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• 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, 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 theyre 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 whove

• 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 theyre 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?

• This MinutePhysics video was supported by CuriosityStream, an affordable subscription

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The video game Portal is built around a sci-fi device that can create a portal connecting

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B2 US portal relative speed cube object stationary