The Portal Paradox

Video game

portal

s are built around science fiction. Portals can be created to connect devices from one location on the wall, ceiling, or floor to another, and in-game objects (or players themselves) can teleport from one end of the

portal

to the other. other. In particular, an object that enters one end of the portal with a certain speed exits the other end with the same speed, but if the portal does not face the same direction, then the object will exit in the new direction. But the speed will be the same. This leads to an apparent

paradox

: what if one end of the portal was moving?

Would a stationary object hit another at the end of the portal, with zero velocity, because it had no velocity before entering? Or, if the orange portal moves downward rapidly, does the cube shoot out of the blue portal with a corresponding relative velocity? It's easy to argue both cases, and I suspect that's why this puzzle is so popular online. Of course, as far as we know, no such portal exists, but assuming it does and obeying the laws of physics, then the question really comes down to this: whether it works for something like entering and exiting the portal in the same way.

So what is measured? Does speed matter? Because in our universe there is no absolute frame of reference for measuring speed and speed itself: speed can only be determined in relation to another object. So here are some options: Maybe when passing through the portal, the object maintains the same speed relative to the surroundings but is redirected to a new direction: this option A. Or maybe the object maintains the same speed relative to the average position of the Portal. Except mathematically it's the same as measuring relative to the environment, as long as the portal is not accelerating, again option A.

Or maybe the speed of the object relative to the portal it enters is the same speed relative with the portal from which it emerges. - This is option B. Alternatively, perhaps objects enter and exit at a relatively constant rate until the end of the portal they are not currently using; This is a valid possibility, although a bit strange. The point is that all of these options are consistent with what you would see in a video game, because in the game the portal barely moves with respect to the environment. My personal opinion is that the most physical natural option is B, where the speed is measured locally relative to the individual ends of the portal, so the cube shoots out of the blue portal.

This is roughly what would be expected if the portal were a wormhole that curved spacetime (as objects would obey the shielded impulse in the curved spacetime), or if the portal were more of a teleportation that scans one end of the problem and reconstructs it. of a 3D printer, at the other end. So I think B is more natural. It's also tempting to think that there is a situation that simply cannot be Option A (an object remaining at the same speed relative to the environment) because how can a stationary object leave a stationary portal when it is stationary?

The object must leave the portal for the same time it takes to enter, otherwise the middle part of the object will flash momentarily, or repeat itself, leaving and entering the same time means that a one meter cube surrounded by portals moving one second must move within a The process of leaving the blue portal per second is equivalent to one movement per second. However, there is a way to make option A work, precisely because the cube does not enter the orange portal all at once, but enters little by little. If those bits coming out of the blue portal didn't move, then they would all appear completely in the plane of the portal, stationary, and continue to pile up, crushing the cube into a flat square.

Or if the cube was rigid and not crushed, then there would be no access. First the orange portal: the portal would bounce! I doubt that option A is actually the way portals are programmed in video games, since measuring speed relative to the global environment (rather than relative to a specific object) is usually the easiest to program, since the game experiments were done within the engine. to try to see what was going on with the game glitches, just not letting solid objects move through portals against them. This may be unsatisfactory, not how you think the portal should work.

But that's okay! To me, the morality of the portal

paradox

is not a paradox: the answer depends on how portals actually work, which, since they are 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. So, I leave you with one last portal riddle to ponder: What if instead of going down? Towards the cube, the orange portal moves sideways on the ground, drop the cube through it. Does the cube go straight through the blue portal, bounce off the orange portal, or shoot from the blue portal at an angle?

This MinutePhysics video is powered by CuriosityStream, an affordable subscription streaming service covering science, documentaries, and non-fiction. I Won't Beat the Jungle - CuriosityStream has in their collection what I think is the best physics documentary I have ever seen "Particle Fever" and you can watch it by visiting Curiositystream.com/Minutephysics and using the promo code "Minutephysics"” Sign Up and you will get your first 30 days completely free. After that, subscribe to CuriosityStream for just $2.99 ​​a month and get unlimited access to over 2,400 other documentary and nonfiction shows, including some you may know! But seriously, go check out Particle Fever by visiting Curiousstream.com/Minutephysics and using the promo code 'Minutephysics'.

Particle Rush is great!