I’m always fascinated at the ginormous arguments that this picture is guaranteed to cause, and I wonder at what kind of experiments you could do with it to investigate people’s different intuitions of physics.
I think the answer B makes more sense. There’s no reason this portal configuration should conserve momentum since it breaks space translation symmetry. On the other hand, if you’re looking at the object from the exit portal then you expect its trajectory to be smooth. More formally, the portal can be implemented by making space into an appropriate Riemannian manifold (with singularity at portal edges) and mechanics with the usual Lagrangian leads to B.
On the other hand, if you’re looking at the object from the exit portal then you expect its trajectory to be smooth.
I’m confused. Both trajectories are smooth.
More formally, the portal can be implemented by making space into an appropriate Riemannian manifold (with singularity at portal edges) and mechanics with the usual Lagrangian leads to B.
Well, yes, but I think the question is concerned with the peculiar implementation of portals in the game, which apparently conserves momentum.
If you’re looking from the exit portal you see the object coming towards you. Therefore, when it crosses the portal you expect it to keep moving with the same velocity rather than suddenly stopping (I assume that the portal is a smooth geometric surgery of space and nothing singular is happening at the boundary except at the edge).
Well, yes, but I think the question is concerned with the peculiar implementation of portals in the game, which apparently conserves momentum.
I have no idea about the game (never played it). I’m just saying what seems more natural from the POV of physics.
If you do it in the Portal 2 engine (Portal 1 doesn’t support moving portals) it seems to be A but with a slight push (google for videos).
The point is, I don’t think the topology of the portals even allows for things like “conservation of momentum” to make sense (anyone can correct me here).
The point is, I don’t think the topology of the portals even allows for things like “conservation of momentum” to make sense (anyone can correct me here).
That’s what I immediately thought, but on further thought I think it might, if you assume portals move things through some kind of force rather than by folding space itself, though something yadda yadda Dirac delta function yadda yadda, but we can assume the portals are very much heavier than the object so… Well, I’d have to work it out.
Yes, I think it can work, if when the object passes the portals the portals gets displaced by -m/M times their distance, where m is the mass of the object and M is the combined mass of the portals. (By “work” I mean it doesn’t need there to be a privileged frame of reference for it to be described.)
(I’m assuming Galilean relativity; I’m not sure it can be made to work in special relativity as well.)
I’m always fascinated at the ginormous arguments that this picture is guaranteed to cause, and I wonder at what kind of experiments you could do with it to investigate people’s different intuitions of physics.
I think the answer B makes more sense. There’s no reason this portal configuration should conserve momentum since it breaks space translation symmetry. On the other hand, if you’re looking at the object from the exit portal then you expect its trajectory to be smooth. More formally, the portal can be implemented by making space into an appropriate Riemannian manifold (with singularity at portal edges) and mechanics with the usual Lagrangian leads to B.
I’m confused. Both trajectories are smooth.
Well, yes, but I think the question is concerned with the peculiar implementation of portals in the game, which apparently conserves momentum.
If you’re looking from the exit portal you see the object coming towards you. Therefore, when it crosses the portal you expect it to keep moving with the same velocity rather than suddenly stopping (I assume that the portal is a smooth geometric surgery of space and nothing singular is happening at the boundary except at the edge).
I have no idea about the game (never played it). I’m just saying what seems more natural from the POV of physics.
(It’s A, right?)
To some extent, ‘folk physics’ has already been studied a fair bit. For example, see the links at the end of http://lesswrong.com/lw/khd/confound_it_correlation_is_usually_not_causation/ about a quiz designed to measure how well people understand Newtonian mechanics and to what extent they succumb to incorrect folk physics beliefs.
If you do it in the Portal 2 engine (Portal 1 doesn’t support moving portals) it seems to be A but with a slight push (google for videos).
The point is, I don’t think the topology of the portals even allows for things like “conservation of momentum” to make sense (anyone can correct me here).
That’s what I immediately thought, but on further thought I think it might, if you assume portals move things through some kind of force rather than by folding space itself, though something yadda yadda Dirac delta function yadda yadda, but we can assume the portals are very much heavier than the object so… Well, I’d have to work it out.
Yes, I think it can work, if when the object passes the portals the portals gets displaced by -m/M times their distance, where m is the mass of the object and M is the combined mass of the portals. (By “work” I mean it doesn’t need there to be a privileged frame of reference for it to be described.)
(I’m assuming Galilean relativity; I’m not sure it can be made to work in special relativity as well.)
The link to Halloun & Hestenes 1985 no longer seems to be valid, although the 1992 paper still seems to be good.
Is this the same paper?
That was fast. But no, that seems to be an earlier paper, I meant http://generative.edb.utexas.edu/classes/knl2011fall/Halloun_Hestenes_FCI.pdf
Yes, assuming portals conserve momentum (which I believe they do in the Portal canon).
Speedy thing goes in, speedy thing comes out :-D
My intuition agrees with Squark’s, but I’ve never played the game either.