grandfather paradox

The grandfather paradox is a paradox of time travel, first described by the science fiction writer René Barjavel in his 1943 book "Le Voyageur Imprudent" ("The Imprudent Traveller").^[1] The paradox is this: Suppose a man traveled back in time and killed his biological grandfather before the latter met the traveller's grandmother. As a result, one of the traveller's parents (and by extension, the traveller himself) would never have been conceived. This would imply that he could not have travelled back in time after all, which in turn implies the grandfather would still be alive, and the traveller would have been conceived, allowing him to travel back in time and kill his grandfather. Thus each possibility seems to imply its own negation, a type of logical paradox.

An equivalent paradox is known (in philosophy) as autoinfanticide — that is, going back in time and killing oneself as a baby — though when the word was first coined in a paper by Paul Horwich it was in the malformed version autofanticide. ^[2]

The grandfather paradox has been used to argue that backwards time travel must be impossible. However, other resolutions have also been advanced.

Scientific theories

Complementary time travel

Since quantum mechanics is governed by probabilities, an unmeasured entity (in this case, your historical grandfather) has numerous probable states. When that entity is measured, the number of its probable states singularises, resulting in a single outcome (in this case, ultimately, you). Therefore, since the outcome of your grandfather is known, you killing your grandfather would be incompatible with that outcome. Thus, the outcome of one's trip backwards in time must be complementary with the state from which one left.^[3]

Novikov self-consistency principle

See the Novikov self-consistency principle and Kip S. Thorne for one view on how backwards time travel could be possible without a danger of paradoxes. According to this hypothesis, the only possible timelines are those which are entirely self-consistent, so that anything a time traveler does in the past must have been part of history all along, and the time traveler can never do anything to prevent the trip back in time from being made since this would represent an inconsistency.

Parallel universes/alternate timelines

There could be "an ensemble of parallel universes" such that when the traveller kills the grandfather, the act took place in (or resulted in the creation of) a parallel universe in which the traveller's counterpart will never be conceived as a result. However, his prior existence in the original universe is unaltered.

Examples of parallel universes postulated in physics are:

• In quantum mechanics, the many-worlds interpretation suggests that every seemingly random quantum event with a non-zero probability actually occurs in all possible ways in different "worlds", so that history is constantly branching into different alternatives. The physicist David Deutsch has argued that if backwards time travel is possible, it should result in the traveler ending up in a different branch of history than the one he departed from.^[4] See also quantum suicide and quantum immortality.

• M-theory is put forward as a hypothetical master theory that unifies the five superstring theories, although at present it is largely incomplete. One possible consequence of ideas drawn from M-theory is that multiple universes in the form of 3-dimensional membranes known as branes could exist side-by-side in a fourth large spatial dimension (which is distinct from the concept of time as a fourth dimension) - see Brane cosmology. It is theorized that when two branes collide it sends a massive ripple of heat and energy throughout the two. This is a possible explanation of what caused the big bang according to the ekpyrotic scenario and the cyclic model. However, there is currently no argument from physics that there would be one brane for each physically possible version of history as in the many-worlds interpretation, nor is there any argument that time travel would take one to a different brane.

Other considerations

Consideration of the grandfather paradox has led some to the idea that time travel is by its very nature paradoxical and therefore logically impossible, on the same order as round squares. For example, the philosopher Bradley Dowden made this sort of argument in the textbook Logical Reasoning, where he wrote:

Nobody has ever built a time machine that could take a person back to an earlier time. Nobody should be seriously trying to build one, either, because a good argument exists for why the machine can never be built. The argument goes like this. Suppose you did have a time machine right now, and you could step into it and travel back to some earlier time. Your actions in that time might then prevent your grandparents from ever having met one another. This would make you not born, and thus not step into the time machine. So, the claim that there could be a time machine is self-contradictory.

However, most philosophers and scientists agree that time travel into the past need not be logically impossible as long as there is no possibility of changing the past, as suggested, for example, by the Novikov self-consistency principle. Bradley Dowden himself revised the view above after being convinced of this in an exchange with the philosopher Norman Swartz.^[5]

Consideration of the possibility of backwards time travel in a hypothetical universe described by a Gödel metric led famed logician Kurt Gödel to assert that time might itself be a sort of illusion.^[6][7] He seems to have been suggesting something along the lines of the block time view in which time does not really "flow" but is just another dimension like space, with all events at all times being fixed within this 4-dimensional "block".

See also

• Causality
• Chronology protection conjecture
• Time loop
• Predestination paradox
• Ontological paradox
• Time travel in fiction
• I'm My Own Grandpa (song)
• The chicken or the egg

References

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