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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

The Portal Paradox

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    wstwr12345 posted on 2020/03/28
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