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.
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.
Really, my argument boils down to what is stated about motion through portals, momentem is conserved. Momentum is only conserved within a fram of reference, two balls bouncing off of eachother in an isolated box make no change in the total momentum of the system… But as soon as you consider that the box is on a truck that is accelerating, then the total momentum for the box is not conserved from the perspective of something inside the box.
If you simplify the system to just the orange portal and the box, then from that perspective, it makes no difference if the box is moving, or if the portal is moving. As soon as you need to account for movement on the other side of the portal, then frame of reference has to include that space in your initial assessment of what is actually moving, otherwise you’re making predictions on a system that you haven’t fully accounted for. If you take away the portal, then the relative velocity between the box, and the area that would have been the exit of the portal, would be 0. Add back in your portal, and the wave it around randomly, and the relative velocity is still 0. Move the portal over the box, and the relative velocity is still zero, because as stated in the game, momentum is conserved for objects passing through the portal. It doesn’t matter how fast the portal is going, the relative movement stays the same, which in this case, is 0.
Ah, if that’s how you’ve been interpreting the explanation, I can see why we’ve been at an impasse. Portals as shown absolutely do seem to violate conservation of momentum in the more global sense.
You don’t even need a complicated set up to do it. Put a portal in empty space, rotate the plane of the exit 90 degrees, then send a box through at a simple constant speed. Assuming the universe isn’t compensating in other ways*, the total momentum of the universe will be different before and after the box went through, so there’s no environment encompassing the portal interactions that will satisfy the zero condition. Only each object’s local experience will keep the condition.
*I can think of a few options for this bit:
The entire universe somehow accelerates the opposite way in response, a fun idea, but it has no meaningful consequences.
Portals behave more like wormholes as scientifically defined. They have mass themselves and, if free-floating, move in reaction to mass sent through them in a way that preserves total momentum. This is enough to run with though. The games’ portals always have to be anchored to other mass. This leaves room for the idea that the portals actually do want to move in response to objects passing though them. They just transmit that force into the mass they’re anchored to, and that force propagating out is where the momentum conservation actually resolves.
Put a portal in empty space, rotate the plane of the exit 90 degrees, then send a box through at a simple constant speed. Assuming the universe isn’t compensating in other ways*, the total momentum of the universe will be different before and after the box went through, so there’s no environment encompassing the portal interactions that will satisfy the zero condition.
Pretty sure the momentum from the perspective of the box stays the same. The game doesn’t explicitly say that momentum for the entire system stays the same, just that "Momentum, a function of mass and velocity, is conserved between portals.” so rotating the exit of the portal in a different direction changes the momentum of the entire system (room, portals, box, etc…), but the box never actually experiences a change in momentum. Maybe a better way to put it, is that the absolute momentum of the box never changes when it passes through a portal.
Pretty sure the momentum from the perspective of the box stays the same.
How exactly are you defining monentum here? “The box sees the entire universe move at velocity V backwards both before and after passing through the portal.” This is probably at least approximately true, but total momentum of the universe minus the box would have to be exactly zero to make this technically correct. “The box never perceived a change in its own momentum.” This is 100% true.
The game doesn’t explicitly say that momentum for the entire system stays the same
Then why are we still talking about this? Lol. I thought that was one of the main points of your position.
the box never actually experiences a change in momentum
Correct, the box never experiences a change in momentum. The box exists in one inertial reference frame and, in going through the portal, is deposited into a different reference frame. Two inertial reference frames that differ in orientation are equally as distinct as two inertial reference frames that differ in velocity. The same logic applies to both.
Maybe a better way to put it, is that the absolute momentum of the box never changes when it passes through a portal.
You’re describing what I labeled as “inherent,” so I’ll take it.
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.
Really, my argument boils down to what is stated about motion through portals, momentem is conserved. Momentum is only conserved within a fram of reference, two balls bouncing off of eachother in an isolated box make no change in the total momentum of the system… But as soon as you consider that the box is on a truck that is accelerating, then the total momentum for the box is not conserved from the perspective of something inside the box.
If you simplify the system to just the orange portal and the box, then from that perspective, it makes no difference if the box is moving, or if the portal is moving. As soon as you need to account for movement on the other side of the portal, then frame of reference has to include that space in your initial assessment of what is actually moving, otherwise you’re making predictions on a system that you haven’t fully accounted for. If you take away the portal, then the relative velocity between the box, and the area that would have been the exit of the portal, would be 0. Add back in your portal, and the wave it around randomly, and the relative velocity is still 0. Move the portal over the box, and the relative velocity is still zero, because as stated in the game, momentum is conserved for objects passing through the portal. It doesn’t matter how fast the portal is going, the relative movement stays the same, which in this case, is 0.
Ah, if that’s how you’ve been interpreting the explanation, I can see why we’ve been at an impasse. Portals as shown absolutely do seem to violate conservation of momentum in the more global sense.
You don’t even need a complicated set up to do it. Put a portal in empty space, rotate the plane of the exit 90 degrees, then send a box through at a simple constant speed. Assuming the universe isn’t compensating in other ways*, the total momentum of the universe will be different before and after the box went through, so there’s no environment encompassing the portal interactions that will satisfy the zero condition. Only each object’s local experience will keep the condition.
*I can think of a few options for this bit:
The entire universe somehow accelerates the opposite way in response, a fun idea, but it has no meaningful consequences.
Portals behave more like wormholes as scientifically defined. They have mass themselves and, if free-floating, move in reaction to mass sent through them in a way that preserves total momentum. This is enough to run with though. The games’ portals always have to be anchored to other mass. This leaves room for the idea that the portals actually do want to move in response to objects passing though them. They just transmit that force into the mass they’re anchored to, and that force propagating out is where the momentum conservation actually resolves.
Pretty sure the momentum from the perspective of the box stays the same. The game doesn’t explicitly say that momentum for the entire system stays the same, just that "Momentum, a function of mass and velocity, is conserved between portals.” so rotating the exit of the portal in a different direction changes the momentum of the entire system (room, portals, box, etc…), but the box never actually experiences a change in momentum. Maybe a better way to put it, is that the absolute momentum of the box never changes when it passes through a portal.
How exactly are you defining monentum here? “The box sees the entire universe move at velocity V backwards both before and after passing through the portal.” This is probably at least approximately true, but total momentum of the universe minus the box would have to be exactly zero to make this technically correct. “The box never perceived a change in its own momentum.” This is 100% true.
Then why are we still talking about this? Lol. I thought that was one of the main points of your position.
Correct, the box never experiences a change in momentum. The box exists in one inertial reference frame and, in going through the portal, is deposited into a different reference frame. Two inertial reference frames that differ in orientation are equally as distinct as two inertial reference frames that differ in velocity. The same logic applies to both.
You’re describing what I labeled as “inherent,” so I’ll take it.