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.
