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 had no speed before entering?
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,
This one’s option A.
Or perhaps objects maintain the same speed
relative to the average position of the portals themselves.
Except that’s mathematically the same as measuring relative to the environment,
as long as the portals aren’t accelerating – so option A.
Or perhaps the speed of 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 move, right?
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 which is not moving.
Or, if the cube were rigid and couldn’t be squished,
又或者 假如小方块是刚性的 无法被压扁
then it simply couldn’t enter the orange portal in the first place,
The blue end of the portal will act like a wall
and the orange 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 doesn’t let solid objects pass through a portal moving towards them.
Which is perhaps unsatisfying answer to a paradox,
and not how you think the portals should work.
But that’s ok!
We don’t have to agree with the game designers.
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?
Does it bounce off the orange portal?
Or does it shoot out of the blue portal at an angle?
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The video game Portal is built around a sci-fi device