Einstein showed that elapsed time depends on how you move. Philosophers had been arguing about whether time flows at all for two thousand years. Here are the puzzles that came out of both, with demos you can run.
One twin flies to a star and back; the other stays home. When they meet again the traveler is younger. Each saw the other’s clock running slow, so why isn’t it symmetric? Because only the traveler turns around and changes frames.
None of these are true contradictions. Each one shows that an everyday assumption about time is wrong.
A 10 m pole flies through an 8 m barn. To the farmer, the pole is length-contracted and fits, so both doors can shut at once with it inside. To the runner carrying it, the barn is contracted and the pole can’t possibly fit. Who’s right?
Newton’s laws work the same forwards and backwards, yet eggs break and never unbreak. In 1876 Josef Loschmidt challenged Ludwig Boltzmann: if every collision is reversible, how can entropy only increase?
The usual answer: the arrow of time comes from the starting conditions, not the laws. The universe began in an extraordinarily low-entropy state, and we live on the long slide away from it. Why it started that way is still open.
Two people walk past each other on Earth. For one, the Andromeda fleet’s launch decision is already “in the past”; for the other it hasn’t been made yet.
At 2.5 million light-years, even walking speed tilts your line of “now” by days on Andromeda. Based on arguments by Rietdijk (1966) and Putnam (1967).
Is time dilation real or a trick of bookkeeping?
Physicists flew cesium atomic clocks around the world in both directions. The eastbound clocks lost about 59 nanoseconds and the westbound gained about 273, matching relativity’s predictions.
Does general relativity allow travel to your own past?
Kurt Gödel found a solution to Einstein’s equations, a rotating universe, where you can loop back to your own past. Wormhole versions followed (Morris, Thorne and Yurtsever, 1988).
Long before atomic clocks, philosophers found that time breaks logic in surprising places.
| Stage | Time added | Total time | Gap left |
|---|
Zeno of Elea (5th century BC) argued that swift Achilles can never catch a tortoise with a head start. By the time he reaches where it was, it has moved on; by the time he reaches that spot, it has moved again, forever. Here Achilles runs 10 m/s and the tortoise 1 m/s with a 100 m lead.
His dichotomy paradox is the same trick backwards: to cross a room you must first cross half, and half of that, so how do you ever start? His arrow paradox asks how a flying arrow moves if at every instant it is motionless.
“What then is time? If no one asks me, I know; if I wish to explain it, I do not know.”
In Confessions Book XI, Augustine notes that the past no longer exists and the future doesn’t exist yet, while the present has no length. So how can we measure a stretch of time at all?
Can an event be past, present and future at once?
J. M. E. McTaggart split time into the A-series (past, present, future, which keep changing) and the B-series (earlier and later, which never change). He argued change needs the A-series, but the A-series is contradictory, since every event has all three properties.
Is “there will be a sea battle tomorrow” already true or false today?
If it is already true, the battle seems unavoidable, and fatalism follows. If it’s neither, logic’s rule that every statement is true or false fails.
A judge says you’ll be hanged on a weekday next week, and it will be a surprise.
You reason it can’t be Friday (you’d know Thursday night), so not Thursday either, and so on, concluding it can’t happen. Then you’re hanged on Wednesday, completely surprised.
Physicists take these seriously because closed timelike curves are allowed by the equations. Each paradox has a proposed escape.
A traveler born in 1990 goes back to 1958 and stops their grandparents from meeting in 1960. Then the traveler is never born, so who went back? Choose a theory and watch what it says happens.
A traveler hands young Shakespeare a copy of Hamlet, which Shakespeare then publishes. Who wrote it?
Information or objects circle in a closed loop with no origin. Named after Robert Heinlein’s story “By His Bootstraps”.
A ball enters a wormhole, exits in the past, and knocks its younger self off course so it never enters.
Physicist Joseph Polchinski posed this grandfather paradox without free will. Echeverria, Klinkhammer and Thorne (1991) found that every starting shot they tried had at least one self-consistent path, often glancing blows, and sometimes infinitely many.
Trying to prevent a prophecy is what fulfils it.
Oedipus’s parents abandon him to avoid a prophecy, which sets up its fulfilment. Time-travel stories use the same loop: the attempt to change history is part of history.
If time travel is ever invented, why haven’t visitors from the future shown up?
Stephen Hawking proposed a chronology protection conjecture: physics, likely quantum effects, prevents time machines. In 2009 he threw a party for time travelers and sent the invitations only afterwards. Nobody came.
Relativity’s lack of a shared “now” pushes many physicists toward the block universe, but the debate is philosophical, not settled by experiment.
Only the present exists. The past is gone, the future isn’t real yet. Matches experience, but clashes with relativity, where observers disagree about what “present” means.
The past and present exist; the future doesn’t yet. Reality grows as new moments are added. Defended by C. D. Broad (1923) and others.
Past, present and future all exist, like places on a map. “Now” is just where you are, the way “here” is. Fits relativity neatly, but makes the feeling of flow hard to explain.