Portal Paradox

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Re: Portal Paradox

Postby HenryS » Sun Oct 26, 2008 9:20 pm UTC

Lines are really geodesics in a space like this, which you can specify by saying that they start at some location with some initial direction, and extend in either direction. E.g. in the left hand diagram there is a vertical line that joins the two red arrows. The geodesic you get on that line just goes around in a circle following the same line from red arrow to red arrow forever.

So what happens to the geodesic which is given by starting at the top of the picture where the vertical red line hits the top, and going vertically downwards from there? As the circle passes by moving to the right, that geodesic will go through the portal and come out on the other side of the portal, in this case I think the geodesic continues coming vertically out of the lower circle. When the yellow arrow has just passed by the position of the red line, the geodesic comes out just to the left of the lower yellow arrow, and as the disk moves across the exit point of the geodesic on the lower circle moves across to the left. When the top circle has passed by the red line, the geodesic is once again just the vertical red line.

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Re: Portal Paradox

Postby Entropy » Sun Oct 26, 2008 9:28 pm UTC

My concern is not about how a laser shown from the top would interact with the hole. My concern is about what happens to the space inside the hole. When you use a hole punch on a piece of paper, you are left with the hole and the little circle that you punched out. If you 'move the hole', some of that circle has to come back somehow.

If you have a flat sheet of rubber, and you punch a hole in it with a hole punch, how can you move the hole? The only way I can see is to put the circle of rubber back, and then punch a new hole.

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Re: Portal Paradox

Postby HenryS » Sun Oct 26, 2008 9:56 pm UTC

Ok, so put the hole back in, punch a new hole epsilon to the right, reconnect the tube... so what? Everything is continuous here, nothing "breaks" as far as I can see...

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Re: Portal Paradox

Postby Entropy » Sun Oct 26, 2008 10:22 pm UTC

The problem with punching new holes is that you punch out bits of the world when you do that. Hence, if there is a guy to the right of the hole, you end up punching bits of him out, and then reassembling him on the left as the hole moves. He never goes 'through' the portal, and part of him ends up being stored on these little rubber discs outside the world.

The problem somewhat goes away if we turn the hole back into a slit, because none of the world gets removed. However, the effect as the slit 'moves' is the same... it cuts through any objects in it's path, leaving them partially on one side of the portal and partially on the other. The only time something goes 'through' the portal is when they move relative to it.

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Re: Portal Paradox

Postby HenryS » Sun Oct 26, 2008 10:47 pm UTC

This is getting kindof close to Zeno's arrow paradox, although maybe we shouldn't go there yet.

Let's go down another dimension for a different example. The world is a 1 dimensional line [imath](-\infty,\infty)[/imath]. Someone opens up a portal entrance and exit. Instead of disks in 2d they are now intervals, say the orange portal covers [imath][-2,-1][/imath] and the blue portal covers [imath][1,2][/imath]. The portals are connected in such a way that -1 links to 1 and -2 links to 2. The world has now been reconfigured into a circle consisting of [imath][-1,1][/imath] (because -1 and 1 are identified), and another infinite line that consists of [imath][-\infty,-2] \cup [2,\infty][/imath] (because -2 and 2 are identified).

Now move the blue portal to the right. The circular part of the world remains a circle, it just gets to be a longer circle. Or if you move the blue portal to the left you get a shorter circle. How is this different from living on a rubber band, which someone is stretching (making the circle longer) or relaxing (making the circle shorter)? You can't even tell where the portal boundary is when living in this space, it would just look the same from anywhere you choose.

Going back to the rubber discs, you're thinking of making very small steps to do motion, I'm thinking of doing a continuous process, of infinitesimally small steps.

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Re: Portal Paradox

Postby Entropy » Sun Oct 26, 2008 11:00 pm UTC

The difference between stretching or shrinking the circle and adding to or removing from the circle is just that: you are inserting or removing fabric at a particular location, rather than contorting it. Moving the blue portal to the left (say from [1, 2] to [0, 1]) removes anything in the range [0, 1] from the circle. If the guy happened to be standing in that range, he would no longer be in the circle.

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Re: Portal Paradox

Postby phlip » Mon Oct 27, 2008 12:57 am UTC

A point of order: the portals in the game are flat zero-width disks... so our lower-dimension analogies should be a line in 2D, or a point in 1D... not a disk and line, respectively.

The point being that zero volume is "removed" from space when a portal is opened. Whether this changes the reasoning at all, I'm not entirely sure, but still, the analogies need work.

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Re: Portal Paradox

Postby Entropy » Mon Oct 27, 2008 1:15 am UTC

phlip wrote:A point of order: the portals in the game are flat zero-width disks... so our lower-dimension analogies should be a line in 2D, or a point in 1D... not a disk and line, respectively.

The point being that zero volume is "removed" from space when a portal is opened. Whether this changes the reasoning at all, I'm not entirely sure, but still, the analogies need work.


That's a good point. Still, as a slit (or point) moves, the fabric on one side has to teleport across it to the other side, which is going to remove things from the contracting part of the space.

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Re: Portal Paradox

Postby jestingrabbit » Mon Oct 27, 2008 2:39 am UTC

0xentropy wrote:
phlip wrote:A point of order: the portals in the game are flat zero-width disks... so our lower-dimension analogies should be a line in 2D, or a point in 1D... not a disk and line, respectively.

The point being that zero volume is "removed" from space when a portal is opened. Whether this changes the reasoning at all, I'm not entirely sure, but still, the analogies need work.


That's a good point. Still, as a slit (or point) moves, the fabric on one side has to teleport across it to the other side, which is going to remove things from the contracting part of the space.


It seems like you're viewing the fabric of space time (to use cliched, hackish, terminology) as something that is, or should be, teleported, whereas henryS is viewing only the matter and energy held on the fabric as something that is teleported.
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Re: Portal Paradox

Postby Darth Eru » Mon Oct 27, 2008 3:01 am UTC

jestingrabbit wrote:
0xentropy wrote:
phlip wrote:A point of order: the portals in the game are flat zero-width disks... so our lower-dimension analogies should be a line in 2D, or a point in 1D... not a disk and line, respectively.

The point being that zero volume is "removed" from space when a portal is opened. Whether this changes the reasoning at all, I'm not entirely sure, but still, the analogies need work.


That's a good point. Still, as a slit (or point) moves, the fabric on one side has to teleport across it to the other side, which is going to remove things from the contracting part of the space.


It seems like you're viewing the fabric of space time (to use cliched, hackish, terminology) as something that is, or should be, teleported, whereas henryS is viewing only the matter and energy held on the fabric as something that is teleported.


No, I think he meant teleport from one edge of the opening to the other edge of the same opening as the portal was moved. Teleport was probably an unfortunate choice of verbiage to use in that way when discussing portals. Besides that, I still think entropy's wrong. If the portal is only 2-d, then as phlip pointed out, no volume of space is actually displaced when opening the portal, so no "fabric" would move around at all. If the portal is truly width-less, I envision it as being able to intersect with solid objects and whatnot without disturbing them at all, unless they approached it from in front and therefore passed through it. (I'm not sure what would happen if a larger object moved into it from the front. Probably a portal-shaped hole would be cut in it. Or, it could resize the portal or the object so the whole thing fit through.)

So I don't think the whole "hole-punch" analogy is really applicable here, since the portal is not, in fact, a hole punch. Rather it's a piece of an infinitely thin cross-section of space that has suddenly disappeared. Since the cross-section is infinitely thin, no space has actually disappeared. Kind of odd to think about, and I could be wrong overall, but under the assumption that portals are 2-d, I believe my reasoning is sound.
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Re: Portal Paradox

Postby Entropy » Mon Oct 27, 2008 3:20 am UTC

Darth Eru wrote:No, I think he meant teleport from one edge of the opening to the other edge of the same opening as the portal was moved. Teleport was probably an unfortunate choice of verbiage to use in that way when discussing portals.


Correct, that is what I was intending to say.

Besides that, I still think entropy's wrong. If the portal is only 2-d, then as phlip pointed out, no volume of space is actually displaced when opening the portal, so no "fabric" would move around at all.


I agree entirely. The difficulty I am seeing is with the space that the slit travels over: nothing in that space should actually be disturbed, or travel 'through the portal' at all.

If the portal is truly width-less, I envision it as being able to intersect with solid objects and whatnot without disturbing them at all, unless they approached it from in front and therefore passed through it. (I'm not sure what would happen if a larger object moved into it from the front. Probably a portal-shaped hole would be cut in it. Or, it could resize the portal or the object so the whole thing fit through.)

So I don't think the whole "hole-punch" analogy is really applicable here, since the portal is not, in fact, a hole punch. Rather it's a piece of an infinitely thin cross-section of space that has suddenly disappeared. Since the cross-section is infinitely thin, no space has actually disappeared. Kind of odd to think about, and I could be wrong overall, but under the assumption that portals are 2-d, I believe my reasoning is sound.


I think that for the most part we agree... the conversation just got sidetracked a bit by using the hole punch as an analogy. The major point I was trying to make is that moving the slit over objects should not cause them to magically get sucked through the slit. The portal should not exhibit portal-like behavior if it's endpoints are the only things moving. In addition, it makes absolutely no sense to move one portal through another, as two portals can no longer create a connection across a fold upon reaching that proximity. Consider: how do you fold a T shape such that the horizontal and vertical line segments line up?

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Re: Portal Paradox

Postby phlip » Mon Oct 27, 2008 3:35 am UTC

0xentropy wrote:The major point I was trying to make is that moving the slit over objects should not cause them to magically get sucked through the slit.
But why not? After all, moving an object over the slit makes it "magically get sucked through the slit"... indeed, that's the whole point of the portals.

Say, in two dimensions... a blue portal as a line from (0,0) to (0,1), opening left... and an orange portal from (0,2) to (0,3), opening right. A point mass at (1,2.5). We move the orange portal to the right, at a speed of 1 unit/second. 1 second later, it hits our point mass. Why shouldn't it get portalled to (0,0.5), moving leftward at 1 unit/second?

Of course, if there's an atmosphere, you'll get a low-pressure pocket behind the moving portal (equivalently, the newly-created "fabric" behind the portal is empty, a vacuum) and the air in front of the portals will have a higher pressure (equivalently, the air in the bits of "fabric" that are destroyed, are bumped off to either side)... but then, the exact same pressure difference happens when you move any object, portals aren't special in that regard. The only difference between this and moving any other object is that the high-pressure area can bleed from one portal to the other.

Another point is that the "fold a piece of paper" thing is itself a loose analogy... there's no particular reason to suspect that the portal gun works by folding the universe through some extra dimension to make the portals line up... space can be contorted without having to be curved around, or through, anything in particular. You can concoct a metric which is Euclidian almost everywhere, but the two lines of a T are the same points in space... and you don't have to find a way to "fold" a piece of paper in 3-space making those two lines coincide to do so.

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Re: Portal Paradox

Postby Entropy » Mon Oct 27, 2008 3:58 am UTC

phlip wrote:
0xentropy wrote:The major point I was trying to make is that moving the slit over objects should not cause them to magically get sucked through the slit.
But why not? After all, moving an object over the slit makes it "magically get sucked through the slit"... indeed, that's the whole point of the portals.


So the objects within the space go through the slit, but the fabric of the space just crosses through it? I'm confused as to why the two should be treated differently.

Say, in two dimensions... a blue portal as a line from (0,0) to (0,1), opening left... and an orange portal from (0,2) to (0,3), opening right. A point mass at (1,2.5). We move the orange portal to the right, at a speed of 1 unit/second. 1 second later, it hits our point mass. Why shouldn't it get portalled to (0,0.5), moving leftward at 1 unit/second?


Because the space it was occupying at (1, 2.5) isn't going anywhere. After the orange portal moves through that space, that space is still going to be there.

Of course, if there's an atmosphere, you'll get a low-pressure pocket behind the moving portal (equivalently, the newly-created "fabric" behind the portal is empty, a vacuum) and the air in front of the portals will have a higher pressure (equivalently, the air in the bits of "fabric" that are destroyed, are bumped off to either side)... but then, the exact same pressure difference happens when you move any object, portals aren't special in that regard. The only difference between this and moving any other object is that the high-pressure area can bleed from one portal to the other.

Another point is that the "fold a piece of paper" thing is itself a loose analogy... there's no particular reason to suspect that the portal gun works by folding the universe through some extra dimension to make the portals line up... space can be contorted without having to be curved around, or through, anything in particular. You can concoct a metric which is Euclidian almost everywhere, but the two lines of a T are the same points in space... and you don't have to find a way to "fold" a piece of paper in 3-space making those two lines coincide to do so.


So wait... physical space can bring two points together without folding? Are we still talking about physical space, or a mathemagical topology in which things can actually teleport?

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Re: Portal Paradox

Postby phlip » Mon Oct 27, 2008 4:18 am UTC

Ah, when I see a portal moving, I don't see the "fabric" it moves through being unaffected... I see the "fabric" in front of it being destroyed (incrementally, of course, with any objects which happen to be in the epsilon-width strip being removed at a given moment in time being sorta "bumped" to one side (so a particle can move over the seam, even as more magical space fabric is being destroyed, suffering merely an infinitesimal perturbation in its path as it crosses the seam). At the same time, "fabric" being created, behind the portal... initially empty (ie, a vacuum), as is the epsilon-width strip of space behind any moving solid.

As for the difference between crazy twisted hypothetical "physical space" and crazy twisted mathematical topologies... I wasn't aware that there was a distinction to be made. You'll have to point me to an axiom set for the former, 'cause I'm only aware of one for the latter.

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Re: Portal Paradox

Postby Entropy » Mon Oct 27, 2008 4:39 am UTC

phlip wrote:Ah, when I see a portal moving, I don't see the "fabric" it moves through being unaffected... I see the "fabric" in front of it being destroyed (incrementally, of course, with any objects which happen to be in the epsilon-width strip being removed at a given moment in time being sorta "bumped" to one side (so a particle can move over the seam, even as more magical space fabric is being destroyed, suffering merely an infinitesimal perturbation in its path as it crosses the seam). At the same time, "fabric" being created, behind the portal... initially empty (ie, a vacuum), as is the epsilon-width strip of space behind any moving solid.


Why do the particles get to be bumped if the space that they occupy is being destroyed? It seems that you are introducing a force here without anything actually applying that force.

As for the difference between crazy twisted hypothetical "physical space" and crazy twisted mathematical topologies... I wasn't aware that there was a distinction to be made. You'll have to point me to an axiom set for the former, 'cause I'm only aware of one for the latter.


There have actually been measurements taken that indicate our 3D space is curved through a higher dimensional space, more-so near very dense objects. I suppose the major difference for me is that a space which is bent or twisted in a higher dimensional space can have a physical realization, but a space defined by an arbitrary set of equations might be impossible to realize physically.

Folding space is the least problematic way that I can imagine to introduce portals without breaking physical laws. Without bringing the points together, you suddenly have to somehow support the idea of teleportation in your set of laws that govern the universe.

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Re: Portal Paradox

Postby phlip » Mon Oct 27, 2008 4:51 am UTC

0xentropy wrote:Why do the particles get to be bumped if the space that they occupy is being destroyed? It seems that you are introducing a force here without anything actually applying that force.

The displacement caused by the "bumping" (and thus the force involved) is infinitesimal though... it goes to zero as we take our time-step (and thus the epsilon width of our strip of space) toward zero. Hence the quote-marks... there isn't an actual bumping involved, it's an approximation caused by viewing a continuous process as a discrete-time process... since the latter is much easier to explain and conceptualise, but means there's a finite nonzero amount of space being destroyed at each step, and thus a finite nonzero probability of matter being in that space, which something has to happen to. The "bumping" is just a solution to that problem that approaches "the stuff just goes through the portal like you'd expect" when dt approaches zero.

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Re: Portal Paradox

Postby Entropy » Mon Oct 27, 2008 4:57 am UTC

But that isn't what I'd expect... I'd expect the matter to get destroyed along with the space. Treating the space and the objects in it differently is the whole difficulty that I am having, and I don't understand the justification for treating them separately.

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Re: Portal Paradox

Postby phlip » Mon Oct 27, 2008 5:09 am UTC

But part of the problem is that you're treating the "fabric" as if it was an object, and I don't see the reason for that, either. Hence the quotes there, too.

I think there should be no difference between an object approaching a portal, and a portal approaching an object. Relativity of position and velocity has been pretty fundamental in Physics since Galileo... the idea that the portal would react differently based on whether it was moving relative to some fixed omnipresent field (whether we call it a "fabric" or just call it the aether and be done with it) sounds dodgy to me.

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Re: Portal Paradox

Postby jestingrabbit » Mon Oct 27, 2008 5:14 am UTC

0xentropy wrote:There have actually been measurements taken that indicate our 3D space is curved through a higher dimensional space, more-so near very dense objects.


You mean objects with large mass and no there haven't been. Just because space-time has negative curvature doesn't mean that its sitting inside some higher dimensional object. Take the hyperbolic plane for instance. One model has it being a sheet of a hyperboloid. But others have it being the unit disc, or the upper half plane. Now, you can think of the disc and the plane as sitting inside a larger space, but you don't have to. They can just have that curvature without being curved in something larger.

I think the reason that there might be a difference in the treatment of the fabric and the objects is because they are different things.
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Re: Portal Paradox

Postby Entropy » Mon Oct 27, 2008 5:29 am UTC

phlip wrote:But part of the problem is that you're treating the "fabric" as if it was an object, and I don't see the reason for that, either. Hence the quotes there, too.

I think there should be no difference between an object approaching a portal, and a portal approaching an object. Relativity of position and velocity has been pretty fundamental in Physics since Galileo... the idea that the portal would react differently based on whether it was moving relative to some fixed omnipresent field (whether we call it a "fabric" or just call it the aether and be done with it) sounds dodgy to me.


Hold on... so you don't want to treat the space as an object, but you want to treat the portal as an object? Isn't the portal a topological feature of the space?

jestingrabbit wrote:
0xentropy wrote:There have actually been measurements taken that indicate our 3D space is curved through a higher dimensional space, more-so near very dense objects.


You mean objects with large mass and no there haven't been. Just because space-time has negative curvature doesn't mean that its sitting inside some higher dimensional object. Take the hyperbolic plane for instance. One model has it being a sheet of a hyperboloid. But others have it being the unit disc, or the upper half plane. Now, you can think of the disc and the plane as sitting inside a larger space, but you don't have to. They can just have that curvature without being curved in something larger.

I think the reason that there might be a difference in the treatment of the fabric and the objects is because they are different things.


My mistake, I did mean mass. And I suppose it is possible to have a flat representation of a curved space. But how could you have a flat representation of a space where two separate points on the space have been glued together?

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Re: Portal Paradox

Postby phlip » Mon Oct 27, 2008 5:41 am UTC

I don't think I need to claim that the portal is an object, in order to claim it should satisfy Galileo/Lorentz/whatever invariance... topological feature or not, it's at a specific point in space, and if that point is stationary in *some* intertial frame, with stuff in motion towards the portal, then it should behave appropriately, and transport that stuff to the other portal. And even if the portal is accelerating, there's a frame where the portal's velocity hit 0 just as a particle hit the portal, and it should work then, too.

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Re: Portal Paradox

Postby Entropy » Mon Oct 27, 2008 6:02 am UTC

phlip wrote:I don't think I need to claim that the portal is an object, in order to claim it should satisfy Galileo/Lorentz/whatever invariance... topological feature or not, it's at a specific point in space, and if that point is stationary in *some* intertial frame, with stuff in motion towards the portal, then it should behave appropriately, and transport that stuff to the other portal. And even if the portal is accelerating, there's a frame where the portal's velocity hit 0 just as a particle hit the portal, and it should work then, too.


In that reference frame, the portal at the other side is moving at the same speed as the particle. How does the particle attain twice the speed and overtake it?

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Re: Portal Paradox

Postby phlip » Mon Oct 27, 2008 6:07 am UTC

The same way a particle moving through non-aligned portals manages to come out moving in a different direction, or a particle moving between two portals at different heights manages to come out with more gravitational potential energy, but its energy state otherwise unchanged... neither of which can be easily explained (and the causes for which are unknown), but that they happen is taken as a given when discussing the portals (the forces and/or extra energy are provided via a large supply of unexplainium in the gun's gubbins).

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Re: Portal Paradox

Postby Entropy » Mon Oct 27, 2008 6:46 am UTC

phlip wrote:The same way a particle moving through non-aligned portals manages to come out moving in a different direction, or a particle moving between two portals at different heights manages to come out with more gravitational potential energy, but its energy state otherwise unchanged... neither of which can be easily explained (and the causes for which are unknown), but that they happen is taken as a given when discussing the portals (the forces and/or extra energy are provided via a large supply of unexplainium in the gun's gubbins).


The difference in those cases is that when the space is viewed as actually being connected at the portal surfaces, the velocity doesn't change at all by going across. It is just the new connectivity of the space that takes what were straight lines and turns them into curves that can end up perpendicular to how they started. As far as I can see, a portal influences connectivity, not velocity.

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Re: Portal Paradox

Postby phlip » Mon Oct 27, 2008 6:50 am UTC

OK, so why is that different to a portal that connects two lines/planes/hyperplanes/whatever in spacetime?

A particle can go in one portal and come out another at a different direction in spacetime (ie, a different speed), just as easily as a particle can go into one portal and come out of another in a different direction in space.

[edit]
Equivalently: a particle can enter one portal, at velocity v, in the reference frame where that portal is stationary... and then, one coordinate transform (Galilean or Lorentz, take your pick) later, leave the second portal at velocity v, in the reference frame where the second portal is stationary.

This can even satisfy the fact that a particle can enter a portal in one direction and leave in another... formally, let S1 be the frame which has the entrance portal stationary, centred on the origin, opening right, and S2 be the frame which has the exit portal stationary, centred on the origin, opening left. Then if a particle enters the portal at position p, velocity v, in frame S1... then it'll leave the portal at position p, velocity v, in frame S2.

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Re: Portal Paradox

Postby Darth Eru » Mon Oct 27, 2008 12:47 pm UTC

I just had an interesting thought. Could an argument be made that once a portal is open, the endpoints must remain stationary with relation to each other, so moving one will move the other, until the portal is closed and reopened (ie by firing the gun again). If that were the case, then you wouldn't have any trouble with accelerating an object without applying force by moving one end of the portal over it, and you wouldn't face the conceptual trouble of having a portal that will only transmit things if they move into it, instead of it moving over them (I just have a hard time imagining this to be true.)

Since a portal would obviously have to be non-stationary relative to something, it could be possible to move it around. That doesn't necessarily mean it would be possible to change the relative position of the two endpoints to each other though. And a strong argument in favour of that would be the fact that being able to bring two portals-end-points together or take them apart or move one over an object while leaving the other alone would allow you to violate far more laws of physics than just being able to construct a portal in the first place.
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HenryS
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Re: Portal Paradox

Postby HenryS » Mon Oct 27, 2008 9:17 pm UTC

I think a lot of this discussion comes down to what rules people are playing by, or rather, the discussion is over what rules we could be playing by. In the game of course, portals do not move continuously, which is one set of consistent rules. We seem to be arguing about or whether they can move or not but haven't described what assumptions we are making about the world that we want to preserve. E.g. conservation of energy, which is already fishy if you can set up an infinite falling loop.

I suggest that we ask of our moving portals physics that they act like the portals we know from the game when they aren't moving, and that their actions be at least defined (that we know what happens given a situation) and consistent (that you cannot approach the same situation from two different points of view and get different results).

If we want to construct systems of portal physics which have more restrictions than this in order to avoid possible problems then that's all good, but without some example that shows that without those restrictions there is no sensible way in which the portals would work, then there is maybe a more general version of portal physics to figure out.

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Re: Portal Paradox

Postby pimanrules » Fri Oct 31, 2008 1:20 am UTC

Thought I might share:

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Re: Portal Paradox

Postby MSTK » Fri Oct 31, 2008 6:31 am UTC

It might be enlightening to postulate a scenario where portal movement gives rise to effective time-travel.

Imagine Portal A and B; each has an attached clock/calendar. A is on a slab that remains stationary. B is on a slab that is taken and put onto a space ship capable of travel near c. The ship then departs and flies at, say, .995c for about a year. Due to time dilation, A's clock will have elapsed about 10 years. B's clock will have elapsed about 1 year.

What does this mean? If A is on Earth and the ship leaves in the year 2008, then after the aforementioned trip, B's calendar will read 2009. But A's calendar will read 2018.

Einsteinian Time Travel is characteristically Forwards-only. If a prospective time traveler is on the ship and steps into his portal, B, in 2009, he will emerge out of Portal A in 2018.
The unconventional time travel here is the fact that this allows for backwards time travel, as well. If a 25-year-old scientist on Earth steps into Portal A in 2018, he will emerge on the Spaceship in 2009.

Now, this might strike you as impractical. Someone who wishes to go back in time to change the past will only walk through the portal to realize that he is .995 light years away from the Earth, unable to actually *do* anything. But suppose he intends to hijack the space ship and then fly it straight back to earth at the same speed, and land the ship next to where A is and still is.

1 ship year later, 10 earth years later, the Earth's calendar will read 2028. The ship's calendar will read 2010.

The time traveler now has portal A and B side-by-side. To Portal A and to the rest of the world, it is the year 2028. To portal B and to him, it is the year 2010.
Now at this point the time traveler will consider himself quite foolish. He departed Earth in 2018 intending to change the past and yet wound up in the year 2028. It is interesting to note that the time traveler himself, born in 1983, is only biologically 26 years old in the year 2028.


But...here's your paradox.

In the first case (when the ship is away), a person who steps into Portal B will emerge from Portal A 9 years later. In the second case, will a person who steps into Portal B emerge from Portal A 18 years later? The case is made seemingly absurd because both portals appear to exist simultaneously, side-by-side. Imagine our character from above stepping into the Portal B he just dragged home from space. Would he come out of Portal A in the year 2046?


Now consider the reverse. In the first case, a person who steps into Portal A will emerge from Potal B 9 years in the past. But what would happen to someone who steps into Portal A in the second case, where they are side-by-side, in 2028? In 2046?

Angelbaka
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Re: Portal Paradox

Postby Angelbaka » Mon Nov 03, 2008 1:07 am UTC

To settle an earlier point:
Portals obey all laws of physics with the SOLE EXCEPTION of conservation of energy, otherwise the game would have been unplayable. This makes sense, as we've never (to my knowledge) actually PROVED conservation of mass-energy, we simply haven't yet disproved(?) it yet. That, and the world makes much less sense if one were able to simply create an explosion with particles to convey the heat and huge kinetic energy. (I personally believe this is why superheros are so awesome, because they aren't actually physically impossible- it's just easier if they are). So, technically, a portal gun isn't actually impossible- we just can't conceptualize how it could be possible.

EDIT: in regards to the ORIGINAL problem: you would reach critical mass sometime before the portals actually touched each other because you cannot have two particles occupying the same space (even non-euclidean and multiple dimensions agree, they'd just disagree that both particles reside in the same space) Either way, you reach critical mass, nuclear explosion(fission)/implosion(fusion), energy is redirected through both portals into each other and eventually (not very long, considering the power of the forces involved) the surfaces they reside on are destroyed and point is null. You, of course, are dead from the nuclear reaction of your body.
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link7927
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Re: Portal Paradox

Postby link7927 » Fri Nov 07, 2008 5:11 pm UTC

i think i have a way to dlove this...whos got G Mod? :D
If any one does, spawn a portal at ur feet, then one above you and have some one move it on top of you. i dont know if the game will give us wat were looking for, it mite just stop at ur head or sumthin, its worth a shot tho =p

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Blatm
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Re: Portal Paradox

Postby Blatm » Sun Nov 09, 2008 1:51 am UTC

leehsl wrote:In regards to the original question: the two walls with portals on them approaching each other is an equivalent of Misner space (like a cylinder, such that entering through one portal brings you to the other side) that is decreasing in radius.

Now, say that the portals are reasonably far apart and they are approaching you at a constant speed. To "escape" this scenario, you must run towards one portal as quickly as possible! You will be running down this "infinite track". As you run however, the walls are steadily approaching each other - which means that you are picking up velocity in respect with the walls. In fact, pretty soon you will be nearing the speed of light in respect to the walls [kind of like the infinite fall via portals, except horizontally, made possible due to approaching walls.]

As you near the speed of light, relativistic effects occur. Thus, you will see the distance between the walls getting much narrower (besides, they are approaching anyway), but to an observer standing still, you will appear thinned (and while that may seem awesome, just think of the mass you've gained). Furthermore, time will be dilated! Whee. If you keep running, and we suppose that Chell has infinite stamina, and never gets tired from running, you will find that you can actually pass through the portals an infinite amount of times in a finite time-span as measured by your heartbeats (as you don't get the luxury of a wrist watch).

And what happens after that finite amount of time? You cross the Cauchy horizon... and things become weird. Very weird. But you will have survived! What happens after you cross the horizon is unknown to me, and I don't care to speculate. Any experts want to further illuminate this situation?


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Irongrip
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Re: Portal Paradox

Postby Irongrip » Sun Nov 09, 2008 2:15 am UTC

MSTK wrote:It might be enlightening to postulate a scenario where portal movement gives rise to effective time-travel.

Imagine Portal A and B; each has an attached clock/calendar. A is on a slab that remains stationary. B is on a slab that is taken and put onto a space ship capable of travel near c. The ship then departs and flies at, say, .995c for about a year. Due to time dilation, A's clock will have elapsed about 10 years. B's clock will have elapsed about 1 year.

What does this mean? If A is on Earth and the ship leaves in the year 2008, then after the aforementioned trip, B's calendar will read 2009. But A's calendar will read 2018.

Einsteinian Time Travel is characteristically Forwards-only. If a prospective time traveler is on the ship and steps into his portal, B, in 2009, he will emerge out of Portal A in 2018.
The unconventional time travel here is the fact that this allows for backwards time travel, as well. If a 25-year-old scientist on Earth steps into Portal A in 2018, he will emerge on the Spaceship in 2009.

Now, this might strike you as impractical. Someone who wishes to go back in time to change the past will only walk through the portal to realize that he is .995 light years away from the Earth, unable to actually *do* anything. But suppose he intends to hijack the space ship and then fly it straight back to earth at the same speed, and land the ship next to where A is and still is.

1 ship year later, 10 earth years later, the Earth's calendar will read 2028. The ship's calendar will read 2010.

The time traveler now has portal A and B side-by-side. To Portal A and to the rest of the world, it is the year 2028. To portal B and to him, it is the year 2010.
Now at this point the time traveler will consider himself quite foolish. He departed Earth in 2018 intending to change the past and yet wound up in the year 2028. It is interesting to note that the time traveler himself, born in 1983, is only biologically 26 years old in the year 2028.


But...here's your paradox.

In the first case (when the ship is away), a person who steps into Portal B will emerge from Portal A 9 years later. In the second case, will a person who steps into Portal B emerge from Portal A 18 years later? The case is made seemingly absurd because both portals appear to exist simultaneously, side-by-side. Imagine our character from above stepping into the Portal B he just dragged home from space. Would he come out of Portal A in the year 2046?


Now consider the reverse. In the first case, a person who steps into Portal A will emerge from Potal B 9 years in the past. But what would happen to someone who steps into Portal A in the second case, where they are side-by-side, in 2028? In 2046?


Has it occurred to you that going in and out of portals does not care for your "time dilation" I'd argue both portals and hence mater that flows through them experience "proper" time.

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Re: Portal Paradox

Postby Apo » Sun Nov 09, 2008 3:07 am UTC

I plotted it again:
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Tass
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Re: Portal Paradox

Postby Tass » Thu Nov 13, 2008 12:54 pm UTC

Irongrip wrote:Has it occurred to you that going in and out of portals does not care for your "time dilation" I'd argue both portals and hence mater that flows through them experience "proper" time.


Trouble is there IS no "proper time" in special relativity. Simultanous events in one inertial frame is not simultanios in another. Using a set of "moving" portals, and another set of "stationary" portals, you could indeed travel back in time. It was earlier discussed that the portals would simply warp space-time and make oddly shaped causality ligthcones, trouble is they could be made to turn back upon themselves.

A world with portals would probably have to be without relativity, yet still hav curved space.

Btw, in my world a portal would be a ring working from both sides. Going in from one side would make you go out on the other, and vice versa. You would have to walk around the edge of the portal two times to get back where you started. That also explaines what happens if you punch through the back of a portal - you simply punch out the back of the other. Also I would have the portal ring it self sourounded by some indestructable matter, sort of like a hulahoop, to avoid nasty cuttingeffects; and my portals would not have any glowing semi-transparent edges, but just the hoop and a clean look into the other place.

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Re: Portal Paradox

Postby qinwamascot » Sat Nov 15, 2008 12:03 am UTC

Portals do violate one concept in relativity automatically-information can't be transferred faster than c. Portals which one end moves relative to the other violate a lot more than that. It would hypothetically require an infinite amount of energy to do. That's why you can get results like backwards time travel. Put simply, portals don't make sense in relativity at all, so speculating over this basically speculation over the in-game physics engine, which we can't know easily.
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Re: Portal Paradox

Postby HenryS » Sat Nov 15, 2008 9:20 am UTC

qinwamascot wrote:Portals do violate one concept in relativity automatically-information can't be transferred faster than c.
I don't think there's a problem here, you get the same effect with wormholes, which afaik are possible in relativity. All you have there is the wrong concept of distance. Space-time with a portal or wormhole has some extra connectivity, in particular there is a short way to get from A to B and a long way to get from A to B. Measured using the long path, yes information is travelling too fast, but measured using the short path it isn't.

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Re: Portal Paradox

Postby darkspork » Wed Nov 19, 2008 4:00 am UTC

I believe I have a solution to our little portals-defying-physics problem. As far as the Enrichment Center is concerned, portals are powered by some kind of generator in the facility to account for the infinite loops possible.

Now, let us suppose that a force Fp exists on any objects near or around the portal, equal to the difference in potential energy of the two sides. Thus, the portals would instead "bend gravity" than allow infinite loops. For example, if you were to place a blue portal on the ground and an orange 100M up, any attempt to walk through the blue portal would fail. It would take the same amount of energy to walk through the portal as it would to climb 100M. This, for a human, would be utterly impossible. However, the effect would lead to airflow in the exact opposite direction that one would expect. An object entering the orange portal would use up the same amount of energy that it would were it to fall down. Basically, if the blue portal were to face a window, then a penny placed gently into the orange would be driven into the glass at well over terminal velocity.

Now, let's apply this principle to the time dilation problem. As the spaceship takes off with the orange portal, the gravitational force field pulling objects through would increase to the gravitational potential energy difference between Earth's ground and space. Surely, this would be enough to force the contents of the spaceship along with (eventually) its hull through the portal. But, ignoring the spaceship's destruction, the massive time dilation of perhaps 9 years would be sure to create an incredible force allowing no object to pass from the blue portal into the yellow portal. Essentially, the orange portal would become a black hole and the blue portal a white.
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Re: Portal Paradox

Postby Quizatzhaderac » Thu Nov 20, 2008 4:37 am UTC

For the orginal question:
If the portals are attached to the walls, the walls would be able to transfer force to the portals which would ordinarily be irrelevant because they have no mass. When the portals close in on you, your right and left shoulders would meet moving relative to each other. The portals' motion would have to constantly reshape space and hence the energy fields in it. As you are compressed, the reshaping of space would exert energy on you. So the energy flow would go wall -> portals -> space -> you.

Regarding the infinite energy issue:
It's important to remember the key differences between game and reality physics. In games (generally) all objects are either immovable or have an innate negative acceleration along the vertical axis. This acceleration has nothing to do with gravity or mass. In games, energy is a property of matter and has no intrinsic reality. In a gravitational field, you are pulled along all paths to the center of gravity, which means in a universe with a hole there is a force pulling you toward the ceiling portal. If the distance between the portals is very small relative to the center of gravity (i.e. if you are on a planet's surface) then there would be basically no gravitational force between the two portals.

Regarding the speed of light:
It would be preserved because by changing the connectivity of space you're changing distances. Relativity is preserved because when you create a (topological) hole in space, the location of the hole is relative. Imagine a circular track 100 meters long. Now imagine at some point along that track you create a portal 5 meters within and 5 meters outside of the tracks. You now have two circular paths, one around the track and one though the portals. Relativity is preserved because it's impossible to say weather you now have a 100 m circular track and two portals 10 m apart, or a 10 m circular track and two portals 100 m apart. (Though in the latter case the portal has a VERY different shape)
Last edited by Quizatzhaderac on Tue Aug 19, 2014 7:02 pm UTC, edited 1 time in total.
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Re: Portal Paradox

Postby spazdor » Thu Nov 27, 2008 10:28 am UTC

Guise, guise, we can restore physical consistency by dropping the idea that portals don't exert a force. In the game, we've only seen portals on surfaces that were pretty sturdy. So what if the portals actually exert a force upon the wall they're on, equal and opposite to whatever force will launch the matter flying through it?

Then the preservation of momentum is restored. Energy is still violated, natch.

Note about the alternative: If this was not the case, you could smush two portals face-to-face very fast, and the air between them would increase in pressure and temperature very rapidly. You could do some atom-splitting with a portal gun like that.


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