Portal Physics

I really want to post with some consistency, even if I'm just rambling. So tonight, I will be rambling about the physics of the popular video game Portal. In case you're unfamiliar, you can read about it online, but basically, you're in an enclosed room, armed with nothing but a special portal gun. Shoot it at a wall to create a bluish portal, and at another wall to create an orangish portal. As if by magic, the two portals will be connected, so that you can send any object, including light, or yourself, through one portal, and it will come out the other. You use this to transport yourself or other objects to places that would otherwise be unreachable. It looks kind of like an FPS, but it's actually more of a puzzle game, which is why I like it. Of course, teleportation in video games isn't new, but what's unique about Portal is that the momentum of objects is also transferred through the portal, which leads to some very interesting solving techniques. For example, if you're on a high "cliff" next to a wide, deep chasm, and you need to get across the chasm, but can't create a portal on the other side (some walls resist the portal gun), you can shoot one portal in the wall next to you, so that it faces across the chasm, then shoot another on the ground of the chasm, way below you. Then jump into the lower portal, and you will soon find yourself shooting out of the wall portal, across the chasm. Of course, almost as much fun as actually completing the game is running through some interesting hypothetical scenarios. I really am just rambling here.

Put one portal on the ceiling, and another on the floor, directly below it. Jump into the floor one, and you'll fall out of the ceiling and into the floor, infinitely many times, moving faster and faster each time. (You can actually do this in the game, and there is apparently some kind of randomization built in that causes you to slightly miss the floor portal after a few iterations. Suppose that didn't happen though.) Suppose you keep your body oriented the normal way. If you look up or down, you see an infinite tunnel of portals, similar to the infinite "hall of mirrors" effect if you stand between two parallel mirrors. Clearly, each time you go through the portal, your kinetic energy is unchanged, but your potential energy increases by your weight times the height of the ceiling. So yes, conservation of energy is being violated, but don't worry about that for now.

As the person goes faster and faster, they measure the distance between the floor and the ceiling to be shrinking, according to special relativity. Eventually, this effect should be so pronounced that, according to the person, two or more parts of the body are at the same place relative to "the" floor. For example, suppose the room has contracted enough that its height is half that of the person. Just as the person's feet are entering the floor portal, his waist is also entering the "previous" floor portal. The person might cite this as evidence that there truly are an infinite number of portals. Meanwhile, an observer sitting quietly in the room would see the portal traveller shrunk to about half his normal height.

I can see that having a basic understanding of special relativity, and almost no understanding of general relativity, is going to be a problem. Still, let's go on. What if the falling portal traveller starts feeling sick, and shoots a portal onto the floor nearby, with the same color as the current floor portal, so they will instantly stop? Putting aside the broken bones and bruises that will likely result, we now have a paradox. If the portal traveller and the stationary observer were both wearing watches, each would have said the other's was running slow. Now that both are in the same frame of reference, which watch has the earlier time, assuming the traveller's watch miraculously didn't break upon impact? Admittedly, no real physical theory should be required to answer this question, as we've already violated conservation of energy, but it's still an interesting thought.

One thing that is completely absent in the game (and probably for good reason) is any significant quantity of liquid. Suppose you have two large tanks. Tank A is full of water, and sits on the ground. Tank B is elevated somewhat, and initially empty. A portal is created that connects the bottom of both tanks. What happens? My first thought is that it works like a siphon, with water "seeking its own level" -- that is, water will flow through the portal, filling tank B, until both tanks have exactly the same water level, relative to the ground. By this logic, if tank A is lifted up after equilibrium is reached, water will again flow from A to B. I can't see why this would happen, so I think a new hypothesis is needed.

One of the first things we learned in PHYS 162 last semester is that electric field lines always diverge from positive charges and converge to negative charges. They never form closed loops, and can only start and end on charges or go out to infinity. Suppose a room contains a single positive charge. If you can trace a field line through a portal, it should come out the corresponding portal, potentially at a different angle. Assume the portals are as in the first situation: one on the ceiling, one on the floor. It seems to me the only way to draw the field lines accurately would have to be by modeling the setup as an infinite set of rooms, stacked one on top of the other, each containing a single positive charge. Further evidence that the portals really do create "copies" of the room, rather than simply connecting two parts of the room which are normally separate.

What if you dropped the positive charge into the portal, the same way we dropped a person through it originally? You would have a moving positive charge, i.e. a current. I suppose this would set up a magnetic field in the room, which would be constantly increasing. If you used two floor portals, instead of a floor and ceiling portal, you would effectively have two nearby AC currents, thus instead of infinite kinetic energy, you could create infinite electromagnetic energy.

I think that's enough for now.