Lol. This will be fun. Glados’ explanation is still correct, but momentum being conserved between portals (or “across portals” as I’d rather phrase it) is exactly what gets you answer B.
“A perspective that encompasses all of the objects involved” is not a thing in reality. No point in space cares about another point in space beyond the forces felt from that direction transmitted through spacetime, and the frame of reference following the left portal moving down and the frame of reference following the stationary right portal are both equally valid and moving relative to each other over the timeframe of the cube transitioning through the portal. I don’t agree that the game is pushing a different model, but if it actually is, then that opens up so many (more) holes in physics that we may as well be debating magic.
I actually addressed the portal stopping halfway in another comment here which I won’t bother to copy here, but the summary is that you shouldn’t think of the box as one item but a mass of particles connected by internal forces. Your answer is indeed “obvious” and intuitive, but accelerating portals do funny things with frames of reference that means intuitive isn’t always right and is the reason this topic always creates the disagreement it does.
As the portal comes down across the top half of the cube with constant relative velocity V and the appropriate momentum for said velocity, all those portaled particles will emerge from the other side of the portal with the same relative velocity V and same associated momentum compared to that side of the portal. Whether the particles maintain velocity relative to the portal because of something intrinsic to how space works at the portal boundary or because particles coming in forcibly displace particles going out in equal measure, the result is the same, fast in = fast out.
When the descending portal suddenly stops halfway, the particles already portaled through don’t “know” this. They’ve still got the momentum of being sent through moments earlier reinforced by all the particles around them doing the same thing, so they “desire” to keep moving away from the portal. The particles of the bottom half of the box are similarly “ignorant” of all the shenanigans above and “want” to maintain the zero momentum they’ve had all along as measured by most of the objects in the scene.
This means the top and bottom halves of the box, despite never losing conservation of momentum, suddenly don’t align with each other. The conflict of the top half “wanting” to keep moving away from the portal at velocity V and the bottom half “wanting” to stay where it is will resolve in one of two ways:
If the cube’s internal forces are strong and “springy” enough to accommodate the disagreement, forces will propagate and equalize throughout the whole cube effectively averaging all “desired” motion out and the cube will fly out of the right portal at velocity ~1/2 V.
If the internal forces are not enough, the two halves of the cube will separate from each other, either cleanly at the portal boundary if the momentum disagreement massively overpowers internal forces or more messily and violently if it barely overpowers them. Obviously we don’t have portals in real life to visualize this, but you can kind of get a feel for the effect through planetary bodies breaking up at Roche limits.
Edit: Wording the overall effect another way: Portals moving relative to each other effectively link two frames of reference to be one and the same over the portal boundary. If one portal changes velocity, the two frames of reference cease to align. This can cause conservation of momentum to appear to have been violated externally while actually being maintained in all the internal reference frames objects actually experienced.
perspective that encompasses all of the objects involved” is not a thing in reality.
Actually it is, that’s exactly what a perspective, or refence is, it’s either this, or you are arguing that there is a universal reference point. There isn’t a universal reference point though, all motion is relative to other objects. The problem with using B as the result of this experiment is it draws a conclusion on the relative motion of the box, without considering the relative motion of everything on the other side of the portal. B only makes “sense” in a system where only the position and motion of the box and the orange portal are considered, any conclusion regarding motion outside this system are invalid when you use a perspective thar excludes everything except the box and the orange portal.
Maybe I’m misinterpreting your use of the phrase, but it seems you’re arguing from applied Newtonian mechanics where objects define a reference frame. A reference frame in that sense is a useful convention but doesn’t actually signify something in reality, hence my comment. Objects don’t care about their velocity relative to other objects or about reference frames suddenly shifting as measured that way. An object’s motion is encoded as an entirely local property in spacetime itself, AKA its worldline. This distinction between object-based reference frames and local reference frames is usually not worthwhile, because they’re usually entirely consistent with each other. The convention just happens to break in situations where worldlines cease to be continuous and consistently differentiated, as in the case of portals.
An object’s motion is encoded as an entirely local property in spacetime itself, AKA its worldline.
Worldline is just a way to describe how an object or point moves in spacetime, since relatively makes everything kinda fucky and hard to follow using newtonian laws of motion, it does not appear to be a replacement for an inertial frame of reference.
Edit: by your argument of what a worldline is, then we would expect A to happen, since there is no motion component “encoded” in the worldline of the cube anyway.
Lol. Serious /uj question: Are you deliberately misreading me to do the rage bait thing? I’m using “worldline” in the first sense you gave. I’ll avoid it and reword the actual main point as this is good practice for me anyway:
Local spacetime is the ultimate thing all velocity maps onto, so any examination of this problem needs to respect spacetime as the primary driver of behavior. Answer A ignores the spacetime the cube is being moved into on the exit side of the portal as a real thing it must maintain inertia within (the critical detail also overlooked in the “Buster Keaton” answers).
Serious /uj question: Are you deliberately misreading me to do the rage bait thing?
No, I’ve been serious since I acknowledged that I was supposed to ragebait people.
Local spacetime is the ultimate thing all velocity maps onto,
Okay, let’s step through this slowly for you, if local spacetime is what all velocity maps to, then it sounds like each object has its own velocity that is independent of other objects (IE, in a universe with a single object in it, it could have a velocity), correct?
Yes, it would have velocity, or at least all the mechanical properties of it. That velocity would be undefined from our perspective since all possible ways you could define it (0, 5 m/s to the right, etc.) would be equally valid depending on the coordinates you choose to put at rest, but that’s a measurement problem, not anything intrinsic to reality.
The important bits are: 1) inertia exists as long as you have the minimum ingredients, an object in spacetime, 2) all possible inertial reference frames are still meaningfully distinct from each other and stay as such, 3) any change in velocity of the object would show up in all possible inertial reference frames, and 4) any such change will stay logically consistent regardless of which inertial reference frame you choose to measure the velocity change in.
Yes, it would have velocity, or at least all the mechanical properties of it.
Okay, so since we have established (in your framework of understanding) that the cube has its own velocity, if the portal is moving towards the cube at 1m/s, how fast is the cube moving?
Lol. This will be fun. Glados’ explanation is still correct, but momentum being conserved between portals (or “across portals” as I’d rather phrase it) is exactly what gets you answer B.
“A perspective that encompasses all of the objects involved” is not a thing in reality. No point in space cares about another point in space beyond the forces felt from that direction transmitted through spacetime, and the frame of reference following the left portal moving down and the frame of reference following the stationary right portal are both equally valid and moving relative to each other over the timeframe of the cube transitioning through the portal. I don’t agree that the game is pushing a different model, but if it actually is, then that opens up so many (more) holes in physics that we may as well be debating magic.
I actually addressed the portal stopping halfway in another comment here which I won’t bother to copy here, but the summary is that you shouldn’t think of the box as one item but a mass of particles connected by internal forces. Your answer is indeed “obvious” and intuitive, but accelerating portals do funny things with frames of reference that means intuitive isn’t always right and is the reason this topic always creates the disagreement it does.
As the portal comes down across the top half of the cube with constant relative velocity V and the appropriate momentum for said velocity, all those portaled particles will emerge from the other side of the portal with the same relative velocity V and same associated momentum compared to that side of the portal. Whether the particles maintain velocity relative to the portal because of something intrinsic to how space works at the portal boundary or because particles coming in forcibly displace particles going out in equal measure, the result is the same, fast in = fast out.
When the descending portal suddenly stops halfway, the particles already portaled through don’t “know” this. They’ve still got the momentum of being sent through moments earlier reinforced by all the particles around them doing the same thing, so they “desire” to keep moving away from the portal. The particles of the bottom half of the box are similarly “ignorant” of all the shenanigans above and “want” to maintain the zero momentum they’ve had all along as measured by most of the objects in the scene.
This means the top and bottom halves of the box, despite never losing conservation of momentum, suddenly don’t align with each other. The conflict of the top half “wanting” to keep moving away from the portal at velocity V and the bottom half “wanting” to stay where it is will resolve in one of two ways:
If the cube’s internal forces are strong and “springy” enough to accommodate the disagreement, forces will propagate and equalize throughout the whole cube effectively averaging all “desired” motion out and the cube will fly out of the right portal at velocity ~1/2 V.
If the internal forces are not enough, the two halves of the cube will separate from each other, either cleanly at the portal boundary if the momentum disagreement massively overpowers internal forces or more messily and violently if it barely overpowers them. Obviously we don’t have portals in real life to visualize this, but you can kind of get a feel for the effect through planetary bodies breaking up at Roche limits.
Edit: Wording the overall effect another way: Portals moving relative to each other effectively link two frames of reference to be one and the same over the portal boundary. If one portal changes velocity, the two frames of reference cease to align. This can cause conservation of momentum to appear to have been violated externally while actually being maintained in all the internal reference frames objects actually experienced.
Actually it is, that’s exactly what a perspective, or refence is, it’s either this, or you are arguing that there is a universal reference point. There isn’t a universal reference point though, all motion is relative to other objects. The problem with using B as the result of this experiment is it draws a conclusion on the relative motion of the box, without considering the relative motion of everything on the other side of the portal. B only makes “sense” in a system where only the position and motion of the box and the orange portal are considered, any conclusion regarding motion outside this system are invalid when you use a perspective thar excludes everything except the box and the orange portal.
Maybe I’m misinterpreting your use of the phrase, but it seems you’re arguing from applied Newtonian mechanics where objects define a reference frame. A reference frame in that sense is a useful convention but doesn’t actually signify something in reality, hence my comment. Objects don’t care about their velocity relative to other objects or about reference frames suddenly shifting as measured that way. An object’s motion is encoded as an entirely local property in spacetime itself, AKA its worldline. This distinction between object-based reference frames and local reference frames is usually not worthwhile, because they’re usually entirely consistent with each other. The convention just happens to break in situations where worldlines cease to be continuous and consistently differentiated, as in the case of portals.
Worldline is just a way to describe how an object or point moves in spacetime, since relatively makes everything kinda fucky and hard to follow using newtonian laws of motion, it does not appear to be a replacement for an inertial frame of reference.
Edit: by your argument of what a worldline is, then we would expect A to happen, since there is no motion component “encoded” in the worldline of the cube anyway.
Lol. Serious /uj question: Are you deliberately misreading me to do the rage bait thing? I’m using “worldline” in the first sense you gave. I’ll avoid it and reword the actual main point as this is good practice for me anyway:
Local spacetime is the ultimate thing all velocity maps onto, so any examination of this problem needs to respect spacetime as the primary driver of behavior. Answer A ignores the spacetime the cube is being moved into on the exit side of the portal as a real thing it must maintain inertia within (the critical detail also overlooked in the “Buster Keaton” answers).
No, I’ve been serious since I acknowledged that I was supposed to ragebait people.
Okay, let’s step through this slowly for you, if local spacetime is what all velocity maps to, then it sounds like each object has its own velocity that is independent of other objects (IE, in a universe with a single object in it, it could have a velocity), correct?
Yes, it would have velocity, or at least all the mechanical properties of it. That velocity would be undefined from our perspective since all possible ways you could define it (0, 5 m/s to the right, etc.) would be equally valid depending on the coordinates you choose to put at rest, but that’s a measurement problem, not anything intrinsic to reality.
The important bits are: 1) inertia exists as long as you have the minimum ingredients, an object in spacetime, 2) all possible inertial reference frames are still meaningfully distinct from each other and stay as such, 3) any change in velocity of the object would show up in all possible inertial reference frames, and 4) any such change will stay logically consistent regardless of which inertial reference frame you choose to measure the velocity change in.
Okay, so since we have established (in your framework of understanding) that the cube has its own velocity, if the portal is moving towards the cube at 1m/s, how fast is the cube moving?
I think I see exactly where you’re going with this, but let’s just say the cube is defined to be at rest with the portal approaching at 1 m/s.