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.
Bit of a gish gallop, but it looks like you are dropping the argument about relative movement not being real, so situation A becomes the only logical choice because the relative movement of the cube to the other side of the portal is the same, regardless of how fast the portal is moving.
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).
Except it’s not moving, it has the appearance of movement, but the actual velocity of the box is 0 m/s. If the box suddenly gained the velocity of the portal, then momentum is no longer conserved, which is directly in contradiction to how the game explains movement through portals.
GLaDOS specifically states “Momentum, a function of mass and velocity, is conserved between portals.”
it looks like you are dropping the argument about relative movement not being real
I’ll chalk that up to me not being as clear as I should have been from the start. Please consider my position to have always been the last point: Motion relative to other objects = convention not directly based on something real but usually useful due to building on things almost always true. Motion relative to local spacetime = the actual real thing on which everything else builds. So…
GLaDOS specifically states “Momentum, a function of mass and velocity, is conserved between portals.”
I’m not disagreeing with this. To break it down further though, mass is just an inherent property of an object, and its velocity is fundamentally expressed in the object’s relation to local spacetime.
Except it’s not moving, it has the appearance of movement, but the actual velocity of the box is 0 m/s.
Declaring an “actual velocity” sounds more like an argument against relativity (again for clarity, the fundamental spacetime geometry based relativity I was never intending to call into dispute). The critical detail you skipped over is that the 1 m/s velocity is seen in the inertial reference frame in which the portal is at rest.
Since this has started retreading the same points, I’ll just go ahead and jump to where I think our understandings actually diverge, how portals relate to spacetime.
Your argument seems to boil down to: The box starts at 0 m/s in its local spacetime, and the portal is a simple hole on top of reality with no power to change this, so the box must end at 0 m/s in the same local spacetime.
My argument boils down to: Portals can momentarily link different inertial reference frames within spacetime together, so the box can seamlessly transition between the two resulting in an apparent momentum change while the actual inherent momentum doesn’t change.
It’s worth adding that static portals already do the same thing. Momentum and velocity have a direction component, not just speed. When an object enters a portal going one direction and comes out in another direction as measured against the wider environment, that’s also an apparent momentum change.
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.
Bit of a gish gallop, but it looks like you are dropping the argument about relative movement not being real, so situation A becomes the only logical choice because the relative movement of the cube to the other side of the portal is the same, regardless of how fast the portal is moving.
Except it’s not moving, it has the appearance of movement, but the actual velocity of the box is 0 m/s. If the box suddenly gained the velocity of the portal, then momentum is no longer conserved, which is directly in contradiction to how the game explains movement through portals.
I’ll chalk that up to me not being as clear as I should have been from the start. Please consider my position to have always been the last point: Motion relative to other objects = convention not directly based on something real but usually useful due to building on things almost always true. Motion relative to local spacetime = the actual real thing on which everything else builds. So…
I’m not disagreeing with this. To break it down further though, mass is just an inherent property of an object, and its velocity is fundamentally expressed in the object’s relation to local spacetime.
Declaring an “actual velocity” sounds more like an argument against relativity (again for clarity, the fundamental spacetime geometry based relativity I was never intending to call into dispute). The critical detail you skipped over is that the 1 m/s velocity is seen in the inertial reference frame in which the portal is at rest.
Since this has started retreading the same points, I’ll just go ahead and jump to where I think our understandings actually diverge, how portals relate to spacetime.
Your argument seems to boil down to: The box starts at 0 m/s in its local spacetime, and the portal is a simple hole on top of reality with no power to change this, so the box must end at 0 m/s in the same local spacetime.
My argument boils down to: Portals can momentarily link different inertial reference frames within spacetime together, so the box can seamlessly transition between the two resulting in an apparent momentum change while the actual inherent momentum doesn’t change.
It’s worth adding that static portals already do the same thing. Momentum and velocity have a direction component, not just speed. When an object enters a portal going one direction and comes out in another direction as measured against the wider environment, that’s also an apparent momentum change.