Original by Michael Weiss.

Our story stars two twins, sometimes unimaginatively named A and B; we prefer the monikers Stella and Terence. Terence sits at home on Earth. Stella flies off in a spaceship at nearly the speed of light, turns around after a while, thrusters blazing, and returns. (So Terence is the terrestrial sort; Stella sets her sights on the stars.)

When our heroes meet again, what do they find? Did time slow down for Stella,
making her years younger than her home-bound brother? Or can Stella declare that the
*Earth* did the travelling, so Terence is the younger?

Not to keep anyone in suspense, Special Relativity (SR for short) plumps unequivocally for the first answer: Stella ages less than Terence between the departure and the reunion.

Perhaps we can make short work of the "travelling Earth" argument. SR does
*not* declare that *all* frames of reference are equivalent, only so-called
*inertial* frames. Stella's frame is not inertial while she is
accelerating. And this is observationally detectable: Stella had to fire her
thrusters midway through her trip; Terence did nothing of the sort. The Ming vase
she had borrowed from Terence fell over and cracked. She struggled to maintain her
balance, like the crew of Star Trek. In short, she *felt* the acceleration,
while Terence felt nothing.

Whew! One short paragraph, and we've polished off the twin paradox. Is that really all there is to it? Well, not quite. There's nothing wrong with what we've said so far, but we've left out a lot. There are reasons for the popular confusion.

For one thing, we've been rather unfair to Stella. We've said why she can't
simply adopt Terence's viewpoint, but we haven't said how things look from her
perspective. It seems passing strange that *Terence* could age several years
just because *Stella* engages her thrusters. The Time
Gap and Distance Dependence Objections put a sharper
edge on this uneasy feeling.

There are versions of the twin paradox where Stella *doesn't* turn on her
thrusters and feels no acceleration (the Slingshot variation, where Stella whips round a
distant star in free fall, and the Magellan variation, where Stella travels round a
cylindrical or spherical universe). These cast doubt on how relevant the
acceleration is in the usual version. (We may add FAQ entries for these variations
sometime in the future, but at the moment they are left as Exercises for the Reader.)

Finally, what about the Equivalence Principle? Doesn't that say that Stella can
*still* claim to be motionless the whole time, but that a huge pseudo-gravitational
field just happened to sweep through the universe when she hit her "thrusters on"
button? (For that matter, Terence experiences Earth's gravity, but his frame can
be considered to be approximately inertial.) Some people claim that the twin paradox
can or even must be resolved *only* by invoking General Relativity (which is built
on the Equivalence Principle). This is not true, but the Equivalence Principle Analysis of the twin paradox does provide
some additional analysis of the subject. The EP viewpoint is nearly mandatory for
understanding some of the twin paradox variations.

Let's lay out a standard version of the paradox in detail, and settle on some terminology. We'll get rid of Stella's acceleration at the start and end of the trip. Stella flashes past Terence in her spaceship both times, coasting along.

Here's the itinerary *according to Terence:*

- Start Event
- Stella flashes past. Clocks are synchronized to 0.
- Outbound Leg
- Stella coasts along at (say) nearly 99% light speed. At 99% the time dilation factor is a bit over 7, so let's say the speed is just a shade under 99% and the time dilation factor is 7. Let's say this part of the trip takes 7 years (according to Terence, of course).
- Turnaround
- Stella fires her thrusters for, say, 1 day, until she is coasting
back towards Earth at nearly 99% light speed. (Stella is the hardy
sort.) Some variations on the paradox call for an instantaneous
turnaround; we'll call that the
*Turnaround Event*. - Inbound Leg
- Stella coasts back for 7 years at 99% light speed.
- Return Event
- Stella flashes past Terence in the other direction, and they compare clocks, or grey hairs, or any other sign of elapsed time.

How much over? Well, Terence says the turnaround took a day. Stella's speed was changing throughout the turnaround, and so her time dilation factor was changing, varying between 1 and 7. So Stella's measurement of the turnaround time will be something between 1 day and 1/7 of a day. If you work it out, it turns out to be a bit over 15 hours.

[Top] [Prev] [Next]