Portal Paradox

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jestingrabbit
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Re: Portal Paradox

Postby jestingrabbit » Thu Nov 27, 2008 10:45 am UTC

HenryS wrote:
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.


I think its actually a significant problem. The problem occurs in the Barn and Pole thought experiment.

http://www.rdrop.com/~half/Creations/Pu ... index.html

Basically, if I can send information from one end of the barn to the other quickly enough (ie faster than light), then there are two distinct versions of reality, one in which the barn can be closed, trapping the pole and its bearer inside (the version from the barn person (...master?)), and the other where that is impossible (the version from the pole bearer).

So the problem still exists it seems to me. I have no idea how the wormhole people resolve this.

A way to resolve it for portals is hazily alluded to earlier.
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Re: Portal Paradox

Postby Token » Thu Nov 27, 2008 1:32 pm UTC

jestingrabbit wrote:Basically, if I can send information from one end of the barn to the other quickly enough (ie faster than light), then there are two distinct versions of reality, one in which the barn can be closed, trapping the pole and its bearer inside (the version from the barn person (...master?)), and the other where that is impossible (the version from the pole bearer).

How does faster-than-light information affect simultaneity? I'm by no means an expert on special relativity, but it looks to me like, if the barn doors were to close at the same time in the barn-master's reference frame, then the door at the far end would close first for the pole-bearer, requiring deceleration (before the near barn door closed) and throwing the entire problem outside the bounds of special relativity.
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Re: Portal Paradox

Postby HenryS » Thu Nov 27, 2008 8:11 pm UTC

jestingrabbit wrote:Basically, if I can send information from one end of the barn to the other quickly enough (ie faster than light), then there are two distinct versions of reality, one in which the barn can be closed, trapping the pole and its bearer inside (the version from the barn person (...master?)), and the other where that is impossible (the version from the pole bearer).
I'm no relativity expert, but since relativity (maybe general relativity) is all supposed to be done in the context of manifolds, and you'd get the same issue with any space that isn't simply connected, I can't imagine there isn't some way around it.

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Re: Portal Paradox

Postby Cavetroll » Sat Nov 29, 2008 3:27 am UTC

Well, I've read through all the posts in this thread. I'm only in high school so a fair number of the posts went right over my head, but I do think I got the general meaning. Forgive me if this interpretation has been presented already.

I've always though of portals as being in front of the surface they are on, as opposed to embedded into them. Kind of like an infinitely thin LCD TV. Except instead of light, it emits matter from the 'camera' side. Actually, I suppose both ends would function as the TV and the camera. In my opinion this would solve the problem of how it would move, it isn't displacing the wall behind it, it's just moving across the surface an infinitely small distance in front of it.

As for the original problem, I can't even begin to comprehend what would happen in a situation like that.

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Re: Portal Paradox

Postby Robert'); DROP TABLE *; » Sat Nov 29, 2008 11:53 am UTC

Cavetroll wrote:I've always though of portals as being in front of the surface they are on, as opposed to embedded into them. Kind of like an infinitely thin LCD TV. Except instead of light, it emits matter from the 'camera' side. Actually, I suppose both ends would function as the TV and the camera. In my opinion this would solve the problem of how it would move, it isn't displacing the wall behind it, it's just moving across the surface an infinitely small distance in front of it.


Nice idea, but if you fire a Portal onto a wall (in the game) that has decals on it, (Like the "Automated Machinary" signs) the decals get bent around the edge of the portal, rather than just getting covered by it.
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Re: Portal Paradox

Postby scikidus » Sat Nov 29, 2008 1:29 pm UTC

I'm pretty sure that portals do not violate the universal "speed limit," because how does one really define distance in this case?

To look at this another way, portals are folding the current dimension through the dimension above. Imagine for a moment that you are a Flatlander, and for simplicity's sake you live on a sheet of newspaper. You are standing on the upper-left corner. I come over and bend over the sides of the newspaper, like so:

Image

From your perspective, I have now made a portal from one end of the paper to the other. Let's say the paper is 186000 miles long. According to you, standing on the newspaper, you can now travel an expanse instantaneously that takes even light almost a second to cross. From your perspective you can now travel faster than light. But are you, really?

--------

For reference, I recommend that every watches this film.

http://www.youtube.com/watch?v=HvgwR9ERCBo
Happy hollandaise!

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Re: Portal Paradox

Postby jestingrabbit » Sat Nov 29, 2008 4:15 pm UTC

Token wrote:How does faster-than-light information affect simultaneity?


I don't see how faster than light information could effect the nature of simultaneity, but I could be wrong.

Token wrote:I'm by no means an expert on special relativity, but it looks to me like, if the barn doors were to close at the same time in the barn-master's reference frame, then the door at the far end would close first for the pole-bearer, requiring deceleration (before the near barn door closed) and throwing the entire problem outside the bounds of special relativity.


The door at the far end would close first in the pole-bearer's reference frame, but I don't see that that forces deceleration, though I do think that you've identified the problematic phenomenon.

Consider a situation in which the pole has a sensor on its aft end, and that sensor informs the barn-master of its passage through the first barn door (it takes time to send that information, but you can make that duration short relative to the other times involved so as not to cause a problem). It is this information, from the sensor, that the barn-master is responding to when he closes the doors. There are now two very different descriptions of the polebearer passing through the barn.

In the barn-masters reference frame, the doors close whilst the pole is within the barn. In the pole bearers reference frame, the event which causes the doors to close has not occured at the time of the fore end of the pole passing through the second barn door. So the doors must close on the pole.

Basically, by creating faster than light communication you have broken causality. There are other ways that I could try and describe this. Its entirely possible that the universe could cope with this one way or another, this is only a model afterall, but the orthodoxy says that this is impossible.

Another problem entirely with the "things go through the portal and appear simultaneously on the other side" account is that if the portals are moving wrt one another, then which simultaneously are we talking about?

@Henry: Whilst there are some manifolds which aren't simply connected, there are a hell of a lot that are, and at least on a macro level the universe resembles one that is.

scikidus wrote:For reference, I recommend that every watches this film.

http://www.youtube.com/watch?v=HvgwR9ERCBo


I'd like to advise everyone to never watch this movie ever. It will actually make you dumber. No comment on you specifically sckidus, but that movie is intensely crap.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

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Re: Portal Paradox

Postby scikidus » Sat Nov 29, 2008 5:31 pm UTC

jestingrabbit wrote:
scikidus wrote:For reference, I recommend that every watches this film.

http://www.youtube.com/watch?v=HvgwR9ERCBo


I'd like to advise everyone to never watch this movie ever. It will actually make you dumber. No comment on you specifically sckidus, but that movie is intensely crap.

And I'd like to applaud you, jestingrabbit, for criticizing the work and not the referencer.

FIH++;
Happy hollandaise!

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Re: Portal Paradox

Postby Token » Sat Nov 29, 2008 6:33 pm UTC

OK, I probably don't understand this properly at all, but here's what I make of this.

Yes, you slightly interfere with causality, in that, in the pole-bearer's reference frame, the door closes before the event that triggers it. However, this is more of a curiosity than a flaw in the nature of the universe. In both reference frames, the aft end of the pole enters the barn, and in both universes, the doors close on either side of the pole. This is not, as far as I can tell, a problem.

So - from the barn-master's reference frame, the pole enters the barn. He triggers the door closing through the wormhole, and both doors close at once, trapping the pole.

From the pole-bearer's reference frame, the far door closes first. The far end of the pole hits the door. At this point, in this reference frame, the near end of the pole has yet to pass through the near barn door, which has yet to close. This is weird, but not a problem, because there is nothing stopping the near end of the pole from continuing to move. Any shockwave from the impact at the far end can still only travel down the pole at the speed of light, wormhole or no. And by the construction of the problem, it cannot reach the near end before that end passes through the near door, which has yet to close. Then the near door closes, and at this point (in the pole reference frame), it has either punched through the far door, or has compressed/broken in a manner that leaves it entirely within the barn. The near end of the pole will still pass through the near door before it closes, and so causality is at least locally preserved. You'll probably get an angry letter from the Librarians of Time and Space, but you're not about to set up a situation in which it's possible to kill your own grandfather.
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Re: Portal Paradox

Postby Saroset » Wed Dec 03, 2008 8:03 am UTC

I'd guess you'd never pass through either portal and just, for the most part, be crushed as if they were simply walls.

As mentioned above, the portal just changes the route you take. Essentially, the distance you can travel remains the same, except for the fact that it can, in my mind, also be considered infinite? Ahh, brain dying. It's like you have an infinite amount of space to travel through, but an ever decreasing amount of space for matter to occupy. You'd squish yourself in a room that, as long as there is any room what-so-ever, has infinite space.

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Re: Portal Paradox

Postby Elmach » Thu Jul 14, 2011 8:44 am UTC

Angelbaka wrote: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.

We haven't proved conservation of mass-energy for the same reason we haven't proved General Relativity.

But conservation of mass-energy is very important!

It is equivalent to the laws of physics changing with time!

I wonder what this means...

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Re: Portal Paradox

Postby zemerick » Thu Jul 14, 2011 5:29 pm UTC

The answer to the barn-pole is indeed that there is actually no paradox. It's one of those thought experiments that requires the full use of relativity to actually solve it:
http://en.wikipedia.org/wiki/Ladder_paradox has the resolution, though it's not the best explanation I've seen of it. I think most of Brian Greenes books include this or some variation of it.

Basically, you have to consider each point of the pole/ladder separately, including acceleration ( or rather deceleration. ) What ends up happening, is the door is closed before the pole comes through. 1 frame of reference would say the pole fits and both doors actually closed at the same time, the other says it is currently too long, but the rear door is still open. Now, the first obviously is already solved. The second however, would be undergoing deceleration. So, by the time the pole comes to a complete stop like it has in the first frame, the pole is small enough to fit and the second door does not close until after this time from this frame of reference.

So, as mentioned, the 2 frames might disagree on the order of events, but they fully agree on the end.

Elmach wrote:
Angelbaka wrote: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.

We haven't proved conservation of mass-energy for the same reason we haven't proved General Relativity.

But conservation of mass-energy is very important!

It is equivalent to the laws of physics changing with time!

I wonder what this means...


Yes, the original problem was properly solved in the first reply. You would simply begin hitting yourself, then, depending on the speed and/or final distance of the 2 plates you could even get fusion or a blackhole. Fusion btw though, is an explosion, not an implosion. Formation of a black-hole is an implosion.

Also, it is true there is nothing in science fully proven. That's the beauty of science itself. Nothing is ( supposed to be ) declared the final end truth without question. Instead, once something is shown to agree with what is seen, it is declared the most accurate model. We actually know for a fact that there is something wrong with general relativity and quantum mechanics, because whenever you combine the 2 you can get crazy answers like infinites and negatives where they just can't be etc. We're working to find the solution, but until we do..they are the most accurate we have. In the case of quantum mechanics, it's rather ridiculously accurate.

It should also be pointed out that Quantum Mechanics does have "portals" in a sense. Quantum Tunneling allows any particle to instantly travel to any other location in the entire universe. It is one of the stranger parts of quantum mechanics. No need to worry about finding yourself on the other side of the universe though: if you ran into a wall every single second, odds are it would take trillions upon trillions of times the age of the universe to pass through it, and greater distances are exponentially less likely. Typically, quantum tunneling occurs on distances smaller than the width of the particle to start with.

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Re: Portal Paradox

Postby LucasBrown » Thu Jul 14, 2011 8:17 pm UTC

No real contribution, just a GIF I found somewhere:
portal-mishap.gif
portal-mishap.gif (65.31 KiB) Viewed 4970 times

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Re: Portal Paradox

Postby jestingrabbit » Fri Jul 15, 2011 3:56 am UTC

zemerick wrote:So, as mentioned, the 2 frames might disagree on the order of events, but they fully agree on the end.


Only if in the pole bearer frame I assume that the doors start closing before the event that triggers their closing. Either you assume that something like retro causality works ie events can be caused by things that happen after them, which is a huge departure from regular causality, or you end up with irreconcilable events. Either way, you've broken physics.
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Re: Portal Paradox

Postby tomonkey4 » Fri Jul 15, 2011 5:30 pm UTC

I am wondering if portals really do break the conservation of energy law. After all, using a permanent magnet you can pass wire through its lines of flux and draw out energy, and you can keep doing this forever getting more and more energy, can't you? So perhaps by using portals to keep gaining energy from the Earths gravitational field is like moving a wire in circles continually drawing energy from the magnet.
If my analogy works, then the magnet is like the earth, and the wire is like whatever you put through the portals. I am choosing to use water. When you pass the wire through the lines of flux, you transfer the electrons out of the wire. When you pass the water through the portals, you are probably removing energy from the portals, since you cannot remove energy from the water or the earth. If this is true, the portals may get smaller due to having less energy, and eventually the water would not pass through because the portals are too small. Then we are left with two very tiny portals until new ones are shot from the portal gun. This leads to the conclusion that all energy comes from the portal gun, and so energy is conserved, but the gun will take a long time to charge.
I'm sure there are many arguments to be found here, and I'd like to hear them.

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Re: Portal Paradox

Postby phlip » Mon Jul 18, 2011 1:01 am UTC

tomonkey4 wrote:After all, using a permanent magnet you can pass wire through its lines of flux and draw out energy, and you can keep doing this forever getting more and more energy, can't you?

But you have to put in energy to move the wire - this isn't just friction, the same magnet inducing a current in the wire also has a braking effect on the wire... that's where the energy comes from. Entirely too many perpetual machine ideas are based on this misconception that if you reduce friction in the generator enough, you'll be able to spin it and draw power out without any drag. Overunity nutters don't know 'bout my Lenz's law.

If an EM analogy must be drawn, it's less like a wire moving through a magnetic field, and more like two magnets, either attracting or repelling. You can get a force out of it, but you can't get infinite work out of it... to get more work out, you have to move the magnets back where they were, which requires putting energy in. But the portal would let you just teleport it back up to the high energy state. On second thoughts this isn't a very useful analogy - it's just identical in all important respects, so it doesn't help at all.

But in short, your suggestion boils down, basically, to "the energy either comes from nowhere or it comes from the portals/portal gun. It can't come from nowhere, so it must come from the portals/portal gun. Therefore it doesn't come from nowhere." Ultimately the idea is reasonable - the energy could be coming from the gun, rather than from nowhere... but it's not exactly proof of anything. While we certainly have no IRL mechanism to get energy from nowhere (and don't believe one exists), we also have no IRL mechanism to draw energy from the portal gun to do what it does. So anything is pure conjecture until the canon says otherwise.

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Re: Portal Paradox

Postby pinochet » Wed Jul 20, 2011 2:01 am UTC

Probably a useful thread necro here, what with portal 2 out recently.

I think the only way to avoid breaking physics is to stop treating the portal like a wormhole and guess at the properties of the technology as created within a coherent realm of physics.

I think the in-game portals are not so much wormholes as some sort of a nonmatter thing. Relevantly, an in-game portal bolt will stop at the interface of a portal rather than travel through it, proving that it has a surface of some sort. I'd guess that a portal-on-a-board being pushed through another portal would just collapse the pair of portals, for similar reasons. Also, we should observe that portals, whatever they actually are, are mounted on matter objects, not into the fabric of spacetime. I don't really know how a literal wormhole would interact with a moving planet, but I'd guess there's a reasonable chance it might try to slide up or down the distorted spacetime of the gravity well, or perhaps decide to "sit still" in some IRF other than the surface of our rotating, orbiting planet in our rotating, moving galaxy. (Does anyone with an actual physics degree know whether the "fabric of spacetime" is stationary with respect to the matter inhabiting it? I'm curious). Anyway, I think Portal portals can't be wormholes.

I would probably try to explain away the conservation of energy violation by assuming that the portals require energy to maintain a portal, and that moving things around within a gravity well charges the potential energy difference to the generator. Therefore, if I place a 1kg beach ball in an infinite 1 m/s terminal velocity fall between two portals separated by 1m, the generator has to kick in 1J every 1s to bring the ball up to the higher level of potential energy. If this isn't supplied, the portal collapses cutting the ball in half wherever it ran out of energy. One could not therefore derive energy from an infinite waterfall and a water wheel, since the infinite waterfall is being "paid for" externally. This also lets us avoid peculiar gravitational and electric field topography around portals; electric and gravitational fields go across the width of a portal like it isn't there, and objects changing potential energy are handled by the generator.

The game is sort of ambiguous about whether portals exert force on the walls behind them, but they almost have to. Considering that air molecules are presumably constantly transiting an portal, a wall with a portal on it either needs to be pushing inwards every time a molecule enters and exits, or else the floor behind the portal is experiencing zero atmospheric pressure from the back surface of the portal. This would rip oval-shaped holes through drywall, or anything else not built like a space shuttle (though it might explain why they felt the need to dig the enrichment center into the bedrock). The atmospheric pressure argument would also mean that any unsecured object with a portal would tend to move around with a force equal to atmospheric pressure times the surface area of a portal. Even if the portal excludes air molecules somehow, one could just as easily propel a car/spacecraft by sticking both orange and blue portals on the inside surface of the rear window, and repeatedly throwing/catching a ball through the portals.

The same goes for the portals-on-pistons pancaking question in the original discussion from '08. If there is no force transferred to the wall/piston, then you can effectively compact any object to an arbitrarily high pressure and temperature for no energy cost (or perhaps two atmosphere-portalsurface-pistonlengths, per the pressure thing above). By making the portal push back against the piston with the pressure of a pancaked experimentee (as compressed skin enters and exits the portal in an equilibrium), we avoid this problem. This similarly keeps us from cheating the delta-volume strokes of internal combustion engines.

As far as relativity, causality, and time travel are concerned, the game obviously does not inform us whether there is a light speed time lag between entering one portal and exiting another. The closest we get to that situation in the game is when...
Spoiler:
GlaDos reaches through to the surface of the moon at the end of portal 2 to pull Chell back to earth, but there is no way to know if she experienced ~500 ms lag in maneuvering her robotic arm,

...making that uninformative. It seems somehow not in the spirit of the game to stick your arm into a portal that connects to the surface of another planet, and wait for a round trip communication delay when you try to wiggle your fingers. But I imagine the physics would work just fine with a delay.

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Re: Portal Paradox

Postby ianfort » Sat Jul 23, 2011 4:27 pm UTC

What interests me about portals is the interesting geometric possibilities they allow for, such as closed 1-sided and 2-sided polygons, and completely flat 1-sided mobius strips. Portal mathematics might be interesting.

Image


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