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Why do portals create pocket dimension when you put a small portal into a bigger portal? — Transcript

by optozorax · 3,423 words · 389 segments · language en · Watch on YouTube

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0:00We already know what happens if you put a portal's exit into its entrance —
0:04it comes out of itself and hits the edge.
0:07But what if you make it small enough, so it fits?
0:10You've asked me this countless times, and I was curious myself.
0:14But it broke in my program, and I had no idea how to solve it.
0:18Until NOW. I finally have the solution.
0:21Let's check it out.
0:22Look at this tiny portal.
0:23It's moving forward, forward, and it emerges somewhere.
0:27Let's revolve around.
0:29Wait. Where did it go?
0:31The portal created a pocket dimension?
0:33Yes. And this is the correct answer,
0:35which we will explore in detail in this video.
0:38The key to all of this is one overlooked portal axiom
0:41that not only explains this result, but also unlocks amazing new possibilities
0:46for other portals and completely flips our understanding of portal physics.
0:51You are on the Optozorax channel. My name is Ilya.
0:53Let's get started.
0:55Let's take two portals.
0:57They can teleport an object.
0:59If we turn off light teleportation, then we can see the teleporting surface.
1:03When crossing this surface,
1:05an object or light teleports to the other portal.
1:07That's exactly how it works in my program: when a light ray hits this surface,
1:12it jumps to another location and keeps going.
1:15In one of my previous videos, I showed an axiom that says
1:18"a portal's behavior doesn't depend on the shape of its surface".
1:22So we can make it hemispherical and nothing really changes.
1:26Let's dive into how this works.
1:29First, let's look at how a light ray behaves
1:31with different surfaces.
1:33A light ray that starts here
1:34and going in this direction does not change at all.
1:37But if we make the shape hemispherical,
1:40the light ray first teleports to the orange portal,
1:43then back to the blue one,
1:45and ends up in exactly the same spot as with the flat surface.
1:49This explains why changing its shape does not affect how portal looks.
1:54Object teleportation works the same way.
1:57But look, with a flat surface, the back part is flat,
2:01but with the other surface it looks completely different.
2:04That does not really match our axiom.
2:06To solve this problem, we can turn the back surface into a portal too.
2:11It turns out, this axiom only works for two-sided portals,
2:14which we have not explored before.
2:17By the way, notice that at some point, the object does not actually teleport,
2:21but it looks like it did,
2:23as if the teleporting surface is drawn around it.
2:26What if we do the same with the portal?
2:29Let's take an ellipsoidal portal with a similar surface and place it
2:33inside itself as far as it can go.
2:36And here is how it looks with light teleportation.
2:39Now it looks like the orange part teleports the blue part.
2:43Although this doesn't actually happen.
2:45Remember how I used to do this before?
2:48I created multiple degrees of teleportation
2:51and filtered them in a special way.
2:54So I could have skipped all that work and just made such teleporting surface
2:58to get the same result?!
2:59Well, it turns out, these approaches are equivalent.
3:03So the next logical step is to take a small portal
3:06with a hemispherical surface and simply place it in the orange part.
3:11And that's the entire solution.
3:13Inside, we get a pocket dimension.
3:16Later in the video, we will discover if it can be moved indefinitely,
3:20figure out how infinite space emerges and conduct many experiments.
3:24But first, I want to tell you how I came to this discovery.
3:28After publishing my previous videos,
3:30I thought I'd shown absolutely everything possible
3:33and there was nothing left to discover about portals.
3:37Scrolling through Twitter, I found this message:
3:39"You can actually put a portal INSIDE itself
3:42fully by using the half-sphere portals."
3:44I thought, "Hmm, nothing interesting.
3:47The guy just moved a portal.
3:49Of course, a small hemisphere will fit in a large one."
3:52But hemispherical portals work exactly the same as flat ones, so
3:57he placed a flat portal inside itself???
4:00I was flabbergasted.
4:02This discovery is what led me to quit my job
4:05and focus on YouTube to make this video.
4:08And this guy deserves credit — he did this using a scene editor to get this result.
4:13Before that, I had tried
4:15to solve the small portal problem in a million ways,
4:18analyzed all possible matrices, tried different calculation methods,
4:23but nothing worked and I eventually gave up.
4:26But let's figure out why exactly this axiom is true —
4:30beyond the fact that it just looks right.
4:32There are two types of portals: scanner-printer and spatial.
4:37A scanner-printer portal scans and destroys an object on one side
4:41and recreates it on the other.
4:43This would need tons of energy,
4:45and this kind of portal could theoretically exist in our world.
4:50But it disobeys our axiom because it has only one active surface,
4:54and its shape affects its behavior.
4:57Later in the video, I'll propose an experiment to measure this surface.
5:02Now about the spatial portal.
5:05I borrowed this clip from the video "The Shape of Space",
5:08which I highly recommend.
5:10It shows how a torus unfolds into a flat sheet of space.
5:14A torus has such a structure that in the flat version,
5:18the right side leads to the left and the top leads to bottom.
5:22You could say this works just like portals.
5:25And these portals create this shape in the form of a torus.
5:29So what would the shape of a space look like for our portals?
5:34To show this, I wrote an entirely new program
5:37capable of simulating this curvature of space.
5:40For example, this is how a flat torus looks in it.
5:44We see that the blue square teleports between top and bottom,
5:47while the green square teleports between the right and left edges.
5:51My program glues left to right and top to bottom.
5:55Then it runs a simulation to which shape this will lead to.
5:59It moves in a funny way and converges to a torus.
6:02With this torus, both squares end up continuous.
6:06Next, let's take this scene on a plane.
6:09Here we have a two-sided portal.
6:11The blue square teleports and moves in a circle,
6:14while the green one simply teleports.
6:16In the simulation, this part of the portal is glued to another part.
6:20I start the simulation and it converges to this shape.
6:24As we can see, the green square doesn't appear to teleport at all.
6:28And if we rotate the view, we can see a cylindrical surface in the back,
6:32and the blue square moves in a circle within it.
6:35And when viewed from this angle,
6:37it resembles a visual representation of a wormhole.
6:41Now let's examine a portal with a different teleporting surface.
6:45Similarly, this surface in one place is glued to this surface in another place.
6:50We start the simulation, and it converges to exactly the same shape.
6:55You could say that portals in this configuration inherently define
6:58this shape, and the teleporting surface is simply our choice
7:03of how we cut through that shape to represent space in a flat way.
7:07This means the teleporting surface is a virtual entity —
7:11something we use for our convenience.
7:14And that's exactly what justifies the axiom introduced in this video.
7:19From here, we can derive many interesting things.
7:22For example, a doorway and a portal represent the same local space.
7:27Furthermore, we could say that a portal doesn't just have one teleporting surface,
7:32but that all possible surfaces exist simultaneously,
7:35and at the same time none of them truly exist.
7:40Also, for a spatial portal, there is no such thing
7:43as "before teleportation" and "after teleportation."
7:47Now let me clarify
7:48that I am using hemispherical portals only because they are easier to program.
7:54In reality, the surface can be anything: flat, hemispherical, zigzagging.
8:00It can even intersect itself.
8:02The only constraint is that the one part must not intersect the other,
8:06as shown here.
8:08But, actually,
8:09even a broken surface like this can be fixed.
8:12We just need to teleport this piece to the orange portal.
8:16However, I avoid doing that
8:18because those are the same calculations as degrees of teleportation,
8:23and they are not easy to implement.
8:25This is just a quick tour of my new space curvature simulation program.
8:30I haven't explained how it works,
8:32why there are holes here,
8:35what the Nash embedding theorem has to do with this, and much more.
8:39In the future, I'd also like to simulate the curvature of space for a portal
8:43inside another portal or for a moving portal.
8:47But all of this will take a lot of time and effort.
8:50Let me know if you want a dedicated video about that.
8:54Now for the experiments.
8:56Let's see how an object passes through such a portal.
8:59Without light teleportation enabled, nothing unusual happens.
9:02The object simply gets bigger.
9:05But when light teleportation is on, we see multiple copies of the object.
9:09It is important to understand that these are only reflections.
9:13There is always just one object. You can't physically duplicate it.
9:17You can even rotate the view inside the portal and look at
9:20all these reflected copies.
9:22This leads us to the next question:
9:24how does infinite space appear inside the portal,
9:27and why is it so dark in there?
9:30I created a new feature for the camera.
9:32Now it can teleport through portal.
9:34To demonstrate this, we rotate inside a portal-within-a-portal scene.
9:39Here is how it looks with light teleportation,
9:43and here it is with both modes enabled.
9:46Each time we teleport, we see only two hemispheres.
9:49But because the portals work so seamlessly,
9:52we don't notice the transition.
9:54This is how infinite space is formed:
9:56with each teleportation, you become smaller and smaller,
9:59which means you can fit infinite space inside a finite volume.
10:05By the way, I want to emphasize
10:07that pocket dimension technically exist right here, between the two portals.
10:12Nothing actually separate from the universe is created.
10:15It just appears that way.
10:17So why is it so dark in there?
10:20Because many light rays get stuck in teleportation loops.
10:23We can demonstrate this by flying in this direction.
10:26Let's turn on the dual-mode display.
10:28As we fly, we see constant teleportation, but no visible exit.
10:33In my program, when a light ray gets trapped and teleports endlessly,
10:37it's rendered as black.
10:40Now, let's take a look at another scene.
10:42Here, the two portals are facing each other,
10:45and the small one enters the larger one head-on.
10:47This resembles that GIF where two portals move toward each other,
10:52or that video you've probably seen.
10:54With flat portals, this would be an unsolvable situation.
10:58But now we can place this small portal inside.
11:01We fly through it and turn around, and we see
11:04a pyramid of all degrees of teleportation stretching in both directions infinitely.
11:09It's still just one portal,
11:11but the space is folded in such a way that we perceive multiple copies.
11:15Just like with the object, there is only one instance.
11:19And can we move this portal forward infinitely?
11:22Let's take this shape and move it.
11:24As soon as it touches its own surface, everything breaks.
11:27One part of the surface begins to intersect the other.
11:30But since the portal is smaller,
11:32we can keep increasing the length of its surface indefinitely,
11:36allowing it to move farther and farther without intersecting anything.
11:40So, yes, the portal can move forward forever.
11:43And this is what it would look like.
11:45Just make sure not to drop anything in such a portal
11:48or it will be lost forever.
11:50For infinite movement in other scenes like this one,
11:53we need to change the shape of the surface in a smarter way.
11:56But it's generally possible.
11:58This is the main limitation of this surface shape approach.
12:02The surfaces must not intersect, otherwise the image breaks and becomes nonsensical.
12:08It turns out we can't come up with a single portal surface
12:11that will work in all cases.
12:13For each individual case, we need a new surface shape.
12:16For example, let's recall these ellipsoidal portals.
12:20Here, the hemispherical surface has reached its limit.
12:23It touches the boundary.
12:25We can't enlarge it anymore.
12:27But with light teleportation,
12:28we see that the portal hasn't fully entered the other portal.
12:32My flat portals with degrees of teleportation
12:35worked perfectly in such situation.
12:37So we need to devise
12:39a new, more complex surface shape for the portal to fully enter here.
12:43Or we need to somehow combine these two approaches into one,
12:47so that it can solve all possible problems.
12:50I've already found a solution, and it's very unusual.
12:54But more on that in the next video.
12:56Also, in the next video,
12:58I'll show whether it's possible to put a normal sized portal inside itself.
13:03So be sure to subscribe, so you don't miss it.
13:06Another reason why this is an incredible discovery
13:10is that this idea can even be generalized to the triple portal,
13:13which I showed in this video.
13:15The regular triple portal is one-sided because it has this closed back surface.
13:21And to make it two sided, you need to add another portal to each part,
13:25so that each part looks like the letter Y.
13:28Now our axiom works for this portal.
13:31This means we can create a non-flat teleportation shape like this,
13:35using a third of a sphere. It's quite non-trivial shape,
13:38but it works exactly the same as ordinary triple portals.
13:43And since we have such a shape, now we can place two portals into another one.
13:47Let's say like this.
13:49Let's get closer, turn on light teleportation,
13:52and we can revolve inside just like we did for other portals.
13:56Here we get such a beautiful and complex fractal,
13:59because the triple portal connects space in a more complex way.
14:04And the same can be done with a cylindrical portal.
14:07Here you can inflate the surface like this,
14:09and the portal will work exactly the same way.
14:12Now, let's shrink one part and place it in the center.
14:16Next, let's fly in.
14:17We see that there is an infinite black space again,
14:21and the portals are arranged in the shape of an hourglass.
14:25Let's turn off light teleportation and inflate the surface again,
14:29so that the portal can move beyond the flat boundaries.
14:33And now the same movement, but with light teleportation turned on.
14:37And from this position, you can rotate this portal.
14:41This new approach is perfect for creating mesmerizing animations.
14:47Or you can rotate it another way.
14:50It's interesting how the angular velocity of rotation
14:53increases to infinity as the size decreases.
14:57Now about the physics.
14:59Let me clarify that I'll be using the terms
15:02"before teleportation" and "after teleportation"
15:05because it's easier to program and reason about
15:07different surfaces. And it's easier to understand
15:10what leads to contradictions and what doesn't.
15:13We need to remember that no place
15:15before or after teleportation exists anymore.
15:19Let's take this scene,
15:21which we've already discussed in one of my previous videos.
15:24There is no gravity or air resistance here.
15:28The portal moves uniformly and in a straight line by inertia.
15:33It has no acceleration and it does not stop anywhere.
15:37Before teleportation,
15:38the object is stationary and it moves after teleportation.
15:42People don't like that the object somehow gains momentum in this scene.
15:47After all, portals work like doorways.
15:50And when a doorway runs into you, nothing happens.
15:53Yes, because in a doorway, the entrance and exit
15:56move at the same speed relative to each other.
15:59But in this case, they move at different speeds.
16:02People probably assume that the portal should behave something like this,
16:07when the object stops immediately after teleportation
16:10to avoid gaining any momentum.
16:13We remember that this can't be the case
16:15because there is no moment after teleportation.
16:19But let's try to follow this logic.
16:21I think everyone agrees that the object should be
16:24stationary BEFORE teleportation right here.
16:28So here is the big brain move —
16:29what if I make a teleporting surface like this?
16:32Here, the object NEVER teleports,
16:34and it's always stationary, but it looks as if it teleported and gained momentum.
16:40As we remember, any law of portals must work the same for all surfaces.
16:45So for this scene, the only working option is the movement after teleportation.
16:50This kind of stopping can only work for one flat surface.
16:55But movement after the teleportation works for any surface.
16:59But this is only if we accept this axiom,
17:02which gives such incredible results as pocket dimension.
17:06Let's continue.
17:07In this scene, the portal moves in a circle instead of a straight line —
17:12which means it is constantly accelerating and changing direction of its speed.
17:16Let's add an object here.
17:18And now the question is:
17:19how will the object move after teleportation?
17:22The first option — it will move in a straight line.
17:26Look, before teleportation, it moved in a circle.
17:29This is the gray trajectory.
17:31And after teleportation,
17:32it started moving in a straight line by inertia and acquired rotation.
17:37This fits a scanner-printer portal,
17:40which have a specific surface that exerted force on the exiting object.
17:44So now it moves according to the normal laws of physics.
17:48And this is a way to measure the surface of a scanner-printer portal
17:51when we can't see it.
17:53In the same situation, we launch multiple objects before teleportation.
17:57They move in a circle, and then they start moving in a straight line.
18:02If the surface were different,
18:03for example, hemispherical, the objects would start moving
18:07in a straight line at a different moment in time.
18:10And by using this, we could calculate this surface.
18:13The second solution to this problem — the object continues to move in a circle.
18:17This fits perfectly for spatial portals.
18:20And that's because we can design such a surface
18:23where the object never teleported, but it looks like it's moving in a circle.
18:28This is even better seen if you stand in the object's position.
18:32So what does this mean?
18:33It looks like action at a distance that applies to everything
18:37that passes through portals.
18:38If you entered a portal and it started moving differently,
18:42then this will affect you from any distance.
18:45This is absurd!
18:46This is a very, very bad result and a real reason to doubt our axiom!
18:51Or something else needs to be rethought.
18:55And now my favorite picture.
18:57If you don't know it, pause and decide what you choose.
19:01I've always been for option B
19:03where the object flies out of the portal with some speed.
19:07And I never understood supporters of option A,
19:10where the object stops immediately after teleportation and slides down.
19:15But now I understand that there is more than meets the eye.
19:19This picture is essentially a combination of the two previous scenes.
19:23First, the portal moves without any acceleration
19:26at a constant speed, and then it stops.
19:29And this stopping moment is what I've been ignoring all this time.
19:33After all, this is accelerated movement,
19:36which gave us an absurd in the previous scene.
19:39Now, what if we make a hemispherical teleporting surface for the portal?
19:43When the portal stops, it never teleported anything
19:46and the object was always in its original place.
19:49So then option B is correct for a flat surface
19:52and the option A is correct for hemispherical surface.
19:56And which one to choose?
19:57I don't have an answer, but I have something better.
20:01Direction to an answer.
20:02Portal gravitational waves.
20:04I think that an accelerating portal should emit something like gravitational waves
20:09that propagate at the speed of light and affect objects.
20:13Thus, we can avoid action at a distance.
20:15It seems that when stopping,
20:17the gravitational wave should somehow slow down the object,
20:21and the final answer should be something in between A and B.
20:24But to research this, one needs to know the theory of relativity and its math.
20:29But I am not familiar with this.
20:32So, my friends, I will leave the physics to you
20:35while I responsible for the geometry.
20:37But, again, this is just an idea.
20:40Maybe I'm wrong, and everything should work differently.
20:43As always, you can try out everything that I showed here in my web demo.
20:49And now there is another one too.
20:52For the next video, most of the work is already done.
20:55It will be coming soon.
20:57By the way, now I have a Discord server where you can chat about portals.
21:03And thanks for watching.

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