I'm so glad you called out the fact portals merely existing already break several laws of physics. Great video! Edit: I really wish commenting this didn't result in further debates in the replies lol people need to chill and just enjoy things more
A portal on a moving surface can only take you to world that looks identical - but where the walls are moving and the piston is static. Two observers in the two worlds give different numbers for objects moving in their worlds - they can't agree on velocities - so I guess we just pick one.
@@JohnnyWednesday Arguably we don't just "pick one", the scenario is defined as the piston moving, so we know which reference frame we're in. It's not that important that another reference frame can come up with another value. Both would see the cube shoot out, at whatever speed it approached (ish), though how that is expressed can change. Consider both portals moving, along the same axis and facing opposite directions. The cube would almost certainly just plop out the other side given the negative velocity of the exit portal, even though it had positive velocity from the input. From the cube's reference frame, it doesn't look too exciting, mostly a teleport. And from the moving portals' perspectives, it does what it always does, and just keeps the speed it had.
@@JohnnyWednesdayYeah, two different observers with two different frames of reference would give you different results. That has nothing to do with the portals though, that's just how motion works
The cube has to move to conserve momentum in one frame, and it has to stay still to conserve momentum in another frame. That's a contradiction and proves the situation is impossible. You can do the same with energy conservation. All frames of reference being equally valid does not mean that what happens in one is irrelevant to what happens in another. Special and General Relativity describe how different frames of reference relate to each other. If you're talking about real physics, the correct answer is "mu". It's a meaningless question due to false premises. If you're talking about a game engine, as mentioned in the video it's a question of how the game engine works. It should be noted that the canonical answer in Portal is also that it's an invalid question due to false premises, as a portal cannot exist on a moving surface relative to the frame of reference of the room/a point on Earth's surface.
@@SnakebitSTI *except for the very notable instance in 2 where this is shown to not actually be an inherent property of portals. Also, what is the frame of reference where the cube with a portal slamming down over it must stay still to conserve momentum? Can the portal itself not be acting on the cube to change its momentum? Bc clearly its momentum _is_ changing, so instead of saying that change came from nowhere and defies physics, why can't we say it came from the portal?
If you think about it in a different reference frame, the portal moving toward the cube is essentially the same as the cube moving toward the portal, so the same physics would apply.
See this is exactly how I visualise it and don't understand why it isn't explained in this way more. A portal pushing into the cube is exactly the same as the cube pushing into the portal because - depending which portal you're looking at - both are occurring.
But there is another equally valid reference frame where the cube is not moving, and then later it is, without any force having acted on it. It always loops back around to "portals are impossible".
Yeah, that's exactly how he solved the problem in the last video, seems like the most sound explanation to me and the most simple to explain too, and this whole thing with particles and bonds seems to follow that.
@@SnakebitSTI Which reference frame? From the reference frame of the seal of the portal (the entrance/exit "surface") the cube is moving towards it (as already said). We cannot describe the movement of the cube from its own reference frame, so you are implying another reference frame.
I always figured the portals were two ends of a wormhole. The path between any two portals is actually a null geodesic. Therefore there is no violation of energy or momentum conservation. It's like how the moon orbiting the earth changes its velocity constantly despite no energy input yet we know this is not a violation of conservation laws, rather it happens because the conservation laws hold.
My main problem with this is that it suggests that gravity should be able to travel through portals, and as such gravity would be able to pull you _up_ through a portal above you if the exit was lower. This would prevent the terminal velocity setup from working, instead making it a 0g zone between the portals.
@@angeldude101 It would not make it a zero G zone necessarily as you still get the gravitational influence from all the ground around the lower portal. You should still pick up speed and hit terminal velocity albeit at a slower rate.
@@ragingfred By necessity of the conservation of energy, you couldn't gain any speed by travelling from a point A to the same point A, even if your path goes through the portal. An object at the point A would always have the same potential energy, so you couldn't get any kinetic energy unless you include an energy source exterior to gravity (even including the Earth's gravity). You can't invent a perpetual motion machine, even in a world with portals. Technically, a free falling closed path that goes through the portal would by necessity sum up to zero gravity. Or if you want to be more precise, the integral of the gravity field throughout the path would sum up to zero, just like the moon does during its orbital path around the Earth. That doesn't mean that the gravity stays at zero G throughout, but it does mean that you can't gain speed between two cycles of a free-falling scenario ; since the integral of an acceleration force throughout the path corresponds to a speed difference, the speed would necessarily be exactly the same at the same point between two cycles. While the Earth does have an influence on the system and does still have a gravity pull, it only has a real influence as you move away from the system. Functionally, the two ends of the wormhole would probably act for gravity in a similar way as the two ends of a magnet act for electromagnetism, where the gravity influence near the wormhole is so intense that the Earth's influence is negligible in comparison. As you approach the system, you only feel the portal's gravitational influence, just like a compass gets fully influenced by a nearby magnet, but as you get away from it, it loses its influence and you can start feeling Earth's gravity again, just like your compass starts pointing North again as you escape the magnet.
The idea of the material fracturing because of a sudden change in portal momentum is scary. If the portal surface was indefinitely thin a sudden change of momentum or position could act as a kinetic “knife” changing the inertia at an infinitesimal plane thinner than a razor. Makes me wonder what might happen if an earthquake or seismic event happened while a person or living thing went through. Worst case could be just as bad as a portal closing mid-transfer… Thanks for helping us think about yet another disaster that could come of this innocuous-looking technology!! 😅
I don't think that would be like a knife under normal conditions or even earthquake . I think that only if portal stops at infinite speed that would be a problem. maybe edge of the portal could be like a knife tho
8:12 It's probably important to note that this isn't necessarily a clean cut along the plane of the portal. The portal isn't acting as a knife, it's the object pulling itself apart.
The discussion of conservation of momentum in the video reminds me of an interesting variant of these sorts of portal shenanigans I once came up with... Say we have our portal set up like this: The blue end of the portal is on a concrete wall, something stable that isn't going to be moving. The orange end of the portal, however, is on a thin wooden board, something we can easily pick up and carry around. Now, on the blue side of the portal, we get a metal pole, and thread it halfway through the portal, so it's sticking out both sides. And then we bolt it to the concrete wall, anchoring it in place on the blue side. So, on the blue side, everything is still anchored in place and cannot move. If we look at the orange end. We have our board, with a portal in it, and a pole sticking out. And we can still pick up that board and wave it around. And I don't think it would be that controversial to claim that if we do that, the end of the pole should move around as well. After all, it's anchored in place on the other end, it's being held in the middle of the blue portal, so it should stay in the middle of the orange portal even as it moves around. But that means the tip of the pole is accelerating around, as you wave the board... which means there has to be some sort of forces being pushed around, some amount of work being done. You pushing on the board to move the portal, is resulting in force being applied to the pole. And Newton's third implies that the reverse must also be true... if you try to move the pole, it should translate back to forces being applied to the portal, and the board it's stuck to. That is... you should be able to grab onto the pole sticking out of the orange portal and lift, and it should pull the board along with it, you could carry the board around just by holding onto the pole. Which feels weird at first, because the pole isn't attached to the board, it's only attached to the wall on the blue side, but I believe it's the only way it can all work. I came up with this scenario while trying to reason through another variant of the portal paradox, where you have _two_ pistons facing each other, with portals on both faces, and crush a cube between them... which can be hard to process. But once you understand that it must be possible for reaction forces to propagate backward from the objects moving through the portals to the portal surfaces themselves, it's a lot simpler.
I'd like to see this channel do a video on this subject. I can sort of wrap my head around it, but I'm interested in how its implications might affect other scenarios. Does this reveal any useful principles that weren't obvious, or is it just a brain twisting implementation of otherwise well understood rules?
to me, i don't think you'd be able to pull the board and portal around by only applying force to the pole, unless it was somehow enough force to move everything the pole is attached to (and even then it would just snap at whatever the weakest connection point was). since it'd functionally be the same as grabbing a metal pole welded to a wall with no portals attached, the board portal would just hang there on it and the pole would be rigid. BUT in that case, that means by moving the board around, the pole is moving with enough force on the other side of the portal to basically crush anything, which still makes more sense to me than the alternative somehow
My take on this is that the rod and the orange portal are connected since the orange portal is connected to the blue portal, which is connected to the wall, which is connected to the rod. Sure, when picking the board and orange portal up by the rod, the connection isn't part of what you pick up, but it is there.
I agree, thats how I've seen this problem all along. But it doesen't apply to the conservation of energy. Never had I considered the infinite portal fall, his example really fucks with my head.
It makes slightly more sense if you assume that the portals are "smart" and "powered" and can somehow - while the momentum of the object imparts some energy upon the surface they're placed - impart appropriate energy on objects moving in/out of them. If I'm understanding this correctly, it's pretty much the only explanation for how they can work at all. I think he had this same thought, and he pretty much says it, but not expressed in much detail. People genuinely arguing about something from a work of fiction that is a physical impossibility in our universe is a pretty silly exercise in futility obviously, but I think this video and what's been said here is the closest approximation to how it should/could work, and I think that's pretty cool lol
To me that would then mean the cube pushes back on the portal as well, so must at least be effectively slowing the portal on the piston down, or requires the piston to push with progressively more force
@@Haps_q I guess it makes more sense when I think about it now. Just the inherent fact of teleporting something to a higher place is an issue, because you're taking an "energy shortcut" when compared to the energy required to lift that object up normally. I agree with the video, there's probably no way to make this consistent with physics without handwaving the energy requirement away like "the portals are powered" or "the portals harvest energy from somewhere else" etc.
That's a force not an energy, and the problem is that in the example with a piston all the energy is already accounted for yet somehow the cube is imparted a force, and thereby given energy proportional to the speed of the piston. This only makes sense if pushing a portal creates a resistance equal to the kinetic energy imparted onto the mass moved through the portal, a lot like air resistance.
i love how this starts out as a chicken and the egg situation and then James goes to prove the point by stating simply "where do you think the chicken came from", making everything else seem relatively obvious in the process. thank you for finally creating a well made solution to this lol
@@urlhnd An almost-chicken. Eggs are eggs, but egg laying animals may or may not be chickens. So an animal that was nearly a chicken laid an egg, from which hatched a chick that grew into a chicken. Egg came first.
@@messymessr exactly, chicken or egg first only seems interesting to people unfamiliar with basic science, educated people understand that the egg came first.
@@SuppaflyZSM Educated people understand that the question is supposed to be understood as "Which came first, the chicken or the chicken egg?", which is impossible to answer because we have no single coherent definition for either of those things when viewed on an evolutionary scale, similarly to how it's impossible to say where one color ends and the other begins on a gradient scale.
@@Lernos1 The "gradient" in this case only advances when new life is created, i.e. the egg. Assuming that 1) When something is born it either is or is not a chicken, whatever that definition is, and 2) that a pre-chicken cannot randomly mutate from radiation or cellular decay into a chicken... Then the chicken egg came first due to random genetic mutations during breeding. If it were possible to say there were a "first" chicken, then whatever that designated chicken is came from an egg.
About conservation of energy: I always assumed from seeing the first trailer for Portal back in the 2000s that the portals required a vast and continuous expenditure of energy by Aperture Science to open and to stay open. The energy comes from unseen machinery behind the scenes which is fuelled by your suspension of disbelief. I also think that the cube getting cut in half by the piston ceasing to thrust it forward would be extremely unlikely to happen unless the cube was made of something really really weak such as paper or the piston was going really really fast, such as breaking the sound barrier. Also, the effect of gravity pulling in different directions on the two sides of the portal should be considered.
Honestly pointing out that the test chambers aren't static kinda cuts the whole line of reasoning off on its own - all portals are moving portals. Whether or not something appears to be moving in our frame of reference has no bearing on the physics operating on it, that's just relativity. In regard to the infinite portal drop conservation of energy thing, the real reason we're able to break conservation of energy there is that we're not simulating the impact of the gravity of matter on one side of the portal on matter on the other side, which implicitly means the portal is constantly using some amount of energy to counter it. There isn't really one physically consistent way to model that though, since space in our universe can't have holes cut in it (and modeling it would break some basic parts of the gameplay anyway).
The answer to the last question is that portals - either as depicted in the games, or as imagined in an attempt to make those depictions physically consistent - inherently violate the laws of physics in some way. As portrayed in the games, and as popularly imagined, the portals connect two regions of space in such a way that the space is completely continuous. However, in the real world, gravitational fields propagate through continuous space, so a "real" portal would also cause gravitational fields to propagate. To make it obvious, imagine the scenario of one end of a portal on Earth, and the other on the Moon: you will of course get a massive flow of air at first, but even faster than that (at the speed of light in fact) you'll also get the Earth's gravitational field propagating through the portal. Needless to say, this is going to do *weird* things if you work through the consequences, e.g. I suspect that the portal ends moving relative to each other would generate gravitational singularities, at least in some circumstances.
The portal "paradox" is only a "paradox" to those who can't understand relativity. If I walk through a doorway at 1 mph, the rate of me going through that doorway is 1 mph. If a doorway is rolled over me at 1 mph, the rate of me going through that doorway is still 1 mph. A portal is just a doorway where the entrance and exit are at two different spots. The rate of going through the doorway still needs to be the same on both sides. That's momentum. And as it is officially stated in the game: The laws of momentum are conserved between portals.
the piston coming down at the cube is the same as the cube accelerating towards the piston. the only question is if our camera (frame of reference) is attached to the platform the cube rests in, or the piston itself. once you attach the camera to the piston, it should become relatively obvious to anyone, i would think
That would be correct if you only attach a frame of reference to the exit portal, but you still have to account for the entrance portal. What makes this problem difficult to think about is that you need two frames of reference interacting at the same time. The right portal is not moving in reference to the original platform and there is no exertion of force from the static platform on the left, therefore the cube cannot launch out of the right side. That's why it's a paradox: Both perspectives are correct but can't coexist.
It is not. All motion is relative, but you can look from multiple points of relativity to determine which object accelerated while the rest is stationary.
From a gameplay standpoint this solves the portal paradox very well, but realistically this is all wrong as it doesn't actually obey the laws of energy conservation. The problem is that energy conservation is being maintained because you're treating the portal as if it has mass and thus velocity, which isn't true. Portals are wormholes, or spatial tubes essentially. What happens if you swing the end of one tube while the other is stationary? It creates a vacuum force and thus momentum--the YT Channel The Action Lab did an experiment showing this. So the actual answer is that both are true. When one portal moves to encase the box, the box will only move if the vacuum force created is strong enough to actually move the box. Then you have to remember that the larger the diameter the tube the greater the speed needed to generate a vacuum force. So then you're left with the 3 following scenarios: 1. Portal moves and encases the box, causing it to exit the other portal and fall via gravity (not a high enough vacuum force). 2. One portal is in space and the atmospheric pressure difference creates a vacuum force to move the cube. 3. The portal is moving at speeds insane enough--due to large diameter spatial tube--to create a strong enough vacuum force to move the cube.
One thing that's interesting about portals is that gravity doesn't seem to pass through them. You don't get pulled by the earth on the other side of the portal until you actually move to that side of the portal. I wonder if having gravity work through portals would solve all the infinite potential energy shenanigans, or if they would just make portals incredibly violently destroy their surroundings, as earth starts being pulled by itself through both ends of the portal.
I think of the portals as wormholes. Drastically curved space(time). You're not teleporting up, you're moving in a straight line. It just so happens that in the way that the curved space is, a straight line leads you back to where you were. Kinda like if you were on a sphere, if you walk forward enough, you'll get back to where you were. It's like that, except the sphere is VERY ununiform, with it being mostly flat, and then a very sharp curve in squished space
@@iinkstain "Quantum tunneling" is a process that has nothing to do with what we see in Portal and was just the writers' way of making it sound cool. It is just easier to think of the portals as we would the kind of wormholes that relativity supports.
This is probably the most logical take and best practical explanation of a "solution" for the portal paradox I've seen. Obviously the portals as seen in Portal would break our universe pretty thoroughly but this seems like the most intuitive and closest approximation to how they would work if they did exist.
So in a world with these types of portals... One portal at the bottom of the ocean, other portal inside the end of a very strong pipe, which leads to a turbine, and then back into the ocean... And now we know why aperture doesn't have any power problems.
What if we considered portals as instead of tying space together, we dissameble the incoming object and reassemble it, spitting it out the other side. This would conserve momentum in the way you describe, and doesn't really violate any laws of physics.
I agree and thats how I think of teleportation. Like the original object is being destroyed and a new one is being created. In that case what the portal does on the other side can be anything it wants to. You could come out as a rubber duck flying 100mph. but in the case of aperture science they wanted to make something more practical
Welp, thanks to this video we can finally have portal 3, a perfect narrative about discovering moving portals and defining it's physics with logic. I'm glad that GladOS is still alive.
The portal does not impart energy at all in this equation, it is doing a third, inexplicable thing: changing the frame of reference for the motion of the cube. All motion is relative, the portal is just changing what the motion is relative to. There is no such thing as a "stationary" object.
I feel like if there was a pair of portals that are ”holes in space”, then gravity would not behave as we expect and then the infinite falling trick might not work?
To figure out where portals get their energy from, there's some information that is relevant: 1. Moon rock is excellent at sustaining portals 2. Other materials can support portals (aperture had portal surfaces before they bought the moon rock) The most promising energy source in moon rock is Helium-3, an isotope of helium that can be used in nuclear fusion reactors. As other nuclear fusion fuels exist, this explains how old aperture panels could support portals, and as there's a limited ammount of Helium-3 in moon rock, it explains why the auto-portals in the early levels turn off (to preserve power), and even why the moon portal closes; The higher energy required to reach and match speed with the moon, combined with unpurified moon rock, results in a portal that only lasts a few seconds. Sure, it's nowhere near enough power, but that's a much smaller handwave than portals just being magic
Maybe this is just my lack of understanding, but I always understood the paradox angle of the box not flying out the other end as being true due to there not actually being any momentum/force applied to it until it comes out the other end. So if it got far enough through the portal, gravity on the other end could pull it the rest of the way out if there's enough of a slant? With gravity really being the only force applied. Thinking of portals kind of like a hula-hoop, where one side just happens to come out in a different place in space. So if you lower a hula-hoop over a box, the hula-hoop doesn't itself apply force to the box because it never actually touches the box. So in my mind the only force being applied to the box in the paradox is the environment on either ends of the portals. But maybe that's nonsense. I just haven't had it ever explained convincingly to me why we are assuming any momentum is coming from the portals themselves. Similarly for the infinite falling thing. You're speeding up as you fall much like you would if you jumped from a large height. The portals themselves aren't contributing to your momentum, the repeated force of gravity is?
My two cents on the conservation of energy problem is that portals fundamentally violate it. There's something called Noether's theorem which shows that symmetry and conservation are equivalent. For example, conservation of momentum is true because of translational symmetry, and vice-versa. Similarly, conservation of energy is due to time invariant symmetry. If portals were to exist in reality as they're shown in the game, you could violate causality by instantly transmitting messages (not a GR expert by any means, but there are some physics stackexchange posts where they explain this better). If you can violate causality, you break time symmetry which breaks conservation of energy. So even if crossing portals used energy, as long as you can break causality, conservation of energy can't be true Fun fact: conservation of energy isn't even true in reality because of the expansion of the universe (also because of Noether's theorem). It just appears to be true at our scale
Portals are just holes in space, the changed momentum vector occurs for the same reason orbiting/falling do and where the energy for that comes from also has the same answer as where does the energy from falling come from. In terms of moving with objects, I would imagine that the portal wouldn't be tethered to the object, but would itself usually be an inertial object. While it has the same momentum as whatever/wherever its being created on/at, as soon as it is actually created it would cease to update it's momentum... or it would if not for the fact that energy has to be provided to keep the portal open, and since the spacetime curvature centers on the energy source, the portal would be dragged along by wherever it's getting energy from via a "gravitational bond". Even without that though the portal still would not fly off since relativity is a thing. This would also explain why portals close when you accelerate the object it's attached to too much, as if the energy source gets too far away from the "center" of the portal before the "center" can "move" itself back to the energy source, the portal would just collapse from the energy no longer being geometrically capable of supporting the curvature. Conservation of energy is inherently violated in any system where the curvature of space can change over time, but in this case a portion of the energy that makes up the cube would be transferred to the entrance portal from a gravitational interaction, and would take an equivalent amount of energy from the exit also via gravitational interaction. You can find a similar interaction in real life by looking at two black holes orbiting each-other, and the orbits decay from gravitational energy loss.
The rest of the issues of where energy comes from/goes to are solved when you consider how non-inertial reference frames in real life actually have similar problems and what the solutions to those problems where (see: the unruh effect).
Instead of thinking about the piston at all, for a second think of the diagonal portal as a regular hole with a piston and a cube attached to it; flinging it out the other end. If the piston portal from the example were to stop halfway, the cube would have no sufficient momentum to pull it through leaving it on the ground with the other half poking through the exit portal.
To all of the confused people: The portal slamming over the cube imparts mimentum to the cube. This is observable in that the cube _must_ move to exit the other side. Any portion of the cube on the exit side has roughly the velocity of the piston. Ignore conservation of energy. These portals are magic; pure logic doesn't map 1:1.
I want to see a serious particle physicist look at the portal paradox and consider things like whether gravity would be transmitted through portals. If anything can pass through a portal, does that include subatomic "messenger" particles like the graviton? If so, then wouldn't the force of gravity pass through the portal? If portals were real, particle physicists would love using them to help with those sorts of theories
concidering that gravity would work from both sides most logical is being directly in it would be felt from the range of 0g to 2g (depending on orientation) and be weaker further you get from it, and probably get closer to be not able to percive any change of gravitation pull since one from the portal would be non direct and changing direction so no longer amplyfing/reducing "ambient" one.
It seems to me that the moving portal would kind of "simulate" all of the space on the other side of itself moving that fast against anything that passes through it.
A portal is just a hole, where the other side of the hole is somewhere else. If you have a cube on a table, cut a hole in a piece of paper and put the paper on the table with the cube going through the hole, the cube doesn't just shoot up.
tough to say. that wouldn’t be opening up any new space for a pressure differential to form, it just gives the air molecules more directions to flow through, while maintaining the exact same state of air pressure after the portals appear.
@@iinkstain There would probably be a slight shift in air as air pressure at the ceiling and floor equalise, since they would be at slightly different pressures due to convection. I do think the air would also fall infinitely downwards though, for the same reason as if you slid a cube into an infinite portal loop of the exact same height as the cube, it should still fall- All the particles are being accelerated by gravity at the same rate, there's no reason to believe the cube would somehow support itself. It probably wouldn't be very fast though since the falling air would be interacting with surrounding air which would slow it down.
@@thevortexcrafter7060 i think now that i imagine it, fitting the cube into that space that squeezes the cube against itself would be extremely difficult. you’d be exacting a squeezing pressure onto it as the opposite edges of the cube push against itself, either crushing it entirely or causing it to erode a thin enough layer to slowly reduce this pressure and form a thin enough floor of air molecules between the spaces of the cubes top and bottom, that the cube will start trying to chase (causing it to fall). i wrote this after a fever dream.
It's nice seeing your reasoning behind this. It almost convinces me that this is the way it should work. The way I see the portals are two sides of one thing. You can't have one without the other. One portal on a wall is not a portal. So it's more like, if a hula hoop fell around you, you wouldn't shoot out the other side.
Except from the perspective of the hula hoop, you DO infact shoot out the other side. It's only from your perspective that you're stationary, just like how the entire earth is moving at extreme velocities yet we are stationary relative to it.
RE: Conservation of Energy Obviously portals aren't actually possible in reality, which means at some point we have to concede that portals are breaking some law or laws of physics. We'd rather it be as few laws as possible so it's as real as possible, but *something* still has to be broken. It obviously must be breaking conservation of energy. And there's no real explanation for that because... it's not real. It's where you need to apply suspension of disbelief and just don't worry about it. Intuitively I don't like the swinging portals thing. But also does that explanation even work if the portals aren't facing the same direction? Like if you put two hanging portals in a V shape (but with enough room to swing freely) and shoot a cube straight in to one of the portals. The entrance portal being pushed back still could make sense, but the exit portal would basically have that momentum applied sideways, even though the cube comes straight out. Or if the exit portal is still just pushed back like your explanation, I don't see how that's conserving momentum since it's a different direction. It seems more like portals just don't conserve the direction part of momentum, just the value. Edit: actually, direction is relative just like speed. So it still keeps the same direction relative to the portal the whole time just like it does with speed. Is that not conservation of momentum?
On the problem of conservation of energy where you get infinite kinetic energy from this 8:57 scenario, I think you could apply this 6:00 to it. If the portals are stuck on a rigid surface, then that pushback would be felt entirely by you instead of the portals moving. Essentially, the portals would absorb your movement kind of like how a magnet falls slowly through a copper pipe or like a non-newtonian fluid. The faster you move through the portal, the more resistance to motion you feel. Of course, this kills all the fun of many if not all puzzles in Portal, so maybe we wouldn't want to implement it.
Correct me if I’m wrong but the infinite falling trick works because when you put a portal on the ceiling and the floor, what you’ve basically done is create an infinite stacked building. just imagine you have a building with a bunch of floors and a hole in each and you dropped a cube all the way down but with the case of the portals it just drops forever That’s how I imagine it
I find the conversation interesting because it views the problem as though portals are a planar barrier, but the Moon moment in Portal 2 (if a bit exaggerated) suggests the sides of the portal can impact each other through differences in pressure and gravity. I've always viewed the transition between portals more like two magnetic fields interacting with each other. If the magnetic fields are similar, then the point where they meet acts almost as if a single magnet. An infinite hole would not be infinitely increasing gravity, but rather a transition between the gravitational force at each height as a gradient. Also, with regards to relative velocity of the portal, you could argue the entrance and exit are both moving simultaneously relative to the object, like dropping a hula hoop over a person. Ultimately I think the biggest, and potentially only, contributor to launching the cube would be the force of Earth counter-acting gravity. You would get that small acceleration as gravity suddenly changes relative direction. If the portal stopped half-way you'd see the cube probably lean over into the edge of the portal as it finds an equilibrium between the two gravitational fields it exists between. (which sounds dangerous if the edge of the portal is infinitely thin!!)
Moving portal imparts its motion onto the object passing through. The energy comes from what the portal is attached to. Oh, you've got account for exceeding the resting forces for the portion of the object that hasn't received energy from the moving portal. So a little less than half, friction is going to be minor, but gravity is going to be the decider. Tumbling is probable. Snapping objects apart is likely going to be a problem of portal misalignment more than speed. 50gs fails to rip a human apart... Actually that's wrong... The relevant concept isn't acceleration but jerk... Closer to spontaneous the change is the greater likelihood of ripping a body apart. Misalignment is more probable but don't be rocket thrusting a portal cart onto a half exposed object. Effective mass that has traversed through the portal at whatever speed it was traveling versus the resting mass with all that force focused at the intersect plain of the midportal object. That's... going to become nasty without much speed on the moving portal. The normal solution for portal like wormholes is them sharing the same origin and then getting stretched across space which allows them never exceed C but allows objects(nonsensically) to effectively exceed C. The origin is the gun. The being able to turn off half and then make anew is.. problematic to parse but not relevant. Wormholes have you traverse through a space between the entrance and exit. Portal portals don't seem to have any such buffer space. That lack of buffer space makes portals moving at opposed speed to what is going through them very problematic... I had a thought about the real issue being realistically applying gravity through the portal. Well, any attractive/repulsive field effect really. They should probably propagate through the portal. But I'm going to be honest... That isn't anything on how a portal changing speed relative to the traversing object is going to play out. Accidentally overwhelming the intermolecular force, the nuclear force?
5:45 The vectors here only work out if the portals are side by side facing the same direction, no? This explanation for the conservation of momentum wouldn't work if you turned one of these panels, say, 90 degrees in another direction.
I liked this video a lot as someone that intuitively agreed with you, and agreed with your argument in the previous video, but it still didn't make sense as to why in my own head. Showing the two boxes made it instantly click. Thanks for all these wonderful videos.
I don't know if it really makes sense to keep the conservation of energy law in a world where (Portal's) portals exist. After all these laws have been determined empirically in our world, without portals. However, I think it would be interesting to consider Newton's laws of motion, especially the 3rd one (action and opposite reaction). This means that with the portals on the ground and ceiling, you are also accelerating Earth in the opposite direction! You could use this technique to accelerate a ship! Regarding the portal stopping in the middle of the cube, snapping the cube in half would also require a lot of energy, spit does not make sense either for that reason. It cannot be instantaneous anyway, so it's ti sane as the cube hoing through the portal at constant speed, and getting progressively decelerated. There must be a reactive force acting on the portal to account for this deceleration.
A possible theory to where the energy comes from is if portals themselves had a mass. Considering the portal funnel effect, this could vaguely support the idea that they have their own gravitational pull. As objects enter and exit the portal its mass would change. In the case of infinity falling through portals, I guess one of the portals would collapse once too much mass is moved through.
For Chell jumping into a portal loop, when something fall down, it moves air upwith turbulences, so infinitely falling would make a upward air stream that would add up and apply resistance to falling, mostly making the object to go out of optimal loop path
concidering gravity it just made you reach maybe higher speeds (since at the frame of the portal you would most likely be influenced by 2g) but as you say it would not make you reach infinite spped due to air resistance
For the question of "How is energy conserved?": What if, it's the gun that provides the initial energy to open the portal, and as it's used, the energy in the 'wormhole' is removed. And then we can explain that the magical portal gun is smart enough to know and measure the current portal locations and puts more energy into those spots to keep it open.
About conservation of energy - in the case of the cube shooting out of the other portal - it would definitely have to come from whatever force pushes the portal in the first place. in the case of teleporting up - I think the obvious solution would be that you *should* need equivalent amount of kinetic energy to even go into such portal in the first place, and you just wouldn't fall into it when stationary, so when you fall through a portal and go up - the needed energy is taken from your kinetic energy, just like when moving up normally. Same with going down - such a portal would "suck you in" (this would require carefully thinking about how air pressure would work but I'm sure it would eventually equalize to *something*).
Actually, thinking about the air pressure thing more - my idea would *fix* air pressure issues, without this you would naturally have air being sucked from a portal below to a portal above, infinitely. This would provide a mechanism to prevent it. I think this would make portals completely physically consistent. But practically may result in some insane tidal forces when a portal goes between places at vastly different heights... so spaghettification by portal? And they would be so much less fun in a game
4:20 where do we draw the line with what gets sliced through a portal? if this diagram is how you believe portals would work then we would all be screwed in that universe cause the portal would split the atoms in the air lmao
7:07 To be honest, I think this video far exceeds an argument, as it's a very entertaining, yet informative breakdown on portal mechanics. So many points you make here I would never of thought about and coupled with the very helpful examples make this a very amazing video. Great video!
Good video and great animations, but this is still definitely incorrect. Portals are canonically wormholes, just the visible borders of an invisible, warped path through space. For all intents and purposes, the two portals are like either side of an infinitely thin hula-hoop. There cannot be a concept of space “between” the portals, because portals simply connect space in arbitrary ways, same as how a doorway is a defined plane that separates the rooms it connects. Going through a portal cannot affect the transversing object under any circumstances, by definition, otherwise they wouldn’t really be portals. For the “redirection” of a moving cube’s momentum through two static portals, the cube is moving in a straight line through space (through portals) that appears disjointed to outside observers. But from the cube’s perspective it never changed direction and there was never a need to accelerate to change the direction of motion. Just because the path of motion appears curved to outside observers doesn’t change the fact that the path was straight. This is just like how light bends around objects with gravity, despite having no mass, since gravity bends spacetime so that a straight path from the light’s perspective is curved to ours. Each atomic slice of the cube goes from blue side to orange side without changing its momentum, and moves out of the way just in time for the next slice to make the transition. The distance between each slice has not been disturbed so the transition through the portals is unnoticeable and only one of color-coding. The same thing is true if both portals are moving in sync, like having a portal on the front and back of a square-faced school bus. If the bus was driving really fast at you, and you did a purely vertical jump, you would land on the ground exactly one bus-length from the point you jumped, regardless of how fast the bus was driving. You never touched or interacted with the bus, and the only force acting on you would be gravity. Each atomic slice of you goes from blue side to orange side without changing its momentum, but the orange portal moves forward just in time for the next slice to be scooped up by the blue side and make the transition. Again, the distance between each slice has not been disturbed so the transition through the portals is unnoticeable. Note that for both portals moving or both portals stationary, you can imagine each object as an atomic slice going from blue side to orange side with no inconsistencies. Either the momentum of each slice makes room for the next, or the momentum of the portals allows the next slice to “appear” right where it’s supposed to without affecting the previous or next slices. But this isn’t true for one portal moving, one portal stationary or any other situation where the portals move relative to each other (a difference in velocity). And the reason is pretty obvious but took me a while to formally explain: we are expanding and contracting the length of the warped path of space connecting the portals. To go back to my initial hula-hoop definition, imagine holding a hula hoop above your head and then dropping it. Every part of you goes from being below the hula-hoop to instantly above the hula-hoop, sequentially and at the same rate. But for portals moving separately, it’s like the faces of the hula-hoop are not in sync, so the rate of space following through gets affected and this has serious consequences. Before we get to the main example covered in the video, let’s go through a simple example to help illustrate the process for thinking through these hypotheticals without confusing portal momentum and cube momentum. Imagine we have a 10m stick in space, the blue portal facing the stick and moving towards it at 40 m/s, and the orange portal facing away from the stick but also moving towards it at 20 m/s. As each whole atomic slice of the stick enters the blue portal, the orange portal has only moved half an atomic slice’s length. This doesn’t matter for the first slice, but the second slice only gets half as much room as it requires. The other side of the portal still has the third slice on it, holding the front half of the second slice against the first slice. The third atomic slice will be forced to “appear” at the original location of the second atomic slice, further sandwiching the second slice between itself and the first slice. Then the fourth atomic slice will be forced to “appear”, with the fifth slice following close behind. Since the exit portal is moving at 1/2 the entrance portal’s velocity, we will end up with a stick half as long (5m) but twice as dense. If we swapped the speeds of the portals, we’d end up with a stick twice as long (20m) that is half as dense. To generalize this, the length contraction factor (LCF) can be represented by the velocity of the exit portal away from the exiting object sections divided by the relative velocity of the entrance portal towards the entering object slices. It is important to note that the length contraction or expansion would happen directly on the surface of the exit portal. Objects would also deform in shape if the exit portal is moving up/down/left/right as an object passes through, like dragging malware popups across a desktop, since the center of each slice would be offset from the previous one. Also note that the bottom of the LCF fraction will always be positive, since an object will only enter the entrance portal if their separation is decreasing. The top portion can be positive, negative, or zero depending on how the exit portal is moving. The main example in the video represents the case where the LCF = 0. The first slice of the cube enters a moving blue portal and appears out of the orange with no momentum. This agrees with the bus-jumping example at first. But then the second slice arrives, and the first slice hasn’t moved relative to the exit portal since both are stationary. This will force the second slice to “appear” in the exact same location as the first, instantly doubling the original density. Then the third slice “appears” in the exact same location as the other two, reaching triple the original density. The gut reaction to this explanation is to ask “Why wouldn’t the newer layers push the previous ones out of the way?” and they would, eventually. But it’s important to remember that the squeeze occurs because the portal-shaped cylindrical volume of space becomes compressed along the length axis, not because of any kind of momentum transfer or acting forces. In LCF = 0 cases, the density would continuously increase until reaching the object’s material stress point and exploding right on the surface of the exit portal to relieve the internal pressure. If the portion of the object yet-to-enter the entrance portal isn’t blown away from the entrance portal, this cycle would probably continue until all of the object had either exploded or become compressed at the exit. Similarly to how low LCFs cause internal pressure stress and explosions, too high an LCF will separate atomic layers and introduce internal stretching strain which could result in sheering off slices of the object as they leave the exit portal if moving fast enough. Negative LCF cases (exit portal moving in the direction of its opening) and cases where the LCF varies across the width/height of the portal (angular rotation of a portal) are even more interesting to think about, but I’ve already spent way way too much time typing this out and so I leave that as an exercise for the reader. The only alternative to this length contraction would be that portals cannot change their relative positions or velocities once they are opened. Under this rule, if one portal was moved independently of its partner, both would instantly destabilize and close, severing anything passing through at the time. This prevents all of these convoluted explanations, but feels very limiting and contradicts the neurotoxin laser cutting and moonshot scenes from the games, which is kinda what spawned these paradox questions in the first place. So yeah, that’s my explanation. TL;DR - There is no momentum shared between portals and objects going through. There are no contradictions in portal behavior if moving in sync (or not at all). When portals move independently, objects passing through get stretched/crushed along axes of portal movement. The stretching and crushing is due to the length expansion and contraction of space itself while passing through portals.
I think the platform you're smashing into the cube is transferring it's energy into the cube through the portal. as you said, because the target portal is stationary while the other is moving, the first portal must be essentially pushing/pulling the object to the other side, and the only reason it's doing that is because it's being moved by the platform. so if this were reality I would expect that the piston encounters resistance similar to the momentum the object is gaining on the other side
how it is tansfering it since it is not touching it? and if it was magnetised than same energy that was pulling it towards portal would pull it backwards towards orange
@@klawypl I view the portal as a rigid membrane that warps light and matter upon contact to the matching membrane, so yes it is touching it otherwise it wouldn't be "going through" the portal
What if the platform with the portal coming down over the cube isn't being pushed, but is free-falling? As the platform with portal falls over the cube, the part of the cube already through the portal pulls on the part that is still on the other side, which is being kept back by gravity. With the right combination of weights (cube and platform) and falling speed, could it happen that the platform stops falling midway over the cube as the forces equal out? This could also change in interesting ways by making the cube bottom- or top-heavy. The one could make the falling platform stop higher up the cube, while the other could make the cube shoot out as soon as its heaviest part is through the portal.
my idea for conservation of energy due to portals: when you pass through portals of different heights, the sudden change in gravitational potential exerts a gravitational force on you normal to the plane of the portal, nearly instantly converting your kinetic energy back into potential energy, or if you're not moving fast enough or pushing hard enough to achieve that potential energy, resisting that you pass through at all. another fun option is if the gravitational field could somehow "flow" through the portals to equalize the potential difference, resulting in a zone of zero gravitational force directly between the portals, and at some horizontal distance, a slight repulsive force near the one on the floor and a slight attractive force near the one on the ceiling.
I'm glad to see you did a follow up to this topic honestly, there's still some intricacies that you're missing, as I had mentioned in my previous comments on the other paradox video, but I'm thrilled to see you came to the same conclusions I did for the most part! I ended up writing down effectively a small essay from when I first sat down to think about the portal paradox and knowing some funky physics points regarding portals given their being based on wormholes and I'd honestly love it if I could sit down some day and have a chat with you on this some time! Especially given there is enough weirdness left to cover regarding the paradox on offer that you could actually make a third video, one thing I'll share adamantly though, all interactions should be considered from the reference point of the portals where the world always moves around them and that they are from their perspectives always static, makes understanding "Speedy thing goes in, speedy thing goes out" a lot easier for the weirder side of the physics, also puts more plainly the moving portal interactions true nature imparting moment of inertia. Please do let me know if you're open to having a chat regarding this given I had a lot of fun breaking down a ton of weird and at times in words of Einstein, spooky interactions and would love to properly share them in a form more readable than a youtube comment.
In my head canon, a portal is just a device that very rapidly analyses every particle entering it, absorbs the particles into some hidden physical storage medium, and sends some information to the exit portal describing those particles, which '3D-prints' them on the other side from some hidden source of matter. From this perspective, the exit portal is effectively functioning as a sort of rocket engine so it makes total sense that the cube going through the portal imparts momentum upon it due to Newton's second law.
So there is one aspect that I think is super important to the problem that actually makes the answer pretty easy. Both sides of the portal have their own respective gravities. The cube on the piston end is being pulled towards the platform, and the cube on the slope side would be pulled with gravity respective to a slope problem. Whether or not the cube follows answer A or B depends on whether or not the piston is accelerating towards the cube, since in order for it to be launched, there needs to be a force that exceeds the force of gravity. its possible that since the piston suddenly stops, there would be impact, but since the cube has both of the gravities acting upon it, and it is moving at a constant velocity, its closer to how an elevator would take you up a floor, but wouldn't launch you into space.
For the piston pushing against the portal, my intuition also tells me that it would come out shooting. The energy could come from the piston's kinetic energy (i.e. slow it down). For the infinite portal drop, it is a bit trickier because you are basically connecting two points in a potential field (gravitational in this case) you would need to penalize the energy somehow (e.g. subtract the potential delta between the portals from the kinetic energy of the object everytime it crosses) I think this is basically a weird discontinuous potential field where the potential increases a constant amount in an infinitesimally thin layer. That would mean you could stand over the portal on the floor, because you have not enough kinetic energy to even cross that layer (boring lol). It would also mean that you would get sucked into the ceiling portal if you crossed a single hand, and you would come out shooting to the same height you were before (that's why I mean the energy is conserved if you have it like this) Other interesting "paradoxes" would arise in virtually all other fielsd of physics. For example in electromagnetism, there are also very important potential fields like the electric field. To put it simply, you could just connect a battery to itself in series infinitely, and you would have the same exact problem/paradox as the infinite falling. For the record I am a physicist, so I should know what I am talking about even if I really don't. Maybe we just cant have portals in real life lol
I think the gravitational field would evolve over time after the portal is formed(you know, gravitational waves, whatever) and result in a stable, continuous boundary through the portal. If you placed a portal on the floor and on the ceiling, you might experience weightlessness and float at some point in between the two portals. Either way, there is necessarily a force from the change in gravitational potential. Otherwise, the portal the portal must effectively transport you to a parallel world where the gravitational potential is offset by a constant value. Because of gravitational time dilation, this means that falling infinitely down portals would mean travelling back in time. Canonically, interdimensional teleportation has been acheived by Black Mesa, and time travel is "_illegal anyway and strictly regulated by time cops_". Aperture Science very much dislikes following regulations, so I think this is somewhat plausible. (ignoring a number of paradoxes) Btw, I am not a physicist, and I have no real understanding of the math behind GR. I've been recently learning some differential geometry and geometric algebra motivated by a (remarkably relevant) problem relating to a bubble with discontinuous curvature, and I hope to someday be able to apply it to portals and spacetime curvature. Honestly extremely rewarding to find connections and apply math to things I genuinely wonder about.
this is just my take on the whole thing because i think its fun to examine these sorts of things and i havent given my thoughts on it, but i think the cube on the bottom wouldnt push out the top cube, just because the bottom cube is exiting the portal doesnt mean its having any additional velocity applied to it to push the top cube, at the same time, its not getting any resistance from the top cube because the top cube is now just existing somewhere else. the cube has no idea its even moved because of the seamless transition of the portal. what would most likely happen, is the top cube would fall instantly before it even has a real chance to fully interact with the bottom cube, then that falling motion would interact with the bottom cube, if tied, it would drag the bottom cube out as it fell downwards and thats just due to gravity, no additional force. also the portal on the floor, portal on the ceiling thing, its just that each pass you make, gravity stacks (like a multiplier) and just keeps adding gravity, because all gravity sees is chell at the top of the portal exit the top portal with a velocity of x, and it adds gravity and then chell goes through the bottom portal with that added velocity, so chell exits the top portal with a velocity of that new x, so gravity sees that and pulls down even more until she goes in the portal again and the sequence continues. its no so much "oh im continuously falling" but rather, "oh i see something falling from the ceiling to the floor 250,000 different times with no break in between, time to add a gravity multiplier" not a scientist but thats just my uneducated theory
I don't see any problem with the violation of conservation of energy. Portal 2 put an exit portal on the *moon*; the portal gun either breaks symmetry or is able to draw an arbitrarily large amount of energy from "somewhere off camera" to pay for its shenanigans. Probably alternate universes or something, if Half-Life is anything to go by.
@6:26-.-That's not how I would argue with this. I instead argue that if 1). Portals are just holes in space and 2). Portals are moving, then C). Moving portals moves space itself. So then the question is: what is the scientific or philosophical difference between an object moving through space vs space moving about an object? I for one see no difference. It's kind of like how what to moving in a river would push objects in the water, it would be a defilement of physics if something was just unaffected by waters movement without any clever work around.
I would argue it's the same thing as shoving a cardboard box with a hole in the bottom of it over a cube. I don't think it would fly out. It would only move because of the shift in gravity on the other side. Edit: I was wrong. It would be like a cardboard box if both of the portals were moving, but the key difference is that the blue portal is stationary, which is what's causing the motion.
but it does fly through it, relative to the surrounding cardboard boundary, until the cardboard accelerates in a way that makes its velocity match that of the cube.
@@drdca8263 I feel like just because the portal moves fast around the cube wouldn't make the cube suddenly fly through it. I feel like the logic is flawed here. How exactly is the portal affecting the cube if it doesn't even touch it?
@@drdca8263 Since portals are just that, portals, imagine that the blue portal is on the immediate other side of the orange one on a suspended platform. Having what is essentially a hoop pass over the cube wouldn't just make it fly upwards, right? Is this really so different from having the blue portal be stationary? Edit: Okay yeah it IS different, because having the blue portal be stationary makes it so that it would fly out because of the pushing explained in the video You're right!
@@pierson9905 what do you mean when you say it doesn’t touch it? The cube goes through a surface with boundary the boundary of the portal. (Now, which surface you associate with it might be a choice.. maybe you don’t have to pick the taut surface connecting to the edge, but could choose some other surface, as long as you pick corresponding surfaces on both sides (would different such choices have the exact same consequences? I feel like maybe, but maybe not), but, there’s still something that the cube passes through at some point, else, if it never interacted with the portal, it would just be hit by the moving object?)
Conservation of Energy is probably a bit easier to deal with. On the infinite portal fall, you're speeding up because gravity is pulling you down. But, your mass too is pulling the source of gravity towards you (the earth presumably in this case), since you have mass you too have your own (very extremely weak) field of gravity. And it's just building up with each loop through the portal. I have to wonder if there would be some sort of multiplication factor with the gravity pulling you through the portal. Since gravity is thought along the lines of warping space, that warp would extend up to the ceiling where the exit portal is, go through the entrance and back up. My instincts tell me it's unlikely to be a continual escalation of gravity build up, but it may have a sort of "higher gravity tube" between the two portals. Buuuuuut, I'm not sure if that would be the case. As for momentum itself, momentum is a bit weird. It could be considered having stored energy, but, from my limited understanding, that energy is more of a differential between two reference points. Like how in a car that is going a constant speed you don't really feel momentum until you come to a sudden stop. You don't actually have actual energy built up in you, but the act of speeding up or slowing down will change your vectors to make you feel like it. So with that in mind, when it comes to portals that are side by side facing the same direction, you can think of it like something along these lines. First imagine a wall between the two portals that don't even let the fabric of space and time to seep through. Then imagine a "space-time grid", with coordinates on it, and it intersects the first portal while one of the axis coordinates increment higher the closer it gets. One of the lines are colored red goes straight through the portal. On the other portal, the space time grid would push through it, and the axis coordinate is now increasing as it gets further from the portal. Now place an object on that line, and launch it forward, it's coordinate on the axis grows and grows as it reaches the portal. And when it exits the otherside, the coordinate continues to grow. Basically, think of it as the reference point the object is, is not in relation to the universe, but to the portal. And after this long write up, I thought of another way to think of the coordinates, think the coordinates for both portals, regardless where they are, as being [0,0], and the object is at [0,10], and moving towards portal A. It's coordinates decrease till it hits [0,0], and when it comes out of Portal B, the axis is now going into the negative numbers till it's at, say, [0,-10]. Even if Portal B was at [100,100] from the perspective of Portal A, from the object's perspective it's only [0,-10], despite being at [100,110] from Portal A. and with that rambling done I think I should leave this comment off here before I ramble more.
you can kinda solve the conservation of energy part by making gravity itself travel through portals. in the example of falling through portals on the ceiling and floor, the area between the portals would either become zero gravity, or gravity on the ceiling portal would pull up instead of down. depending on how large of an area this affects, this may also rip the earth in half. might also set off those gravity-wave-detector-thingies.
Love your videos on the Portal demake, but these videos are also great! Big fan of educational UA-cam channels like VSauce, MinutePhysics, Veritasium, etc. You did a great job in this video of combining two types of content I enjoy. Keep up the great work. Excited to see more from you in the future!
For conservation of energy in an infinite portal fall, I think the conservation of momentum answer can still be applied. As Earth exerts a gravitational force on you to accelerate you from the top portal to the bottom, you exert the same force back onto it to accelerate it up; the continuous stream of potential energy being converted into your kinetic energy comes out of the kinetic energy of the earth. The real problem presented by portals then becomes how this almost definitely can be used to decrease entropy, thus breaking thermodynamics.
On the last question, could you view portals kind of like how you view mirrors in physics? Mirrors can be viewed has not redirecting a laser beam, but instead on each side of the mirror there is the space, but mirrored. as a result the laser seems to take a straight path. could this be considered the same for portals? imagining the portals as not a hole through space, but a way to move from one area in space to another, identical, area in space? in the infinite portals example, this would be like an infinitely high stack of rooms one on top of each other, so from the pov of the object falling, its the same as just falling off a large tower?
From the POV of the falling object, yes, that works fine. Until it moves sideways and hits the ground of one of those "rooms" at high speed. Where does the energy contained in that speed come from? Arguably, it would be from the portal itself, but the transfer mechanism is not clear, since the portal doesn't directly interact with the falling object.
Mirrors "can be viewed as ..." may be a useful *model* for some considerations, but it doesn't reflect reality, as in reality, there is no such thing as a copy of space. If the laser beam is reflected and heats up an object after that, the object that gets heated up is the one in the "original" space. The laser doesn't interact with anything in another space. I agree with his ideas that energy must be provided by whatever device is sustaining the portals
@andremello The kinetic energy comes from gravity. Normally the kinetic energy gravity can give to an object is finite, but the portal keeps resetting the height.
There actually are parity symmetry violations in particle physics, i.e. there are cases where, if the mirror were a reflected universe, the particle in your universe would go to your right and the reflected particle would go to your left - opposite directions. The "mirror universe" thing is just a convenient geometry trick sometimes used to model optics.
@@luna010 what does it mean for "gravity" to give energy though? I think that sentence is flawed. The usual interpretation is that the object itself has "potential" energy stored in it, by virtue of being at a certain height, and that energy is converted to kinetic energy as the object falls. What is strange about the portal situation is that suddenly the object regains that potential energy, because it is suddenly at a higher height again, and where does that energy come from? Conceptually, it's the portal doing work by transporting the object to a higher height, just like one can transfer energy by lifting the object. But since the portal does not "touch" the object, or interact in any way we can detect, that energy transfer is mysterious. It is also unclear what it means for the portal to lose energy. I suspect the solution is to include the gravity field itself in the geometry, so in the volume between the two portals we have the gravity field pointing in two opposite directions, thus cancelling itself. The object wouldn't fall at all. Note this doesn't contradict James' solution to the moving portal.
I think matpat's explanation of mass as the means of conserving energy is a good solution. Each time you enter a portal, your mass is added to that portal and subtracted from the exit portal. So a negative mass makes up for the energy gained from falling
I think in most interpretations I have seen of portals they are seen more as doorways. They don't reconstruct you on the other side, they don't teleport your particles, etc. You literally move through them as though you move through a doorway. What the portals do is they contort spacetime so that the two portals are directly on the other side of each other spatially. Essentially imagine the universe is a piece of paper, they severely bend the paper back on themselves and then poke a hole, you as the player traverse through the hole. Momentum is conserved in that case, since you did actually walk through a door in the same direction. If you were to draw a line and then have the line"fall down the hole" spatially it's a straight line however, from our perspective it is not. It's the portal equivalent of a straight line on a curved surface does not look straight on a flat surface. If you look at it from this way and it is the idea of a door frame just falling on a cube, things start to make a little more sense.
@@LineOfThy You have the same global universe relative movement problem with teleportation, I don't think non-absolute (perfect) teleportation could exist?
I've always imagine that portals kind "add a copie of the room right behind it", rotated depending of the or rotation they have to each other. The object passing the portals will just go in a straight line, kinda going in the "other/same" room using a wormhole-like path. So for the paradox, it will need that the room need to "move" AND to stand still at the same time, so both of the solutions would kinda works, but that's clearly messed up so they are all wrong too
The thing about conservation of energy is that portals "move" matter instantly through spacetime. But nothing can go faster than light. You would need an infinite amout of energy just to go beyond that limit. So, the simple existence of the portals, as presented in the original game, doesn't follow conservation of energy (we can assume that they store/create an infinite amout of energy). Maybe they should work differently, maybe like wormholes but we don't know if wormholes actually could exist and how they would operate. Anyway, I really like your project and how you are giving your best to make the game engine as good as possible. Keep up the good work !!
For the momentum conservation with stationary portals, you should think that the vector is relative to the object, not to the "world". Think about it from another point of view: when Chell cross a portal, she's facing forward from the secondary (target) portal, not from the primary (origin) one. If you use shapes like cubes or spheres, it's a little hard to imagine it as all the faces are the same, but if you use a person, or an irregular shape, you'll see that everything is relative to the shape and not to the world. Also, for the gravity thing, it's the same. You conserve the speed/momentum when you pass the portals, then, you gain more speed because of the gravity force, next, you pass again the portals, and so on until you reach the terminal speed, it's not magic (except for being able to create a portal, yet), just think about it as a infinite fall from a precipice.
The way I see it, portals burn their "charge" as things go thru, as suggested by the sizzling edges, that constant sizzle probably because of air currents, light, subatomic particles etc. They likely get their charge from the hawking radiation of the microblackhole that powers the portal gun ( I think GLaDOS mentions the microblackhole at some point, not sure, it was a long time ago); and I would expect that if otherwise undisrupted, portals would eventually fizzle out spontaneously at some point, sooner if lots of energy or heavy things keep going thru, but probably lasting more than a human life-time, or maybe simply for some duration longer than the time since the game came out, as I suspect if someone had been running the game since it launched, there wouldn't be code in it to have make them close spontaneously at any point. Infinite falls don't violate conservation of energy because the energy is being extracted from the portals.
before watching the video i'm gonna say it still gets launched at about half velocity since the molecules that get pushed out the other portal have velocity and pull the stationary ones along but gravity exists too which would lower the velocity a bit too
since it isn’t expanding the capacity of the room in any way, it should maintain the same exact state even after putting portals top and bottom. or you know what actually, gravity is still pulling all water to the bottom, with the bottom having the greatest amount of pressure. i imagine it to be an endless loop of having the pressure constantly try and equalise coming through the hole in the bottom and pushing against the water in the top. nah bro idk it’s too late at night for this
In Valve's games: The Cube would instantly jump while teleporting (if the piston is fast enough). In real life Physics: the portal would teleport without adding any additional movement / momentum. Note that I just said "additional"..., meaning that current momentum and forces and velocity are conserved and transferred between Portals. The cube would just "appear there in its new place quick". That's my theory. Notice that there cannot be any friction between the Portal itself and it's surface (i.e.: it's a HOLE): that's why the Portal itself cannot add additional movement (or momentum) to any Object, per se.
I love this beautiful visualization. Next time I will just push the tip through a portal and see it continue forever (without acceleration).... assuming no gravity and no air.
I got this theory off tv short from a long time ago but I can't remember what it was since I was so young. This was just about teleportation and not the game. Basically it explained portals as destroying and recreating things on the other side. The energy to do this would come from the material that makes the portal and would not last forever. They would be still be limited by the speed of light and basically what happens at the other side of the portal can be anything aperture science they want it to be, but in this case they make it seem like you teleport. You don't die when you enter it because the portal is creating everything you need to just before it destroys it. But you could think of the object on the other side of the portal as not the original its self but a replica. If a portal ran out of energy while you where between it you would be chopped at the point it ran out of energy. If anyone knows the tv spot I got this from that would be helpful, i think it was animated.
Well the fact that the edges of the portals are fiery could help your explanation on the conservation of energy. Maybe the portal gun shoots a goo that burns slowly, and the burn rate adjusts based on the energy needs of what goes in and out of it, but it's always lit, like a pilot light of some sort. But now we're really getting into the weeds of scifi technology. We'd probably need to crossreference it with Half Life Lore and get Xen Magic Space Rocks involved
My logic is probably wrong here for one reason or another, but the diagram at 5:38 made me think about normal force because of the arrows. This probably applies better to your portal piston problem than this diagram though. If each particle in the cube were to actually be colliding with the surfaces both portals are attached to (yet have no resistance moving through the portals), the force from the entrance portal surface on the portal (F1) is applied to the cube and the surface it is sitting on. The surface the cube is sitting on applies a normal force (F2) with equal magnitude to F1 on the cube, making the net force 0. As the cube moves through the portal, the force F1 is also applied to the surface of the exit portal providing a normal force (F3) also equal in magnitude to F1. Since F1 is pointed away from the entrance portal, the applied force would be pointed towards the exit portal, making F3 point away from the exit portal. This would result in the force F3 to be applied to cube as it passes through the portal, launching it. Example with portal on a piston: For simplicity, the cube will be sitting on a flat surface at rest with the entrance portal moving on a piston straight down with a force of 1N (in xyz: F1 = [0,-1,0]) with a horizontal exit portal pointed right (+x). F1=[0,-1,0], Cube applies F1 to surface, F2=[0,1,0], F1+F2=[0,0,0], F3=[1,0,0], F1+F2+F3=[0+0+1,-1+1+0,0+0+0]=[1,0,0] Example with stationary portals and a moving cube: For simplicity, both portals will be horizontal, pointed right (+x). F2 is the force applied to the cube, pointed left (-x) with a magnitude of 1N (F2=[-1,0,0]). F2=[-1,0,0], F1=[1,0,0], F2+F1=[0,0,0], F3=[1,0,0], F2+F1+F3=[1,0,0]
I think we can wave away the seemingly breaking of conservation of energy by just saying that the portals are some hyper-dimensional connection along what can only be assumed to be hyperbolic space, such that there is no energy loss... which basically just equates to "magic science did it" now that I think about it :p
I feel like relativity would solve all of the problems. The direction is relative to the portal, the speed is relative to the portal, and the kinetic energy would also be relative.
there is slight problem with the 2 cubes one, both are resting, they do not move per se, just swich places, first one isn't pushed, its resting on the first one (also in this example it would slide down due to gravity but thats beside the point since we may be talking abou high speeds) only moment they get any energy would be probably last miliseconds that portals slams and create solid surface
At 2:26 when the first box exits the other end of the portal the gravity in that frame of reference takes hold and the box falls over. 5:10. No it's not true for stationary portals. Momentum is maintained, the direction of that vector changes, but physics doesn't care what direction you're going so long as energy isn't created or destroyed, it's why potential energy exists, energy can change form infinitely so long as it isn't gained or lost. Black Holes which suck in spinning matter gain rotation, it doesn't matter what direction the object that fell in was spinning though, the angular momentum of the black hole will always increase when added to. 5:20, and no a cube changing direction mid-air wouldn't violate momentum either, but there's no way to change the vector of the momentum in classical physics. Portals allow for this because you're splicing two pieces of space together. You might as well argue that walking through a doorway breaks conservation of momentum because once you're no longer in the room and that's somehow problematic. 5:27 yes, momentum is a vector, and the direction does matter for moving through space to determine where an object will be from time A to time B, but it doesn't matter for conservation of momentum where all that matters is the magnitude. Gyroscopes are an example of this. Spin up a big gyroscope whine in a spinning chair, tilt it left to right. The magnitude of the angular momentum doesn't change (except by dissipation through other means such as heat from friction) but the direction does change and that isn't an issue. 5:37 Your solution is effectively saying that if I walk through a doorway, I'm imparting momentum on the doorway. That's really wrong. Portals are 4 dimensional connections in space, they're not physical things, they don't ever impart forces or allow you to impart forces that aren't normally happening, they just allow taking shortcuts through three dimensional space. 6:00 that's not how portals work at all. 6:29 in which game? Portal or the one you made? If it's the one you made then ofc the argument is moot, it's your game, portals work however you want, and if it's the Valve Game Portal then you're wrong because Portals can't move at all so the entire experiment is moot. If you take the concept of a Portal as presented in the game Portal by Valve, the explanation given is that they are just interconnected pieces of space and would work opposite of your explanations. 6:40 this argument is moot because nothing sits absolutely still in space, space is constantly expanding. Regardless whether or not a portal is moving isn't relevant to what two positions it connects to. 7:00 in the clip you're showing, by your logic, the portals moving should apply an angular diffraction past the portal exit to the beams since the portal is moving. That clip kind of blows up your theory since as you can see, the light isn't getting bent at all. 7:10, yes because people pointed out why you were wrong and now you're pulling up examples that prove yourself wrong as evidence that you're right. Weird. The ultimate answer to partway protrusion is that the side that exits will have a different gravitational frame of reference and get pulled accordingly and if enough mass is on the other side it'll plop out as expected. Here's an easy way to explain your argument being wrong. Take a wall, put a portal on either side, making it effective a doorway. Slide that wall horizontally to make a stationary box pass through it. Now take a doorway and do the same to the box with the doorway. The results of the experiment should be identical, in your example, the portal doorway sees the box go sliding perpendicular to the wall while the regular doorway does nothing, *that's wrong*.
maybe that's why you can only place portals on some surfaces. Portals need the right chemical composition on the surface they attach to, so that they can convert chemical energy into kinetic/potential energy for moving stuff around
Momentum of the object is conserved because the portal's function is to teleport an object from one location to another without affecting its velocity magnitude, only its velocity direction. Magnitude of a cube-at-rest's velocity is still zero. The velocity at which a portal moves at you is of no affect because the contents of the portal are both volumes of air that are both having their velocity magnitudes preserved as particles move about back and forth across the boundary. It's like if a bucket fell on a small object, the object isn't going to just hop into the air as the bucket comes over it because neither the air nor floor moved to exert a force on it. Same here.
You are forgetting the major reason for the breaking of conservation, its the frame of reference, relativity. the portals allow the change in reference frame for the object from one side to the other. with the piston example: * the stationary cube is accelerating constantly at 1g, but the platform is pushing back with an equal force (ie the ground) so it is stationary *as the piston drops the section of the cube passing through has its reference frame altered to that of 45 degrees local gravitational constant, so now the top half has an acceleration pulling the top of the cube to the side at that 45deg *also the mass of the top of the cube is is being accelerated by the emerging lower section of the cube (which you explained, but forgot the next bit) which is being pushed upwards by the stationary platform. THIS is where the momentum comes from for the emerging cube, the stationary platform is pushing the cube through the moving portal (the moving change in reference frame) with the opposing portal example the momentum is conserved because the reference frame of the cube (from the cubes perspective) doesn't change, from the observers perspective the reference frame itself of the cube changes when passing through the portal. So to be clear, the cube is in a box (its reference frame) the box has no mass or energy cuz is a reference to space time relativity of the objects within it. so from the cubes perspective the universe flips around 180deg and it just continues as it was without any force being applied to it. when playing with portals you need to remember that the frame of reference is the thing that is altered when passing the event horizon and not the object, and if the net forces on an object do not match the resulting net forces of the object on the other sides frame of reference than there will be an change in acceleration imparted proportional to the moment of inertia (mass) on either side of the portal.
I'm so glad you called out the fact portals merely existing already break several laws of physics. Great video!
Edit: I really wish commenting this didn't result in further debates in the replies lol people need to chill and just enjoy things more
A portal on a moving surface can only take you to world that looks identical - but where the walls are moving and the piston is static. Two observers in the two worlds give different numbers for objects moving in their worlds - they can't agree on velocities - so I guess we just pick one.
@@JohnnyWednesday Arguably we don't just "pick one", the scenario is defined as the piston moving, so we know which reference frame we're in. It's not that important that another reference frame can come up with another value. Both would see the cube shoot out, at whatever speed it approached (ish), though how that is expressed can change.
Consider both portals moving, along the same axis and facing opposite directions. The cube would almost certainly just plop out the other side given the negative velocity of the exit portal, even though it had positive velocity from the input. From the cube's reference frame, it doesn't look too exciting, mostly a teleport. And from the moving portals' perspectives, it does what it always does, and just keeps the speed it had.
@@JohnnyWednesdayYeah, two different observers with two different frames of reference would give you different results. That has nothing to do with the portals though, that's just how motion works
The cube has to move to conserve momentum in one frame, and it has to stay still to conserve momentum in another frame. That's a contradiction and proves the situation is impossible. You can do the same with energy conservation.
All frames of reference being equally valid does not mean that what happens in one is irrelevant to what happens in another. Special and General Relativity describe how different frames of reference relate to each other.
If you're talking about real physics, the correct answer is "mu". It's a meaningless question due to false premises.
If you're talking about a game engine, as mentioned in the video it's a question of how the game engine works. It should be noted that the canonical answer in Portal is also that it's an invalid question due to false premises, as a portal cannot exist on a moving surface relative to the frame of reference of the room/a point on Earth's surface.
@@SnakebitSTI *except for the very notable instance in 2 where this is shown to not actually be an inherent property of portals.
Also, what is the frame of reference where the cube with a portal slamming down over it must stay still to conserve momentum? Can the portal itself not be acting on the cube to change its momentum? Bc clearly its momentum _is_ changing, so instead of saying that change came from nowhere and defies physics, why can't we say it came from the portal?
If you think about it in a different reference frame, the portal moving toward the cube is essentially the same as the cube moving toward the portal, so the same physics would apply.
See this is exactly how I visualise it and don't understand why it isn't explained in this way more. A portal pushing into the cube is exactly the same as the cube pushing into the portal because - depending which portal you're looking at - both are occurring.
But there is another equally valid reference frame where the cube is not moving, and then later it is, without any force having acted on it.
It always loops back around to "portals are impossible".
Yeah, that's exactly how he solved the problem in the last video, seems like the most sound explanation to me and the most simple to explain too, and this whole thing with particles and bonds seems to follow that.
@@SnakebitSTI Which reference frame? From the reference frame of the seal of the portal (the entrance/exit "surface") the cube is moving towards it (as already said). We cannot describe the movement of the cube from its own reference frame, so you are implying another reference frame.
thats the same as saying
moving through a door is the same as an open door coming towards you
how is that the same
I always figured the portals were two ends of a wormhole. The path between any two portals is actually a null geodesic. Therefore there is no violation of energy or momentum conservation. It's like how the moon orbiting the earth changes its velocity constantly despite no energy input yet we know this is not a violation of conservation laws, rather it happens because the conservation laws hold.
My main problem with this is that it suggests that gravity should be able to travel through portals, and as such gravity would be able to pull you _up_ through a portal above you if the exit was lower. This would prevent the terminal velocity setup from working, instead making it a 0g zone between the portals.
@@angeldude101 It would not make it a zero G zone necessarily as you still get the gravitational influence from all the ground around the lower portal. You should still pick up speed and hit terminal velocity albeit at a slower rate.
@@angeldude101 Cool thought experiment, I hope someone can make a simulation of it!
Probably not on n64, though.
@@ragingfred By necessity of the conservation of energy, you couldn't gain any speed by travelling from a point A to the same point A, even if your path goes through the portal. An object at the point A would always have the same potential energy, so you couldn't get any kinetic energy unless you include an energy source exterior to gravity (even including the Earth's gravity). You can't invent a perpetual motion machine, even in a world with portals.
Technically, a free falling closed path that goes through the portal would by necessity sum up to zero gravity. Or if you want to be more precise, the integral of the gravity field throughout the path would sum up to zero, just like the moon does during its orbital path around the Earth. That doesn't mean that the gravity stays at zero G throughout, but it does mean that you can't gain speed between two cycles of a free-falling scenario ; since the integral of an acceleration force throughout the path corresponds to a speed difference, the speed would necessarily be exactly the same at the same point between two cycles.
While the Earth does have an influence on the system and does still have a gravity pull, it only has a real influence as you move away from the system. Functionally, the two ends of the wormhole would probably act for gravity in a similar way as the two ends of a magnet act for electromagnetism, where the gravity influence near the wormhole is so intense that the Earth's influence is negligible in comparison. As you approach the system, you only feel the portal's gravitational influence, just like a compass gets fully influenced by a nearby magnet, but as you get away from it, it loses its influence and you can start feeling Earth's gravity again, just like your compass starts pointing North again as you escape the magnet.
@@jAujAl1I would love to see someone work out the math for energy-conserving portals and implement a demo
The idea of the material fracturing because of a sudden change in portal momentum is scary. If the portal surface was indefinitely thin a sudden change of momentum or position could act as a kinetic “knife” changing the inertia at an infinitesimal plane thinner than a razor. Makes me wonder what might happen if an earthquake or seismic event happened while a person or living thing went through. Worst case could be just as bad as a portal closing mid-transfer…
Thanks for helping us think about yet another disaster that could come of this innocuous-looking technology!! 😅
Pure nightmare fuel there.
Forget earthquakes, even step vibrations could be a problem.
I don't think that would be like a knife under normal conditions or even earthquake . I think that only if portal stops at infinite speed that would be a problem. maybe edge of the portal could be like a knife tho
8:12 It's probably important to note that this isn't necessarily a clean cut along the plane of the portal. The portal isn't acting as a knife, it's the object pulling itself apart.
that would’ve been good to add as a footnote as i feel others could be mislead, since the example footage shows closed portals
The discussion of conservation of momentum in the video reminds me of an interesting variant of these sorts of portal shenanigans I once came up with...
Say we have our portal set up like this: The blue end of the portal is on a concrete wall, something stable that isn't going to be moving. The orange end of the portal, however, is on a thin wooden board, something we can easily pick up and carry around.
Now, on the blue side of the portal, we get a metal pole, and thread it halfway through the portal, so it's sticking out both sides. And then we bolt it to the concrete wall, anchoring it in place on the blue side. So, on the blue side, everything is still anchored in place and cannot move.
If we look at the orange end. We have our board, with a portal in it, and a pole sticking out. And we can still pick up that board and wave it around. And I don't think it would be that controversial to claim that if we do that, the end of the pole should move around as well. After all, it's anchored in place on the other end, it's being held in the middle of the blue portal, so it should stay in the middle of the orange portal even as it moves around.
But that means the tip of the pole is accelerating around, as you wave the board... which means there has to be some sort of forces being pushed around, some amount of work being done. You pushing on the board to move the portal, is resulting in force being applied to the pole. And Newton's third implies that the reverse must also be true... if you try to move the pole, it should translate back to forces being applied to the portal, and the board it's stuck to.
That is... you should be able to grab onto the pole sticking out of the orange portal and lift, and it should pull the board along with it, you could carry the board around just by holding onto the pole.
Which feels weird at first, because the pole isn't attached to the board, it's only attached to the wall on the blue side, but I believe it's the only way it can all work.
I came up with this scenario while trying to reason through another variant of the portal paradox, where you have _two_ pistons facing each other, with portals on both faces, and crush a cube between them... which can be hard to process. But once you understand that it must be possible for reaction forces to propagate backward from the objects moving through the portals to the portal surfaces themselves, it's a lot simpler.
Without thinking too much about it it does make sense to me.
I'd like to see this channel do a video on this subject. I can sort of wrap my head around it, but I'm interested in how its implications might affect other scenarios. Does this reveal any useful principles that weren't obvious, or is it just a brain twisting implementation of otherwise well understood rules?
to me, i don't think you'd be able to pull the board and portal around by only applying force to the pole, unless it was somehow enough force to move everything the pole is attached to (and even then it would just snap at whatever the weakest connection point was). since it'd functionally be the same as grabbing a metal pole welded to a wall with no portals attached, the board portal would just hang there on it and the pole would be rigid. BUT in that case, that means by moving the board around, the pole is moving with enough force on the other side of the portal to basically crush anything, which still makes more sense to me than the alternative somehow
My take on this is that the rod and the orange portal are connected since the orange portal is connected to the blue portal, which is connected to the wall, which is connected to the rod.
Sure, when picking the board and orange portal up by the rod, the connection isn't part of what you pick up, but it is there.
To me the energy that flings the cube forward is just the energy that propels the portal down in the first place.
I agree, thats how I've seen this problem all along.
But it doesen't apply to the conservation of energy. Never had I considered the infinite portal fall, his example really fucks with my head.
It makes slightly more sense if you assume that the portals are "smart" and "powered" and can somehow - while the momentum of the object imparts some energy upon the surface they're placed - impart appropriate energy on objects moving in/out of them. If I'm understanding this correctly, it's pretty much the only explanation for how they can work at all. I think he had this same thought, and he pretty much says it, but not expressed in much detail. People genuinely arguing about something from a work of fiction that is a physical impossibility in our universe is a pretty silly exercise in futility obviously, but I think this video and what's been said here is the closest approximation to how it should/could work, and I think that's pretty cool lol
To me that would then mean the cube pushes back on the portal as well, so must at least be effectively slowing the portal on the piston down, or requires the piston to push with progressively more force
@@Haps_q I guess it makes more sense when I think about it now. Just the inherent fact of teleporting something to a higher place is an issue, because you're taking an "energy shortcut" when compared to the energy required to lift that object up normally.
I agree with the video, there's probably no way to make this consistent with physics without handwaving the energy requirement away like "the portals are powered" or "the portals harvest energy from somewhere else" etc.
That's a force not an energy, and the problem is that in the example with a piston all the energy is already accounted for yet somehow the cube is imparted a force, and thereby given energy proportional to the speed of the piston. This only makes sense if pushing a portal creates a resistance equal to the kinetic energy imparted onto the mass moved through the portal, a lot like air resistance.
i love how this starts out as a chicken and the egg situation and then James goes to prove the point by stating simply "where do you think the chicken came from", making everything else seem relatively obvious in the process.
thank you for finally creating a well made solution to this lol
But who laid the egg?
@@urlhnd An almost-chicken. Eggs are eggs, but egg laying animals may or may not be chickens. So an animal that was nearly a chicken laid an egg, from which hatched a chick that grew into a chicken. Egg came first.
@@messymessr exactly, chicken or egg first only seems interesting to people unfamiliar with basic science, educated people understand that the egg came first.
@@SuppaflyZSM Educated people understand that the question is supposed to be understood as "Which came first, the chicken or the chicken egg?", which is impossible to answer because we have no single coherent definition for either of those things when viewed on an evolutionary scale, similarly to how it's impossible to say where one color ends and the other begins on a gradient scale.
@@Lernos1 The "gradient" in this case only advances when new life is created, i.e. the egg. Assuming that 1) When something is born it either is or is not a chicken, whatever that definition is, and 2) that a pre-chicken cannot randomly mutate from radiation or cellular decay into a chicken... Then the chicken egg came first due to random genetic mutations during breeding. If it were possible to say there were a "first" chicken, then whatever that designated chicken is came from an egg.
I think the two cube experiment is the perfect way to demonstrate and solve this paradox, same way as dropping something. All the particles together.
Dropping bound masses is the exact thought experiment used to prove fall speed does not depend on mass.
About conservation of energy: I always assumed from seeing the first trailer for Portal back in the 2000s that the portals required a vast and continuous expenditure of energy by Aperture Science to open and to stay open. The energy comes from unseen machinery behind the scenes which is fuelled by your suspension of disbelief.
I also think that the cube getting cut in half by the piston ceasing to thrust it forward would be extremely unlikely to happen unless the cube was made of something really really weak such as paper or the piston was going really really fast, such as breaking the sound barrier.
Also, the effect of gravity pulling in different directions on the two sides of the portal should be considered.
Maybe, except chell shot a portal to the moon.
Honestly, I wouldn't put it padt Apperture to make a machine literally powered by suspension of disbelief
@@azieg9ygeb Being able to shoot a portal to the moon just means the tech has a really really long range.
@@MrBenMcLean expecialy if moon dust is its best conductor
Honestly pointing out that the test chambers aren't static kinda cuts the whole line of reasoning off on its own - all portals are moving portals. Whether or not something appears to be moving in our frame of reference has no bearing on the physics operating on it, that's just relativity.
In regard to the infinite portal drop conservation of energy thing, the real reason we're able to break conservation of energy there is that we're not simulating the impact of the gravity of matter on one side of the portal on matter on the other side, which implicitly means the portal is constantly using some amount of energy to counter it. There isn't really one physically consistent way to model that though, since space in our universe can't have holes cut in it (and modeling it would break some basic parts of the gameplay anyway).
The answer to the last question is that portals - either as depicted in the games, or as imagined in an attempt to make those depictions physically consistent - inherently violate the laws of physics in some way.
As portrayed in the games, and as popularly imagined, the portals connect two regions of space in such a way that the space is completely continuous. However, in the real world, gravitational fields propagate through continuous space, so a "real" portal would also cause gravitational fields to propagate. To make it obvious, imagine the scenario of one end of a portal on Earth, and the other on the Moon: you will of course get a massive flow of air at first, but even faster than that (at the speed of light in fact) you'll also get the Earth's gravitational field propagating through the portal. Needless to say, this is going to do *weird* things if you work through the consequences, e.g. I suspect that the portal ends moving relative to each other would generate gravitational singularities, at least in some circumstances.
The portal "paradox" is only a "paradox" to those who can't understand relativity.
If I walk through a doorway at 1 mph, the rate of me going through that doorway is 1 mph.
If a doorway is rolled over me at 1 mph, the rate of me going through that doorway is still 1 mph.
A portal is just a doorway where the entrance and exit are at two different spots. The rate of going through the doorway still needs to be the same on both sides. That's momentum. And as it is officially stated in the game: The laws of momentum are conserved between portals.
the piston coming down at the cube is the same as the cube accelerating towards the piston.
the only question is if our camera (frame of reference) is attached to the platform the cube rests in, or the piston itself.
once you attach the camera to the piston, it should become relatively obvious to anyone, i would think
That would be correct if you only attach a frame of reference to the exit portal, but you still have to account for the entrance portal. What makes this problem difficult to think about is that you need two frames of reference interacting at the same time. The right portal is not moving in reference to the original platform and there is no exertion of force from the static platform on the left, therefore the cube cannot launch out of the right side. That's why it's a paradox: Both perspectives are correct but can't coexist.
It is not. All motion is relative, but you can look from multiple points of relativity to determine which object accelerated while the rest is stationary.
@@adamsfusion put both portals in different rooms.
put a camera in both rooms.
Attach one camera to the piston, and one to the exit portal.
From a gameplay standpoint this solves the portal paradox very well, but realistically this is all wrong as it doesn't actually obey the laws of energy conservation. The problem is that energy conservation is being maintained because you're treating the portal as if it has mass and thus velocity, which isn't true. Portals are wormholes, or spatial tubes essentially. What happens if you swing the end of one tube while the other is stationary? It creates a vacuum force and thus momentum--the YT Channel The Action Lab did an experiment showing this.
So the actual answer is that both are true. When one portal moves to encase the box, the box will only move if the vacuum force created is strong enough to actually move the box. Then you have to remember that the larger the diameter the tube the greater the speed needed to generate a vacuum force. So then you're left with the 3 following scenarios:
1. Portal moves and encases the box, causing it to exit the other portal and fall via gravity (not a high enough vacuum force).
2. One portal is in space and the atmospheric pressure difference creates a vacuum force to move the cube.
3. The portal is moving at speeds insane enough--due to large diameter spatial tube--to create a strong enough vacuum force to move the cube.
the kinetic energy added to the system comes from the nuclear reactor at the heart of the facility
One thing that's interesting about portals is that gravity doesn't seem to pass through them. You don't get pulled by the earth on the other side of the portal until you actually move to that side of the portal. I wonder if having gravity work through portals would solve all the infinite potential energy shenanigans, or if they would just make portals incredibly violently destroy their surroundings, as earth starts being pulled by itself through both ends of the portal.
I think of the portals as wormholes. Drastically curved space(time). You're not teleporting up, you're moving in a straight line. It just so happens that in the way that the curved space is, a straight line leads you back to where you were. Kinda like if you were on a sphere, if you walk forward enough, you'll get back to where you were. It's like that, except the sphere is VERY ununiform, with it being mostly flat, and then a very sharp curve in squished space
except it unfortunately has been debunked and they are actually not curved spacetime, it’s actually macro scale quantum tunnelling
@@iinkstain "Quantum tunneling" is a process that has nothing to do with what we see in Portal and was just the writers' way of making it sound cool. It is just easier to think of the portals as we would the kind of wormholes that relativity supports.
This is probably the most logical take and best practical explanation of a "solution" for the portal paradox I've seen. Obviously the portals as seen in Portal would break our universe pretty thoroughly but this seems like the most intuitive and closest approximation to how they would work if they did exist.
I don’t know how the portal paradox is so popular as a “paradox” even though it’s solution is so simple to figure out.
would the piston portal pushing down into the cube not just be the same as throwing it? then the energy conservation would make sense
So in a world with these types of portals... One portal at the bottom of the ocean, other portal inside the end of a very strong pipe, which leads to a turbine, and then back into the ocean... And now we know why aperture doesn't have any power problems.
Breaking the portal paradox down at the particle level was a great explanation, very easy to understand!
Honestly, I don't even get how this is a discussion, how can people think the cube will stop..
What if we considered portals as instead of tying space together, we dissameble the incoming object and reassemble it, spitting it out the other side. This would conserve momentum in the way you describe, and doesn't really violate any laws of physics.
I agree and thats how I think of teleportation. Like the original object is being destroyed and a new one is being created. In that case what the portal does on the other side can be anything it wants to. You could come out as a rubber duck flying 100mph. but in the case of aperture science they wanted to make something more practical
i want someone to describe to me how this works with photons
Welp, thanks to this video we can finally have portal 3, a perfect narrative about discovering moving portals and defining it's physics with logic.
I'm glad that GladOS is still alive.
The portal does not impart energy at all in this equation, it is doing a third, inexplicable thing: changing the frame of reference for the motion of the cube. All motion is relative, the portal is just changing what the motion is relative to. There is no such thing as a "stationary" object.
Editing and animations in this vid were fantastic, hope to see more similar vids soon
What about relativity and reference frames? From the cube's perspective, there *is* no portal! It just sees uninterrupted space.
I feel like if there was a pair of portals that are ”holes in space”, then gravity would not behave as we expect and then the infinite falling trick might not work?
To figure out where portals get their energy from, there's some information that is relevant:
1. Moon rock is excellent at sustaining portals
2. Other materials can support portals (aperture had portal surfaces before they bought the moon rock)
The most promising energy source in moon rock is Helium-3, an isotope of helium that can be used in nuclear fusion reactors.
As other nuclear fusion fuels exist, this explains how old aperture panels could support portals, and as there's a limited ammount of Helium-3 in moon rock, it explains why the auto-portals in the early levels turn off (to preserve power), and even why the moon portal closes; The higher energy required to reach and match speed with the moon, combined with unpurified moon rock, results in a portal that only lasts a few seconds.
Sure, it's nowhere near enough power, but that's a much smaller handwave than portals just being magic
Maybe this is just my lack of understanding, but I always understood the paradox angle of the box not flying out the other end as being true due to there not actually being any momentum/force applied to it until it comes out the other end. So if it got far enough through the portal, gravity on the other end could pull it the rest of the way out if there's enough of a slant? With gravity really being the only force applied. Thinking of portals kind of like a hula-hoop, where one side just happens to come out in a different place in space. So if you lower a hula-hoop over a box, the hula-hoop doesn't itself apply force to the box because it never actually touches the box. So in my mind the only force being applied to the box in the paradox is the environment on either ends of the portals. But maybe that's nonsense. I just haven't had it ever explained convincingly to me why we are assuming any momentum is coming from the portals themselves.
Similarly for the infinite falling thing. You're speeding up as you fall much like you would if you jumped from a large height. The portals themselves aren't contributing to your momentum, the repeated force of gravity is?
My two cents on the conservation of energy problem is that portals fundamentally violate it. There's something called Noether's theorem which shows that symmetry and conservation are equivalent. For example, conservation of momentum is true because of translational symmetry, and vice-versa. Similarly, conservation of energy is due to time invariant symmetry. If portals were to exist in reality as they're shown in the game, you could violate causality by instantly transmitting messages (not a GR expert by any means, but there are some physics stackexchange posts where they explain this better). If you can violate causality, you break time symmetry which breaks conservation of energy. So even if crossing portals used energy, as long as you can break causality, conservation of energy can't be true
Fun fact: conservation of energy isn't even true in reality because of the expansion of the universe (also because of Noether's theorem). It just appears to be true at our scale
Portals are just holes in space, the changed momentum vector occurs for the same reason orbiting/falling do and where the energy for that comes from also has the same answer as where does the energy from falling come from. In terms of moving with objects, I would imagine that the portal wouldn't be tethered to the object, but would itself usually be an inertial object. While it has the same momentum as whatever/wherever its being created on/at, as soon as it is actually created it would cease to update it's momentum... or it would if not for the fact that energy has to be provided to keep the portal open, and since the spacetime curvature centers on the energy source, the portal would be dragged along by wherever it's getting energy from via a "gravitational bond". Even without that though the portal still would not fly off since relativity is a thing. This would also explain why portals close when you accelerate the object it's attached to too much, as if the energy source gets too far away from the "center" of the portal before the "center" can "move" itself back to the energy source, the portal would just collapse from the energy no longer being geometrically capable of supporting the curvature. Conservation of energy is inherently violated in any system where the curvature of space can change over time, but in this case a portion of the energy that makes up the cube would be transferred to the entrance portal from a gravitational interaction, and would take an equivalent amount of energy from the exit also via gravitational interaction. You can find a similar interaction in real life by looking at two black holes orbiting each-other, and the orbits decay from gravitational energy loss.
The rest of the issues of where energy comes from/goes to are solved when you consider how non-inertial reference frames in real life actually have similar problems and what the solutions to those problems where (see: the unruh effect).
Instead of thinking about the piston at all, for a second think of the diagonal portal as a regular hole with a piston and a cube attached to it; flinging it out the other end.
If the piston portal from the example were to stop halfway, the cube would have no sufficient momentum to pull it through leaving it on the ground with the other half poking through the exit portal.
To all of the confused people:
The portal slamming over the cube imparts mimentum to the cube. This is observable in that the cube _must_ move to exit the other side. Any portion of the cube on the exit side has roughly the velocity of the piston.
Ignore conservation of energy. These portals are magic; pure logic doesn't map 1:1.
I want to see a serious particle physicist look at the portal paradox and consider things like whether gravity would be transmitted through portals. If anything can pass through a portal, does that include subatomic "messenger" particles like the graviton? If so, then wouldn't the force of gravity pass through the portal? If portals were real, particle physicists would love using them to help with those sorts of theories
concidering that gravity would work from both sides most logical is being directly in it would be felt from the range of 0g to 2g (depending on orientation) and be weaker further you get from it, and probably get closer to be not able to percive any change of gravitation pull since one from the portal would be non direct and changing direction so no longer amplyfing/reducing "ambient" one.
It seems to me that the moving portal would kind of "simulate" all of the space on the other side of itself moving that fast against anything that passes through it.
A portal is just a hole, where the other side of the hole is somewhere else. If you have a cube on a table, cut a hole in a piece of paper and put the paper on the table with the cube going through the hole, the cube doesn't just shoot up.
This is my thoughts exactly
the cube does shoot up though, relative to the paper (until the paper stops when it hits the table)
@@drdca8263 exactly but the cube doesn't fly off the table or even leave the surface of the table.
the "infinite portal fall" should apply to air too, right? as soon as you place your portals, you should expect a wind tunnel will form.
tough to say. that wouldn’t be opening up any new space for a pressure differential to form, it just gives the air molecules more directions to flow through, while maintaining the exact same state of air pressure after the portals appear.
@@iinkstain There would probably be a slight shift in air as air pressure at the ceiling and floor equalise, since they would be at slightly different pressures due to convection. I do think the air would also fall infinitely downwards though, for the same reason as if you slid a cube into an infinite portal loop of the exact same height as the cube, it should still fall- All the particles are being accelerated by gravity at the same rate, there's no reason to believe the cube would somehow support itself. It probably wouldn't be very fast though since the falling air would be interacting with surrounding air which would slow it down.
@@thevortexcrafter7060 i think now that i imagine it, fitting the cube into that space that squeezes the cube against itself would be extremely difficult. you’d be exacting a squeezing pressure onto it as the opposite edges of the cube push against itself, either crushing it entirely or causing it to erode a thin enough layer to slowly reduce this pressure and form a thin enough floor of air molecules between the spaces of the cubes top and bottom, that the cube will start trying to chase (causing it to fall). i wrote this after a fever dream.
It's nice seeing your reasoning behind this. It almost convinces me that this is the way it should work.
The way I see the portals are two sides of one thing. You can't have one without the other. One portal on a wall is not a portal. So it's more like, if a hula hoop fell around you, you wouldn't shoot out the other side.
Except from the perspective of the hula hoop, you DO infact shoot out the other side. It's only from your perspective that you're stationary, just like how the entire earth is moving at extreme velocities yet we are stationary relative to it.
RE: Conservation of Energy
Obviously portals aren't actually possible in reality, which means at some point we have to concede that portals are breaking some law or laws of physics. We'd rather it be as few laws as possible so it's as real as possible, but *something* still has to be broken. It obviously must be breaking conservation of energy. And there's no real explanation for that because... it's not real. It's where you need to apply suspension of disbelief and just don't worry about it.
Intuitively I don't like the swinging portals thing. But also does that explanation even work if the portals aren't facing the same direction? Like if you put two hanging portals in a V shape (but with enough room to swing freely) and shoot a cube straight in to one of the portals. The entrance portal being pushed back still could make sense, but the exit portal would basically have that momentum applied sideways, even though the cube comes straight out. Or if the exit portal is still just pushed back like your explanation, I don't see how that's conserving momentum since it's a different direction.
It seems more like portals just don't conserve the direction part of momentum, just the value.
Edit: actually, direction is relative just like speed. So it still keeps the same direction relative to the portal the whole time just like it does with speed. Is that not conservation of momentum?
On the problem of conservation of energy where you get infinite kinetic energy from this 8:57 scenario, I think you could apply this 6:00 to it. If the portals are stuck on a rigid surface, then that pushback would be felt entirely by you instead of the portals moving. Essentially, the portals would absorb your movement kind of like how a magnet falls slowly through a copper pipe or like a non-newtonian fluid. The faster you move through the portal, the more resistance to motion you feel.
Of course, this kills all the fun of many if not all puzzles in Portal, so maybe we wouldn't want to implement it.
Correct me if I’m wrong but the infinite falling trick works because when you put a portal on the ceiling and the floor, what you’ve basically done is create an infinite stacked building. just imagine you have a building with a bunch of floors and a hole in each and you dropped a cube all the way down but with the case of the portals it just drops forever
That’s how I imagine it
Yes, you are correct, and you speed up due to gravity.
I find the conversation interesting because it views the problem as though portals are a planar barrier, but the Moon moment in Portal 2 (if a bit exaggerated) suggests the sides of the portal can impact each other through differences in pressure and gravity.
I've always viewed the transition between portals more like two magnetic fields interacting with each other. If the magnetic fields are similar, then the point where they meet acts almost as if a single magnet. An infinite hole would not be infinitely increasing gravity, but rather a transition between the gravitational force at each height as a gradient. Also, with regards to relative velocity of the portal, you could argue the entrance and exit are both moving simultaneously relative to the object, like dropping a hula hoop over a person.
Ultimately I think the biggest, and potentially only, contributor to launching the cube would be the force of Earth counter-acting gravity. You would get that small acceleration as gravity suddenly changes relative direction. If the portal stopped half-way you'd see the cube probably lean over into the edge of the portal as it finds an equilibrium between the two gravitational fields it exists between. (which sounds dangerous if the edge of the portal is infinitely thin!!)
Moving portal imparts its motion onto the object passing through. The energy comes from what the portal is attached to. Oh, you've got account for exceeding the resting forces for the portion of the object that hasn't received energy from the moving portal. So a little less than half, friction is going to be minor, but gravity is going to be the decider. Tumbling is probable.
Snapping objects apart is likely going to be a problem of portal misalignment more than speed. 50gs fails to rip a human apart... Actually that's wrong... The relevant concept isn't acceleration but jerk... Closer to spontaneous the change is the greater likelihood of ripping a body apart. Misalignment is more probable but don't be rocket thrusting a portal cart onto a half exposed object.
Effective mass that has traversed through the portal at whatever speed it was traveling versus the resting mass with all that force focused at the intersect plain of the midportal object. That's... going to become nasty without much speed on the moving portal.
The normal solution for portal like wormholes is them sharing the same origin and then getting stretched across space which allows them never exceed C but allows objects(nonsensically) to effectively exceed C. The origin is the gun. The being able to turn off half and then make anew is.. problematic to parse but not relevant. Wormholes have you traverse through a space between the entrance and exit. Portal portals don't seem to have any such buffer space. That lack of buffer space makes portals moving at opposed speed to what is going through them very problematic...
I had a thought about the real issue being realistically applying gravity through the portal. Well, any attractive/repulsive field effect really. They should probably propagate through the portal. But I'm going to be honest... That isn't anything on how a portal changing speed relative to the traversing object is going to play out. Accidentally overwhelming the intermolecular force, the nuclear force?
5:45 The vectors here only work out if the portals are side by side facing the same direction, no? This explanation for the conservation of momentum wouldn't work if you turned one of these panels, say, 90 degrees in another direction.
this is the exact pedantry ive been wanting to see someone say and explain why this is the answer. i feel a sense of relief to know that others know
I liked this video a lot as someone that intuitively agreed with you, and agreed with your argument in the previous video, but it still didn't make sense as to why in my own head. Showing the two boxes made it instantly click. Thanks for all these wonderful videos.
I don't know if it really makes sense to keep the conservation of energy law in a world where (Portal's) portals exist. After all these laws have been determined empirically in our world, without portals.
However, I think it would be interesting to consider Newton's laws of motion, especially the 3rd one (action and opposite reaction). This means that with the portals on the ground and ceiling, you are also accelerating Earth in the opposite direction! You could use this technique to accelerate a ship!
Regarding the portal stopping in the middle of the cube, snapping the cube in half would also require a lot of energy, spit does not make sense either for that reason. It cannot be instantaneous anyway, so it's ti sane as the cube hoing through the portal at constant speed, and getting progressively decelerated. There must be a reactive force acting on the portal to account for this deceleration.
A possible theory to where the energy comes from is if portals themselves had a mass. Considering the portal funnel effect, this could vaguely support the idea that they have their own gravitational pull. As objects enter and exit the portal its mass would change. In the case of infinity falling through portals, I guess one of the portals would collapse once too much mass is moved through.
For Chell jumping into a portal loop, when something fall down, it moves air upwith turbulences, so infinitely falling would make a upward air stream that would add up and apply resistance to falling, mostly making the object to go out of optimal loop path
concidering gravity it just made you reach maybe higher speeds (since at the frame of the portal you would most likely be influenced by 2g) but as you say it would not make you reach infinite spped due to air resistance
For the question of "How is energy conserved?": What if, it's the gun that provides the initial energy to open the portal, and as it's used, the energy in the 'wormhole' is removed. And then we can explain that the magical portal gun is smart enough to know and measure the current portal locations and puts more energy into those spots to keep it open.
About conservation of energy - in the case of the cube shooting out of the other portal - it would definitely have to come from whatever force pushes the portal in the first place.
in the case of teleporting up - I think the obvious solution would be that you *should* need equivalent amount of kinetic energy to even go into such portal in the first place, and you just wouldn't fall into it when stationary, so when you fall through a portal and go up - the needed energy is taken from your kinetic energy, just like when moving up normally. Same with going down - such a portal would "suck you in" (this would require carefully thinking about how air pressure would work but I'm sure it would eventually equalize to *something*).
Actually, thinking about the air pressure thing more - my idea would *fix* air pressure issues, without this you would naturally have air being sucked from a portal below to a portal above, infinitely. This would provide a mechanism to prevent it. I think this would make portals completely physically consistent. But practically may result in some insane tidal forces when a portal goes between places at vastly different heights... so spaghettification by portal?
And they would be so much less fun in a game
4:20 where do we draw the line with what gets sliced through a portal? if this diagram is how you believe portals would work then we would all be screwed in that universe cause the portal would split the atoms in the air lmao
Nothing gets sliced tho, the material is still in one piece
7:07 To be honest, I think this video far exceeds an argument, as it's a very entertaining, yet informative breakdown on portal mechanics. So many points you make here I would never of thought about and coupled with the very helpful examples make this a very amazing video. Great video!
Well you can just consider wormholes and it solves it all. They’re holes in space that move.
Good video and great animations, but this is still definitely incorrect. Portals are canonically wormholes, just the visible borders of an invisible, warped path through space. For all intents and purposes, the two portals are like either side of an infinitely thin hula-hoop. There cannot be a concept of space “between” the portals, because portals simply connect space in arbitrary ways, same as how a doorway is a defined plane that separates the rooms it connects. Going through a portal cannot affect the transversing object under any circumstances, by definition, otherwise they wouldn’t really be portals.
For the “redirection” of a moving cube’s momentum through two static portals, the cube is moving in a straight line through space (through portals) that appears disjointed to outside observers. But from the cube’s perspective it never changed direction and there was never a need to accelerate to change the direction of motion. Just because the path of motion appears curved to outside observers doesn’t change the fact that the path was straight. This is just like how light bends around objects with gravity, despite having no mass, since gravity bends spacetime so that a straight path from the light’s perspective is curved to ours. Each atomic slice of the cube goes from blue side to orange side without changing its momentum, and moves out of the way just in time for the next slice to make the transition. The distance between each slice has not been disturbed so the transition through the portals is unnoticeable and only one of color-coding.
The same thing is true if both portals are moving in sync, like having a portal on the front and back of a square-faced school bus. If the bus was driving really fast at you, and you did a purely vertical jump, you would land on the ground exactly one bus-length from the point you jumped, regardless of how fast the bus was driving. You never touched or interacted with the bus, and the only force acting on you would be gravity. Each atomic slice of you goes from blue side to orange side without changing its momentum, but the orange portal moves forward just in time for the next slice to be scooped up by the blue side and make the transition. Again, the distance between each slice has not been disturbed so the transition through the portals is unnoticeable.
Note that for both portals moving or both portals stationary, you can imagine each object as an atomic slice going from blue side to orange side with no inconsistencies. Either the momentum of each slice makes room for the next, or the momentum of the portals allows the next slice to “appear” right where it’s supposed to without affecting the previous or next slices.
But this isn’t true for one portal moving, one portal stationary or any other situation where the portals move relative to each other (a difference in velocity). And the reason is pretty obvious but took me a while to formally explain: we are expanding and contracting the length of the warped path of space connecting the portals. To go back to my initial hula-hoop definition, imagine holding a hula hoop above your head and then dropping it. Every part of you goes from being below the hula-hoop to instantly above the hula-hoop, sequentially and at the same rate. But for portals moving separately, it’s like the faces of the hula-hoop are not in sync, so the rate of space following through gets affected and this has serious consequences.
Before we get to the main example covered in the video, let’s go through a simple example to help illustrate the process for thinking through these hypotheticals without confusing portal momentum and cube momentum. Imagine we have a 10m stick in space, the blue portal facing the stick and moving towards it at 40 m/s, and the orange portal facing away from the stick but also moving towards it at 20 m/s. As each whole atomic slice of the stick enters the blue portal, the orange portal has only moved half an atomic slice’s length. This doesn’t matter for the first slice, but the second slice only gets half as much room as it requires. The other side of the portal still has the third slice on it, holding the front half of the second slice against the first slice. The third atomic slice will be forced to “appear” at the original location of the second atomic slice, further sandwiching the second slice between itself and the first slice. Then the fourth atomic slice will be forced to “appear”, with the fifth slice following close behind. Since the exit portal is moving at 1/2 the entrance portal’s velocity, we will end up with a stick half as long (5m) but twice as dense. If we swapped the speeds of the portals, we’d end up with a stick twice as long (20m) that is half as dense.
To generalize this, the length contraction factor (LCF) can be represented by the velocity of the exit portal away from the exiting object sections divided by the relative velocity of the entrance portal towards the entering object slices. It is important to note that the length contraction or expansion would happen directly on the surface of the exit portal. Objects would also deform in shape if the exit portal is moving up/down/left/right as an object passes through, like dragging malware popups across a desktop, since the center of each slice would be offset from the previous one. Also note that the bottom of the LCF fraction will always be positive, since an object will only enter the entrance portal if their separation is decreasing. The top portion can be positive, negative, or zero depending on how the exit portal is moving.
The main example in the video represents the case where the LCF = 0. The first slice of the cube enters a moving blue portal and appears out of the orange with no momentum. This agrees with the bus-jumping example at first. But then the second slice arrives, and the first slice hasn’t moved relative to the exit portal since both are stationary. This will force the second slice to “appear” in the exact same location as the first, instantly doubling the original density. Then the third slice “appears” in the exact same location as the other two, reaching triple the original density.
The gut reaction to this explanation is to ask “Why wouldn’t the newer layers push the previous ones out of the way?” and they would, eventually. But it’s important to remember that the squeeze occurs because the portal-shaped cylindrical volume of space becomes compressed along the length axis, not because of any kind of momentum transfer or acting forces. In LCF = 0 cases, the density would continuously increase until reaching the object’s material stress point and exploding right on the surface of the exit portal to relieve the internal pressure. If the portion of the object yet-to-enter the entrance portal isn’t blown away from the entrance portal, this cycle would probably continue until all of the object had either exploded or become compressed at the exit.
Similarly to how low LCFs cause internal pressure stress and explosions, too high an LCF will separate atomic layers and introduce internal stretching strain which could result in sheering off slices of the object as they leave the exit portal if moving fast enough. Negative LCF cases (exit portal moving in the direction of its opening) and cases where the LCF varies across the width/height of the portal (angular rotation of a portal) are even more interesting to think about, but I’ve already spent way way too much time typing this out and so I leave that as an exercise for the reader.
The only alternative to this length contraction would be that portals cannot change their relative positions or velocities once they are opened. Under this rule, if one portal was moved independently of its partner, both would instantly destabilize and close, severing anything passing through at the time. This prevents all of these convoluted explanations, but feels very limiting and contradicts the neurotoxin laser cutting and moonshot scenes from the games, which is kinda what spawned these paradox questions in the first place. So yeah, that’s my explanation.
TL;DR - There is no momentum shared between portals and objects going through. There are no contradictions in portal behavior if moving in sync (or not at all). When portals move independently, objects passing through get stretched/crushed along axes of portal movement. The stretching and crushing is due to the length expansion and contraction of space itself while passing through portals.
I think the platform you're smashing into the cube is transferring it's energy into the cube through the portal. as you said, because the target portal is stationary while the other is moving, the first portal must be essentially pushing/pulling the object to the other side, and the only reason it's doing that is because it's being moved by the platform. so if this were reality I would expect that the piston encounters resistance similar to the momentum the object is gaining on the other side
how it is tansfering it since it is not touching it? and if it was magnetised than same energy that was pulling it towards portal would pull it backwards towards orange
@@klawypl I view the portal as a rigid membrane that warps light and matter upon contact to the matching membrane, so yes it is touching it otherwise it wouldn't be "going through" the portal
@@AfonsodelCB myself i see it more like a door or a hole you step thro
@@klawypl but one explains it the other doesn't
What if the platform with the portal coming down over the cube isn't being pushed, but is free-falling? As the platform with portal falls over the cube, the part of the cube already through the portal pulls on the part that is still on the other side, which is being kept back by gravity. With the right combination of weights (cube and platform) and falling speed, could it happen that the platform stops falling midway over the cube as the forces equal out? This could also change in interesting ways by making the cube bottom- or top-heavy. The one could make the falling platform stop higher up the cube, while the other could make the cube shoot out as soon as its heaviest part is through the portal.
I definitely was thinking it wouldn’t move but your idea totally made sense and it changed my mind! First time I am interested in physics.
my idea for conservation of energy due to portals: when you pass through portals of different heights, the sudden change in gravitational potential exerts a gravitational force on you normal to the plane of the portal, nearly instantly converting your kinetic energy back into potential energy, or if you're not moving fast enough or pushing hard enough to achieve that potential energy, resisting that you pass through at all. another fun option is if the gravitational field could somehow "flow" through the portals to equalize the potential difference, resulting in a zone of zero gravitational force directly between the portals, and at some horizontal distance, a slight repulsive force near the one on the floor and a slight attractive force near the one on the ceiling.
I'm glad to see you did a follow up to this topic honestly, there's still some intricacies that you're missing, as I had mentioned in my previous comments on the other paradox video, but I'm thrilled to see you came to the same conclusions I did for the most part!
I ended up writing down effectively a small essay from when I first sat down to think about the portal paradox and knowing some funky physics points regarding portals given their being based on wormholes and I'd honestly love it if I could sit down some day and have a chat with you on this some time!
Especially given there is enough weirdness left to cover regarding the paradox on offer that you could actually make a third video, one thing I'll share adamantly though, all interactions should be considered from the reference point of the portals where the world always moves around them and that they are from their perspectives always static, makes understanding "Speedy thing goes in, speedy thing goes out" a lot easier for the weirder side of the physics, also puts more plainly the moving portal interactions true nature imparting moment of inertia.
Please do let me know if you're open to having a chat regarding this given I had a lot of fun breaking down a ton of weird and at times in words of Einstein, spooky interactions and would love to properly share them in a form more readable than a youtube comment.
In my head canon, a portal is just a device that very rapidly analyses every particle entering it, absorbs the particles into some hidden physical storage medium, and sends some information to the exit portal describing those particles, which '3D-prints' them on the other side from some hidden source of matter. From this perspective, the exit portal is effectively functioning as a sort of rocket engine so it makes total sense that the cube going through the portal imparts momentum upon it due to Newton's second law.
So there is one aspect that I think is super important to the problem that actually makes the answer pretty easy. Both sides of the portal have their own respective gravities. The cube on the piston end is being pulled towards the platform, and the cube on the slope side would be pulled with gravity respective to a slope problem. Whether or not the cube follows answer A or B depends on whether or not the piston is accelerating towards the cube, since in order for it to be launched, there needs to be a force that exceeds the force of gravity. its possible that since the piston suddenly stops, there would be impact, but since the cube has both of the gravities acting upon it, and it is moving at a constant velocity, its closer to how an elevator would take you up a floor, but wouldn't launch you into space.
For the piston pushing against the portal, my intuition also tells me that it would come out shooting. The energy could come from the piston's kinetic energy (i.e. slow it down).
For the infinite portal drop, it is a bit trickier because you are basically connecting two points in a potential field (gravitational in this case) you would need to penalize the energy somehow (e.g. subtract the potential delta between the portals from the kinetic energy of the object everytime it crosses) I think this is basically a weird discontinuous potential field where the potential increases a constant amount in an infinitesimally thin layer. That would mean you could stand over the portal on the floor, because you have not enough kinetic energy to even cross that layer (boring lol). It would also mean that you would get sucked into the ceiling portal if you crossed a single hand, and you would come out shooting to the same height you were before (that's why I mean the energy is conserved if you have it like this)
Other interesting "paradoxes" would arise in virtually all other fielsd of physics. For example in electromagnetism, there are also very important potential fields like the electric field. To put it simply, you could just connect a battery to itself in series infinitely, and you would have the same exact problem/paradox as the infinite falling.
For the record I am a physicist, so I should know what I am talking about even if I really don't.
Maybe we just cant have portals in real life lol
I think the gravitational field would evolve over time after the portal is formed(you know, gravitational waves, whatever) and result in a stable, continuous boundary through the portal. If you placed a portal on the floor and on the ceiling, you might experience weightlessness and float at some point in between the two portals.
Either way, there is necessarily a force from the change in gravitational potential.
Otherwise, the portal the portal must effectively transport you to a parallel world where the gravitational potential is offset by a constant value. Because of gravitational time dilation, this means that falling infinitely down portals would mean travelling back in time.
Canonically, interdimensional teleportation has been acheived by Black Mesa, and time travel is "_illegal anyway and strictly regulated by time cops_". Aperture Science very much dislikes following regulations, so I think this is somewhat plausible. (ignoring a number of paradoxes)
Btw, I am not a physicist, and I have no real understanding of the math behind GR. I've been recently learning some differential geometry and geometric algebra motivated by a (remarkably relevant) problem relating to a bubble with discontinuous curvature, and I hope to someday be able to apply it to portals and spacetime curvature. Honestly extremely rewarding to find connections and apply math to things I genuinely wonder about.
this is just my take on the whole thing because i think its fun to examine these sorts of things and i havent given my thoughts on it, but i think the cube on the bottom wouldnt push out the top cube, just because the bottom cube is exiting the portal doesnt mean its having any additional velocity applied to it to push the top cube, at the same time, its not getting any resistance from the top cube because the top cube is now just existing somewhere else. the cube has no idea its even moved because of the seamless transition of the portal. what would most likely happen, is the top cube would fall instantly before it even has a real chance to fully interact with the bottom cube, then that falling motion would interact with the bottom cube, if tied, it would drag the bottom cube out as it fell downwards and thats just due to gravity, no additional force.
also the portal on the floor, portal on the ceiling thing, its just that each pass you make, gravity stacks (like a multiplier) and just keeps adding gravity, because all gravity sees is chell at the top of the portal exit the top portal with a velocity of x, and it adds gravity and then chell goes through the bottom portal with that added velocity, so chell exits the top portal with a velocity of that new x, so gravity sees that and pulls down even more until she goes in the portal again and the sequence continues. its no so much "oh im continuously falling" but rather, "oh i see something falling from the ceiling to the floor 250,000 different times with no break in between, time to add a gravity multiplier"
not a scientist but thats just my uneducated theory
I don't see any problem with the violation of conservation of energy. Portal 2 put an exit portal on the *moon*; the portal gun either breaks symmetry or is able to draw an arbitrarily large amount of energy from "somewhere off camera" to pay for its shenanigans. Probably alternate universes or something, if Half-Life is anything to go by.
@6:26-.-That's not how I would argue with this. I instead argue that if 1). Portals are just holes in space and 2). Portals are moving, then C). Moving portals moves space itself. So then the question is: what is the scientific or philosophical difference between an object moving through space vs space moving about an object? I for one see no difference. It's kind of like how what to moving in a river would push objects in the water, it would be a defilement of physics if something was just unaffected by waters movement without any clever work around.
I would argue it's the same thing as shoving a cardboard box with a hole in the bottom of it over a cube. I don't think it would fly out. It would only move because of the shift in gravity on the other side.
Edit: I was wrong. It would be like a cardboard box if both of the portals were moving, but the key difference is that the blue portal is stationary, which is what's causing the motion.
but it does fly through it, relative to the surrounding cardboard boundary, until the cardboard accelerates in a way that makes its velocity match that of the cube.
@@drdca8263 I feel like just because the portal moves fast around the cube wouldn't make the cube suddenly fly through it. I feel like the logic is flawed here. How exactly is the portal affecting the cube if it doesn't even touch it?
@@drdca8263 Since portals are just that, portals, imagine that the blue portal is on the immediate other side of the orange one on a suspended platform. Having what is essentially a hoop pass over the cube wouldn't just make it fly upwards, right? Is this really so different from having the blue portal be stationary?
Edit: Okay yeah it IS different, because having the blue portal be stationary makes it so that it would fly out because of the pushing explained in the video
You're right!
@@pierson9905 what do you mean when you say it doesn’t touch it? The cube goes through a surface with boundary the boundary of the portal. (Now, which surface you associate with it might be a choice.. maybe you don’t have to pick the taut surface connecting to the edge, but could choose some other surface, as long as you pick corresponding surfaces on both sides (would different such choices have the exact same consequences? I feel like maybe, but maybe not), but, there’s still something that the cube passes through at some point, else, if it never interacted with the portal, it would just be hit by the moving object?)
Conservation of Energy is probably a bit easier to deal with.
On the infinite portal fall, you're speeding up because gravity is pulling you down. But, your mass too is pulling the source of gravity towards you (the earth presumably in this case), since you have mass you too have your own (very extremely weak) field of gravity.
And it's just building up with each loop through the portal.
I have to wonder if there would be some sort of multiplication factor with the gravity pulling you through the portal. Since gravity is thought along the lines of warping space, that warp would extend up to the ceiling where the exit portal is, go through the entrance and back up. My instincts tell me it's unlikely to be a continual escalation of gravity build up, but it may have a sort of "higher gravity tube" between the two portals. Buuuuuut, I'm not sure if that would be the case.
As for momentum itself, momentum is a bit weird. It could be considered having stored energy, but, from my limited understanding, that energy is more of a differential between two reference points. Like how in a car that is going a constant speed you don't really feel momentum until you come to a sudden stop. You don't actually have actual energy built up in you, but the act of speeding up or slowing down will change your vectors to make you feel like it.
So with that in mind, when it comes to portals that are side by side facing the same direction, you can think of it like something along these lines. First imagine a wall between the two portals that don't even let the fabric of space and time to seep through. Then imagine a "space-time grid", with coordinates on it, and it intersects the first portal while one of the axis coordinates increment higher the closer it gets. One of the lines are colored red goes straight through the portal. On the other portal, the space time grid would push through it, and the axis coordinate is now increasing as it gets further from the portal.
Now place an object on that line, and launch it forward, it's coordinate on the axis grows and grows as it reaches the portal. And when it exits the otherside, the coordinate continues to grow.
Basically, think of it as the reference point the object is, is not in relation to the universe, but to the portal. And after this long write up, I thought of another way to think of the coordinates, think the coordinates for both portals, regardless where they are, as being [0,0], and the object is at [0,10], and moving towards portal A. It's coordinates decrease till it hits [0,0], and when it comes out of Portal B, the axis is now going into the negative numbers till it's at, say, [0,-10]. Even if Portal B was at [100,100] from the perspective of Portal A, from the object's perspective it's only [0,-10], despite being at [100,110] from Portal A.
and with that rambling done I think I should leave this comment off here before I ramble more.
there's something that makes me unexplainably happy about the little companion particles
Now assume a perfectly spherical cube.
If I see a man balance two perfectly balanced spheres, I'm calling the police
you can kinda solve the conservation of energy part by making gravity itself travel through portals.
in the example of falling through portals on the ceiling and floor, the area between the portals would either become zero gravity, or gravity on the ceiling portal would pull up instead of down.
depending on how large of an area this affects, this may also rip the earth in half.
might also set off those gravity-wave-detector-thingies.
Love your videos on the Portal demake, but these videos are also great!
Big fan of educational UA-cam channels like VSauce, MinutePhysics, Veritasium, etc.
You did a great job in this video of combining two types of content I enjoy. Keep up the great work. Excited to see more from you in the future!
For conservation of energy in an infinite portal fall, I think the conservation of momentum answer can still be applied. As Earth exerts a gravitational force on you to accelerate you from the top portal to the bottom, you exert the same force back onto it to accelerate it up; the continuous stream of potential energy being converted into your kinetic energy comes out of the kinetic energy of the earth. The real problem presented by portals then becomes how this almost definitely can be used to decrease entropy, thus breaking thermodynamics.
On the last question, could you view portals kind of like how you view mirrors in physics? Mirrors can be viewed has not redirecting a laser beam, but instead on each side of the mirror there is the space, but mirrored. as a result the laser seems to take a straight path. could this be considered the same for portals? imagining the portals as not a hole through space, but a way to move from one area in space to another, identical, area in space? in the infinite portals example, this would be like an infinitely high stack of rooms one on top of each other, so from the pov of the object falling, its the same as just falling off a large tower?
From the POV of the falling object, yes, that works fine. Until it moves sideways and hits the ground of one of those "rooms" at high speed. Where does the energy contained in that speed come from? Arguably, it would be from the portal itself, but the transfer mechanism is not clear, since the portal doesn't directly interact with the falling object.
Mirrors "can be viewed as ..." may be a useful *model* for some considerations, but it doesn't reflect reality, as in reality, there is no such thing as a copy of space. If the laser beam is reflected and heats up an object after that, the object that gets heated up is the one in the "original" space. The laser doesn't interact with anything in another space.
I agree with his ideas that energy must be provided by whatever device is sustaining the portals
@andremello
The kinetic energy comes from gravity. Normally the kinetic energy gravity can give to an object is finite, but the portal keeps resetting the height.
There actually are parity symmetry violations in particle physics, i.e. there are cases where, if the mirror were a reflected universe, the particle in your universe would go to your right and the reflected particle would go to your left - opposite directions.
The "mirror universe" thing is just a convenient geometry trick sometimes used to model optics.
@@luna010 what does it mean for "gravity" to give energy though? I think that sentence is flawed. The usual interpretation is that the object itself has "potential" energy stored in it, by virtue of being at a certain height, and that energy is converted to kinetic energy as the object falls. What is strange about the portal situation is that suddenly the object regains that potential energy, because it is suddenly at a higher height again, and where does that energy come from?
Conceptually, it's the portal doing work by transporting the object to a higher height, just like one can transfer energy by lifting the object. But since the portal does not "touch" the object, or interact in any way we can detect, that energy transfer is mysterious. It is also unclear what it means for the portal to lose energy.
I suspect the solution is to include the gravity field itself in the geometry, so in the volume between the two portals we have the gravity field pointing in two opposite directions, thus cancelling itself. The object wouldn't fall at all. Note this doesn't contradict James' solution to the moving portal.
I think matpat's explanation of mass as the means of conserving energy is a good solution. Each time you enter a portal, your mass is added to that portal and subtracted from the exit portal. So a negative mass makes up for the energy gained from falling
I think in most interpretations I have seen of portals they are seen more as doorways. They don't reconstruct you on the other side, they don't teleport your particles, etc. You literally move through them as though you move through a doorway.
What the portals do is they contort spacetime so that the two portals are directly on the other side of each other spatially.
Essentially imagine the universe is a piece of paper, they severely bend the paper back on themselves and then poke a hole, you as the player traverse through the hole.
Momentum is conserved in that case, since you did actually walk through a door in the same direction. If you were to draw a line and then have the line"fall down the hole" spatially it's a straight line however, from our perspective it is not. It's the portal equivalent of a straight line on a curved surface does not look straight on a flat surface.
If you look at it from this way and it is the idea of a door frame just falling on a cube, things start to make a little more sense.
Isn't this just wormhole vs teleportation? Teleportation will shoot the cube out, while a theoretical perfect connection of bent 3d space will not.
A perfect connection can’t really move
@@LineOfThy You have the same global universe relative movement problem with teleportation, I don't think non-absolute (perfect) teleportation could exist?
@@McKay1901 hmmm
I've always imagine that portals kind "add a copie of the room right behind it", rotated depending of the or rotation they have to each other. The object passing the portals will just go in a straight line, kinda going in the "other/same" room using a wormhole-like path.
So for the paradox, it will need that the room need to "move" AND to stand still at the same time, so both of the solutions would kinda works, but that's clearly messed up so they are all wrong too
The thing about conservation of energy is that portals "move" matter instantly through spacetime. But nothing can go faster than light. You would need an infinite amout of energy just to go beyond that limit.
So, the simple existence of the portals, as presented in the original game, doesn't follow conservation of energy (we can assume that they store/create an infinite amout of energy).
Maybe they should work differently, maybe like wormholes but we don't know if wormholes actually could exist and how they would operate.
Anyway, I really like your project and how you are giving your best to make the game engine as good as possible. Keep up the good work !!
For the momentum conservation with stationary portals, you should think that the vector is relative to the object, not to the "world".
Think about it from another point of view: when Chell cross a portal, she's facing forward from the secondary (target) portal, not from the primary (origin) one. If you use shapes like cubes or spheres, it's a little hard to imagine it as all the faces are the same, but if you use a person, or an irregular shape, you'll see that everything is relative to the shape and not to the world.
Also, for the gravity thing, it's the same. You conserve the speed/momentum when you pass the portals, then, you gain more speed because of the gravity force, next, you pass again the portals, and so on until you reach the terminal speed, it's not magic (except for being able to create a portal, yet), just think about it as a infinite fall from a precipice.
The way I see it, portals burn their "charge" as things go thru, as suggested by the sizzling edges, that constant sizzle probably because of air currents, light, subatomic particles etc. They likely get their charge from the hawking radiation of the microblackhole that powers the portal gun ( I think GLaDOS mentions the microblackhole at some point, not sure, it was a long time ago); and I would expect that if otherwise undisrupted, portals would eventually fizzle out spontaneously at some point, sooner if lots of energy or heavy things keep going thru, but probably lasting more than a human life-time, or maybe simply for some duration longer than the time since the game came out, as I suspect if someone had been running the game since it launched, there wouldn't be code in it to have make them close spontaneously at any point.
Infinite falls don't violate conservation of energy because the energy is being extracted from the portals.
before watching the video
i'm gonna say it still gets launched at about half velocity since the molecules that get pushed out the other portal have velocity and pull the stationary ones along
but gravity exists too which would lower the velocity a bit too
I think it's interesting to imagine what happens to the air, or what if the room was filled with water etc.
since it isn’t expanding the capacity of the room in any way, it should maintain the same exact state even after putting portals top and bottom.
or you know what actually, gravity is still pulling all water to the bottom, with the bottom having the greatest amount of pressure. i imagine it to be an endless loop of having the pressure constantly try and equalise coming through the hole in the bottom and pushing against the water in the top. nah bro idk it’s too late at night for this
In Valve's games: The Cube would instantly jump while teleporting (if the piston is fast enough).
In real life Physics: the portal would teleport without adding any additional movement / momentum. Note that I just said "additional"..., meaning that current momentum and forces and velocity are conserved and transferred between Portals. The cube would just "appear there in its new place quick". That's my theory.
Notice that there cannot be any friction between the Portal itself and it's surface (i.e.: it's a HOLE): that's why the Portal itself cannot add additional movement (or momentum) to any Object, per se.
I love this beautiful visualization. Next time I will just push the tip through a portal and see it continue forever (without acceleration).... assuming no gravity and no air.
I got this theory off tv short from a long time ago but I can't remember what it was since I was so young. This was just about teleportation and not the game.
Basically it explained portals as destroying and recreating things on the other side. The energy to do this would come from the material that makes the portal and would not last forever. They would be still be limited by the speed of light and basically what happens at the other side of the portal can be anything aperture science they want it to be, but in this case they make it seem like you teleport. You don't die when you enter it because the portal is creating everything you need to just before it destroys it. But you could think of the object on the other side of the portal as not the original its self but a replica.
If a portal ran out of energy while you where between it you would be chopped at the point it ran out of energy. If anyone knows the tv spot I got this from that would be helpful, i think it was animated.
Well the fact that the edges of the portals are fiery could help your explanation on the conservation of energy. Maybe the portal gun shoots a goo that burns slowly, and the burn rate adjusts based on the energy needs of what goes in and out of it, but it's always lit, like a pilot light of some sort. But now we're really getting into the weeds of scifi technology. We'd probably need to crossreference it with Half Life Lore and get Xen Magic Space Rocks involved
My logic is probably wrong here for one reason or another, but the diagram at 5:38 made me think about normal force because of the arrows. This probably applies better to your portal piston problem than this diagram though. If each particle in the cube were to actually be colliding with the surfaces both portals are attached to (yet have no resistance moving through the portals), the force from the entrance portal surface on the portal (F1) is applied to the cube and the surface it is sitting on. The surface the cube is sitting on applies a normal force (F2) with equal magnitude to F1 on the cube, making the net force 0. As the cube moves through the portal, the force F1 is also applied to the surface of the exit portal providing a normal force (F3) also equal in magnitude to F1. Since F1 is pointed away from the entrance portal, the applied force would be pointed towards the exit portal, making F3 point away from the exit portal. This would result in the force F3 to be applied to cube as it passes through the portal, launching it.
Example with portal on a piston: For simplicity, the cube will be sitting on a flat surface at rest with the entrance portal moving on a piston straight down with a force of 1N (in xyz: F1 = [0,-1,0]) with a horizontal exit portal pointed right (+x). F1=[0,-1,0], Cube applies F1 to surface, F2=[0,1,0], F1+F2=[0,0,0], F3=[1,0,0], F1+F2+F3=[0+0+1,-1+1+0,0+0+0]=[1,0,0]
Example with stationary portals and a moving cube: For simplicity, both portals will be horizontal, pointed right (+x). F2 is the force applied to the cube, pointed left (-x) with a magnitude of 1N (F2=[-1,0,0]). F2=[-1,0,0], F1=[1,0,0], F2+F1=[0,0,0], F3=[1,0,0], F2+F1+F3=[1,0,0]
ok, I wasn't convinced before, but the thought experiment of the portals on walls suspended on ropes convinced me.
I think we can wave away the seemingly breaking of conservation of energy by just saying that the portals are some hyper-dimensional connection along what can only be assumed to be hyperbolic space, such that there is no energy loss... which basically just equates to "magic science did it" now that I think about it :p
Very fitting for the Half-Life universe, considering that Xen exists.
To be fair, the Portal gun is canonically powered by a miniature black hole.
I feel like relativity would solve all of the problems. The direction is relative to the portal, the speed is relative to the portal, and the kinetic energy would also be relative.
there is slight problem with the 2 cubes one, both are resting, they do not move per se, just swich places, first one isn't pushed, its resting on the first one (also in this example it would slide down due to gravity but thats beside the point since we may be talking abou high speeds) only moment they get any energy would be probably last miliseconds that portals slams and create solid surface
At 2:26 when the first box exits the other end of the portal the gravity in that frame of reference takes hold and the box falls over. 5:10. No it's not true for stationary portals. Momentum is maintained, the direction of that vector changes, but physics doesn't care what direction you're going so long as energy isn't created or destroyed, it's why potential energy exists, energy can change form infinitely so long as it isn't gained or lost. Black Holes which suck in spinning matter gain rotation, it doesn't matter what direction the object that fell in was spinning though, the angular momentum of the black hole will always increase when added to. 5:20, and no a cube changing direction mid-air wouldn't violate momentum either, but there's no way to change the vector of the momentum in classical physics. Portals allow for this because you're splicing two pieces of space together. You might as well argue that walking through a doorway breaks conservation of momentum because once you're no longer in the room and that's somehow problematic. 5:27 yes, momentum is a vector, and the direction does matter for moving through space to determine where an object will be from time A to time B, but it doesn't matter for conservation of momentum where all that matters is the magnitude. Gyroscopes are an example of this. Spin up a big gyroscope whine in a spinning chair, tilt it left to right. The magnitude of the angular momentum doesn't change (except by dissipation through other means such as heat from friction) but the direction does change and that isn't an issue. 5:37 Your solution is effectively saying that if I walk through a doorway, I'm imparting momentum on the doorway. That's really wrong. Portals are 4 dimensional connections in space, they're not physical things, they don't ever impart forces or allow you to impart forces that aren't normally happening, they just allow taking shortcuts through three dimensional space. 6:00 that's not how portals work at all. 6:29 in which game? Portal or the one you made? If it's the one you made then ofc the argument is moot, it's your game, portals work however you want, and if it's the Valve Game Portal then you're wrong because Portals can't move at all so the entire experiment is moot. If you take the concept of a Portal as presented in the game Portal by Valve, the explanation given is that they are just interconnected pieces of space and would work opposite of your explanations. 6:40 this argument is moot because nothing sits absolutely still in space, space is constantly expanding. Regardless whether or not a portal is moving isn't relevant to what two positions it connects to. 7:00 in the clip you're showing, by your logic, the portals moving should apply an angular diffraction past the portal exit to the beams since the portal is moving. That clip kind of blows up your theory since as you can see, the light isn't getting bent at all. 7:10, yes because people pointed out why you were wrong and now you're pulling up examples that prove yourself wrong as evidence that you're right. Weird. The ultimate answer to partway protrusion is that the side that exits will have a different gravitational frame of reference and get pulled accordingly and if enough mass is on the other side it'll plop out as expected. Here's an easy way to explain your argument being wrong. Take a wall, put a portal on either side, making it effective a doorway. Slide that wall horizontally to make a stationary box pass through it. Now take a doorway and do the same to the box with the doorway. The results of the experiment should be identical, in your example, the portal doorway sees the box go sliding perpendicular to the wall while the regular doorway does nothing, *that's wrong*.
maybe that's why you can only place portals on some surfaces. Portals need the right chemical composition on the surface they attach to, so that they can convert chemical energy into kinetic/potential energy for moving stuff around
Momentum of the object is conserved because the portal's function is to teleport an object from one location to another without affecting its velocity magnitude, only its velocity direction. Magnitude of a cube-at-rest's velocity is still zero. The velocity at which a portal moves at you is of no affect because the contents of the portal are both volumes of air that are both having their velocity magnitudes preserved as particles move about back and forth across the boundary. It's like if a bucket fell on a small object, the object isn't going to just hop into the air as the bucket comes over it because neither the air nor floor moved to exert a force on it. Same here.
How am I just discovering this channel? Great work!!!
You are forgetting the major reason for the breaking of conservation, its the frame of reference, relativity. the portals allow the change in reference frame for the object from one side to the other.
with the piston example:
* the stationary cube is accelerating constantly at 1g, but the platform is pushing back with an equal force (ie the ground) so it is stationary
*as the piston drops the section of the cube passing through has its reference frame altered to that of 45 degrees local gravitational constant, so now the top half has an acceleration pulling the top of the cube to the side at that 45deg
*also the mass of the top of the cube is is being accelerated by the emerging lower section of the cube (which you explained, but forgot the next bit) which is being pushed upwards by the stationary platform. THIS is where the momentum comes from for the emerging cube, the stationary platform is pushing the cube through the moving portal (the moving change in reference frame)
with the opposing portal example the momentum is conserved because the reference frame of the cube (from the cubes perspective) doesn't change, from the observers perspective the reference frame itself of the cube changes when passing through the portal. So to be clear, the cube is in a box (its reference frame) the box has no mass or energy cuz is a reference to space time relativity of the objects within it. so from the cubes perspective the universe flips around 180deg and it just continues as it was without any force being applied to it.
when playing with portals you need to remember that the frame of reference is the thing that is altered when passing the event horizon and not the object, and if the net forces on an object do not match the resulting net forces of the object on the other sides frame of reference than there will be an change in acceleration imparted proportional to the moment of inertia (mass) on either side of the portal.