Physics of Portals in Real Life
Everyone who has played these games knows that momentum is conserved when you pass through the portals - enter portal fast, exit portal fast. It is a major part of the game. The also matches up with the real-world conservation of momentum.
However, I was thinking about this when i realised something. In the real world, momentum is mass time velocity. Velocity is a vector quantity - is has both direction and magnitude. This means that going into a portal and coming out of a portal facing a different direction has not conserved momentum, as your momentum is now in a different direction.
This can still work, if you assume that by passing through the portal, you have exerted an impulse on the surface that the portal was on - i.e, you have change direction, because you were "pushed" round a corner - in much the same way as if you had just bounced off the surface that the portal was on. You have pushed the wall back, and in doing so have changed your own momentum.
I'm not going to go into specifics of how this might happen, because I have no idea how portals actually work. But I'm pretty sure that this could cause some problems with the way portals work if you think about it. For example, if you put a portal on a loose object, the object should move as you pass into the portal, which would affect the way in which you come out of the exit portal.
Another quick question, is there a way to know if you are going through a portal, or is it indistinguishable from just moving through space as you normally do? (If that makes sense). Can you tell if you are going through a portal, if you can't see the edges of the portal (maybe its a VERY big portal?).
And yeah, I know it's just a game, it doesn't need to be realistic, but I find this interesting, and would like to know what you think about this.
Interesting theories.
I do think that momentum would work just the way it works in-game. You would simply go through one portal at a certain velocity and exit the other portal with the same momentum. I don't think the universe would object and stop you in your tracks. I don't think that putting a portal on a loose object and travel through it would push back the object though, as it's just a matter of transporting / disassemble & reassemble the particles going through the portal, not really a matter of force going through the portal.
That's also interesting. How the hell would portal technology work? Do the particles transport through the portals or do they simple reassemble on the other side? If that is the case then you wouldn't be built up from the same atoms as you once were. Mindfuck xD
@Squiffy:
Well, first of all, I agree about your momentum interpretation by means of vectors, it's very ilustrative. But I don't agree that momentum is not conseved when you fling out the exit portal that has a different direction than the entry portal. My point is that when you change from the entry portal to the exit portal it seems to happen what you could interpret by the 2 following valid happenings:
- Portals open a connection between 2 areas, entry-exit, the vector that describes momentum should not have to be conceived from the long distance (up 500 unit for example) to the first portal entry line, I think there's a continuum and the vector tresspass the entry portal and continues from the exit portal onwards.
- But overall: as the entry and exit portals are connecting two areas and there's no friction, objects or whatever in the middle, you have a force in the moment that you enter one portal that cannot simply disappear when you go out the other portal, this force continues: you exit the portal with the same intrinsic force that you had when you entered the first portal. The change of direction only affects that intrinsic force producing friction because of gravity, but if for example you have 2 floor portals, the same gravity that pulls you down, is the same exact force that pushes you up again... In the case you have a floor portal and a wall portal, this gravity will pull you down to the floor after getting out of the wall portal, landing on the floor again...
Regarding the knowledge that you are going through portals if you cannot see the edges, if I understood you well, hmmm... I think that supposition looks more similar to the world portals than the portals themselves; and no, I don't think you'll notice. If on the other hand you would being into a momentum you'll surely notice, but only because of the wind against your ears...
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Relative to the world, not the player.
It's actually really easy, the momentum you have is a vector that is perpendicular (on a 90 degree angle) with the portal. You also leave the other portal with the same perpendicular angle, you keep that same vector through the portal thus you keep your momentum.
The infinite fall would give a problem: air friction will slow you down, and if you fall to fast you might get lit because of the gigantic heat the air friction will give you.
I think you won't see the difference: light goes through the portals, the only thing you could notice is that you're suddenly seeing penguins where you were in the desert 5 seconds ago (and no, not in the zoo)
In this case, relative to the portal 
One of newtons laws: An object will remain at a constant velocity unless an external force acts upon it. By going through a portal and changing direction, velocity has been altered. Whar is the external force? There isn't one? (I discuss more below)
I was thinking more along the "particles travel through the portals" line. Kind of like a wormhole. That and people talking about momentum relative to the player set me thinking...
Take a laser that goes through a portal, then crosses over itself, at 90 degrees. If you look at the point when the laser crosses its self, you would see that it is going in 2 different directions, and conclude that it must have turned a corner at some point. However, if you were too stand by the laser emitter, and look along the length of the beam, through the portals, it is straight, and therefore you would conclude that it hasn't turned a corner. Both observations could be said to be correct, depending on your perspective
Now take the laser to be the direction of the player's momentum as they pass through the portal. To someone one watching, it would appear that they are going a different direction when the exit the portal. However, to the player, it would appear that they are going the same direction, and the world has moved instead. Again, both observations are correct. So perhaps momentum is conserved, depending on how you look at it.
It would appear to me, that the portal is using a dimension above our 3. (4 including time). Imagine if the portals were to bring the 2 areas in 3d space together in 5d space. To illustrate this, imagine a stickman walking across a page of paper. If you fold the paper in half, to make a cylinder, the stickman could walk all the way round back to where he was, even though from his perspective, with no concept of the 3d space through which the paper is folded, he has been going in a straight line. I think that the same happens with portals, but with higher dimensions. This means that the laser is going in a straight line through 3d space, but is curved in 5d. And momentum is conserved, because there is no tuning in 3d, and the momentum is a 3d vector. No external force in 3d space is needed, it can happen in 5d, and can be exerted by the portal gun (or something) instead, with no observable effect in 3d space.
I have confused myself now. If I'm not making any sense, please say...
Nah, you make sense, and the folded paper analogy is apt. The portal itself is the anomaly, twisting space; relative to the space-created-by-the-portal through which the player is travelling Newton's laws are adhered to.
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you have two positions: player: no change in angle, observer 90 degrees change.
If both persons close their eyes and cannot see what happens and randomly one of the two gets to see what happens there is a superposition (quantum mechanics)
That means that the angle is SQRT((90degrees)?+(0degrees)?) = +/- 90 degrees.
(If you don't understand this: google schr?dinger's cat.)
Then the average of -90 and 90 is 0 so on average the angular change is 0 degrees!
Hooray for science 
I think we should really challenge the assumpting that going through a portal on a wall and coming out of the floor is a change in direction: as mad as it seems, To change direction a force must be applied on your particle to change its velocity and a direction. From you and your point of view, you have travelled in a straight line: it is the world which is the wrong way up.
I think this would solve the conservation of momentum problem, as momentum hasn't changed, but the laser example is a problem. If people who are thinking about the laser don't see what's wrong, imagine that it is polarised light...
I found this really interesting when I did an essay on dimensions (yeah, I was a nerd...). I won't add part 2 just to save some space on the forum.
NOTE: This doesn't really explain the paints above. But it's interesting nonetheless.
Now I really wish I had a portal gun :/