?

There is no single or clear answer to this question that satisfies both physicists and philosophers, or more precisely, philosophers and physicists that are interested in finding a resolution. The problem is this; the paradox consists of two disparate, and seeming irreconcilable propositions, the first being that backward time travel might be possible, and the other being that it might be possible to side step the causality problem.

Let’s us therefore explore the philosophical, time relativity and quantum mechanics aspects of this paradox further!

Philosophical Aspects of the Grandfather Paradox

Philosophical treatments of the grandfather paradox highlight that changing the past would subsequently results in a logical contradiction to the timeline’s history. It is argued that a time traveler would therefore be unable to change the past, and could only act in a way that is consistent with what has already happened.

Compossibility theory

Compossibility theory basically states that since history happened in a certain way, it cannot happen in any other way. Naturally, this means that it would be impossible to kill one’s own grandfather in some past time simply because one is descended from him, and therefore exist in the present.

Novikov Self-consistency Principle

Named after Igor Dmitrievich Novikov, who formulated it, this principle states that history is immutable, and therefore cannot be changed by the action of a time traveler from the future. Put another way, since persons or objects exist in the present, they must necessarily have been part of the history that created them. Therefore, any act that changes history, such as killing one’s grandfather in the past, will effectively prevent one’s existence in the future, thereby making it impossible for a grandson to travel back in time to kill his grandfather. Obviously because the grandson will never exist in the first place.

However, Novikov’s principle does allow for conditions in which a time traveler’s actions might affect only his own past, which may or may not be cause of circular causation that affect events only in the time traveler’s own life. This proposition is the potential basis for Predestination or ontological paradoxes such as the Bootstrap Paradox.

Nevertheless, the guiding principle in Novikov’s work is the fact that the local laws of physics in any region of space-time that contains travelers or objects from the future can never be different from the local laws of physics in regions of space-time in which travelers or objects from the future are not present. This seems to be self-evident.

Novikov’s self-consistency principle states that the universal laws of physics must apply inside closed timelike curves (time machines) so that coherent events may occur. Novikov even used Joseph Polchinski’s billiard ball example to show that the situation can be solved in a consistent way that avoids the grandfather paradox. Adding to the discussion, theoretical physicist Stephen Hawking (1992) explains:

“By traveling in a space ship on one of these closed timelike curves, one could travel into one’s past. This would seem to give rise to all sorts of logical problems, if you were able to change history. For example, what would happen if you killed your parents before you were born. It might be that one could avoid such paradoxes by some modification of the concept of free will. But this will not be necessary if what I call the chronology protection conjecture is correct: The laws of physics prevent closed timelike curves from appearing.”

Time Relativity Aspects of the Grandfather Paradox

When exploring the grandfather paradox from a relativistic point of view, one of the main questions that has to be considered is whether time travel is actually possible. Many physicists have been at great pains to point out that the Theory of General Relativity does not exclude the possibility of time travel. In fact, Relativity actually predicts the possibility that time might flow at different rates for different observers in different frames of reference. This is known as time dilation and has been confirmed countless times in hundreds of experiments and measurements.

Is Time Travel to the Future Possible?

The degree of time dilation experienced depends both on the relative velocities of the traveler and the observer, and the length of time that a traveler is moving faster than a stationary observer. A good example of this is the Twins Paradox, in which one twin that travels at near-light speed ages at a lower rate than the twin that remained on Earth. For instance, if the traveling twin spends one year traveling at near light speed, several tens of thousands of years will pass on Earth. In this paradox then, the traveling twin will have aged by only one year, while his twin on Earth will have died of old age tens of thousands of years before he returns to Earth.

It should be noted though that time dilation occurs in a forward direction. In other words, when the traveling twin arrives back on Earth he arrives in his own future, and while he had hardly aged from his own perspective, Earth, and everything on it has aged by several tens of thousands of years. From the perspective of historians and historical records on Earth, however, the traveling twin will have arrived from somewhere in Earth’s distant past. It is exactly this contradiction that makes it so difficult to resolve the Grandfather Paradox in terms of timing.

Is Time Travel to the Past Possible?

Let us assume that our time traveler needs to go from 2019, to say, 1945 to be in a position to kill his grandfather before he can sire his son, our time traveler’s father. Thus, if we accept that it might be possible to use time dilation as a sort of time machine, our time traveler would need to exceed the speed of light in order to theoretically travel back in time.

Putting that limit aside for now, a time traveler would only needs to spend a few seconds traveling faster than the speed of light to cause 72 years (the difference between 1945 and 2019) to pass on Earth. In theory then, traveling at faster-than-light speed for a few seconds would cause our time traveler to travel back in time and place him in a position where  it might be possible to kill his grandfather. However, the problem is that during the few seconds our time traveler spends traveling at near light speed, his grandfather will have aged at the same rate as everybody else on Earth. In practice, this means that due to imprecise scientific calculations the grandfather might have already sired a son when our time traveler arrives sometime in 1945, which makes it pointless for our time traveler to kill his grandfather.

One way around this conundrum would be to construct a time machine that can travel at high multiples of the light speed. In theory, this could require our time traveler to spend only a few microseconds traveling at several times the speed of light, but the problem with this is that with the current state of our technology the speed of light cannot be exceeded. Moreover, even if we do find a way to exceed the speed of light, our time traveler will not survive the initial acceleration, or if by some miracle he does survive, he will definitively be killed by the effects of Einstein’s equation (E=Mc2) long before he reaches light speed. Regardless of what kills him though, dying effectively prevents him from killing his grandfather.

Quantum Mechanics Aspects of the Grandfather Paradox

Let us assume however, that ways have been discovered that allow us to travel back to past times. For instance, either by building a faster-than-light (FTL) time machine or via a hypothetical passage in space-time known as a wormhole. The time traveler would then need to travel backwards in time to the same world he inhabited. This is an important distinction because according to some philosophers and scientists, traveling to a slightly different world will eliminate historical paradoxes and/or inconsistencies.

Let us therefore look at this proposition, which is known as the Many-Worlds Interpretation (MWI) of Quantum Mechanics.

The Multi-world Interpretation

This multi-world interpretation is predicated on the idea that since killing one’s own grandfather will prevent one’s own existence in the present, it might be possible to find a different, but largely similar world in the past where historical conditions are sufficiently similar to allow grand-patricide without creating an historical inconsistency.

The problem with this notion is off course the fact that one needs an almost infinite number of worlds in order to:

  • create “sufficiently similar” historical contexts
  • find a world where the grandfather-to-be-killed is actually one’s biological grandfather
  • find a world where the act of killing one’s grandfather does not affect or prevent one’s own existence in the present

While there are several serious problems with the multiple-world interpretation, the most pressing issue is the possibility that time will almost certainly not be defined by the number of vibrations of a caesium atom as it is on this world. Therefore, if one’s grandfather lives on a world in a different timeline, and it is possible to locate and kill him, it is very difficult to see how doing so would not create an historical inconsistency on two worlds- one’s own, and the world on which the grandparent lived. Killing his grandfather would therefore be pointless since the murder would have no context or meaning in the time traveler’s’ own world.

Conclusion

Many physicists take paradoxes  seriously because in terms of the logistics involved for time travel to be possible, there is nothing in general relativity that expressly precludes the possibility of closed time-like curves or white holes that could conceivably deliver a time traveler to a time before he was born. Similarly, general relativity also does not preclude the possibility that wormholes in space-time might exist, through which time travelers might be delivered to both past and future times. However, it must be stated that general relativity does not envision conditions under which such anomalies might exist. This is in itself paradoxical in the sense that it does not follow that since general relativity does not exclude time travel, general relativity must therefore allow time travel.

In terms of the more philosophical leaning to the grandfather paradox, people regard paradoxes as intriguing riddles that are often fun to contemplate and resolve. The Grandfather Paradox is a case in point. Therefore, I will leave you with one suitably astute piece of logic suggested by David Lewis, who wrote the respected article called the ‘Paradoxes of Time Travel. Lewis believes that a traveler in time may be able to affect the past, but could never alter or change a timeline’s history, and as he stated in the American Philosophical Quarterly (1976):

“Could a time traveler change the past? It seems not: the events of a past moment could no more change than numbers could. Yet it seems that he would be as able as anyone to do things that would change the past if he did them. If a time traveler visiting the past both could and couldn’t do something that would change it, then there cannot possibly be such a time traveler.” (Lewis 1976).

Lewis resolved the contradiction by concluding that the time traveler being able to both kill and not kill his grandfather is true in one sense and false in another sense. Nevertheless, the statement is not both true and false at any time. After all, in a nod to compossibility theory, it does not contradict history and the fact he did not kill his grandfather after all.

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