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Another Portal Paradox
Another Portal Paradox
minutephysics
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4:57 · Aug 4, 2022
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The
video
game
Portal
is
a
puzzle
game
built
around
a
sci-fi
device
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0:01
The video game Portal is a puzzle game built around a sci-fi device
0:04
that can create a portal connecting one place on the wall
0:06
or ceiling or floor to another,
0:08
and portals are great for cooking up paradoxes and apparent paradoxes!
0:11
I already made a video about a particularly popular paradox (& also about how
0:14
the portals might actually work from a physics perspective),
0:17
but oh boy are there more interesting portal paradoxes.
0:20
Ok, so objects entering one end of a portal with a certain speed leave
0:23
the other end with the same speed,
0:25
and if the portals aren’t oriented in the same direction,
0:27
then the object will exit in the new direction,
0:29
but the speed will be the same.
0:31
In my first portal paradox video,
0:33
I argued this should apply regardless of frame of reference,
0:35
so the orange portal moving towards a cube is the same
0:38
as a cube moving towards the orange portal -
0:40
that is,
0:40
both cause the cube to shoot out of the blue portal with the corresponding
0:44
relative speed.
0:45
Obviously portals are fictional and there's no correct answer,
0:48
but I think the cube shooting out of the blue portal makes the most
0:50
sense given the possible ways portals could work within the physics of our universe.
0:54
BUT there's another paradox hiding in the middle of this one - literally.
0:58
What would happen if the orange portal stopped halfway?
1:01
Does the cube stay put?
1:02
Does it tear itself in half?
1:04
Does it shoot out of the blue portal anyway,
1:06
"pulling" itself the rest of the way through?
1:08
Or something else?
1:09
I'll give you a second to pause
1:11
and decide what you think... again there's no correct answer:
1:14
portals are fictional and you can imagine them to work however you like.
1:18
But for physically realistic portals,
1:20
I think the best way to analyze the "portal stopping halfway paradox" is to
1:24
instead imagine there are two cubes attached by a rope
1:27
and the orange portal stops between the cubes.
1:29
In this case, the top cube will unequivocally shoot out of the blue portal
1:32
at full speed before yanking the rope taut
1:34
and pulling upwards on the bottom cube.
1:36
If the rope is weak then it'll break,
1:38
but if it's strong
1:39
[and if the cubes are the same mass]
1:40
then it'll accelerate the bottom cube
1:41
and slow down the top cube,
1:42
so the cubes will both shoot out of the blue portal,
1:44
but at half speed.
1:46
So if instead the orange portal stops halfway through a single cube,
1:49
then if the cube is super fragile it should tear in half,
1:52
but more likely it'll just shoot out of the blue portal with half the
1:54
speed.
1:55
If the portal stops a third of the way through,
1:57
the cube'll shoot out with 1/3 the speed.
1:59
Etc.
2:00
Paradox solved.
2:01
The next paradox is a bit more subtle:
2:04
what if you try to sandwich a cube between two portals?
2:07
Does the cube disappear?
2:09
Do the portals bounce or stop?
2:11
Or something else?
2:12
Again, I think a change of perspective is helpful - imagine instead
2:16
that you extend a piston through the blue portal.
2:18
Eventually it comes back and hits itself from behind.
2:20
The piston can't keep extending into the portal
2:22
because there is no "inside" of the portal - "inside" the blue portal is
2:26
"outside" the orange portal,
2:27
and vice versa: everything always exists outside the portals, and there's nowhere to hide.
2:32
At this point one of three things could happen.
2:35
If the piston is weak it should crumple,
2:37
the same as if it were pushing against a solid wall.
2:39
If the piston is rigid and the portals are super heavy,
2:42
then the piston will just stop expanding (since it can't lengthen any more without
2:44
the portals moving farther apart).
2:44
But the orange portal is clearly "pushing" the piston out of it to the
2:47
right,
2:47
so Newton's "equal and opposite" law of motion means the piston is pushing the
2:49
orange portal to the left - "kind of like what happens
2:49
when you throw a ball".
2:49
Similarly, the blue portal is somehow absorbing the momentum of the piston entering it,
2:50
and so should be pushed to the right - like what happens
2:50
when you catch a ball.
2:50
So if the portals aren't heavy (and aren't on super heavy objects),
2:51
then the logical (if weird) conclusion is that the portals themselves get pushed apart!
2:51
Newton's laws also apply to the paradox of sandwiching a cube:
2:53
the blue portal moving towards the cube causes the cube to emerge from the
2:54
orange portal like a piston,
2:55
until the cube hits itself.
2:55
At which point, if the cube is weak, it will crumple.
2:55
If it's strong, the portals will stop or even get pushed apart - aka,
2:55
they'll bounce!
2:55
I should say that neither of these paradoxes are my original ideas:
2:55
the sandwich portal paradox was sent to me by somebody who tried it out
2:55
in a sandbox version of the portal video game
2:55
and got some very trippy
2:55
(and non-physicsy) results/glitches,
2:55
and the "halfway through the cube" paradox was in fact posed to me by
2:55
the “portal physics & rendering” programmer on the team
2:55
that made Portal 1 & 2!
2:55
Apparently they thought about having moving portals in the game,
2:55
but ended up deciding not to.
2:55
Which is lucky for us,
2:55
because that means we don't actually know how moving portals "officially" work,
2:55
and we instead get to hypothesize
2:55
and debate and analyze portal paradoxes to our hearts' content.
2:55
Another thing you might want to debate is your favorite way to draw molecules
2:56
- do you prefer ball & stick?
2:57
structural formulas?
2:57
Skeletal?
2:57
Ribbon diagrams?
2:57
Space-filling?
2:57
Or maybe you're into the simplicity of a lewis dot diagram?
2:58
Whatever your preference, you can learn all about the pros (& cons) of each
2:58
of these molecular representations on Brilliant,
2:58
this video's sponsor, where we just launched a new
2:58
and very special course created by Ever Salazar,
2:58
MinuteEarth illustrator and molecular representation fanatic.
2:58
Can I just say, I've never seen such beautiful molecules,
2:58
and you should definitely go check them out.
2:58
Which you can!
2:58
You can sign up for Brilliant for free at Brilliant.org/minutephysics,
2:58
and the first 200 people will get 20% off an annual Premium subscription with
2:58
full access to all of Brilliant’s courses
2:58
and puzzles,
2:58
including our molecule drawing course!
2:58
Again, that's Brilliant.org/MinutePhysics -
2:58
and thanks to Brilliant for letting us take over one of their courses.
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