Let’s assume that the PD is maintaining the portals. It’s got a power source that can supply some finite level of power, and the PD itself is required to keep the portals open so that they are not self-sustaining. The technology is pretty magical, but we want to keep it from obviously and flagrantly violating physics.
Tossing a concrete block into the portal so that exits ten meters in the air – further from the Earth – is just like moving your bike to the top of the hill for free. You can’t do that. Once that heavy object is a little distance away, you can capture (some of) that potential energy when you let the object fall again. We need to make sure our PD pays for the potential energy we get for transporting objects up. (Lateral moves can, I believe, continue to be free1.)
If we need to define a rationale for the energy usage, it could be something along these lines: Imagine that mass passing through the portal makes it unstable. There is a difference between the gravity on the object as it enters the “bottom” versus when it exits the “top”. The object has unaccountably changed its relationship with other gravitational actors. This causes minute ripples in the surface of the portal. If both portals were made back-to-back on the same 2d plane (so that the portal didn't go anywhere) then the ripples on both sides would match and the portal would not be destablized at all. But once you move one above the other, the shape of the ripples change compared to one another. It order to maintain the portal within these gravitational “ripples”, you need to add power. It will work out that the power required is always more than you gained from moving the object up.
At any rate, if the portal device can’t come up with the power to allow the mass through, the portal needs to fail. We haven’t worked out how yet – we’ll get to that in a second. The important point here is that it needs to stop “giving” energy the moment we stop “paying” for it2.
Ok, we now have a portal which doesn’t let us create energy when we pass through, which is a step in the right direction. One problem left. What happens when the portal closes?
This leaves us with slicing. However, that means the edge of the portal needs to be capable of slicing through any object occupying the opening, and it must be able to do so without any further energy from the PD. We can say that opening a portal requires some energy, just as lifting the blade of a guillotine does, and that shutting down a portal is simply releasing that energy by allowing the blade to fall. I think this should allow a two-dimensional surface to cut through any given three-dimensional object regardless of mass, but I have no idea how to prove it. (Assuming doing so is even possible.)
That’s my take on how the PD needs to work. Now someone get out there and build me one. For the sake of science!3
1. Lateral moves can’t be completely free, of course. All objects exert gravitational force on each other, so moving a brick fifty feet away means moving it away from my gravitational field which, despite my recent weight loss, is still non-zero. However, the energy needed to overcome this miniscule. It needs to be paid for, but it’s nothing compared to Earth gravity.
2. I’m not suggesting that the portal should be designed with these limits, on purpose. I’m suggesting that if some clever researcher figured out how to make one, she should quickly discover that these limits are unavoidable. As in, “we can build a portal device, but we will have to provide this energy in such-and-such a manner in order for it to work.”
3. By “science” I mean this.
While not part of any test protocol, we are pleased to present you with this complementary Aperture Science bonus fact: Using a portal device, it would be possible to make a genuine Klein Bottle without resorting to the rather unsightly nexus required by the immersion of the Klein Bottle into our sadly limited 3d space. Unfortunately, one of the portals would need to go inside of the bottle (which is one-sided and therefore the concept of “inside” is a bit daft) and would therefore make the thing a royal pain to use. Not that I have any idea what you’d use it for.
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