Another Portal Paradox

The video game Portal is a puzzle game built around a sci-fi device

that can create a portal connecting one place on the wall

or ceiling or floor to another,

and portals are great for cooking up paradoxes and apparent paradoxes!

I already made a video about a particularly popular paradox (& also about how

the portals might actually work from a physics perspective),

but oh boy are there more interesting portal paradoxes.

Ok, so objects entering one end of a portal with a certain speed leave

the other end with the same speed,

and if the portals aren’t oriented in the same direction,

then the object will exit in the new direction,

but the speed will be the same.

In my first portal paradox video,

I argued this should apply regardless of frame of reference,

so the orange portal moving towards a cube is the same

as a cube moving towards the orange portal -

that is,

both cause the cube to shoot out of the blue portal with the corresponding

relative speed.

Obviously portals are fictional and there's no correct answer,

but I think the cube shooting out of the blue portal makes the most

sense given the possible ways portals could work within the physics of our universe.

BUT there's another paradox hiding in the middle of this one - literally.

What would happen if the orange portal stopped halfway?

Does the cube stay put?

Does it tear itself in half?

Does it shoot out of the blue portal anyway,

"pulling" itself the rest of the way through?

Or something else?

I'll give you a second to pause

and decide what you think... again there's no correct answer:

portals are fictional and you can imagine them to work however you like.

But for physically realistic portals,

I think the best way to analyze the "portal stopping halfway paradox" is to

instead imagine there are two cubes attached by a rope

and the orange portal stops between the cubes.

In this case, the top cube will unequivocally shoot out of the blue portal

at full speed before yanking the rope taut

and pulling upwards on the bottom cube.

If the rope is weak then it'll break,

but if it's strong

[and if the cubes are the same mass]

then it'll accelerate the bottom cube

and slow down the top cube,

so the cubes will both shoot out of the blue portal,

but at half speed.

So if instead the orange portal stops halfway through a single cube,

then if the cube is super fragile it should tear in half,

but more likely it'll just shoot out of the blue portal with half the

speed.

If the portal stops a third of the way through,

the cube'll shoot out with 1/3 the speed.

Etc.

Paradox solved.

The next paradox is a bit more subtle:

what if you try to sandwich a cube between two portals?

Does the cube disappear?

Do the portals bounce or stop?

Or something else?

Again, I think a change of perspective is helpful - imagine instead

that you extend a piston through the blue portal.

Eventually it comes back and hits itself from behind.

The piston can't keep extending into the portal

because there is no "inside" of the portal - "inside" the blue portal is

"outside" the orange portal,

and vice versa: everything always exists outside the portals, and there's nowhere to hide.

At this point one of three things could happen.

If the piston is weak it should crumple,

the same as if it were pushing against a solid wall.

If the piston is rigid and the portals are super heavy,

then the piston will just stop expanding (since it can't lengthen any more without

the portals moving farther apart).

But the orange portal is clearly "pushing" the piston out of it to the

right,

so Newton's "equal and opposite" law of motion means the piston is pushing the

orange portal to the left - "kind of like what happens

when you throw a ball".

Similarly, the blue portal is somehow absorbing the momentum of the piston entering it,

and so should be pushed to the right - like what happens

when you catch a ball.

So if the portals aren't heavy (and aren't on super heavy objects),

then the logical (if weird) conclusion is that the portals themselves get pushed apart!

Newton's laws also apply to the paradox of sandwiching a cube:

the blue portal moving towards the cube causes the cube to emerge from the

orange portal like a piston,

until the cube hits itself.

At which point, if the cube is weak, it will crumple.

If it's strong, the portals will stop or even get pushed apart - aka,

they'll bounce!

I should say that neither of these paradoxes are my original ideas:

the sandwich portal paradox was sent to me by somebody who tried it out

in a sandbox version of the portal video game

and got some very trippy

(and non-physicsy) results/glitches,

and the "halfway through the cube" paradox was in fact posed to me by

the “portal physics & rendering” programmer on the team

that made Portal 1 & 2!

Apparently they thought about having moving portals in the game,

but ended up deciding not to.

Which is lucky for us,

because that means we don't actually know how moving portals "officially" work,

and we instead get to hypothesize

and debate and analyze portal paradoxes to our hearts' content.

Another thing you might want to debate is your favorite way to draw molecules

- do you prefer ball & stick?

structural formulas?

Skeletal?

Ribbon diagrams?

Space-filling?

Or maybe you're into the simplicity of a lewis dot diagram?

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of these molecular representations on Brilliant,

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Again, that's Brilliant.org/MinutePhysics -

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