Portal Physics

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yes but relativity relies on frames of reference and the frame of reference is never only the portal and the box, but also the room around them,

in relation to the room the box never has any actual momentum, only the portal does.

Ok, attempt #2. I still think that "B" is the right answer.

The barber pole is attached to the same wall that the lower portal is 'painted' onto (was too lazy to make it blue). And there's a rat that's running along the top of the pole.

The rat's velocity is before it goes through the portal is v1, with respect to the pole. If that relative velocity is to be maintained (since the rat's feet are only touching the pole), then when it emerges from the lower portal it's velocity will have to be v1+v2 w.r.t. the wall.

Also, if "A" were correct, then the first infinitesimal slice of the pole, upon emerging from the lower portal, would have zero velocity. The rest of the pole would then "pile up" behind the that first slice, preventing the pole from proceeding further. So, either the pole would be crushed, or the moving portal would meet a back-force sufficient enough to stop it. Essentially, if "A" is true, then no 3-D object can pass through (but a 2-D or less object could if oriented the right way).


(Ok, there are some +/- sign problems with my diagram, so consider the 'velocities' to be speeds which are given the appropriate sign by the arrow associated with it.)

More precisely, it depends on inertial frames of reference. In other the frames have to be moving at constant speeds relative to each other without forces acting on them. B in the first picture doesn't make sense in my mind because there is no force acting on the cube that would cause it to fly into the air.

Yes, I think the barber pole would be emerging from the portal at the same speed that the other portal mouth would be moving towards it. However, I don't think the situation in your diagram is analogous to the first one.

excactly.

that would be a much better way of putting it as well

The fast moving top portal should make no difference. Relative to the rest of the world the box remains stationary so using that logic the answer is A.

However, in that drawing, the exit portals are lower than the entry portal. Therefore the box has lost potential energy and that energy has to go somewhere. It could be lost as heat in the system, in which case the answer is A or it could be converted to kinetic energy, in which case the box would exit the portal at the same speed that it would have if it was dropped the same distance.

A problem with both your diagrams:

1. Does the portal even have mass? If not, than it might only have energy on the edges, but not in the center. The opening is nothing more than open space. I'm pretty sure the portal is supposed to be a weapon of entropy. Let's put it this way, 'observe the universe.' There are some 'frames of reference' showing objects moving to distances greater than is possible than the speed of light. Are they actually moving faster than the speed of light? The answer to that is a resounding 'NO.' Entropy is causing a reference artifact by expanding the space between objects.

Portals are no different. They are simply highly controlled versions of entropy.

A simple example:

Sit on a secured pole, as in your second demonstration. Then, have a crane carry a large window with a wall on it over your position. Do you suddenly go flying upon moving through window? The portal is no different, but what is wrong is your apparent expectations. Your assuming the portal exists in a bland, equalized 3d universe. However, my understanding of portals is that they all require at least a 3d universe with entropy(which could would be considered a 4th dimension). In other words all points within the entire universe can be considered infinitely expanded or infinitely small in space. All that changes while the portal moves is the fabric of space-time, nothing more.

Another problem I see with your expectations:

If it were possible, than a portal that moves at the speed of light toward an object would automatically violate causality.

...it's a Portal quote. <.<


Also, and forgive me if it's a fun killer, but discussing laws of nature after altering some of them doesn't really make sense. You can't just remove gravity or friction and pretend everything else will behave normally. Even if it's fun.

That being said, I still say the box will just plop. XD

agreed that this is only entertaining

but the portal is as such the only thing "off" gravity, momentum force and everything else is simulated as closely as possible with the average cpu in mind,

so the only actual assumption here is that of a stable portal, that in itself is stranger than some actual physical phenomena

Portal doesn't conserve energy that way. In fact, it flatly violates the conservation of energy. If you create a portal at the bottom of a staircase and another at the top, when you enter the top one, you don't come out of the lower one with any additional kinetic energy. Also, you can do the reverse and gain potential energy from nowhere.

Hmm, well consider if there are no portals, but rather that the orange portal (in the first diagram) is simply a doorway into an identical room. In that case the second room would be moving w.r.t. the original room. If you were inside the second room looking through the doorway at the box, you would see it moving toward you, and once it passed through the doorway it would continue moving with that same velocity -- since no force acted on it. If the box stopped as it passed through the portal then it would appear to have had forces acting on it, if you were sitting in a chair in the second, moving room.

Of course, the weirdness is that there is no second room, it's just that Portal allows you reconnect space to itself in bizarre ways, which leads to problems like being able to jump between 2 different inertial frames with no forces or changes in energy or momentum.

Ugh, I can't remember the mathematical term, but it's like a path integral where you can take any path you want, but only the starting and ending points matter. Portal breaks that. You can have a hill that is 100 feet high if you walk up one side, and 10 feet high if you walk up the other, even if both starting points are at sea level.

I'll buy that explanation.


Also,

^^

My guess is that the guy would be crushed (by his own body, no less).

If the blue portal were displaced upwards 1/2 of it's diameter, he would crushed by his own butt. [/juvenile mode]

I also thought about it that way but there is a reason why I emphasized that the frames must be inertial. Here's my full explanation:

Let's consider the portal as simply a doorway between 2 identical rooms just like you have above. Now, let's go over your analysis again. You are sitting in the second room, looking through the doorway at the box in the original room. That first room, and hence the box as well, is moving towards you. Now, in accordance with Newton's first law of motion, the box has to continue moving at the same speed, and hence fly into the air, when that room suddenly stops moving. This is precisely the prediction that you came up with in your analysis above, so far so good. However, now let's consider the analogous situation from the point of view of the other room. Imagine you are sitting in the first room, watching the doorway to the second room moving towards the stationary (that means not moving) box next to you. In this situation, the second room is moving towards a stationary cube and not the other way round. Since the cube is stationary, it has to remain stationary (again by Newton's first law) even when the second room stops moving, unless of course, a force acts on it, causing it to fly into the air. Now we seem to have a paradox as it appears as though both A and B in the first diagram could be true, depending on from which "room" you are observing the box.

The solution to the above conundrum basically comes down to this:

As long as two frames of reference are moving at constant speeds relative to each other, with the frames being the two identical "rooms" in the description above, the description of the physics in both frames can be considered identical would still be consistent. However, in order for one of the rooms to stop moving with respect to the other one, it has to decelerate until it's speed reaches zero. During this time of deceleration, even if it were just an instant, room is essentially slowing down and therefore no longer moving at constant speed, hence the frame is no longer inertial and descriptions using identical physics are no longer valid. Usually, when comparing non-inertial reference frames, one would have to make a choice of a preferred frame and then introduce inertial forces (also called fictitious forces) in the other one in order to resolve paradoxes like the one above.

For example, let's say you were in a passenger seat of car that's moving along at a constant speed. Now the driver slams on the breaks. Relative to the road, you have to continue moving at constant speed in accordance to Newtons first law of motion. However, relative to the reference frame of the car, one has to introduce a fictitious force that flings you forward, meaning of course that we've chosen the road as our preferred reference frame. Now the choice of a preferred frame is not arbitrary and in the case of this car example, we've chosen the road as our preferred frame because when the driver slams on the breaks, a force is applied to the car, not the road and the rest of the outside world, in order to decelerate it. This, by the way, is also why one needs to add a centrifugal force in a rotating frame.

Now getting back to our original problem. I would associate force responsible for decelerating one of the "rooms" to a force acting on the moving pillar with the orange portal on it. Therefore, to me "room" 2 appears to be the logical choice as the accelerating frame since it's the room "behind" the orange portal, thus making the original room, where the box is stationary, my preferred frame. Well, if that's my preferred frame, then the laws of physics should hold in that frame without including any extra forces. On the other hand, there must be some kind of inertial force that would stop the box from flying in the other frame. Thus I arrive at A as my final answer.

As for your diagram with the barber pole, that appears correct as velocities V1 and V2 remain constant. However, as soon as the one portal, and hence the barber pole, stops moving, I think there will be an inertial force acting on the rat to keep it from flying forward. I guess it can be hard to get your head around the the fact that the two frames are essentially the same room, it's just that the portals connect different places in 3 dimensional space to each other.

Here is a video showing exactly what happens in-game http://www.youtube.com/watch?v=S85nudR6D-Y

As for real life, I have no idea

Doesn't that completely disregard the nature of relativity?