Work and World

The Twins Paradox Hands-On Explanation | Special Relativity Ch. 8

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.
Video source: https://www.youtube.com/watch?v=LKjaBPVtvms

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