In our universe, when you change from a non-moving perspective to a moving one, or vice versa,
that change of perspective is represented by a what's called Lorentz transformation,
which is a kind of squeeze-stretch rotation of spacetime that I've mechanically implemented
with this spacetime globe.
The spacetime globe illustrates many of the features of special relativity, like length
contraction and time dilation and the twins paradox is...
The twins paradox is a linguistically confusing situation that can arise in special relativity
when somebody learns about time dilation - the fact that in our universe,...(that) things
moving relative to each other each view the other's time as passing more slowly (which
is called “time dilation”).
As the paradox goes “if each person views time as passing more slowly for the other,
then if my twin travels away from earth for a while and then comes back, who's actually
younger when we meet again?”
When you have a potentially confusing situation in relativity, it's really helpful to actually
draw a spacetime diagram to understand what's going on.
So we'll use the spacetime globe.
The situation is this: you're sitting on earth for, let's say, 12 seconds.
Your twin travels out at a third of the speed of light for what you measure to be 6 seconds,
then they turn around and come back at a third the speed of light for what you again measure
to be 6 seconds.
So what does your twin think?
Well, to understand the situation from their moving perspective we need to transform the
spacetime diagram so they no longer appear to be moving – that is, so that their worldline
is vertical.
That's what it means for the spacetime diagram to represent their perspective.
Having done so for the outward leg of their journey, it's clear that your twin would say
that leg of their journey took them – I dunno, what's that look like?
About 5 and 2/3 seconds?
And then they turned around and headed back to earth, which corresponds to a different
moving perspective.
Let's transform things to see how they look from that perspective; that is, so that the
worldline of that leg of the journey is vertical.
Having done so, it's clear that your twin would say that the return leg of their journey
took them – again, looks like about 5 and 2/3 seconds.
So from the perspective of your twin, their whole journey takes 5.66+5.66=11.3 seconds,
while for you it took 12 seconds.
So you, who stayed put, are older.
The key to why the two of you do in fact age differently is that your traveling twin has
two separate perspectives during their journey, while you, staying put, only have one.
And that's the resolution to the linguistically confusing twins situation, demonstrated with
a hands-on spacetime diagram - I want to say that even though I knew and understood the
math and physics behind this, my belief in the true-ness of the solution to the twins
paradox went up a million times the first time I actually measured the times each twin
experienced with my hands, in real life like this.
So I hope that I've managed to capture even a small percentage of that gut level belief
in this video.
You also don't have to use Lorentz transformations to figure out the solution to the twins paradox
if you know about proper time (spacetime intervals), because spacetime intervals are/proper time
is a way of calculating the time that passes for somebody according to their perspective.
So in the case of your twin, on each leg of their journey they take 6 seconds to travel
the distance light would travel in two seconds (or, 2 light-seconds), and taking the square
root of the difference of those numbers squared gives a proper time of 5.66 seconds for each
leg of their journey – exactly what we measured on the spacetime globe!
If you're interested in a little more insight into how the “each person views time as
passing more slowly for the other” part of the paradox actually makes sense (and I
promise, it does), I have another pair of videos diving into more detail on the twins
paradox that I highly recommend you check out!
And to deepen your personal understanding of the resolution to the twins paradox, I
highly recommend Brilliant.org's course on special relativity.
There, you can work through the calculations I've glossed over in a step-by-step guided
exploration, giving you essential hand-on experience with spacetime intervals and other
tools of relativity along the way.
The special relativity questions on Brilliant.org are specifically designed to help you go deeper
on the topics I'm including in this series, and you can get 20% off of a Brilliant subscription
by going to Brilliant.org/minutephysics.
Again, that's Brilliant.org/minutephysics which gets you 20% off premium access to all
of Brilliant's courses and puzzles, and lets Brilliant know you came from here.