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 cube has uniform density].
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!
[But the solutions to the paradoxes are mine] 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?
Whatever your preference, you can learn all about the pros (& cons) of each of these molecular
representations on Brilliant, this video's sponsor, where we just launched a new and
very special course created by Ever Salazar, MinuteEarth illustrator and molecular representation
fanatic.
Can I just say, I've never seen such beautiful molecules, and you should definitely go check
them out.
Which you can!
You can sign up for Brilliant for free at Brilliant.org/minutephysics, and the first
200 people will get 20% off an annual Premium subscription with full access to all of Brilliant’s
courses and puzzles, including our molecule drawing course!
Again, that's Brilliant.org/MinutePhysics - and thanks to Brilliant for letting us take
over one of their courses.