I'm blown away by how you manage to go from a seemingly impossible problem to understanding it intuitively, mathematically and computationally in 20 minutes. Just amazing.
I love how you start with the example of a door. You are absolutely correct, it is a portal. The sign of a good teacher is being able to immediately connect their students to a familiar concepts. You, sir, are very good at this indeed. I wish you the best and am happy to be here under 1k subs
I was like "ayyy i have seen this video before!" but then i saw the date of creation and thought "wait... so i haven't seen this vi-" but before i could even finish the sentence, i looked and stared at the sub count and my mind completely filled up with "UNDERRATED, UNDERRAT-"
The analytical approach works for rasterization too, just make a shader that sets the transparency to 1 on the backside of the portal. This is how it actually works in-game.
I love this and hope you get the attention you deserve. This is a great example of how most people hear that something is impossible and then leave it. You have such a clear and intuitive explanation that I think most people quickly gave up looking for.
This is an absolutely fantastic video, HELLA underrated. I was completely captured by this demonstration the entire way through, and then I look down and see only 6.6k views, and 364 subs (365 now). This was an incredibly easy to follow explanation of the portal-in-portal paradox, 10/10
Thinking portals as just one doorway split in half is a very good way of explaining it. For the portals, they are just one same thing. Also, about the moving portals thing. Portals connect space together, and when you move one of them you kind of move space which confuses the hell out of people. It is very hard to think both with portals and with relativity in mind. Very nice video.
The moving portal onto a stationary block problem at around 3:00 is a quite simple thing to do if you simply remove gravity. The mass of the block and velocity of the portal then do not matter for the problem at all. What the problem is effectively asking is if the object retains its momentum relative to the portal or relative to the space around the portal. And the answer is clearly B.
@@optozorax_en my argument for B is simply "well, it would feel better gameplay-wise!" i think your average player would be pretty disappointed if a portal crushing a cube wouldn't launch it into the stratosphere
@@optozorax_en here is an unbeatable proof. The cube ALWAYS go out based in the OBJECT speed, not the portal, if the object speed is zero it can't get out of the portal. If you say otherwise, you're objectively wrong, because the game is coded like this, and you can test it
@@arekrekas213 I would say that depends how you look at it. If you replace the cube with a person, some may want them to fly out, others would want to be stationary relative to the environment.
3:00 no matter what, the cube must exit the blue portal at the velocity that the orange portal was moving, right? it can't exit the blue portal at a different rate, because then there would be a point in time where part of the cube is missing or duplicated. air resistance shouldn't really matter, because as the orange portal moves, i imagine air would be pushed through it, so when the cube goes through, the air around it would be matching its velocity.
The cube can't exit the portal. The objects maintain its velocity, no matter if the portal is moving. If the velocity of the cube is zero, it doesn't get out of the portal
@@rennangandara7697 velocity is relative. it has one velocity relative to the orange portal, and another velocity relative to the rest of its environment. there is no solution where neither of these is forced to change.
@@rennangandara7697the cube must exit the second portal at the same speed as the cube entering the first portal relative to the portals. For example: cube stationary, orange portal moves at 1m/s then cube must exit blue portal at 1m/s relative to blue portal If 2 portals are placed back to back and the orange portal(bottom one) passed through a cube at 1m/s, then the cube won't be launched out of the blue portal at 1m/s because the blue(exit) portal is already moving away from the cube at 1m/s
Interesting. I think another con of the analytical method is that adding more than one portal will be very difficult. Now, Instead of just "how many times did this get teleported", you have to consider "this got teleported through A, then B, then A twice, then B inverted". This might be too many "levels"
You think of the portals the way I always thought of them. I found many of the explanations people have done before presumptious... Especially the one about "how the object behaves going through". Speed out of the portal should always be relative to your speed into a portal.
If your channel is too new to put links in the description, does that mean that they are in the older Russian version of the channel? I don't know Russian but it shouldn't be to hard to find a link in a description.
Interesting, I never thought of such an... even more unusual case. There are a few possible outcomes I can think of right now (depending on the behavior of the teleporters and the teleportation concept it self). ((Though, I might change my mind if I give it a little more thought.)) I am now assuming that what goes into one portal comes out of the other portal at the same scale ratio relative to the portals perspective. Or in other terms: Let's assume a door-like portal: - Entry portal: 1m (x-axis) x 2m (y-axis) - Exit portal: 2m (x-axis) x 1m (y-axis) If you're now pushing a square cube (1m x 1m) through it, the surface area of the entry portal covered by the square is: - 100% of the x-axis and 50% of the y-axis. -- But by my assumption, the cube would have to cover the sames surface aerea of the exit Portal, - 100% of the x-axis and 50% of the y-axis of the exit portal, then the dimensions of the cube change to 2m x 0.5m. From here, the material and the teleportation method determine what could happen. - If teleportation works on a microscopic level, you could probably get away with a few materials. For example, water would be plausible, and even some raw resources like metal. However, it's very likely that those objects would get insanely hot due to the internal friction at molecular levell. Though a faster pass through the portal, would equal in more heat Potentially leading to melting or even combustion. - If teleportation works on an atomic level, things could get volatile pretty quick. Reshaping atomic bonds might even lead in to a nuclear reaction. (Those hypothetical mind plays would require an chemist to give share his thought. I have no clue about the possibilities there, but I wouldn't be surprised if they were devastating/dooming.) (Also, I'm relatively sure I'm missing something important for my assumption on microscopic level. The laws of physics teach us there is never energy without an opposing equal energy. And I am missing those in my predicted scenario for the most part.)
You can definitely "squish" or smoothly deform any flat portal into every another flat portal shape. Problem is that everything coming through such portals would squish or distort accordingly, so "physical" objects wouldn't really like that and cause a really nasty explosions (even air molecules would disintegrate in funny ways). But for light only, there could be some nice optical effects.
Ah, I swore I've seen the original video pop up but did not watch it because of language, glad you've adapted it! Amazingly explained and with several perspectives too Did you modify the style of Imgui for Rust (egui) or is that default for it? It looks great
3:50 I'm screaming in horror at the idea of a portal being able to move a stationary object outside of itself. I mean it mathematically makes sense, but my brain and eyes don't want to accept it. Kind of like how light travels at the same speed in every frame of reference.
Yoo let this guy cook I skipped to the end thinking it was the video i had already watched and was like: wait a minute, so i went back to the start and got absorbed by it! Really good video! 👍 i like the accent too
3:21 it doesn't matter the speed or mass, if the only thing moving is the portal the answer is always a Imagine a portal like a hoola hoop, no matter the weight of the object and nomatter how fast you slam down the hoop (ignoring air flow and bouncing from impact force) the object stays where it is because it's the portal thats moving not the object. If a doorway breaks out of a wall and falls around you you don't suddenly fly away do you? No lol Portals are just disconnected ends of a hole, you fly in one end you fly our the other, it flies at YOU from your perspective you haven't moved at all. Simple really
Right, I don't see how he so triumphantly concludes his point at 4:10. In his interpretation it seems that if you move a portal through an object, but stop halfway, that object will continue to move through the portal (assuming no gravity/ friction) because it has somehow transferred momentum to the object. But I can only imagine that if you did that you would just end up with a stationary object halfway through a portal.
the thing is, because the orange portal is moving from your perspective the blue portal would be moving at the same speed from your perspective, and therefore the room it's attached to, so that's why you do fly out with speed and b is correct
Here's a question about portals I've never received a satisfying answer to: Let's say that two portals are facing each other at a set distance. You take a metal pole of a particular length and insert it halfway into one portal such that it's other half is in-line with the first. You hold it in this position. Then, you take a separate pole of sufficient length to join the two tips of the first, and weld the ends together. What happens to the pole? Is it now of infinite length? Is it recursive/a loop? Is it still possible to change the pole's orientation? Could it be removed from the portal? What happens if you stop holding it in position?
Well, it couldn't be infinite length, because there is no such thing as 'inside' a portal. In the video, we saw how as soon as one part of a triangle entered one portal it came put the other, meaning that even though it looks like it would go on forever, the only parts that would exist are the two rods. I *think* that trying to change the pole's orientation would be impossible without bending it. I imagine that as soon as one end moves down, the other end is yanked down too, making it stay perpendicular to the portals. That means that if you tried to remove the pole from the portals by pulling it out, it would just bump against the side of the portals. Finally, I really have no idea what would happen if you let go.
@googooblabla100 I think these are reasonable responses, but for the first I have to ask, then: how long would the pole now be, if not infinite? You're right that a portal has no "inside", but from an outside observer's perspective the pole would appear to strech on in infinite length through the portals. It would no longer have an identifiable terminus, and thus would have to be infinite in length, I imagine. You could feed it in either direction through the portal and never run out of pole, simply arriving back at the point you started. Which I suppose makes it recursive like a loop or a Mobius strip, but physically it would still be a perfectly straight pole. I suppose you could answer that it's only the length of the original pole in addition to the connecting piece, but would that still technically be measurably accurate if the pole never actually terminates? I agree that the pole would now be impossible to reorient out of plane, it just wouldn't be dimensionally possible given the constraints of the portals and the bar without somehow bending it (if doing so is even possible while keeping the bar whole). But I feel like this has ramifications on determining the "length" of the bar, in a way I can't quite articulate at the moment. I suppose gravity would take affect and the bar would just drop, but I don't know if it is possible for an object to rest on the "rim" of a portal. Perhaps it would become perfectly and cleanly severed such that it is now the exact length between the two "surfaces" of the portals. What's more troubling is considering what would happen if the same was done while the portals were orientated such that the pole was vertical from the observer's perspective. I imagine the pole would "fall" forever, constantly feeding itself between the two portals seamlessly until it eventually drifted near the portals edge.
@@the_real_Kurt_Yarish to answer your first question, imagine for a second that the pole turns into rubber, so that it can be bent while keeping it's original length. Now, move one of the portals so that it is on the backside of the other portal, like it has become a door. The rubber pole would bend into a ring, which passes through the doorway. I imagine that in the same way that the ring has no definite 'start' or 'end' but can still have it's length measured, the bar does not have a start or end but can still be measured. If you want I'll try to make an animation to explain. (I'll probably make it either way, just for fun) The other questions i really think depend on how the portals work, especially when taking about hitting the portals sides. Hope my explanations help you!
Moving one of the portals further apart while the rod connects them, I imagine would require the other portal to get drug along in the same direction. Forces acting on one portal would have to also act on the other, or else you really would get infinite rod, duplicating X units of material for just moving one of the portals X units further away.
@@googooblabla100 I understand the visualization you're giving, and indeed the pole would have to work similarly if it is actually recursive. Problem is, is that that the pole isn't actually curved; every point of the pole is parallel with itself. If you were to draw a ray from any point on the pole emanating in any direction other than directly along the pole, it would never come into contact with the pole again. An axiom which isn't true for your looped pole. Meaning it can't actually be a true loop, yet it behaves like one.
This is fucking sick I've been looking for more intuitive explanations of portals and other spatial shenanigans for a comic I'm writing up, and this just gave me a bonfire of inspiration I hope you can get those links soon man!
The issue I still have with moving portals moving an object is that you are creating energy from nothing. There is no equal reaction. A moving portal MUST be slowed by an equal amount of energy to that imparted on the object.
3:18 mass and speed is irrelevant, as the box is never touched by anything, no kinetic energy is transferred, only it's gravitational reference frame shifts/rotates, so only A can be correct. From the box's POV, the platform is on just rotates 45 degrees, slice by slice from the boxes top to bottom.
3:55, this can only be true if the triangle is attached to the blue wall, otherwise what would move the triangle? Portals don't cause movement, they connect space. Even Portal 1 said so: speedy thing comes in, speedy thing goes out. Momentum is maintained, and that triangle had no momentum.
Auto-generated shaders is complete insanity. It makes me wonder if you can do something similar for higher degree teleportations. Amazing work. This really makes my head spin, and it puts into perspective why the Valve team decided not to touch moving portals with a 10 foot pole, lol. EDIT: This is your _first video!?_ Strong start!
Now in portal in portal scene there's a for loop, where I automatically process all teleportation degrees without necessity of writing them down. If you open it, you will see slider to change amount of teleportation degrees.
But what happens when there is a triangle between two portals that move towards each other. That’d create a singularity right? Unless u decide that the portals stop being ablr to move if the independent object touches itself
This question is basically asking whether portals can feel a reaction force from objects inside them. Yes, it could create a singularity buuuut in most cases, it just deforms the object into a flat as fuck sheet
5:57 What if we deformed anything that comes out of the other end so it maps perfectly to other shape? Say we have O shape portal side and L shaped end... If I stick a stick in O I should get hockey stick coming out of L
I know you prefaced this with the caveat that you're looking at this as a purely geometric/mathematical problem, but I think there's already an issue with this. Relativity isn't just a property of physical objects, it's a mathematical fact pertaining to anything in a geometric space. The idea that there is no universal frame of reference (FoR) requires that you pick some FoR to base everything else on, but since portals make that choice self-referential, when one portal moves the rest of the universe has to "move" in reference to that motion. Since all FoRs have to be equally valid, and considering the stipulated rules of portals, one portal's FoR necessarily violates the other's. The whole universe should be moving if one portal is moving, but since both portals are in the same universe, and there is no universal FoR, you have to make some arbitrary choice about which FoR "matters" based on each portal's velocity or something... which is also relative... Can somebody else validate or disprove this assertion? My head hurts.
I wonder if a particle based approach would give even more intuitive results (basically simulating atoms/clusters of atoms) Of course, performance would suffer greatly, especially with higher resolutions. It also begs the question: are portals made of atoms?
@optozorax_en In that case, If a portal teleports/moves particles but a portal isn't made out of particles (because it's just space), that means you can't put a portal through a portal. You can't put a hole in a hole. Edit: If portals bend the space itself, I have no idea how you'd compute that. In that case you might have to re-imagine the coordinate system to be entirely relative. That's just my intuition tho.
ahhh, I love the visualizer and demos in this video. Very excited to think about those new portals you teased at the end. One quick note about 3:00, I'm quite sure the question the comic asks is just if the cube has any amount of momentum coming out of the blue portal, it is not asking how much. It's just intended to exercise your understanding of portals, perspective, and paradoxes. It is not asking you to calculate how much momentum, so there is no need for variables like cube mass etc. From the perspective of watching the blue portal, the cube is moving at the same speed of the orange portal. When the two platforms contact and stop, the cube must preserve momentum, so the answer must be B. But where did the energy to launch the cube come from? The platform that the orange portal is attached to just exerted all its energy into the landing platform, not into the cube, so the answer must also be A.
It's worth noting that when the orange portal lands, it is no longer interacting with the cube since it has just finished passing through the portal. it truly only puts energy into the platform it lands on. Since you can view the universe both outside of the portal and inside the portal, I like to think portals have the same inertia as the entire universe. so when the yellow portal lands, maybe everything starts flying away from the cube and the cube stays in place. 😂
hello mysterious internet user that I don't know from anywhere in particular perhaps the act of an object passing through a portal results in a force being applied to the portal, like a drag of sorts this could be a solution to the energy problem in scenario B if the math is reasonable
In the game portal, since objects cannot be subdivided (there can only be one linear and rotational force each acting on the center of mass), and there is a universal reference frame (the hammer grid), the situation of a moving portal must always be A. I understand not wanting to use the mechanics from portal, but that is what makes the question interesting (since a 'physical' interpretation must either be B with mutable portals (not the kind in the game) or impossible). To me introducing relativity is erroneous because that's a law of our world, not portal's, and certainly not all potential games with portals. The portal games already intentionally display infinite gravitational energy due to the displacement of falling objects, so conservation of energy/momentum is irrelevant.
Very interesting but I think the output shape should be distorted when different shapes are used as portals. So you might be able to put a square Into a triangle and get a circle. Idk but also it's probably different shapes coming out depending on which one is bigger
I’m confused why you need to keep track of teleportation degree at all, let alone why it’s forced to work a certain way. I’d love another video exploring that more
what about Gravity? what if you put the portals on the ceiling and will be half in one, and half in another? you'll be suspended in the air? what if you put the portals on different heights?
I'm very skeptical that each of the 11 degrees has to be more copies of essentially the same code. See if you can turn it into an unbounded loop that terminates when no more intersections remain.
Portals cannot preserve energy conservation as the conserved quantity of energy emerges from spacetime symmetry, and anything but perfectly flat spacetime does not have spacetime symmetry, which obviously includes portals lol. Great video though! :)
EDIT: 6:56 - oh maybe you have already thought about what I was saying below here. EDIT 2: Ok, no, not quite. You do consider cutting portals but it seems like you aren't following that to its logical conclusion just yet. Either way, very cool approach! 5:59 I wonder if there is a way to relax this a bit? My guess is that what you need here is some sort of differentiable map between both portals so you know how one portal might deform an object compared to another: You should always be able to split up a portal pair into many tiny portal pairs without a change, right? It makes no difference whether you walk through a big doorway or many tiny doorways where the ones that directly neighbour other doorways have their frames removed, so long as both ends of the multiple doorways are attached in this way (otherwise you might end up cutting shapes. However, even then you aren't *removing* shapes: All pieces will always be accounted for, so maybe even that can be relaxed, though it would be violent) But once you have this sort of process, splitting one large portal into many tiny ones, you can consider what happens "in the limit" and you can get *curved* portals and even *closed up* portals (like a spherical portal - that would actually be a classic wormhole) And furthermore, you can consider *small* and *continuous* deformations of one side of the portal which should still work out. You'd just get deformations as an object goes through. A simple case would be two rectangular portals where one is a tall rectangle and the other is wide. You can completely fulfill all your rules in this case if you allow objects passing through to get stretched and skewed. You just don't want to *delete* the object. Every piece always must have *some* place to go. And mass conservation isn't a problem here either: You are simply affecting the density.
It can be relaxed for linear transformations: scaling, mirroring. But non-linear transformations are evil, they violate some nice portal properties. I have plans to make a video about this non-linear transformations in the future, already have a scene for that (mapping sphere onto a plane).
@@optozorax_en Mapping a sphere to a plane breaks the topology as one finite point is gonna be mapped to a point at infinity, or two points are smeared out into an entire line each, or any other number of distortions corresponding to various maps. No matter what, you have at least one singularity. It makes sense to me that you might need to retain topology. But what if you, say, mapped from a perfectly smooth round sphere to a ripply one? Still the exact same topology, but the geometry is deformed. I think this should be possible if you consider your "copying the coordinate frame" concept by, effectively, giving every single point within an object (including portals) its own coordinates and continuing paths according to parallel transport when one frame's origin coincides with another's. After that you might have to consider some physics to predict the evolution correctly: Passing from a smooth to a ripply portal (or vice-versa) would mean a solid object gets locally squashed or stretched, and so you'd have to consider tension forces and such to predict how the object works afterwards. By the way, if you take the door frame analogy entirely seriously, you really only ought to depend on the frame itself: The surface inside is kind of arbitrary. Like, if you took the door frame to be the shape of a bubble wand, any sort of bubble attached to that frame should be permissible as cutoff surface. - The flat connections you are using here are a matter of simplicity, but if you considered a warped door that's nevertheless flush with the frame as your cutting surface, everything ought to work the exact same still. The situation to me reads a bit like the Stokes-Cartan theorem where you can freely switch, for instance, between an integral over a closed surface and an integral over its enclosed volume. Or between an integral over a loop in space and an integral over *any* arbitrary surface that has this loop as its boundary. *Any* such surface will do. And I think that's true for your portals here too. You just have to be able to consistently draw the corresponding cutting surface on *both* sides of the portal. And I think for that you need preservation of topology and a diffemorphism (i.e. a function that describes how to smoothly go from one surface to the other in a consistent way) (This is just me seeing some connections to, for instance, electromagentic fields (where you'd frequently use variations of the Stokes-Cartan theorem), as well as general relativity (where you work with diffeomorphisms), I certainly didn't do all that portal math nor implemented anything like this, so I'm looking forward to what your future videos will bring)
@@optozorax_en I believe what's really going on is that you need *locally* linear transformations. A map from a sphere to a plane is not locally linear for the entire region. But imagine you split up a portal into thousands of tiny cells: You could apply a linear transformation to every single one of those tiny sub-portals. Nothing should break then. As long as you keep them all connected up, any objects will pass through just fine as well. That's gonna mean your linear transformations have to vary smoothly such that neighbouring cells are transformed into a sufficiently similar way. So long as you have, for every single point, a neighbourhood that transforms in a linear fashion, things ought to hold up.
I love smart viewers like you, write more. You absolutely right about that portal surface is arbitrary, I already have scene for that, in my demo: Load -> Basics -> "Surface portals???". The integral analogy is a good one. About mapping sphere to a plane - I can remove infinity points by using borders. Also this thing this removes this nice property that you can choose arbitrary teleportation surface, because in that case you can definitely observe the surface and find its exact shape in an experiment (feel when passing material is being tensed).
@@optozorax_en I see what you are saying. I think that *should* be fixable still, *but* it effectively requires some sort of force field to keep things consistent despite arbitrary surfaces. I *think* that's sort of how gravity actually works in general relativity: Space itself is curved and as a result you get tidal forces. - in order to keep the portals consistent under somewhat arbitrary surface deformations, you'd end up defining some tidal forces because you are necessarily in an accelerated frame. The cross section of that field through any sort of arbitrary surface is gonna change in a continuous fashion such that, while you can feel the effects of bent space (effectively gravity), there would not be any point where you suddenly get the impression of a fixed sharp surface (because everything is continious still) At best you get an event horizon type situation but importantly for those, for an observer right in the scene, those do not occur. They are only an issue from an outside observer looking at the scene from a distance
Thanks for this amazing analysis and demonstration optozorax! I would love to see what would happen to an object if it was partway through a portal and one entrance abruptly accelerated. I suspect it would be capable of breaking an object in half at an atomic scale (assuming an infinitely thin portal and instantaneous change in portal velocity) but I’d be curious to see your analysis! How would that compare to pushing/pulling an object in a traditional way?… I dunno, but if there’s one person who could figure it out I think that’s you! Either way I look forward to your follow-up on moving portals :)
I think accelerating portal should produce some kind of gravitational waves that affects objects and passes energy and momentum to it. This can be derived from one really neat property of a portal that I will make future video about. Right now I'm not ready to answer that question.
Wow! If you have the entrance to a portal facing the exit of the same portal and 2D object in between them. Where does the object go when you bring the portals together and then move both portals away? Like bringing two slices of bread together around some jam and then moving the sandwich away.
I would make world made out of small cells, so there won't be a problem of cutting, and i will make all coordinates integers, getting rid of floats and most math, portal will be just set of teleport points 6 sided, and if someone goes through its edge it comes out of bounded other side.. I think all agreed that if something goes half to portal, and then portal closes/it goes through edge, it cuts?
The REAL portals should NOT be movable. Not because of some abstract rule, but because portals are connecting different points in the same space. If portal is moving relative to another, it would mean space itself would be moving relative to itself, which would mean either deformation of space or overlap and holes in space. For example, in your visualisation, one portal moves past the object, but without touching it, and object keeps moving on other side after passing through. It means that it's spatially anchored to original portal. Space that it takes moves through the stationary space in the other side of the portal. In that case, there should be hole in space behind the moving portal, or space should be stretched and compressed around it. Either way, in static space, portals are fixed. After all, you cannot move a hole in the paper without deforming the paper. P.S. In that case, portal entering portal would mean simply folding the space inside portal, making it concave; the portals will never actually intersect.
All those degrees are virtual, they don't really exists. There are always only one blue portal. But in implementation, there may be infinitely many of them.
i mean you could just make a weight attached to a pulley that spins a generator and the fact you can move a heavy weight from the ground to the top of a building with little effort using a portal means you can generate as much electricity as you want
I disagree with you @4:00 the conservation of momentum is missing when the portal is moving and the object is stationary. when the object is moving it exists the other side portal WITH conservation of it's momentum, which is NOT 0. however if the object has 0 momentum and the portal is moving all pieces of the object will exit the other side with 0 momentum and basically cash into eachother at the edge of the exit portal because the have no momentum and not was imparted on them by the portal.
I've visualised this in my head before but I could never imagine what happens if you ignore the fact that the portals knock into eachother, what happens if you keep pushing? Edit: Nevermind, I didn't watch far enough. Thank you for showing it :D
maybe it could be solved by using objects made of voxels instead of meshes ? this would be closer to an actual simulation and could fix the triangle issue
@@optozorax_en if you remember tell me i might try to make one myself too also going voxel is very good for ray tracing application since you do check on a data structure instead of every triangle in scene
My fire mastered painting a sound, While studying squares that claim to be round, With my professor who was a cloud, Who couldn't teach circles how to be round.
It is, it just written in plaintext, see closely, youtube does not allow new channels to have links :( When it allows me, I will update the description.
One contradiction with reality that portals create is infinite energy with falling objects, but if you think about it, portals should be able to teleport gravitational fields too. This could possibly fix that contradiction. I imagine you'd basically be floating if you were between horizontal portals. A new video perhaps?
We can't move portals because they are not wormholes but rather quantum tunneling. And because it is quantum tunneling it needs to be really cold and since temperature is just the movement of atoms it means you can't move a portal.
I would argue that an object staying still and a portal moving into it would not affect it's speed. If we are assuming the definition of a portal as a doorway, and that a portal should work the same as a normal doorway, when you have a doorframe and move it through an object, the object does not magically change in speed, it keeps the same speed despite appearing on the other side. A portal simply teleports matter and energy through space, therefore it should not add kinetic energy to an object. If we think about this using newton's first law, an object that is at rest should stay at rest unless it's acted upon by external force. because a regular doorway would not produce force onto an object, by your definition a portal shouldn't either.
I feel like there's no problem in reality, not math, if you break portals. It's just called entanglement. A big portal is just many spacial points being entangled in an ordered way. When you cut the portal you still have 2 portals and you can keep cutting them until atomic scales
3:50 The triangle that passed the portal and made it to the other has a velocity V w.r.t to the camera The part that has not entered the portal has a velocity 0 w.r.t to the camera But parts of the triangle must have zero relative velocity w.r.t to all the other points within the triangle. How do you reason this works?
Basically after the intro I said that this is translation and improvement over my russian video. Did you really watch the russian video with english subtitles? Because I've seen basically no english comments and emptiness on the analytics.
@@optozorax_en ой, извините, я скипнул через дисклеймер сразу к середине видео чтобы убедиться что это то видео что я уже смотрел. Я говорю на обоих языках, но не смотрел российских видео уже много лет, и труба мне их не предлагает очень давно, за исключением вашего, и я просто напросто не запомнил на каком языке оно было, только содержание! Sorry for not engaging on the original channel, I just must not have had any thoughts to add. Just subscribed to this new translated channel, and I'm sure it's gonna pick up, cuz the work you did there is very juicy. Good luck!
I'm blown away by how you manage to go from a seemingly impossible problem to understanding it intuitively, mathematically and computationally in 20 minutes. Just amazing.
This was a great explanation. I hope minutephysics sees this.
I love how you start with the example of a door. You are absolutely correct, it is a portal.
The sign of a good teacher is being able to immediately connect their students to a familiar concepts. You, sir, are very good at this indeed. I wish you the best and am happy to be here under 1k subs
I was like "ayyy i have seen this video before!" but then i saw the date of creation and thought "wait... so i haven't seen this vi-" but before i could even finish the sentence, i looked and stared at the sub count and my mind completely filled up with "UNDERRATED, UNDERRAT-"
I swear i've seen it before as well
первое видео на эту тему было три года назад. и оно было на русском
maybe you've seen the russian one?
@@dinhero21 i remember seeing an English one
Yeah, I remember an English one too.
Edit: It's by minutephysics, this is also a very well made video on the subject though.
The analytical approach works for rasterization too, just make a shader that sets the transparency to 1 on the backside of the portal. This is how it actually works in-game.
immediately recognized egui
egui is so cool
SAME
Came here to post the same hahaha. Made me so happy
Is that Rust's imgui or something?
@defeatSpace yeah
I love this and hope you get the attention you deserve. This is a great example of how most people hear that something is impossible and then leave it. You have such a clear and intuitive explanation that I think most people quickly gave up looking for.
I am so thankful for this... UNIMAGINABLY underrated video. This has answered every question about portals I've had over the years, and I was RIGHT.
This is an absolutely fantastic video, HELLA underrated.
I was completely captured by this demonstration the entire way through, and then I look down and see only 6.6k views, and 364 subs (365 now).
This was an incredibly easy to follow explanation of the portal-in-portal paradox, 10/10
Thinking portals as just one doorway split in half is a very good way of explaining it. For the portals, they are just one same thing.
Also, about the moving portals thing. Portals connect space together, and when you move one of them you kind of move space which confuses the hell out of people. It is very hard to think both with portals and with relativity in mind. Very nice video.
The moving portal onto a stationary block problem at around 3:00 is a quite simple thing to do if you simply remove gravity.
The mass of the block and velocity of the portal then do not matter for the problem at all.
What the problem is effectively asking is if the object retains its momentum relative to the portal or relative to the space around the portal.
And the answer is clearly B.
Of course it's B, but there are so many A people that I decided not to say anything until I have an unbeatable math proof.
@@optozorax_en my argument for B is simply "well, it would feel better gameplay-wise!" i think your average player would be pretty disappointed if a portal crushing a cube wouldn't launch it into the stratosphere
@@optozorax_en here is an unbeatable proof. The cube ALWAYS go out based in the OBJECT speed, not the portal, if the object speed is zero it can't get out of the portal. If you say otherwise, you're objectively wrong, because the game is coded like this, and you can test it
I'm talking about abstract pure portals, not about some game (that was answer to someone's comment, and they deleted it)
@@arekrekas213 I would say that depends how you look at it.
If you replace the cube with a person, some may want them to fly out, others would want to be stationary relative to the environment.
of course it's made by a rust nerd 😅
We need blazing speed 🚀 for quantum physics
"for science, you monster"
Rust > Java
@@SalzmanSoftware there is literally nothing similar about them, why would you even create this comparison XD
Because.
Truly an amazing video. I reckon this channel will gain thousands of subscribers in not time
criminally underrated channel. excited to see what you have for us next!
Amazing video! I hope this blows up and more people get to see this!
3:00 no matter what, the cube must exit the blue portal at the velocity that the orange portal was moving, right? it can't exit the blue portal at a different rate, because then there would be a point in time where part of the cube is missing or duplicated.
air resistance shouldn't really matter, because as the orange portal moves, i imagine air would be pushed through it, so when the cube goes through, the air around it would be matching its velocity.
my view also. the exit speed will always be the relative velocity
The cube can't exit the portal. The objects maintain its velocity, no matter if the portal is moving. If the velocity of the cube is zero, it doesn't get out of the portal
@@rennangandara7697 velocity is relative. it has one velocity relative to the orange portal, and another velocity relative to the rest of its environment. there is no solution where neither of these is forced to change.
@@rennangandara7697the cube must exit the second portal at the same speed as the cube entering the first portal relative to the portals.
For example: cube stationary, orange portal moves at 1m/s then cube must exit blue portal at 1m/s relative to blue portal
If 2 portals are placed back to back and the orange portal(bottom one) passed through a cube at 1m/s, then the cube won't be launched out of the blue portal at 1m/s because the blue(exit) portal is already moving away from the cube at 1m/s
> the cube must exit the blue portal at the velocity that the orange portal was moving
Of course
Now i also see that bounded portal plane are a hulahoop of extreme sharpness. I love the video, amazing works.
Interesting. I think another con of the analytical method is that adding more than one portal will be very difficult. Now, Instead of just "how many times did this get teleported", you have to consider "this got teleported through A, then B, then A twice, then B inverted".
This might be too many "levels"
You think of the portals the way I always thought of them. I found many of the explanations people have done before presumptious... Especially the one about "how the object behaves going through". Speed out of the portal should always be relative to your speed into a portal.
If your channel is too new to put links in the description, does that mean that they are in the older Russian version of the channel? I don't know Russian but it shouldn't be to hard to find a link in a description.
The only link you need is demo - and it's written in plaintext here, you just need to write dots and slashs
@@optozorax_en Oh, sorry I missed that. But also thank you!
This is great work bro! Instant-subscribe. and can't wait to see what else you can do :)
Could you not have different shaped portals that then warp and distort light and objects that pass through?
You don't wanna enter that portal, it will distort you alive
Interesting, I never thought of such an... even more unusual case.
There are a few possible outcomes I can think of right now (depending on the behavior of the teleporters and the teleportation concept it self).
((Though, I might change my mind if I give it a little more thought.))
I am now assuming that what goes into one portal comes out of the other portal at the same scale ratio relative to the portals perspective.
Or in other terms:
Let's assume a door-like portal:
- Entry portal: 1m (x-axis) x 2m (y-axis)
- Exit portal: 2m (x-axis) x 1m (y-axis)
If you're now pushing a square cube (1m x 1m) through it,
the surface area of the entry portal covered by the square is:
- 100% of the x-axis and 50% of the y-axis.
-- But by my assumption, the cube would have to cover the sames surface aerea of the exit Portal,
- 100% of the x-axis and 50% of the y-axis of the exit portal,
then the dimensions of the cube change to 2m x 0.5m.
From here, the material and the teleportation method determine what could happen.
- If teleportation works on a microscopic level, you could probably get away with a few materials. For example, water would be plausible, and even some raw resources like metal. However, it's very likely that those objects would get insanely hot due to the internal friction at molecular levell. Though a faster pass through the portal, would equal in more heat Potentially leading to melting or even combustion.
- If teleportation works on an atomic level, things could get volatile pretty quick. Reshaping atomic bonds might even lead in to a nuclear reaction.
(Those hypothetical mind plays would require an chemist to give share his thought. I have no clue about the possibilities there, but I wouldn't be surprised if they were devastating/dooming.)
(Also, I'm relatively sure I'm missing something important for my assumption on microscopic level. The laws of physics teach us there is never energy without an opposing equal energy. And I am missing those in my predicted scenario for the most part.)
You can definitely "squish" or smoothly deform any flat portal into every another flat portal shape. Problem is that everything coming through such portals would squish or distort accordingly, so "physical" objects wouldn't really like that and cause a really nasty explosions (even air molecules would disintegrate in funny ways). But for light only, there could be some nice optical effects.
Ah, I swore I've seen the original video pop up but did not watch it because of language, glad you've adapted it!
Amazingly explained and with several perspectives too
Did you modify the style of Imgui for Rust (egui) or is that default for it? It looks great
That's default
Объяснение понятное и детальное, спасибо 👍
Impressive, thanks for sharing the explanation *and* code!
but what happens if the other portal is smaller, and faces to the orange portal and completely goes trough the orange portal
Finally, REAL questions, not some physics bullshit! I have very very COOL solution to that and will make a video about it in first months of the 2025
3:50 I'm screaming in horror at the idea of a portal being able to move a stationary object outside of itself. I mean it mathematically makes sense, but my brain and eyes don't want to accept it. Kind of like how light travels at the same speed in every frame of reference.
interesting, I never had that reaction and didn't think that someone intuition would work like that
Yoo let this guy cook
I skipped to the end thinking it was the video i had already watched and was like: wait a minute, so i went back to the start and got absorbed by it! Really good video! 👍 i like the accent too
3:21 it doesn't matter the speed or mass, if the only thing moving is the portal the answer is always a
Imagine a portal like a hoola hoop, no matter the weight of the object and nomatter how fast you slam down the hoop (ignoring air flow and bouncing from impact force) the object stays where it is because it's the portal thats moving not the object.
If a doorway breaks out of a wall and falls around you you don't suddenly fly away do you? No lol
Portals are just disconnected ends of a hole, you fly in one end you fly our the other, it flies at YOU from your perspective you haven't moved at all.
Simple really
Right, I don't see how he so triumphantly concludes his point at 4:10.
In his interpretation it seems that if you move a portal through an object, but stop halfway, that object will continue to move through the portal (assuming no gravity/ friction) because it has somehow transferred momentum to the object. But I can only imagine that if you did that you would just end up with a stationary object halfway through a portal.
@ exactly, his assertion makes no sense, especially when he says a portal is a basically just doorway in the video
the thing is, because the orange portal is moving from your perspective the blue portal would be moving at the same speed from your perspective, and therefore the room it's attached to, so that's why you do fly out with speed and b is correct
The games are simplified a lot by fixed wall placement so they don't have to compute any crazy collisions
Here's a question about portals I've never received a satisfying answer to:
Let's say that two portals are facing each other at a set distance. You take a metal pole of a particular length and insert it halfway into one portal such that it's other half is in-line with the first. You hold it in this position. Then, you take a separate pole of sufficient length to join the two tips of the first, and weld the ends together. What happens to the pole? Is it now of infinite length? Is it recursive/a loop? Is it still possible to change the pole's orientation? Could it be removed from the portal? What happens if you stop holding it in position?
Well, it couldn't be infinite length, because there is no such thing as 'inside' a portal. In the video, we saw how as soon as one part of a triangle entered one portal it came put the other, meaning that even though it looks like it would go on forever, the only parts that would exist are the two rods. I *think* that trying to change the pole's orientation would be impossible without bending it. I imagine that as soon as one end moves down, the other end is yanked down too, making it stay perpendicular to the portals. That means that if you tried to remove the pole from the portals by pulling it out, it would just bump against the side of the portals. Finally, I really have no idea what would happen if you let go.
@googooblabla100 I think these are reasonable responses, but for the first I have to ask, then: how long would the pole now be, if not infinite? You're right that a portal has no "inside", but from an outside observer's perspective the pole would appear to strech on in infinite length through the portals. It would no longer have an identifiable terminus, and thus would have to be infinite in length, I imagine. You could feed it in either direction through the portal and never run out of pole, simply arriving back at the point you started. Which I suppose makes it recursive like a loop or a Mobius strip, but physically it would still be a perfectly straight pole. I suppose you could answer that it's only the length of the original pole in addition to the connecting piece, but would that still technically be measurably accurate if the pole never actually terminates?
I agree that the pole would now be impossible to reorient out of plane, it just wouldn't be dimensionally possible given the constraints of the portals and the bar without somehow bending it (if doing so is even possible while keeping the bar whole). But I feel like this has ramifications on determining the "length" of the bar, in a way I can't quite articulate at the moment.
I suppose gravity would take affect and the bar would just drop, but I don't know if it is possible for an object to rest on the "rim" of a portal. Perhaps it would become perfectly and cleanly severed such that it is now the exact length between the two "surfaces" of the portals. What's more troubling is considering what would happen if the same was done while the portals were orientated such that the pole was vertical from the observer's perspective. I imagine the pole would "fall" forever, constantly feeding itself between the two portals seamlessly until it eventually drifted near the portals edge.
@@the_real_Kurt_Yarish to answer your first question, imagine for a second that the pole turns into rubber, so that it can be bent while keeping it's original length. Now, move one of the portals so that it is on the backside of the other portal, like it has become a door. The rubber pole would bend into a ring, which passes through the doorway. I imagine that in the same way that the ring has no definite 'start' or 'end' but can still have it's length measured, the bar does not have a start or end but can still be measured. If you want I'll try to make an animation to explain. (I'll probably make it either way, just for fun)
The other questions i really think depend on how the portals work, especially when taking about hitting the portals sides. Hope my explanations help you!
Moving one of the portals further apart while the rod connects them, I imagine would require the other portal to get drug along in the same direction. Forces acting on one portal would have to also act on the other, or else you really would get infinite rod, duplicating X units of material for just moving one of the portals X units further away.
@@googooblabla100 I understand the visualization you're giving, and indeed the pole would have to work similarly if it is actually recursive. Problem is, is that that the pole isn't actually curved; every point of the pole is parallel with itself. If you were to draw a ray from any point on the pole emanating in any direction other than directly along the pole, it would never come into contact with the pole again. An axiom which isn't true for your looped pole. Meaning it can't actually be a true loop, yet it behaves like one.
This is fucking sick
I've been looking for more intuitive explanations of portals and other spatial shenanigans for a comic I'm writing up, and this just gave me a bonfire of inspiration
I hope you can get those links soon man!
The issue I still have with moving portals moving an object is that you are creating energy from nothing. There is no equal reaction. A moving portal MUST be slowed by an equal amount of energy to that imparted on the object.
That's exactly what I tried to express on 3:20
3:18 mass and speed is irrelevant, as the box is never touched by anything, no kinetic energy is transferred, only it's gravitational reference frame shifts/rotates, so only A can be correct. From the box's POV, the platform is on just rotates 45 degrees, slice by slice from the boxes top to bottom.
3:55, this can only be true if the triangle is attached to the blue wall, otherwise what would move the triangle? Portals don't cause movement, they connect space. Even Portal 1 said so: speedy thing comes in, speedy thing goes out. Momentum is maintained, and that triangle had no momentum.
So, how will you draw this animation?
such a good video! keep it up
Great video!
this is awesome!! :0
The incursion music! Peak nostalgia.
Auto-generated shaders is complete insanity. It makes me wonder if you can do something similar for higher degree teleportations. Amazing work. This really makes my head spin, and it puts into perspective why the Valve team decided not to touch moving portals with a 10 foot pole, lol.
EDIT: This is your _first video!?_ Strong start!
Now in portal in portal scene there's a for loop, where I automatically process all teleportation degrees without necessity of writing them down. If you open it, you will see slider to change amount of teleportation degrees.
@@optozorax_en 12 steps ahead. Awesome 😄
But what happens when there is a triangle between two portals that move towards each other. That’d create a singularity right? Unless u decide that the portals stop being ablr to move if the independent object touches itself
This is more of a physics questions, because triangle will collide with itself, I don't really know how exactly this should be implemented
This question is basically asking whether portals can feel a reaction force from objects inside them.
Yes, it could create a singularity buuuut in most cases, it just deforms the object into a flat as fuck sheet
где-то я уже это видел
🤫
Тоже самое хотел написать)
Dude, in 100 years, when there are portals in RL, this will be considered groundwork.
5:57 What if we deformed anything that comes out of the other end so it maps perfectly to other shape? Say we have O shape portal side and L shaped end... If I stick a stick in O I should get hockey stick coming out of L
I know you prefaced this with the caveat that you're looking at this as a purely geometric/mathematical problem, but I think there's already an issue with this. Relativity isn't just a property of physical objects, it's a mathematical fact pertaining to anything in a geometric space. The idea that there is no universal frame of reference (FoR) requires that you pick some FoR to base everything else on, but since portals make that choice self-referential, when one portal moves the rest of the universe has to "move" in reference to that motion. Since all FoRs have to be equally valid, and considering the stipulated rules of portals, one portal's FoR necessarily violates the other's. The whole universe should be moving if one portal is moving, but since both portals are in the same universe, and there is no universal FoR, you have to make some arbitrary choice about which FoR "matters" based on each portal's velocity or something... which is also relative...
Can somebody else validate or disprove this assertion? My head hurts.
I don't see how moving portals may violate relativity, you still can have no absolute frame of reference
I wonder if a particle based approach would give even more intuitive results (basically simulating atoms/clusters of atoms) Of course, performance would suffer greatly, especially with higher resolutions.
It also begs the question: are portals made of atoms?
I think portals are made of space organized in some clever way (like wormholes), but not exactly like wormholes
@optozorax_en In that case, If a portal teleports/moves particles but a portal isn't made out of particles (because it's just space), that means you can't put a portal through a portal.
You can't put a hole in a hole.
Edit: If portals bend the space itself, I have no idea how you'd compute that. In that case you might have to re-imagine the coordinate system to be entirely relative.
That's just my intuition tho.
Hopefully someone at Valve sees this. Then if we get a Portal 3, we may get some very cool portal physics.
ahhh, I love the visualizer and demos in this video. Very excited to think about those new portals you teased at the end.
One quick note about 3:00, I'm quite sure the question the comic asks is just if the cube has any amount of momentum coming out of the blue portal, it is not asking how much. It's just intended to exercise your understanding of portals, perspective, and paradoxes. It is not asking you to calculate how much momentum, so there is no need for variables like cube mass etc.
From the perspective of watching the blue portal, the cube is moving at the same speed of the orange portal. When the two platforms contact and stop, the cube must preserve momentum, so the answer must be B. But where did the energy to launch the cube come from? The platform that the orange portal is attached to just exerted all its energy into the landing platform, not into the cube, so the answer must also be A.
It's worth noting that when the orange portal lands, it is no longer interacting with the cube since it has just finished passing through the portal. it truly only puts energy into the platform it lands on.
Since you can view the universe both outside of the portal and inside the portal, I like to think portals have the same inertia as the entire universe. so when the yellow portal lands, maybe everything starts flying away from the cube and the cube stays in place. 😂
Open my demo, Load -> Physics -> Speed model, click "Stopping" checkbox. This is A. Don't you think it's wrong?
hello mysterious internet user that I don't know from anywhere in particular
perhaps the act of an object passing through a portal results in a force being applied to the portal, like a drag of sorts
this could be a solution to the energy problem in scenario B if the math is reasonable
Either energy simply isn’t preserved in a space with portals, or portals take a massive amount of energy to be on.
In the game portal, since objects cannot be subdivided (there can only be one linear and rotational force each acting on the center of mass), and there is a universal reference frame (the hammer grid), the situation of a moving portal must always be A.
I understand not wanting to use the mechanics from portal, but that is what makes the question interesting (since a 'physical' interpretation must either be B with mutable portals (not the kind in the game) or impossible).
To me introducing relativity is erroneous because that's a law of our world, not portal's, and certainly not all potential games with portals. The portal games already intentionally display infinite gravitational energy due to the displacement of falling objects, so conservation of energy/momentum is irrelevant.
Very interesting but I think the output shape should be distorted when different shapes are used as portals. So you might be able to put a square Into a triangle and get a circle. Idk but also it's probably different shapes coming out depending on which one is bigger
Fantastic video
Amazing video
This is awesome
very good video, very underrated also.
Amazing stuff dude
I’m confused why you need to keep track of teleportation degree at all, let alone why it’s forced to work a certain way. I’d love another video exploring that more
I think it's so the shaders are finite
what about Gravity? what if you put the portals on the ceiling and will be half in one, and half in another? you'll be suspended in the air? what if you put the portals on different heights?
I'm very skeptical that each of the 11 degrees has to be more copies of essentially the same code. See if you can turn it into an unbounded loop that terminates when no more intersections remain.
In my new version I wrote this as a for loop with ability to set any amount of teleportation degrees
Portals cannot preserve energy conservation as the conserved quantity of energy emerges from spacetime symmetry, and anything but perfectly flat spacetime does not have spacetime symmetry, which obviously includes portals lol. Great video though! :)
This is why I don't touch physics...
Fair enough ¯\_(ツ)_/¯
EDIT: 6:56 - oh maybe you have already thought about what I was saying below here.
EDIT 2: Ok, no, not quite. You do consider cutting portals but it seems like you aren't following that to its logical conclusion just yet. Either way, very cool approach!
5:59 I wonder if there is a way to relax this a bit? My guess is that what you need here is some sort of differentiable map between both portals so you know how one portal might deform an object compared to another:
You should always be able to split up a portal pair into many tiny portal pairs without a change, right? It makes no difference whether you walk through a big doorway or many tiny doorways where the ones that directly neighbour other doorways have their frames removed, so long as both ends of the multiple doorways are attached in this way (otherwise you might end up cutting shapes. However, even then you aren't *removing* shapes: All pieces will always be accounted for, so maybe even that can be relaxed, though it would be violent)
But once you have this sort of process, splitting one large portal into many tiny ones, you can consider what happens "in the limit" and you can get *curved* portals and even *closed up* portals (like a spherical portal - that would actually be a classic wormhole)
And furthermore, you can consider *small* and *continuous* deformations of one side of the portal which should still work out. You'd just get deformations as an object goes through.
A simple case would be two rectangular portals where one is a tall rectangle and the other is wide. You can completely fulfill all your rules in this case if you allow objects passing through to get stretched and skewed. You just don't want to *delete* the object. Every piece always must have *some* place to go.
And mass conservation isn't a problem here either: You are simply affecting the density.
It can be relaxed for linear transformations: scaling, mirroring. But non-linear transformations are evil, they violate some nice portal properties. I have plans to make a video about this non-linear transformations in the future, already have a scene for that (mapping sphere onto a plane).
@@optozorax_en Mapping a sphere to a plane breaks the topology as one finite point is gonna be mapped to a point at infinity, or two points are smeared out into an entire line each, or any other number of distortions corresponding to various maps. No matter what, you have at least one singularity. It makes sense to me that you might need to retain topology.
But what if you, say, mapped from a perfectly smooth round sphere to a ripply one? Still the exact same topology, but the geometry is deformed.
I think this should be possible if you consider your "copying the coordinate frame" concept by, effectively, giving every single point within an object (including portals) its own coordinates and continuing paths according to parallel transport when one frame's origin coincides with another's.
After that you might have to consider some physics to predict the evolution correctly: Passing from a smooth to a ripply portal (or vice-versa) would mean a solid object gets locally squashed or stretched, and so you'd have to consider tension forces and such to predict how the object works afterwards.
By the way, if you take the door frame analogy entirely seriously, you really only ought to depend on the frame itself: The surface inside is kind of arbitrary. Like, if you took the door frame to be the shape of a bubble wand, any sort of bubble attached to that frame should be permissible as cutoff surface. - The flat connections you are using here are a matter of simplicity, but if you considered a warped door that's nevertheless flush with the frame as your cutting surface, everything ought to work the exact same still. The situation to me reads a bit like the Stokes-Cartan theorem where you can freely switch, for instance, between an integral over a closed surface and an integral over its enclosed volume.
Or between an integral over a loop in space and an integral over *any* arbitrary surface that has this loop as its boundary. *Any* such surface will do. And I think that's true for your portals here too. You just have to be able to consistently draw the corresponding cutting surface on *both* sides of the portal. And I think for that you need preservation of topology and a diffemorphism (i.e. a function that describes how to smoothly go from one surface to the other in a consistent way)
(This is just me seeing some connections to, for instance, electromagentic fields (where you'd frequently use variations of the Stokes-Cartan theorem), as well as general relativity (where you work with diffeomorphisms), I certainly didn't do all that portal math nor implemented anything like this, so I'm looking forward to what your future videos will bring)
@@optozorax_en I believe what's really going on is that you need *locally* linear transformations. A map from a sphere to a plane is not locally linear for the entire region. But imagine you split up a portal into thousands of tiny cells: You could apply a linear transformation to every single one of those tiny sub-portals. Nothing should break then.
As long as you keep them all connected up, any objects will pass through just fine as well. That's gonna mean your linear transformations have to vary smoothly such that neighbouring cells are transformed into a sufficiently similar way. So long as you have, for every single point, a neighbourhood that transforms in a linear fashion, things ought to hold up.
I love smart viewers like you, write more. You absolutely right about that portal surface is arbitrary, I already have scene for that, in my demo: Load -> Basics -> "Surface portals???". The integral analogy is a good one.
About mapping sphere to a plane - I can remove infinity points by using borders. Also this thing this removes this nice property that you can choose arbitrary teleportation surface, because in that case you can definitely observe the surface and find its exact shape in an experiment (feel when passing material is being tensed).
@@optozorax_en I see what you are saying. I think that *should* be fixable still, *but* it effectively requires some sort of force field to keep things consistent despite arbitrary surfaces. I *think* that's sort of how gravity actually works in general relativity: Space itself is curved and as a result you get tidal forces. - in order to keep the portals consistent under somewhat arbitrary surface deformations, you'd end up defining some tidal forces because you are necessarily in an accelerated frame. The cross section of that field through any sort of arbitrary surface is gonna change in a continuous fashion such that, while you can feel the effects of bent space (effectively gravity), there would not be any point where you suddenly get the impression of a fixed sharp surface (because everything is continious still)
At best you get an event horizon type situation but importantly for those, for an observer right in the scene, those do not occur. They are only an issue from an outside observer looking at the scene from a distance
Thanks for this amazing analysis and demonstration optozorax!
I would love to see what would happen to an object if it was partway through a portal and one entrance abruptly accelerated. I suspect it would be capable of breaking an object in half at an atomic scale (assuming an infinitely thin portal and instantaneous change in portal velocity) but I’d be curious to see your analysis!
How would that compare to pushing/pulling an object in a traditional way?… I dunno, but if there’s one person who could figure it out I think that’s you!
Either way I look forward to your follow-up on moving portals :)
I think accelerating portal should produce some kind of gravitational waves that affects objects and passes energy and momentum to it. This can be derived from one really neat property of a portal that I will make future video about. Right now I'm not ready to answer that question.
What if you connect two portals, one big and one small, and have them go through each other without any rotation?
Will explore this in a new video
If you make a portal out of both sides of each portal, does that break the rules you set?
Wow! If you have the entrance to a portal facing the exit of the same portal and 2D object in between them. Where does the object go when you bring the portals together and then move both portals away? Like bringing two slices of bread together around some jam and then moving the sandwich away.
My gut guess would have been that the portals would simply collide like solid objects. This is an interesting alternative to that?
I would make world made out of small cells, so there won't be a problem of cutting, and i will make all coordinates integers, getting rid of floats and most math, portal will be just set of teleport points 6 sided, and if someone goes through its edge it comes out of bounded other side..
I think all agreed that if something goes half to portal, and then portal closes/it goes through edge, it cuts?
great job! have you seen todepond’s screens video? there are some interesting analogous questions for 2d portals with scaling and rotation
Just watched it - it's really nice
2 portals moving at the same speed in opposite directions is weird to think about if they preserve momentum
Can you pretty please update egui macroquad
The REAL portals should NOT be movable. Not because of some abstract rule, but because portals are connecting different points in the same space. If portal is moving relative to another, it would mean space itself would be moving relative to itself, which would mean either deformation of space or overlap and holes in space.
For example, in your visualisation, one portal moves past the object, but without touching it, and object keeps moving on other side after passing through. It means that it's spatially anchored to original portal. Space that it takes moves through the stationary space in the other side of the portal.
In that case, there should be hole in space behind the moving portal, or space should be stretched and compressed around it. Either way, in static space, portals are fixed. After all, you cannot move a hole in the paper without deforming the paper.
P.S. In that case, portal entering portal would mean simply folding the space inside portal, making it concave; the portals will never actually intersect.
and the portals will have to not move relative to what? The universe is always in motion
@NauzRem As I SAID, to each other.
Great video : )
What happens if you shoot a portal on someone and have them jump into the other one?
What’s the maximum amount of degrees a portal can be teleported?
All those degrees are virtual, they don't really exists. There are always only one blue portal. But in implementation, there may be infinitely many of them.
@ wow, wow, wow… wow… how would that look?
of course the second portal is an object, and is placed in the space of the first portal, and then works normally. no time/space loop issues.
Is this a reupload? I think i saw this video before.
awesome video
Ура, ты сделал английскую версию!😊
Этот акцент просто имба!
В плохом или хорошем смысле?
@optozorax_en Если честно, его не помешало бы чуууточку подтянуть)
Can an atom between two portals bond to itself?
Wow, that's deep. It's the same as creating infinite rod that is welded with its own end after being put halfway through portal
Can we make an electricity generator if we drop a magnet on a portal and then another portal above will spit it out.
i mean you could just make a weight attached to a pulley that spins a generator and the fact you can move a heavy weight from the ground to the top of a building with little effort using a portal means you can generate as much electricity as you want
I disagree with you @4:00 the conservation of momentum is missing when the portal is moving and the object is stationary. when the object is moving it exists the other side portal WITH conservation of it's momentum, which is NOT 0. however if the object has 0 momentum and the portal is moving all pieces of the object will exit the other side with 0 momentum and basically cash into eachother at the edge of the exit portal because the have no momentum and not was imparted on them by the portal.
I've visualised this in my head before but I could never imagine what happens if you ignore the fact that the portals knock into eachother, what happens if you keep pushing?
Edit: Nevermind, I didn't watch far enough. Thank you for showing it :D
I show exactly that later in the video
@@optozorax_en I know, I didn't watch far enough, thank you for showing it :]
1:46 Cut the red wire from a to 3, do not cut the other two
maybe it could be solved by using objects made of voxels instead of meshes ? this would be closer to an actual simulation and could fix the triangle issue
That was my first idea! But it had some fundamental flaw which I don't remember...
@@optozorax_en if you remember tell me i might try to make one myself too also going voxel is very good for ray tracing application since you do check on a data structure instead of every triangle in scene
@@ElKariboosama well, I have like 20 triangles in my scenes 😅, so don't know about performance of the voxel renderer
My fire mastered painting a sound,
While studying squares that claim to be round,
With my professor who was a cloud,
Who couldn't teach circles how to be round.
1:00 There is no link in the description.
It is, it just written in plaintext, see closely, youtube does not allow new channels to have links :( When it allows me, I will update the description.
@@optozorax_en i suggest putting newlines at least
At first iteration youtube doesn't even allow newlines! It automatically removes them
@@optozorax_en I am very dumb.
I love how he says portal
Bounced on my boys portal for hours to this
Portals are actually easy to do with raytracing, if a ray hits a portal then just teleport it to the other portal.
Yes. I tried creating portal in portal using OpenGL and it was a nightmare, but I did it: github.com/optozorax/portals_opengl
One contradiction with reality that portals create is infinite energy with falling objects, but if you think about it, portals should be able to teleport gravitational fields too. This could possibly fix that contradiction. I imagine you'd basically be floating if you were between horizontal portals. A new video perhaps?
Yes! I have an idea how to teleport gravity using gravitons, there will be video about it in some future
In the source engine the mass of the cube is actually defined.
So I have to be cut a seemingly infinite number of times to pass through a portal? Sounds more like a Star Trek teleporter to me lol
Капец, я уж подумал, что твой видос украл какой-то англоязычный ютубер
а уже украли, только не полностью и перерисовали типа от руки
@@NauzRem 😢
We can't move portals because they are not wormholes but rather quantum tunneling. And because it is quantum tunneling it needs to be really cold and since temperature is just the movement of atoms it means you can't move a portal.
I would argue that an object staying still and a portal moving into it would not affect it's speed. If we are assuming the definition of a portal as a doorway, and that a portal should work the same as a normal doorway, when you have a doorframe and move it through an object, the object does not magically change in speed, it keeps the same speed despite appearing on the other side. A portal simply teleports matter and energy through space, therefore it should not add kinetic energy to an object.
If we think about this using newton's first law, an object that is at rest should stay at rest unless it's acted upon by external force. because a regular doorway would not produce force onto an object, by your definition a portal shouldn't either.
I feel like there's no problem in reality, not math, if you break portals. It's just called entanglement. A big portal is just many spacial points being entangled in an ordered way. When you cut the portal you still have 2 portals and you can keep cutting them until atomic scales
Im here before 1k subs !
3:50
The triangle that passed the portal and made it to the other has a velocity V w.r.t to the camera
The part that has not entered the portal has a velocity 0 w.r.t to the camera
But parts of the triangle must have zero relative velocity w.r.t to all the other points within the triangle.
How do you reason this works?
I'm confused, is this a reupload? I swear I watched this a while ago?
Basically after the intro I said that this is translation and improvement over my russian video. Did you really watch the russian video with english subtitles? Because I've seen basically no english comments and emptiness on the analytics.
@@optozorax_en ой, извините, я скипнул через дисклеймер сразу к середине видео чтобы убедиться что это то видео что я уже смотрел. Я говорю на обоих языках, но не смотрел российских видео уже много лет, и труба мне их не предлагает очень давно, за исключением вашего, и я просто напросто не запомнил на каком языке оно было, только содержание!
Sorry for not engaging on the original channel, I just must not have had any thoughts to add. Just subscribed to this new translated channel, and I'm sure it's gonna pick up, cuz the work you did there is very juicy. Good luck!
This is great
Yay, I don’t need to watch with subtitles anymore