Portals maintain velocity. Velocity is relative. Therefore the velocity they maintain is the relative velocity of the portal and the subject. Any other way and there would be no consistent way to pass any moment when passing through a portal.

The reason this is so confusing with different answers is that the portals don't really exist, so inherently whether you say a or b is gonna depend on assumptions. In game they aren't allowed to move so we have nothing to base it on to match game physics.

Here's my take, momentum is a product of velocity. Velocity needs a reference frame. Without it, there's no real difference in saying the portal has a velocity of 0 and the people tied up have a the velocity and therefore momentum, or the other way around. If we assume velocity with respect to the portal is what matters and is the momentum carried forward, then it should be B. If it's relative to the earth or tied up people, then A.

C, it combines the victim into a horrible overlapping monster of body parts

If I stick my arm in a stationary (relative to earth surface) portal, I expect my arm to stick out of the exit portal. If the exit portal is moving at 10m/s over the earth, I expect my arm to also be moving 10m/s over the earth. My arm is stationary relative to the portal, but the portal is moving.

If that portal is moving toward a standing person and I make a fist, I expect my fist to hit that person at 10m/s. I am stationary relative to the earth; they are stationary relative to the earth, but my fist is moving at 10m/s relative to the earth. From their perspective, I punched them. From my perspective, they ran into my fist.

If I look through the portal, I will see them approaching me at 10m/s. They will see me inside the portal, approaching them at 10m/s. When the portal passes around them, they will not feel any change in their velocity, they will just collide with me immediately after the portal passes around them. To them, the earth will seem to suddenly be moving at 10m/s.

All motion is relative. To understand how the people will move, we need to look at them relative to the portal. If the trolly is moving at 5 m/s relative to the ground, then the people are moving at 1 m/s relative to it. So they enter the portal moving at 1 m/s and exit at the same speed.

I think Portal solved this conundrum by saying portals can't move.

Energy is relative when there is a frame of reference.
When the tram-portal is the frame of reference, the person has the energy. And speedy thing goes in, speedy thing comes out.
Using Portals canon, the person cannot be the frame of reference (ie 0 energy), because the portal has to move for that scenario - which is Portal-ly impossible. So the person has to come flying out.
If you break Portals canon and say that portals can move, then then the person would likely be super-compacted (matter transporting on top of existing matter) into a singularity or just destroyed.

Frames of reference matter. Whether the train or the people moving happened it doesnt matter to the portal. There is net movement and the momentum is the mass of the person moving x the speed of the train.

Imagine the train was moving the speed of light. If the person exiting the other end of the portal wasnt coming out at the speed of light their body would come out like a soup. All the atoms in their body compressing to escape at some randomly low speed... actually it might make a tiny black hole on the other end as the atoms compress infinitely.

It's hard to overstate my satisfaction

Yes, but portals violate basic physics anyway.

A portal that faces downwards into another portal is effectively a perpetual motion machine. Drop a ferromagnetic object into the loop and wrap some wires around the loop, now you have an infinite electric generator.

It's all relative.

I would imagine that the relative motion between the entry/exit portal would be more important than the absolute motion of the two portals.

So if portals didn't have a distance maximum, assuming that they twist through some higher dimension or into an alternate universe and back or something like that, it would make sense that you could open a portal on Earth and on Mars and anything you push through that portal would maintain its velocity relative to Earth.

Which could result in some hilarious events where things basically detonate the instant they are pushed through as they are slammed into the surface of Mars at potentially ten of thousands of miles an hour depending on the Earths and Mars' relative velocities.

Despite that, there would also undoubtedly be times where their velocities synchronize due to their varying rotational locations and orbital velocities around the solar system, during which times you could conceivably quite easily step from Earth to Mars in a single go.

The safe thing to do though would be to decant from the Earth into a portal that is in orbit around Mars far enough away that at the worst you would experience some relatively gentle abrasion from the smattering of hydrogen atoms in the space surrounding Mars and then parachute down from orbit.

Why the /s?

It's true. Obviously it makes for simpler puzzle design plus was easier to ignore the full capability (even the version in 2 seems to just work enough to allow the set-piece), so it seems silly to use developer limitation as a gotcha.

But how would the objects get on the other side then? The receiving side isn't moving, so the objects essentially need to be pushed through the portal at the speed at which the train is moving, resulting in B. The only way A could work would be both portals moving at the same relative speed.

Here's how I always phase it. Imagine you have a shovel and you are using that shovel to flick some dog shit into your neighbours garden.

With no portal the shit hits the shovel and you flick it, transfering the speed of the shovel into the turds. You stop the shovel and the turds fly away.

Now imagine the shovel has a big rusty hole in it. So it's like a n shape. No portal yet. You go to flick the dog dumps but you just pass straight over them with the hole and the dumps go nowhere. The dumps have gained no momentum because nothing touched them and transferred that to them.

Now put a portal on the end of the shovel. As you sweep it over the cack has anything touched them? Has any object transferred it's momentum to the dog eggs? No, so the dumps just gently tumble out of the other side of the portal.

Speed, and by extension momentum, is relative. I'm sorry, but Einstein got you.

Except the momentum changes with portals most of the time anyway. Momentum is a vector, not just a scalar, meaning momentum has both a scalar and a direction component. And that direction component usually must be conserved as well. But portals change the direction of momentum all the time relative to the orientation of the entering and exiting portals. If the direction of the momentum of the object is relative to the orientation of the portal, then it makes as much sense that the scalar of the momentum would be relative to the velocity of the portal as well.

Energy is not conserved either, which is why the infinite falling box arrangement means the box keeps accelerating downwards gaining kinetic energy even though it started out with a much smaller, finite potential energy. Portals and conservation do not mix well.

As the people on the track are moving at an accelerated speed of 0 m/s, normally a train would apply the full force of the train moving to the meat bags human ethic problems on the tracks.

As newton's first law states F = m*a, or Force = Mass * acceleration

F = x * 0 = 0 N of force

thus, they could just plop out as if falling after having a chair removed.

It's two dimensional in the sense that the surface of the portal is a plane, through which things pass.

So as things pass through the portal, conservation of momentum is either preserved or it isn't, with respect to a constant observer. What happens as they partly enter the portal in both of these situations?

If momentum is preserved, and they have zero momentum going in to the portal, then they are motionless as they exit the portal. There is nothing to cause your hand to move out of the way for your arm. Scaled down to the atomic level, you become a paste.

So you say that your hand moves out of the way because it is connected to your arm. The fact that it moves out of the way fast enough to make room for your arm means that it has velocity, and therefore momentum. The momentum means that it (and you) would get launched into the air, but conservation of momentum was violated.

There is no scenario where you exit the portal motionless but intact.

I really think you didn't read my full comment, because I explained the problem with this exact scenario.

First, in your hoolahoop example both sides of the hoop are moving with the same velocity (this is essentially option 3 I described). But the entire thought experiment is "what if the two sides didn't move with the same velocity"

If you've played the game, you know that you don't instantly teleport when you touch the portal, you can be half in the portal. This means that when something enters the portal, it is deposited on the surface of the other portal. So as your arm enters the portal, your hand needs to move out of the way to make space for your arm.

If your hand doesn't move out of the way to make room for your arm (it is still because it has the same momentum that it had when it entered) then your arm will materialize in the same space as your hand. Now scale that down to the atomic level, if the atoms of your fingertips don't move for the next atoms, everything will be deposited in a 1 atom thick film.

If your hand does move out of the way fast enough to make room for your arm, then it is moving at the same speed that the train was moving. Your momentum from that speed would fling you into the air.

In no scenario do you just pop out intact but motionless.

Fuck, you just made me question the whole thing. Cave Johnson must be turning in his grave.

... fuck. You're absolutely right. All my theorems - flushed down the drain.

Think of a portal as a door, if someone brings an open door up to you (idk maybe it's on wheels or something) and you go through it, you don't suddenly fly through the frame.

Another violation is that they conserve speed, not velocity. Put 2 portals 90° apart. Travel into the first perpendicular to the surface. You'll exit the second perpendicular to its surface. That means you accelerated to change direction, which takes energy. Portals don't conserve momentum or energy.

No way, the portal displaces space meaning it just allows gravity to work unimpeded adding more kinetic energy to the object. The potential energy during a "falling cycle" is infinite but infinitely removed when the spacial disruption is broken.

Lets say the tennis racket has 2 portals. One in the front and one in the back. When you swing the racket, the front portal moves forwards with some speed V. The portal on the back is moving backwards with the same speed, so -V (same speed V, but in opposite direction). A stationary ball, suspended in mid-air would have 0 speed. The racket portal approaches the ball at speed V, so the ball has a relative speed V to the racket. The portal on the back has a speed of -V and ven you combine that with the ball's speed of V, we get -V+V=0. And so the ball stays put. The portals in the image are not both in motion. The front portal is approaching the people with a speed of V and so the relative speed of the people to the portal is V. The exit portal has a speed of 0, relative to the people. When the people go through the portal, their speed is 0+V=V, meaning they get launched out the exit portal with the same speed the entrance portal hit them.

Yeah but the momentum is relative to the portal.

If the blue exit portal was behind the wagon and so moving at the velocity of the orange entry portal, then I would agree that it's A because they move at the same velocity and in the same direction.

But since the blue exit portal is static and the orange one is moving, the people will enter the portal at a relative velocity to the portal which will be transferred to the blue one. Meaning B will occur.

If the portals were on two wagons going in the opposite directions at the same X velocity, then the people would enter at X relative velocity and exit at 2X velocity.

Right, in perspective of the initial orange portal the people are moving. They aren't at rest compared to the portal. The portal is at rest.

The energy would come from the trolley. The people would launch out at approximately the same speed as the trolley interacts with them and the trolley would slow down in response to how much kinetic energy was transferred to the people.

This guy is thinking with portals!

Then they can't enter at all and have to be flattened by the portal, because they must have motion too exit the other portal

Except the people aren't moving so aren't speedy

No momentum goes in, no momentum comes out

Think of it as a pole entering the portal, the end will have to exit at high speeds and so it will need to drag the rest of it out at that speed

They didn't do the math.

They just mentioned some of the formulas.

It's the difference between reading a book and knowing the book exists.

But, "speedy" relative to what? Relative to the walls of the room your are inside? What if you are in a falling elevator? Relative to the rotating surface of the earth? To the center of the solar system? "Relative to the portal" is the only answer to that question that makes sense.

But if we use coordinates relative to the orange hole, the whole world, including the rails and people on them, is moving, and the people are moving towards the hole with a speed of the train.

This can't apply because unlike the portals, both sides of the ring are moving at the same speed/direction.

Except there is no concept of "individual momentum," it's all relative to something. Not to mention, technically speaking, any specific reference point that isn't the blue portal will actually show it has infinite speed as it instantly moves from one spot to another. I think the most intuitive answer is to imaging standing in front of the blue portal, and look through it. From your perspective, the victims are being hurled at you, propelled by the ground. As soon as they go through the portal, no linger being in contact with the ground, they are effectively projectiles. By no means a hard proof, but this video has a compelling argument for that interpretation.

Except it is wrong

By that logic you have to account for the earths speed as it moves through the universe... That doesn't sound accurate.

Its just a hole though. If you have a tennis racket with no strings and swing it over something stationary the object doesnt move

There is one segment in Portal 2 where you need to cut some tubes that transport neurotoxin, and for that small segment only, the game allows moving portals. https://youtu.be/OrAHvenjZpA

if I take a hoop/window and place it quickly over an object

Then the velocity of the object relative to the "exit" of the hoop would be the same as the velocity of the object relative to the "entrance" of the hoop, which is option B.

In your analogy, option A would mean the object has a relative velocity of entering the hoop but suddenly no relative velocity exiting it, so the object magically starts following the hoop.

Yeah, but that's because both sides of the window are traveling at the same speed. If the blue portal was on the other end of the tram, they'd plop.

If you strap a camera to the window, it will appear as if the object launches from the camera's perspective.

Momentum is relative too, since it's equal to mass times velocity (in classical mechanics, of course)

Yes, if the speed you go in wouldn't the speed you go out, you'd be ripped apart.

In portal (the whole point of this joke), it happens instantly an works like walking through a door. If your hand is through, it's at the other side and the rest of your body isn't.

If you would travel at the same direction and speed of the train, you could step through and be stationary at the other side. If you stand still and the train travels to you, the only "logical" answer is that you fly out the other side or be ripped apart.

Like that episode of myth busters where they fired a canon backwards out of a moving vehicle

The train.

As the object enters the first portal then the inertia of the far end of the object that is forced to pass through will need to be accelerated in the space outside the second portal to pass through, acceleration which is induced by being pushed by the other end of the object still outside the first portal.

In other words, pushing a portal onto an object pushes that object with half the speed of the portal. This will likely require energy put into the portal itself to maintain it, which needs to come from the train.

The hole in space between the portals.

But it gains the momentum when it exits. It's moving at it exits the blue portal. Meaning it has momentum at the exit point.

It's probably dependent on the reference frame of the first portal, or the portal gun.

Games and real life are the same! Now if you'll excuse me I'm going to jump off a bridge then use an energy drink to heal my broken bones.

Then I could imagine a sport where you have a racquet with a portal on it, and you swipe at a suspended ball, with a target somewhere beyond the other portal.

Think of a portal like a doorway or just a frame of one. Stepping through it seamlessly puts you on the other side. If you were standing still, and the door went around you, would any force be exerted upon you, causing you to move? That's why I think it would be A. Nothing is applying any force to you, you're just basically teleporting. You may not even actually fully emerge from the portal, being trapped on the threshold, since no force is moving you beyond the point where the two ends meet.

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Not with that attitude!

Let's say the train moves at 100mph, therefore your body needs to exit the other portal at 100mph. Otherwise it would be compressed. What happens to the energy of this movement if you just stop on the other end?

So?

Holes don't transfer energy, speedy thing in, speedy thing out.

No, the speed of the pedestrians relative to the portal is not zero.

The whole thing would just be relative to the portal, though. Relative to the portal, they come in fast and out fast.

Not relative to the train. From the trains perspective, they are moving towards the train with the same speed they see the train moving.

There is no single correct reference frame. All reference frames are equally correct. If you want to argue that something is stationary, you have to explain what it is stationary relative to. There is no absolute "stationary".

The portal is a connection of two spaces, but the spaces themselves are not moving. It's hard to say though because some sort of force would have to push you into place, but momentum is conserved so... Who knows.

But the object doesn't enter at speed here it's stationary. If a hoop is thrown at an object and passes around the object the object is still stationary. The speed of the portal relative to the object does not impart movement on the object.

The quicker the portal moves the quicker the object appears on the other side but for the object to shoot out it means energy is being transfered from the car to the object.

If you're right then what happens If the two portals are moving at equal and opposite speeds?

If you jump into a portal, YOU have momentum, these people are stationary and therefore have no momentum, the answer is A.

Portals don't abide by physics, but people still do. Even in the infinite fall scenario there isn't infinite energy because the object accelerating is still subject to terminal velocity, and it's change in momentum comes from gravity. For the people to change their velocity, there has to be energy imparted onto them. My theory is that the train would have to slow.

If the ground disappears from under your feet at 60 miles per hour, the moment you start falling are you falling at 60 miles per hour?