The video game Portal is built around a sci-fi device that can create a portal connecting
one place on the wall or ceiling or floor to another, and objects in the game (or the
player themselves) can pass essentially instantaneously from one end of the portal to the other.
In particular, an object entering one end of a portal with a certain speed leaves the
other end with the same speed, though if the portals aren’t oriented in the same direction,
then the object will exit in the new direction.
But the speed will be the same.
And this leads to an apparent paradox: what happens if one of the ends of the portal is
itself moving?
Does a stationary object plop out the other end of the portal with zero speed, since it
Or if the orange portal moves quickly downwards, does the cube shoot out of the blue portal
with the corresponding relative speed?
It’s easy to argue in favor of either case, which I suspect is why this puzzle is so popular
on the internet!
Of course, as far as we know such portals don’t exist, but supposing they did, and
obeyed the laws of physics, then the question really boils down to this : if objects have
to enter and exit the portals with the same speed, then what’s that speed being measured
relative to?
Because in our universe there’s no absolute reference frame from which to measure speeds
and velocities on their own - velocities can only be determined relative to another object.
So here are a few options: perhaps when passing through a portal, the object maintains the
same speed relative to the environment, though redirected in a new direction - this one’s
option A . Or perhaps objects maintain the same speed relative to the average position
of the portals - except that’s mathematically the same as measuring relative to the environment,
as long as the portals aren’t accelerating - so option A again.
Or perhaps the speed an object has relative to the portal it enters is the same as the
speed it has relative to the portal it exits - - this one is option B . Or, perhaps objects
enter and exit at a constant speed relative to the end of the portal they’re NOT using
at the moment - it’s a valid possibility, although it’s kind of weird.
The thing is, all of these options are consistent with what you see in the video game, because
in the game the portals pretty much never move relative to the environment.
My personal opinion is that the most physically natural option is B , where the velocity is
locally measured relative to the individual ends of the portals, and so the cube shoots
out of the blue portal.
This would be roughly what you’d expect if the portals were wormholes bending spacetime
(because the objects then would obey conservation of momentum in a curved spacetime), or if
the portals were more of a teleportation device that scans the matter coming in one end and
reconstructs it, kind of like a 3D printer, at the other end.
So, I think B is more natural.
It’s also tempting to think that there’s simply no way it can be option A - the one
where objects keep their same speed relative to the environment - because how could a stationary
object exit a stationary portal while remaining stationary?!
The object would have to exit the portal in the same amount of time it takes to enter,
otherwise the middle part of the object would temporarily blink out of existence, or be
duplicated, and exiting and entering in the same amount of time would mean that a one
meter cube that’s enveloped by the moving portal over the course of one second must
exit the blue portal over the course of a second, which is equivalent to moving at one
meter per second.
However, there is a way for option A to work, precisely because the cube doesn’t enter
the orange portal all at once - it goes in bit by bit.
And if those bits come out of the blue portal not moving, then they all appear exactly in
the plane of the portal, stationary, and they would keep on piling up against each other,
squishing the cube into a flat square!
Or, if the cube were rigid and couldn’t be squished, then it simply couldn’t enter
the orange portal in the first place - the portal would bounce off of it!
And I suspect option A is actually how the portals are programmed in the video game itself,
both because measuring speeds relative to the global environment (as opposed to relative
to a particular object) is typically the easiest thing to program, and because people who’ve
done experiments within the game engine to try to see what happens have discovered that
the game glitches and simply doesn’t let solid objects pass through a portal moving
towards them.
Which is perhaps unsatisfying, and not how you think the portals should work.
But that’s ok!
To me, the moral is that the portal paradox is not a paradox - the answer depends on how
the portals themselves actually work, which, since they’re fictional, is up to you to
decide.
What you think should happen says more about you, and whether you think more like a programmer,
or more like a physicist!
And so, I leave you with a final portal puzzle to ponder: what if instead of moving down
towards the cube, the orange portal is moving sideways on the ground and you drop the cube
through it.
Does the cube shoot straight up through the blue portal, bounce off the orange portal,
or shoot out of the blue portal at an angle?
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