A proof that hyperspace cannot transport matter

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Arminius
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A proof that hyperspace cannot transport matter

Postby Arminius » Thu Sep 04, 2014 4:57 pm UTC

Whilst thinking about a paradoxical machine that I had been pondering about for some time I realized a simple fact.
"Hyperspace travel", as described in movie and tv shows is impossible, with a simple though experiment.

Imagine a rock, entering such a "portal" on the ground an reappearing on the top of a building. It would have increased its potential energy "magically", thus violating the principle of conservation of energy. Does this also disprove the idea of supplementary spatial dimensions in string theory?

(I do know that this is borderline physicis but supplementary space dimensions is part of string theory.)

Is this reasoning flawed?

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Re: A proof that hyperspace cannot transport matter

Postby Dopefish » Thu Sep 04, 2014 5:23 pm UTC

Well, one could try to do some handwaving in the details so that energy goes into/out of the portal itself (or is otherwise accounted for somewhere in the mechanism) so that energy is conserved or something along those lines.

Still even lacking that, conservation of energy isn't necessarily a law of the universe. We think it is since all of our experiences and understanding of physics as we know it implies that it is, but physics as we know it isn't necessarily the complete picture, and it could (albeit improbably) be the case that energy can be created/destroyed via the mechanisms of portals/hyperspace.

Hyperspace/portals/etc aren't consistently described the same way in science fiction either, and almost never actually get into the gritty details. Some descriptions might be specific enough that one could show they're inconsistent with themselves (and thus disprove them), but for the most part one would probably just show that such devices would violate conservation of energy, which I don't feel is strictly speaking equivalent to a proof that they can't exist.

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Re: A proof that hyperspace cannot transport matter

Postby LaserGuy » Thu Sep 04, 2014 5:52 pm UTC

Well, there's a few possibilities. It's possible that the act of opening/entering the portal could invariably cost equal or more energy to having objects pass through it. Or it's possible that in energy is just not conserved in such systems.

If there was no time delay in the object's disappearance and appearance through the portal, then there's causality to consider as well--ie. it would be possible to construct a situation where an object would appear out of the portal before you put it into it.

If the portal doesn't violate conservation of energy or causality, OTOH, for the purposes of moving your rock, it's basically the same thing as a crane, which isn't a very interesting portal from a sci-fi point of view.

Note that this has no effect on extra dimensions in String Theory, because String Theory (AFAIK) does not predict the existence such portals. The extra dimensions in String Theory have somewhat different properties from the usual dimensions of space and time. There aren't really any applications to macroscopic (or even, to a very significant extent, microscopic) phenomena that these dimensions are particularly relevant to.

Pretty much any time your hear the word "dimension" used in science fiction, they're using it wrong, as far as real science/mathematics is concerned.

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Re: A proof that hyperspace cannot transport matter

Postby Yakk » Thu Sep 04, 2014 6:15 pm UTC

It is impossible to travel on subways.

Someone goes down a "portal" into the subway, travels on a train, then somewhere else comes up another "portal". This is a clear violation of conservation of energy, because what if the object at those two "portals" have different gravitational potentials?

It is impossible to fly in the air. Same argument.

In short, the reasons why "hyperspace teleportation" don't work are not the one you listed.
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Re: A proof that hyperspace cannot transport matter

Postby schapel » Thu Sep 04, 2014 6:32 pm UTC

Arminius wrote:Imagine a rock, entering such a "portal" on the ground an reappearing on the top of a building. It would have increased its potential energy "magically", thus violating the principle of conservation of energy.

If the kinetic energy were changed into potential energy, no it would not violate the conservation of energy. If the rock were falling through a vacuum, then when it appeared out of the top portal it would have the velocity it had when it was last at that height. If the rock were falling through an atmosphere, it would have less vertical velocity each time through the portal, until it wasn't able to fully exit the top portal -- at this point it would then go back up through the top portal and re-emerge at the bottom portal traveling upwards at a velocity that would not be enough to make it back up to the top portal. It would continue oscillating with the velocity dying down until it was resting atop the bottom portal.

Maybe another way to think about it is to think of the bottom portal as a trampoline. But if the rock fell onto the trampoline with sufficient velocity, it would be transported at the speed of light to the top portal with the downward velocity it would have had if it had bounced off the trampoline and traveled through its trajectory in a vacuum.

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Re: A proof that hyperspace cannot transport matter

Postby Hypnosifl » Thu Sep 04, 2014 7:13 pm UTC

Arminius wrote:Imagine a rock, entering such a "portal" on the ground an reappearing on the top of a building. It would have increased its potential energy "magically", thus violating the principle of conservation of energy. Does this also disprove the idea of supplementary spatial dimensions in string theory?

The closest analogue to a "portal" in theoretical physics is probably a traversable wormhole, and the wiki article does say in the section on time travel that:
An object traveling through a wormhole could carry energy or charge from one time to another, but this would not violate conservation of energy or charge in each time, because the energy/charge of the wormhole mouth itself would change to compensate for the object that fell into it or emerged from it.[24][25]

Meanwhile, for a general concept of "hyperspace" not involving any sort of specific portal (like theories that say certain particle interactions can create particles that escape our "brane" and travel off into a higher dimension), why can't you just say that conservation of energy applies to the larger space that includes our brane? Although some form of conservation of energy is likely to be part of any future theory of physics because of Noether's theorem (which implies that as long as the laws of physics don't change with time, energy should be conserved), I don't think there's any good a priori reason to rule out the idea that it isn't always conserved within our own "brane" if that brane is just a surface in a higher-dimensional space, as long as the deviations from perfect energy conservation within the brane are small enough that none of our experiments so far would have detected them.

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Re: A proof that hyperspace cannot transport matter

Postby eSOANEM » Thu Sep 04, 2014 8:53 pm UTC

In GR, energy is only conserved locally (or more accurately, the stress-energy tensor is divergence-free). You could posit that at the boundary, energy is calculated modulo the difference in potential energies between the two ends in which case the requirement is simply that the force field is smooth at the boundary.

I believe it's been suggested that QM deals with timelike separated wormholes by exploiting energy differences and getting a feedback effect of virtual particles.
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Re: A proof that hyperspace cannot transport matter

Postby Goemon » Fri Sep 05, 2014 12:17 am UTC

Meh - rock that comes out the top is colder than the rock that went in at the bottom.
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Re: A proof that hyperspace cannot transport matter

Postby Copper Bezel » Fri Sep 05, 2014 2:21 am UTC

No, no! Then you'll use it to break thermodynamics! Don't throw rocks at thermodynamics - it's not nice!
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Re: A proof that hyperspace cannot transport matter

Postby schapel » Fri Sep 05, 2014 2:21 am UTC

Goemon wrote:Meh - rock that comes out the top is colder than the rock that went in at the bottom.

I think that would violate thermodynamics -- turning heat into energy that can be used to do work, without heat flowing from a hot object to a cold object. Come to think of it, you could make a perpetual motion machine that also acts as a refrigerator that requires no energy source with such a portal, so it violates many laws of physics.

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Re: A proof that hyperspace cannot transport matter

Postby thoughtfully » Fri Sep 05, 2014 2:59 am UTC

Yeah, but we already broke conservation of energy. That kinda opens things up for perpetual motion devices and painfully twerking thermodynamics.
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Re: A proof that hyperspace cannot transport matter

Postby eSOANEM » Fri Sep 05, 2014 6:16 pm UTC

Yeah, the temperature thing means you conserve energy globally (in flat space) but you break the second law of thermodynamics.
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Re: A proof that hyperspace cannot transport matter

Postby schapel » Fri Sep 05, 2014 6:48 pm UTC

thoughtfully wrote:Yeah, but we already broke conservation of energy. That kinda opens things up for perpetual motion devices and painfully twerking thermodynamics.

I thought I came up with a way for portals to work that broke no known laws of physics. In other words, I answered the original question of whether hyperspace cannot transport matter because it would break conservation of energy -- it is false because portals could still conserve energy if the kinetic energy of the falling rock was used to raise it back up to the higher gravitational potential. If you try to use the thermal energy of the rock to raise it back up to the higher gravitational potential, it breaks another law of physics.

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Re: A proof that hyperspace cannot transport matter

Postby doogly » Fri Sep 05, 2014 9:03 pm UTC

There's no proposal for a wormhole which "magics" something from one place to another. It would move across a nice smooth curved manifold, just one that has weird wormhole shapes. But the gravity (and gravitational potential energy) would just smoothly move from one end to the other. It wouldn't just all of a sudden notice "hey I need some potential energy" when it pops out the other end. There isn't even a well defined other "end," it's continuous. (Or smooth. Or C^2, maybe that's enough, I heard a talk on this once, analysis is hard.)
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Re: A proof that hyperspace cannot transport matter

Postby schapel » Fri Sep 05, 2014 9:22 pm UTC

doogly wrote:There's no proposal for a wormhole which "magics" something from one place to another. It would move across a nice smooth curved manifold, just one that has weird wormhole shapes. But the gravity (and gravitational potential energy) would just smoothly move from one end to the other. It wouldn't just all of a sudden notice "hey I need some potential energy" when it pops out the other end. There isn't even a well defined other "end," it's continuous. (Or smooth. Or C^2, maybe that's enough, I heard a talk on this once, analysis is hard.)

No, it wouldn't pop out the other end and then notice that it needs potential energy to do that. It would be just like pushing the rock up from the bottom portal to the top portal, or like throwing the rock up from the bottom to the top portal, but the rock would be taking some other route. When work is performed on the rock, the rock changes position because the work has been performed. That route between portals could be a "wormhole" that connects the two portals, or a teleportation mechanism that converts the rock into some other form to send it to the other portal. The kinetic energy of the rock falling, or the work done on pushing the rock into the bottom portal, would provide the energy needed to get the rock to the top. The rock would travel through the portal because of the work done -- it wouldn't go through the portal and then suddenly realize, "Wait! I need energy from somewhere to do this!"

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Re: A proof that hyperspace cannot transport matter

Postby doogly » Fri Sep 05, 2014 9:23 pm UTC

Yes. That is not different from anything I said.
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Re: A proof that hyperspace cannot transport matter

Postby schapel » Fri Sep 05, 2014 10:51 pm UTC

I've been wondering what it would be like to sit at the bottom portal and push a stationary rock down into it. When you place the rock on the portal, a little bit would go through, until the weight of the remaining rock balanced the force pushing the rock up (because the part of the rock pushed through wants to "fall" from the top portal). It would oscillate a bit as it found the right balance of forces. Then if you pressed down at all, more of the rock would go through, so you'd have to apply more force because there's less rock remaining to provide the force needed to get the rock to the top. If you let go, the rock could snap back forcefully -- if you let go when the rock was almost through, it would snap back with enough velocity to make it nearly fly up to the top portal.

Likewise, if you stood at the top portal and pushed the rock up through it, it would be "sucked" into the portal, appearing at the bottom with enough velocity to return it nearly to its starting position.

I was about to say that due to the difference in air pressure, there would be a constant stream of wind from the bottom portal to the top, also. But would the difference in gravitational potential exactly make up for the difference in pressure?

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Re: A proof that hyperspace cannot transport matter

Postby doogly » Sat Sep 06, 2014 1:06 am UTC

schapel wrote:I've been wondering what it would be like to sit at the bottom portal and push a stationary rock down into it. When you place the rock on the portal, a little bit would go through, until the weight of the remaining rock balanced the force pushing the rock up (because the part of the rock pushed through wants to "fall" from the top portal).

Oh no you're still thinking of something close to magic. It's a smooth transition. "Portal" is a videogame, totally different ballgame.
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Re: A proof that hyperspace cannot transport matter

Postby Goemon » Sat Sep 06, 2014 4:42 am UTC

Copper Bezel wrote:No, no! Then you'll use it to break thermodynamics! Don't throw rocks at thermodynamics - it's not nice!


Well, as thoughtfully says, if you're going to break the law, why be so fussy about which particular law gets shattered?

Actually I was looking at it like this: if you're at the lower portal looking through it at somebody standing on the other side (who is therefore at a higher altitude), then his wristwatch is ticking faster than yours. Time itself is passing faster on the far side of the portal. So if you stick a rock halfway through, what happens to the molecules that are vibrating at the boundary? Since time is running faster on the far side, the denizen of the higher plane would perceive that the rock's molecules to be moving more slowly than expected as the rock comes through the portal - e.g., they measure it to be colder when it crosses over than it was before.

The rock would also shrink slightly (in one direction anyway) as it passes through the portal as the tidal forces acting to stretch it are suddenly reduced, and probably other fun stuff...

EDIT: and it occurs to me that we could just suppose that the portal exerts an opposing force on the rock as you try to push it through which is proportional to the delta height - you have to do work to shove the rock through which is exactly equal to the change in its potential energy.
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Re: A proof that hyperspace cannot transport matter

Postby Xanthir » Mon Sep 08, 2014 10:33 am UTC

doogly wrote:
schapel wrote:I've been wondering what it would be like to sit at the bottom portal and push a stationary rock down into it. When you place the rock on the portal, a little bit would go through, until the weight of the remaining rock balanced the force pushing the rock up (because the part of the rock pushed through wants to "fall" from the top portal).

Oh no you're still thinking of something close to magic. It's a smooth transition. "Portal" is a videogame, totally different ballgame.

If I understand correctly, the gravity at the "portal surface" should basically be null, due to the directions cancelling from the two sides, right? And it smoothly scales up to full normal gravity again at a distance from the portal, with potentially some odd directional effects close but just off to the side of the portal?
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Re: A proof that hyperspace cannot transport matter

Postby Hypnosifl » Thu Sep 11, 2014 9:23 pm UTC

Goemon wrote:Actually I was looking at it like this: if you're at the lower portal looking through it at somebody standing on the other side (who is therefore at a higher altitude), then his wristwatch is ticking faster than yours. Time itself is passing faster on the far side of the portal. So if you stick a rock halfway through, what happens to the molecules that are vibrating at the boundary? Since time is running faster on the far side, the denizen of the higher plane would perceive that the rock's molecules to be moving more slowly than expected as the rock comes through the portal - e.g., they measure it to be colder when it crosses over than it was before.

That isn't how it would work in general relativity with traversable wormholes, though. In this case, if you're next to the lower mouth of the wormhole, and your friend is standing next to the upper mouth far above you, then if you aim your telescope at him to observe his watch using light that traveled through the "normal" space outside the wormhole, you will see his watch running faster...but if you look at him directly through the mouth near you, you'll see his watch running at the same rate as yours. So over time, the version of him you see looking through the wormhole will get progressively more out-of-sync with the version of him you see looking through the telescope. This is exactly why traversable wormholes could be used to break causality in GR--eventually the increased speed of the watch you see through the telescope will balance out the fact that there is a delay in the image due to the time the light has to get from you to him if it takes the "long way" outside the wormhole, and at that point you'll actually start seeing a version of your friend who's slightly ahead of the one who appears to be right next to you through the wormhole, meaning you can do things like warning your friend through the wormhole about future things you've seen happen to the version of him you see through the telescope.

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Re: A proof that hyperspace cannot transport matter

Postby lgw » Fri Sep 12, 2014 5:56 pm UTC

doogly wrote:There's no proposal for a wormhole which "magics" something from one place to another. It would move across a nice smooth curved manifold, just one that has weird wormhole shapes. But the gravity (and gravitational potential energy) would just smoothly move from one end to the other. It wouldn't just all of a sudden notice "hey I need some potential energy" when it pops out the other end. There isn't even a well defined other "end," it's continuous. (Or smooth. Or C^2, maybe that's enough, I heard a talk on this once, analysis is hard.)


Now I have Michael Jackson's "Smooth Criminal" stuck in my head, with the lyric "Smooth Manifold". I blame Doogly.

I've always seen wormholes as going a bit farther in this direction, actually. The path through the wormhole becomes the ordinary path between those endpoints. The only sensible way to measure distance must now include the path through the wormhole as a possible "shortest path", or said in another way, straight lines between a large set of points will pass through the wormhole. Everything acting across a distance where the wormholes are somehow along the path now would see the "path of least action" as passing through the wormholes. You've changed the metric of space, and "distance" would be measured differently than before. That's such an astonishing change in the potential energy of, well, everything, that it seems unlikely you could create a wormhole pair if conservation of energy is real, plus they'd get rather hot - I'm not sure you'd need a feedback loop to get arbitrary energy levels. (Very early in the universe it might have been easy to form wormholes, that maybe could persist today, except I think we'd see very obvious lensing effects if any were large.)

The other sane option is that wormholes aren't actually a short cut. Sort of a boring option for SF, unless you consider their potential for time machines. Since Noether tells us that energy is conserved if mechanics are time-invariant, either they stop being time-invariant when wormholes are around, or the Hamiltonian (the thing actually conserved) isn't what we thought. Doogly reminds us that GR has already changed what's conserved, rather dramatically, so further modifications to account for wormholes (and add even more complexity) wouldn't surprise me at all.

You know, I've always wanted to find some argument from Neother's theorem for the existence of something that could be called aether - just to confuse future generations of students with a "Noether aether theorem".
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Re: A proof that hyperspace cannot transport matter

Postby Hypnosifl » Fri Sep 12, 2014 6:34 pm UTC

lgw wrote: Since Noether tells us that energy is conserved if mechanics are time-invariant, either they stop being time-invariant when wormholes are around, or the Hamiltonian (the thing actually conserved) isn't what we thought. Doogly reminds us that GR has already changed what's conserved, rather dramatically, so further modifications to account for wormholes (and add even more complexity) wouldn't surprise me at all.

As I mentioned in post #6, the way in which wormholes would avoid violating energy conservation has already been worked out--according to GR, the wormhole mouth itself would change mass in a way that balances out the mass of anything traveling in or out of it (and its mass could actually become negative if enough positive-mass objects came out of it).

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Re: A proof that hyperspace cannot transport matter

Postby doogly » Sun Sep 14, 2014 9:49 pm UTC

"conservation of energy" isn't a thing in GR.
The closest thing is the local conservation of energy, dT=0, and that is compatible with wormholes. And pretty certainly true.
But if there is an energy condition like ANEC that is true, then no wormholes. ANEC is
int T_ab e^a e^b dl > 0
where e is a tangent vector to a null geodesic, and l is an affine parameter along the geodesic. If this integral is > 0 (or =) for all null geodesics, ANEC is said to hold.

The vernacular for it is "no net negative energy."
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Re: A proof that hyperspace cannot transport matter

Postby Hypnosifl » Sun Sep 14, 2014 11:30 pm UTC

doogly wrote:"conservation of energy" isn't a thing in GR.
The closest thing is the local conservation of energy, dT=0, and that is compatible with wormholes. And pretty certainly true.

The article here says that it can be made to work in a more global sense if you include an "energy pseudo-tensor" although there are reasons to think pseudo-tensors unphysical, but it also notes that "In certain special cases, energy conservation works out with fewer caveats. The two main examples are static spacetimes and asymptotically flat spacetimes." And aren't wormholes usually modeled as being in asymptotically flat spacetimes (where the spacetime curvature approaches zero at large distances from the wormhole) for simplicity?

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Re: A proof that hyperspace cannot transport matter

Postby doogly » Mon Sep 15, 2014 12:57 am UTC

Sure, but if it's only conserved (or even well defined at all) sometimes, then it's not really much of a conservation law.
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Re: A proof that hyperspace cannot transport matter

Postby PM 2Ring » Thu Sep 18, 2014 1:11 am UTC

doogly wrote:"conservation of energy" isn't a thing in GR.
The closest thing is the local conservation of energy, dT=0, and that is compatible with wormholes. And pretty certainly true.
But if there is an energy condition like ANEC that is true, then no wormholes. ANEC is
int T_ab e^a e^b dl > 0
where e is a tangent vector to a null geodesic, and l is an affine parameter along the geodesic. If this integral is > 0 (or =) for all null geodesics, ANEC is said to hold.

The vernacular for it is "no net negative energy."


I haven't heard of ANEC before.

A Semiclassical ANEC Constraint On Classical Traversable Lorentzian Wormholes
The present article lies at the interface between gravity, a highly nonlinear phenomenon, and quantum field theory. The nonlinear field equations of Einstein permit the theoretical existence of classical wormholes. One of the fundamental questions relates to the practical viability of such wormholes. One way to answer this question is to assess if the total \emph{volume} of exotic matter needed to maintain the wormhole is finite. Using this value as the lower bound, we propose a modified semiclassical volume Averaged Null Energy Condition (ANEC) constraint as a method of discarding many solutions as being possible self-consistent wormhole solutions of semiclassical gravity. The proposed constraint is consistent with known results. It turns out that a class of Morris-Thorne wormholes can be ruled out on the basis of this constraint.

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