GLaDOS specifically states “Momentum, a function of mass and velocity, is conserved between portals.”
If scenario B was correct (which it is not) then if the portal was put on an object lighter than the box and then quickly moved over the box, the box would be launched at a speed equal to the speed of the lighter object, while it has more mass, this is not a conservation of momentum.
The best way to explain movement through portals is that momentum is only conserved from a perspective that encompasses all of the objects involved, this is true for regular physics as well actually. Consider this, what if the portal was shoved very quickly over the box down to it’s halfway point? The obvious answer is that the box would only appear halfway out of the other portal, but if you subscribe to the “logic” that leads to answer B, then the box is actually sucked up by the portal, while the actual logical and intuitive answer is that only half the box sticks out of the portal, and it stays where it was placed.
Portals aren’t objects, they don’t have mass, or even a velocity, they are a shortcut in space, and that was what GLaDOS was explaining when she said that momentum was conserved. Although B seems to initially make sense, it is not correct from a game lore perspective, nor from an actual physical perspective.
It’s not about whether portals have mass or not. It’s about the box’s velocity relative to the space on the other side of the portal. In the game, as you move toward a portal, you also move toward the objects on the other side of the portal. Therefore you have velocity relative to those objects, and that’s the momentum that is conserved as you pass through.
This would suggest that portals in the game Portal are flat paintings, but it’s not. As you move around or toward the portal, your distance and angle to the objects on the other side of the portal move in your frame of reference. Therefore you have velocity relative to those objects. Not to the portal itself, not to the universe behind the portal as a point mass, but to the spatially separated objects on the other side of thr portal individually.
This would suggest that portals in the game Portal are flat paintings
No, it doesn’t imply that portal are flat paintings at all.
As you move around or toward the portal, your distance and angle to the objects on the other side of the portal move in your frame of reference.
Yes, but only technically so because those distances and angles change outside of the portal. Your path through the portals isn’t real, it’s a shortcut through space. This is why an object that is moved through a portal has momentum, but an object that a portal is moved over does not, the two scenarios are not the same when you have a frame of reference that includes the space on the other side of the portal. They are the same if you ignore that space in your frame of reference, but then any conclusion you come to about things outside that frame of reference are invalid.
Yes, but only technically so because those distances and angles change outside of the portal.
Ah, so you’re saying Portals are not flat paintings, they’re flat TV screens which project a representation of the universe behind them like based on where the observer is. Upon impact with an object they then store the objects momentum relative to the TV screen, teleport the object to another point in the universe, and then transfer the momentum to the teleported object. Got it!
One minor inconsistency is that in the Portal universe, objects transition smoothly through portals and can stop halfway through. But that’s okay since we’re just making shit up anyway.
This is why an object that is moved through a portal has momentum, but an object that a portal is moved over does not, the two scenarios are not the same when you have a frame of reference that includes the space on the other side of the portal.
Circular argument. You’re using your preferred conclusion as evidence for your flawed reasoning.
They are the same if you ignore that space in your frame of reference, but then any conclusion you come to about things outside that frame of reference are invalid.
Velocity is a relative property between two objects. There’s no “I’m moving toward the portal, therefore I have momentum” versus “The portal is coming toward me, therefore I have no momentum”.
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?
If momentum is conserved then neither A or B is correct, the box should be an infinity thin sheet. If the portal is half way through the box if it maintains it’s thickness the box has to be moving at the speed of the portal out of it.
Except it’s not moving out of the portal, the portal is moving over the box. I get it when people say that it doesn’t matter if the portal is moving, or of the box is moving, and they are right, up to a point. As soon as you need to account for the movement on the other side of the portal, you have to include that space in your frame of reference, and relative to that space, the velocity of the box is 0.
As I explained here…
The best way to explain movement through portals is that momentum is only conserved from a perspective that encompasses all of the objects involved, this is true for regular physics as well actually.
Incorrect. The answer is A, and here is why.
GLaDOS specifically states “Momentum, a function of mass and velocity, is conserved between portals.” If scenario B was correct (which it is not) then if the portal was put on an object lighter than the box and then quickly moved over the box, the box would be launched at a speed equal to the speed of the lighter object, while it has more mass, this is not a conservation of momentum.
The best way to explain movement through portals is that momentum is only conserved from a perspective that encompasses all of the objects involved, this is true for regular physics as well actually. Consider this, what if the portal was shoved very quickly over the box down to it’s halfway point? The obvious answer is that the box would only appear halfway out of the other portal, but if you subscribe to the “logic” that leads to answer B, then the box is actually sucked up by the portal, while the actual logical and intuitive answer is that only half the box sticks out of the portal, and it stays where it was placed.
Portals aren’t objects, they don’t have mass, or even a velocity, they are a shortcut in space, and that was what GLaDOS was explaining when she said that momentum was conserved. Although B seems to initially make sense, it is not correct from a game lore perspective, nor from an actual physical perspective.
It’s not about whether portals have mass or not. It’s about the box’s velocity relative to the space on the other side of the portal. In the game, as you move toward a portal, you also move toward the objects on the other side of the portal. Therefore you have velocity relative to those objects, and that’s the momentum that is conserved as you pass through.
Well, the box’s velocity relative to the space on the other side of the portal is 0, so that is why it does not move.
That’s what this statement means.
This would suggest that portals in the game Portal are flat paintings, but it’s not. As you move around or toward the portal, your distance and angle to the objects on the other side of the portal move in your frame of reference. Therefore you have velocity relative to those objects. Not to the portal itself, not to the universe behind the portal as a point mass, but to the spatially separated objects on the other side of thr portal individually.
No, it doesn’t imply that portal are flat paintings at all.
Yes, but only technically so because those distances and angles change outside of the portal. Your path through the portals isn’t real, it’s a shortcut through space. This is why an object that is moved through a portal has momentum, but an object that a portal is moved over does not, the two scenarios are not the same when you have a frame of reference that includes the space on the other side of the portal. They are the same if you ignore that space in your frame of reference, but then any conclusion you come to about things outside that frame of reference are invalid.
Ah, so you’re saying Portals are not flat paintings, they’re flat TV screens which project a representation of the universe behind them like based on where the observer is. Upon impact with an object they then store the objects momentum relative to the TV screen, teleport the object to another point in the universe, and then transfer the momentum to the teleported object. Got it!
One minor inconsistency is that in the Portal universe, objects transition smoothly through portals and can stop halfway through. But that’s okay since we’re just making shit up anyway.
Circular argument. You’re using your preferred conclusion as evidence for your flawed reasoning.
Velocity is a relative property between two objects. There’s no “I’m moving toward the portal, therefore I have momentum” versus “The portal is coming toward me, therefore I have no momentum”.
Nope, they aren’t flat screens either. They are shortcuts in space. How many more times will I need to state this for you?
It’s okay, we can terminate this interaction here.
Agreed.
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?
If momentum is conserved then neither A or B is correct, the box should be an infinity thin sheet. If the portal is half way through the box if it maintains it’s thickness the box has to be moving at the speed of the portal out of it.
Except it’s not moving out of the portal, the portal is moving over the box. I get it when people say that it doesn’t matter if the portal is moving, or of the box is moving, and they are right, up to a point. As soon as you need to account for the movement on the other side of the portal, you have to include that space in your frame of reference, and relative to that space, the velocity of the box is 0.
As I explained here…
I must applaud your diligent rage baiting, well done