Another Portal Paradox

Fun fact: there is actually one (and only one) instance in the games where a portal can move. It's in the neurotoxin generator room in Portal 2. They apparently just hard coded that one room's panels to work differently.

I love how you casually dropped at the end that one of these questions was posed to you directly by a portal developer. It's as if they were trying to get you to debug the concept.

2:30 "Everything exists outside the portal, there is no place to hide." This sounds like a threat.

I always imagined portals as a doorway. When you run through a doorway, you don't push the doorway, and likewise if the doorway was moving towards you, you wouldn't be pushed. Momentum can only be created outside of the system, since there is no "inside" of a portal, just how there isn't an "inside" of a two-dimensional doorway

2:55 I've never thought of portals as anything like this. They're just tying two points of space together. So the idea of the portals ever moving by a force that's on the objects passing through is very strange.

I think a lot of the paradox comes from thinking of the portals as physical things (like a mirror) as opposed to a non-Euclidean connection in space. The portals should theoretically stay in a non-accelerating reference frame in space (but not necessarily spacetime) and are not exerting a force on anything passing through them—that eliminates any paradox that has to do with portals accelerating or decelerating. Of course that introduces other problems like what happens when one portal passes through another one—which I think the answer should just be it crushes anything between them, possibly explosively or to the point of a black hole, before the two portals cancel each other out.

During paradox 2, I would imagine that the portals have no physical interaction, that they simply displace two different points of space. The idea that they are affected by the forces applied by something between them seems to be incorrect. The portals should represent a closed system and therefore the forces of the piston would only be exerted on itself and itself alone. The idea that a portal can have a mass or momentum is interesting, as I think a portal isn't an entity in and of itself any more than a magnetic field. A portal would be induced by a device or phenomenon that causes the displacement of space itself, meaning that essentially the portal doesn't exist in the same sense as a physical object and that it requires no mass to exist. Another way to think about it is that a portal is simply a hole. A hole has no mass, and is somehow treated as a separate entity rather than as part of the ground. It has physical dimensions but no mass. A portal is a hole (rather, a tunnel) that is part of space and can therefore follow the same pattern. A portal therefore has no physical properties except for its dimensions. Interesting thoughts 🤔.

About your second "paradox" the portals are not connected to the object in anyway and the object would just crush itself.

I disagree with the notion that the piston pushes on the portal. You don't interact with a window by jumping through it. I'd argue that the "space between the portals" is simply reduced and when sandwiched by a portal you get crushed by space because there is not enough of it for you to exist in any longer.

3:50 Something worth mentioning here though, Portal 2 actually does have 2 cases in which portals are moving relative to one another. The neurotoxin sabotage has you use a static portal and moving portal to cut the neurotoxin pipes with laser. And at the end of the game you have one portal on Earth and one portal on the Moon. So while they didn't have it as a more tangible element in the game, it is still possible in the game's setting, so these paradoxes definitely a thing to think about.

I don't think that the portals would move in the piston instance. Portals act like a hole in a wall. If the piston is pushing through a hole in the wall the wall is unaffected, it does not matter how hard the piston is pushing, or if it overcomes whatever it is pushing on, the hold in the wall is unaffected. As for the sandwiching paradox, it is about how strong the wall the the portal is on is pushing. If the wall the portal is on is pushing with enough force it will crush the item with itself, if the wall is coming towards the item at a force that is too weak, it will stop when the item hits itself.

I feel like some of these paradoxes only exist because we have different definitions and understandings of the concept of portals. Mine is more like a doorway. Like if someone moved a hula hoop over my head. I don't think it's that either of us are wrong though, since it's a fictional technology. If we knew how portals actually worked we would be having a very different discussion haha

Some of these scenarios get into whether portals have their own mass. I always thought of them like a "hole" within the universe that connects around, but if they have mass to them, where an object entering them move them around, then that would change the physics of how they work.

Conservation of energy does not apply to portals, so why would the forces transfer to the portals? It makes more sense to presume the object would be squished out the sides as though it were in a hydraulic press.

3:26 that's voice crack hurt me

As I understood it, the portal just bridges two spaces. Like something going through goes through with only ITS momentum. So the portal doesn’t change the momentum of the object at all. I personally think of it like walking through the moving portal you are still moving the same speed and so would exit at the same speed only in a different place. Not sure if this really is understandable but it is just my interpretation of the quote “Speedy thing goes in, speedy thing comes out.”

The piston has no way to assert force onto the portal. It just asserts the same force into itself, so it can block itself (Edit: THROUGH the portal), but not move the portals at all.

1. For the orange portal to stop halfway, there has to be a force of deceleration effecting it. The same force can be applied to the object, making it stop halfway through. 2. An object going through a portal can't put force on the portal. The force just gets tunneled to the other end/portal (still okay for newtons law i guess). And Therefore sandwiching a cube between two portals is the same as sandwiching two cubes without portals (crumble, if the force is sufficient)

Honestly the "very trippy and non physical" reaction from the game seems more "realistic" than your solution. I definitely get how you arrived at that conclusion and it makes sense too, and like you said, they aren't real so on some level it's pointless to worry about. That said, I think you're ignoring the fact that objects passing through a portal don't convey any forces on the portal itself. A portal isn't pushed back by something thrown through it. So an object blocked on the other side wouldn't be able to stop the movement of the portal. I'd assume the object would be crushed to a smaller space and higher density. That or like it was handled in the game the object folds over itself recursively which would work like we see for rendered textures in the game. It was actually right. It's just a real physical object occupying space can't do that. It would just go flat and maybe spark some fusion reaction or insane state of matter like a neutron star. I'd assume as you approach infinitely close all matter is converted to energy and blown out the sides.

Tbh I see portals as connected holes so basically it’s like throwing a ball through a hole 3:12