Special Relativity’s Twin Paradox Explained – And How It's Resolved

One of the essential features of Einstein’s theory of special relativity is that time appears to travel differently for two observers depending on their relative velocity. This phenomenon is known as time dilation. This isn’t just the subjective experience that driving dangerously fast can age an unwilling and terrified passenger. Instead, both clocks and human perception run slow in a vehicle moving at a significant fraction of the speed of light.

Many science fiction writers have made use of this concept. If concepts like “hyperdrive” or “warp speed” turn out to be impossible or impractical, the “time dilation” special relativity predicts might be one of the few realistic ways humans could visit other star systems. To visit a planet 40 light-years away would take a minimum of 40 years to get there to an observer on Earth, and another 40 years to get back. 

That means that for any astronaut on such a trip, most of their loved ones would be dead by the time they returned. Without time-dilation, however, things would be equally grim for the astronaut, probably. Even 40 years one-way would pose a problem for astronaut effectiveness.

However, special relativity predicts that if you travel close enough to the speed of light, the Earthly observer’s 40 years could be over in a matter of months, or even hours, to those onboard, depending on speed. Many of the greats of science fiction have had a go at considering the effects on society of people reuniting with loved ones who have aged very differently from themselves.

Where’s the paradox?

The concept of time dilation may be strange to us, since none of us travels fast enough for it to become noticeable. Nevertheless, plenty of explainers have been made positing two twins, one of whom stays on Earth and ages normally, while the other makes a long voyage and returns still youthful.

This all sounds fine as long as you’re thinking of it from a perspective where the Earth is the point against which everything is compared. The journeying twin travels fast, while the Earthbound twin hardly moves. 

That, however, is not how the astronaut twin sees it. To them, the Earth appears to be moving away while their spaceship stays still. Why then should they not age normally, and their counterpart on Earth barely experience a change in time? 

To reframe the paradox in a way that might be clearer, imagine two astronauts, Ash and Bee. Both go into space, but Ash’s ship moves slowly, while Bee’s engages a more advanced drive and accelerates to near lightspeed, relative to their original position. Each twin sees the other moving away at close to the speed of light. To Bee, it is Ash that appears to be traveling, and therefore should experience time dilation. When they meet again, each expects the other to have barely changed while they have aged, because to each, the other is the one who traveled while they stayed still.

One of the aspects of special relativity that shocked the world (to the extent that Einstein’s Nobel Prize was awarded for less controversial work) was the recognition that two observers could see apparently contradictory things and both be right. That does not apply here, however: Ash is right and Bee is wrong, and when they meet again, Ash’s body will be much older than Bee’s, as clocks on the two spaceships will attest.

The paradox asks how it is that Bee’s movement is privileged over Ash’s when each saw the other moving away. After all, we live in a universe where everything is moving relative to everything else, and there is no one still point that can serve as a privileged frame of reference.

Many non-physicists, on encountering this topic, have thrown up their hands and declared that special relativity must be wrong (we sometimes get their emails at IFLScience). However, the operations of GPS and experiments with subatomic particles traveling at close to the speed of light confirm that, whatever doubts there may be about Einstein's theory of general relativity, special relativity matches reality.

Einstein himself was one of the many physicists who sought to explain the situation, although he denied it was a paradox.

Resolving the twin paradox

Einstein called his initial theory of relativity “Special” because he was dealing with the special case in which there was no acceleration (and therefore no gravitational field) to worry about. He produced the theory in the same year as two unrelated major breakthroughs and was presumably at least a little distracted by his job as a patent clerk. General relativity, addressing acceleration and gravity, was so much harder that it took him another 11 years of much more focused attention,

Despite its absence from the original theory, acceleration is key to most efforts to resolve the paradox. In our example, Ash and Bee do not merely drift apart randomly. Bee’s rockets accelerate the ship to near-lightspeed. It is this acceleration that causes Bee’s clocks to move more slowly than Ash’s, these explanations conclude.

Satisfactory as this has been to many physicists, others have constructed more complex versions of the thought experiment where two astronauts pass each other at constant speed, and synchronize their clocks as they do so. Resolutions to these versions rely on the fact that, for the two twins to meet again, one of them must turn around. They argue that it is in the change of direction that the time dilation occurs, although how this works in practice is a matter of some debate.

This means that no universally accepted resolution of the paradox exists. However, few physicists doubt that, if we had spacecraft capable of traveling at even a few percent of the speed of light, we could perform the experiment and would indeed find one twin more aged than the other.

That’s a long way off; however, the fastest spacecraft humanity has ever built travels at 0.06 percent of the speed of light, relative to Earth, and it wouldn’t fit an astronaut anyway.

About The Kelly Twins

Mark and Scott Kelly are identical twins, each of whom completed NASA’s astronaut training and went into space. When Mark decided to leave the program and eventually become a Senator, NASA spotted an opportunity. They sent Scott into space again, this time for much longer, and compared the effects on his body with the consequences of staying on the ground for Mark. Their near-identical DNA made Mark a far better control for his brother than any other astronaut could supply.

It’s easy to conflate this experiment with the Twins Paradox. Indeed, a photo of the two currently greets you on the Wikipedia page describing the paradox. That’s because Scott did experience time dilation effects that meant he aged less than Mark. However, the difference was just 8.6 milliseconds, not enough to notice without sophisticated equipment. The difference would have been larger (although still not detectable to humans) if only the special relativistic effects of traveling 27,000 kilometers per hour were considered. Under general relativity, a stronger gravitational field, such as Mark experienced on Earth, slows time down, partially counteracting Scott’s speed.

However, a few milliseconds doesn’t change the body’s biological age in any meaningful way. The real point of the experiment was to see how the extra exposure to cosmic rays above the atmosphere and the consequences of living so long without much gravity affected Scott. The negative consequences for Scott’s health observed have much bigger implications for future voyages to Mars and elsewhere in the Solar System than the tiny relativistic effects.