The Grandfather Paradox

Suppose someone hands you a working time machine and one instruction: go back to 1935 and stop your grandfather from ever meeting your grandmother.

You arrive. You find him — young, alive, no idea who you are. You do the deed, whatever it is. He never marries. Your mother is never born. You are never born.

But if you were never born, who went back to 1935?

Nobody. So your grandfather lives, meets your grandmother, and your mother is born, and so are you. And you have a time machine and an instruction. So you go back and stop him. So you are never born. So you go back. So you are never born.

The loop has no stable state. It is not that the story ends badly; it is that the story cannot end at all. Every version contradicts the version that produced it.

The obvious response is: well, that just proves time travel is impossible. It is a decent response. It is also not quite good enough, for a reason that has kept physicists busy since 1988.

Einstein's general theory of relativity — the best theory of gravity we have, confirmed to spectacular precision — does not straightforwardly forbid loops in time. Solutions to its equations exist in which you can travel forward, always forward, into your own past. They were found by Kurt Gödel in 1949 and by others since. They may all be physically unrealistic. Nobody has been able to prove it.

So the question stops being "what a fun story" and becomes: if the equations allow the trip, what stops the murder?

What kind of paradox this is

Notice that the grandfather paradox is not a puzzle about the strangeness of time. It is a straightforward logical contradiction: a proposition and its negation both follow. "Your grandfather dies childless in 1935" and "your grandfather has children" cannot both be facts about the same history.

That already tells you something important. Whatever else is true, the contradictory history does not happen. Contradictions are not events that occur with low probability; they are not events at all. So the real question is never "what happens if you succeed?" It is: given that you cannot succeed, what is the mechanism?

Everything interesting is in that word "mechanism". Four serious answers are on offer, and they disagree with one another substantially.

Answer 1: You go back, and you fail

This is the Novikov self-consistency principle, named for the Russian astrophysicist Igor Novikov and developed with Kip Thorne's group at Caltech in the late 1980s.

The idea: if closed timelike curves exist, then the only histories that occur are globally self-consistent ones. You can travel to 1935. You can try to kill your grandfather. You will fail — not because a force field stops you, but because the history in which you succeed is not a history. The gun jams. Your hand shakes. You shoot the wrong man. You get the year wrong. You discover, mid-attempt, that the man you shot was not your grandfather after all, and that your grandmother's first husband died in exactly this way, which is family legend.

The philosopher David Lewis made the corresponding point in 1976. Can you kill him? Relative to your skills, the loaded gun, and the clear line of sight — yes, in exactly the sense in which anyone can do anything. Relative to the further fact that he did not die then — no. Both are true, of different senses of "can". There is no contradiction in a person who is able to do something and does not do it. What is impossible is only the conjunction of the whole history.

The uncomfortable feature is the statistics. If you make a thousand attempts, all thousand fail, and the failures will look like an implausible run of coincidence. Consistency is enforced by improbable-looking accident. Novikov's response is that improbable is not impossible, and that a constraint on global solutions is no stranger than any other boundary condition in physics — no stranger, he argued, than the fact that you cannot walk through a wall.

Friedman, Novikov, Thorne and colleagues gave this real technical support in 1990. They studied billiard balls sent through a wormhole time machine on trajectories that would knock their earlier selves off course — the mechanical version of grandfather murder. What they found was striking: for the initial conditions they examined, self-consistent solutions always existed. Typically many of them. A ball aimed to deflect itself instead receives a glancing blow that sends it through the wormhole at just the angle needed to deliver that glancing blow. The apparently paradoxical setups turned out to have consistent completions, not none.

That result cuts both ways. It supports consistency, but it also means the classical initial-value problem near a time machine has no unique answer — which is its own kind of breakdown.

Answer 2: You go back to a different history

Time travel takes you to a branch. You kill the grandfather of that branch's version of you, who is now never born there. Your own history, in which your grandfather survived, is untouched. You still exist, because you came from somewhere else.

This dissolves the contradiction cleanly, because the two claims are now about different histories. Nothing says P and not-P about the same world.

Two very different things are called "branching", and they are worth separating.

The fiction version is a free-floating multiverse in which the past is alterable. It is the standard of countless films, and it has no support in any current physical theory. It also throws away the thing that made time travel interesting: you are no longer changing your past, merely visiting somebody else's.

The physics version is Deutsch's, and it is more disciplined.

Answer 3: Deutsch's quantum resolution

David Deutsch showed in 1991 that quantum mechanics changes the problem substantially.

The classical difficulty is that a system on a closed timelike curve must arrive in the same state it departed in, and grandfather-style dynamics have no such state — a bit that goes back and flips itself has no fixed point among {0, 1}.

Quantum states are not restricted to 0 and 1. They can be mixed — a statistical combination. And a general quantum operation on a finite-dimensional system always has at least one fixed point among mixed states. Deutsch's condition is that the density matrix of the system entering the closed timelike curve must equal the density matrix coming out. For the grandfather circuit, the fixed point is the even mixture: half of the time you exist and go back, half of the time you do not. Self-consistency is restored, always, with no exceptions and no coincidences required.

Deutsch reads this in Everettian terms: the traveller who emerges in the past is in a different branch of the wave function from the one they left. You kill a grandfather; the grandfather you kill is not the one who fathered you, because "the one who fathered you" is in the branch you departed from. Nothing needs to jam anyone's gun.

The proposal is not free of cost. Deutsch's condition makes closed-timelike-curve computers implausibly powerful — Scott Aaronson and John Watrous showed in 2009 that they would let a classical or quantum computer solve every problem in PSPACE, which most researchers regard as a warning rather than a feature. It also introduces discontinuities: nearby input states can be forced to wildly different fixed points, and the map from input to output is non-linear, which sits badly with the rest of quantum mechanics. An alternative proposal by Seth Lloyd and collaborators — post-selected teleportation, or "P-CTCs" — keeps linearity but gives different answers, and is likewise unproven.

Answer 4: The trip never happens

Chronology protection. Stephen Hawking's 1992 conjecture is that the laws of physics conspire to prevent closed timelike curves from forming in the first place, so that the question of what you would do in 1935 never arises.

The argument is a calculation, not a preference. As a spacetime approaches the moment when a time machine would switch on — the chronology horizon — vacuum fluctuations of quantum fields can circulate around the incipient loop, again and again, each pass amplifying the last. Hawking found that the expectation value of the stress-energy tensor diverges on the horizon. The back-reaction of that energy on the geometry would destroy the machine at exactly the moment it was about to work.

He put it memorably: chronology protection "makes the universe safe for historians."

The conjecture is not proved. Establishing it in general appears to need a full theory of quantum gravity, since the divergence occurs precisely where the semiclassical approximation stops being trustworthy. Some models evade the divergence. Hawking himself noted the strongest supporting evidence available: "we have not been invaded by hordes of tourists from the future."

The bootstrap paradox — the paradox's mirror image. A traveller takes a copy of Shakespeare's plays to 1590 and gives them to a young William Shakespeare, who copies them out. Where did the plays come from? Nobody wrote them. They are a consistent loop — no contradiction anywhere — but information appears with no origin.

This is instructive because it shows self-consistency is not sufficient for comfort. Novikov's principle permits bootstrap loops; they violate no logic. What they violate is a strong intuition that information and structure must be produced somewhere. They also seem to violate the second law of thermodynamics in spirit, since order appears without a source. Fully consistent, still deeply odd.

The billiard ball, worked through. A ball rolls towards a wormhole mouth. It emerges from the other mouth three seconds earlier and strikes its younger self, knocking it away from the entrance so it never enters.

Paradox — until you look for the consistent alternative. Suppose the emerging ball delivers only a glancing blow, deflecting the younger ball onto a slightly different path that still enters the wormhole, but at the angle needed to emerge exactly where it must to deliver that glancing blow. Friedman, Novikov and colleagues found such solutions for essentially every initial condition they tried. Often infinitely many.

The lesson: what looks like "no possible history" is usually "a history you did not think of". The classical worry is not that solutions fail to exist. It is that they multiply.

The self-consistent assassin. You go back to kill Hitler in 1908. You wait in Linz with a rifle. A bird startles you; the shot misses; the noise sends the young man into a doorway where he meets someone who lends him a book. Every element is a perfectly ordinary event. The improbability is not in any single step but in the fact that some such chain must occur every time.

Novikov accepts this. His critics — including Hawking — find it a strange picture of physical law: not a force preventing you, but reality's stubborn refusal to be arranged the way you arranged it.

A comparison.

Response	Can you go back?	Can you try?	What stops the contradiction	Status
Novikov consistency	Yes	Yes	Only self-consistent global histories exist	Well-defined, technically supported, statistically odd
Deutsch quantum CTC	Yes	Yes, and you succeed	Fixed-point density matrix; you land in another branch	Well-defined, has awkward consequences
Chronology protection	No	—	Quantum back-reaction destroys the machine	Conjecture, unproven, needs quantum gravity
Fiction branching	Yes	Yes, and you succeed	Different timeline entirely	No physical support