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 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? This MinutePhysics video was supported by
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The cube will have the same speed as the platform but not the same direction. In the game, you can't leave à portal on a moving surface except to cut the neurotoxins pipes.
Why is there so many portal paradoxes / problems on my front page all of a sudden? Did portal get a resurgence of some kind?
Its B, the portals already allows you to generate momentum without moving by the infinity falling loop, why would it not generate momentum in this case
Unless the dimensions of the cube change, it must maintain the same speed relative to the portal at both ends. It must emerge from one at the same speed as it enters the other, otherwise it would temporarily shrink or elongate. This means it maintains its momentum relative to the portal and thus B is correct. The only way A could happen is if the momentum is maintained but then magically lost the instant it finishes emerging from the portal - there's no way this could really happen.
The answer is A, and here's why (ignoring the fact that portals can't remain on most moving platforms):
The platform that the cube is resting on does not appear to be moving (no "movement lines" trailing under it). This means the cube is at rest, and an object at rest will remain at rest until moved.
Portals preserve momentum between them. That's why if you fall into a portal, you come out at the same speed. Likewise, an object not moving through a portal would not move on the other side (theoretically).
So when the portal on the moving platform (ignoring that it is a moving platform) meets the platform with the cube, it's essential to remember the cube has no momentum entering the portal. You cant just create momentum magically, and a portal is just a wormhole where you are eliminating a wall and linking the two locations seamlessly. It's essentially like if you dropped a large donut hole around the cube: the cube still had no momentum.
Then, since portality is in question, after the cube has entered the portal on the platform, the effects of gravity on a slope will come into play, and the cube will plop on the ground in scenario A.
For those mentioning the momentum of the moving platform: that doesn't just magically create momentum. All the speed of the platform will do is change the speed of the transfer of the cube from Orange to Blue portals. No created momentum, just faster transferring. Portals are like teleportation, and the platform's momentum is the rate it takes to transfer the object.
Lastly, if we put the "portals can't be on moving platforms" caveat back in, this entire situation is basically null and void, unless we replace the moving portal platform with Skull Kid dropping the entire goddamn moon (with a portal) on top of the cube.
It's A - think of it as a door frame falling on top of you. You will get squished, but you won't gain any speed.
Edit: please don't downvote me because I have an unpopular opinion :(
It's definitely B. You'll get pushed out of the blue portal at the same speed as the orange portal "hit" you.
A because cube's speed=0
A. Plop
The cube has no momentum.