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?
Sorry. Lol. I used some shorthand I didn’t think I’d need to defend based on earlier statements, but for clarity:
Movement relative to other objects is in itself not a real thing.
Movement relative to local spacetime geometry is always real.
Spacetime geometry is usually continuous.
The usual continuity of spacetime allows for the convention of defining movement relative to other objects with the underlying connecting spacetime element left unstated.
Breaking any underlying assumptions about spacetime continuity also breaks the convention, but the convention is still valid across spaces where the underlying assumptions are not broken.
Expanding out my last statement:
The box is initially moving 0 m/s in the inertial reference frame we defined to be at rest.
The portion of the box that has not yet crossed the portal boundary is moving 1 m/s in the inertial reference frame the entry portal is currently at rest in (valid due to the continuity in spacetime across the measurement between them).
The portion of the box that has already crossed the portal boundary is moving 1 m/s in the inertial reference frame the exit portal is currently at rest in (valid due to the continuity in spacetime across the measurement between them).
There are additional possible declarations to make if the portal boundary is a non-zero volume instead of a plane of instantaneous transition, but the games’ interpretation of portals constrains that to either be zero or close enough to zero to not matter for the end result. Let me know if you want me to expand on that too.
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.
Alright. Cube is moving at 0 m/s (or at rest) and the portal moves over the cube. How fast is the cube moving?
0 m/s relative to the chosen inertial reference frame, 1 m/s relative to the portal entry, and 1 m/s relative to the portal exit.
Woah woah woah woah. I thought relative movements were not real. We’re talking in terms your worldlines here.
This was you BTW…
So please, I ask again, how fast is the box moving when the portal is passed over it at 1 m/s?
Sorry. Lol. I used some shorthand I didn’t think I’d need to defend based on earlier statements, but for clarity:
Movement relative to other objects is in itself not a real thing.
Movement relative to local spacetime geometry is always real.
Spacetime geometry is usually continuous.
The usual continuity of spacetime allows for the convention of defining movement relative to other objects with the underlying connecting spacetime element left unstated.
Breaking any underlying assumptions about spacetime continuity also breaks the convention, but the convention is still valid across spaces where the underlying assumptions are not broken.
Expanding out my last statement:
The box is initially moving 0 m/s in the inertial reference frame we defined to be at rest.
The portion of the box that has not yet crossed the portal boundary is moving 1 m/s in the inertial reference frame the entry portal is currently at rest in (valid due to the continuity in spacetime across the measurement between them).
The portion of the box that has already crossed the portal boundary is moving 1 m/s in the inertial reference frame the exit portal is currently at rest in (valid due to the continuity in spacetime across the measurement between them).
There are additional possible declarations to make if the portal boundary is a non-zero volume instead of a plane of instantaneous transition, but the games’ interpretation of portals constrains that to either be zero or close enough to zero to not matter for the end result. Let me know if you want me to expand on that too.