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wormholes: wrap up

The sci-fi film we've been talking about making at work has to do with the many worlds interpretation of quantum mechanics. I can't go into details (because they have involved many hours of conversations), but basically it starts from the premise that somehow, a group of hackers tinkering with various electrical equipment accidentally stumble upon a way to communicate with other decoherent branches of the multiverse, and this opens pandora's box in a lot of ways.

I was asked to evaluate how this could be made realistic from a physics perspective, and we had many conversations about it. What my coworker pointed out, which sounds right, is that it seems like communicating between different branches of the multiverse would have to involve some kind of non-linear modifications of quantum mechanics. This led us to read up a little on how realistic such modifications would be. Most physicists assume that quantum mechanics is an exact description of the world, but many are open to the possibility that there are slight modifications to it at the scale of quantum gravity which haven't been detected yet. Unfortunately, every time someone has explored this possibility theoretically, they tend to be led to the conclusion that any kind of non-linear modification, no matter how slight, tends to lead to problems that make the whole theory inconsistent and incompatible with other more sacred laws of physics such as thermodynamics.
My advisor's advisor was one who went down this path and eventually concluded it was probably a blind alley.

It appears that there are a lot of connected things that happen when you monkey with the laws of physics as we know them. For example, if you add non-linear modifications to quantum mechanics, you tend to violate the 2nd law of thermodynamics. In creating a lot of negative energy, you also tend to violate the 2nd law of thermodynamics. And in creating a wormhole, you tend to create the possibility for closed timelike loops. David Deutsch and others have analyzed what might happen theoretically if closed timelike loops (CTC's) were possible, and the conclusion is that you'd be able to solve NP complete problems in polynomial time, ie it implies P=NP. Closed timelike loops also violate the 2nd law of thermodynamics, because entropy cannot always increase within a closed loop of time. Either entropy would have to remain constant throughout the whole loop, or increase for a while and then suddenly decrease. It's like one of those staircases from an Escher painting: the staircase that always goes up cannot connect to itself in a circle. Either it doesn't go up, or it goes up and then comes back down. The same with entropy.

So many things are connected here. Non-linear modifications of quantum mechanics, negative energy, perpetual motion, antigravity, time travel, traversable wormholes, and P=NP. The more I read about these (and especially when I read Scott Aaronson's stuff) the more it seems like either you have to accept all of them or none of them.

There are actually multiple connections between computational complexity and wormholes I've found, not just via the connection between CTC's and P=NP. For example, there is the ER=EPR conjecture which is a very exciting proposal by two of the world's greatest living theoretical physicists, Leonard Susskind and Juan Maldacena. They have found a possible way in which wormholes are the same thing as quantum entanglement. Again, I don't have time to delve into the details, but this has to do with the blackhole firewall paradox. Many physicists have been worried that if there are no modifications to quantum mechanics (ie, information is never lost in black holes) then this would imply the existence of "blackhole firewalls" where an infalling observer would reach a flaming wall of fire at the event horizon. This violates a central principle of general relativity known as "the equivalence principle" which states that physics is the same in all reference frames.

But what Susskind says is that maybe firewalls don't actually form inside a black hole, and aren't needed to resolve the information paradox. Instead, the explanation for how things like the no-cloning theorem are preserved in the context of quantum mechanics in a black hole is that the interior of the black hole is protected by an "armor of computational complexity" (as Scott Aaronson puts it). You could try to send messages from the outside to the interior non-locally via quantum entanglement (or equivalently, through a traversable wormhole), but it would require you to solve a computational problem which is so complex it's in the complexity class known as QSZK (Quantum Statistical Zero Knowledge). If I understand correctly, the only reason you cannot send such a message is because quantum computers are not powerful enough to solve problems in this class.

I mentioned in my previous post that while it seems crystal clear that there's no way an advanced civilization could ever build a macroscopic wormhole that something the size of a human could pass through, it's a lot less clear why they couldn't build a microscopic traversable wormhole and use it to send information faster than light. If they could do that, then they could also create timelike loops and hence solve P=NP problems. So maybe the only reason why they couldn't do it is also related to computational complexity. Maybe it's the same general reason Susskind suggests in the context of black hole physics: somehow, computational complexity prohibits the transmission of meaningful information through such a wormhole, even though it would otherwise appear to be possible to build one.

Shortly after writing my last entry on this, I discovered an interesting recent paper from May 2014 on traversable wormholes from a physicist at Cambridge. He wrote the paper in an attempt to construct a stable wormhole geometry using the throat of the wormhole itself to generate the required negative energy to stabilize it. He ended up finding that it was not possible to completely stabilize it, for the particular parameters he was using. But he argues that even though it isn't stable, it would collapse slowly enough that a beam of light would still have a chance to pass through it before it completely collapsed. So if you could somehow construct that geometry (a daunting task), maybe it could be considered "traversable" in that light could temporarily pass through it. He also speculates that maybe you could find other geometries with less symmetry where the whole thing could be stabilized, but this seems like wishful thinking to me. The possibility of having some kind of temporary closed timelike loop while an unstable microscopic wormhole is collapsing I find very intriguing, and unlike the large wormholes of Interstellar it's not something I would completely rule out as a possibility. However, again... if you accept that then it seems like you'd have to accept all of the above weird violations of physics, including P=NP. And to me, it seems more likely that somehow, this armor of computational complexity Susskind and Aaronson are talking about comes into play and stops the beam of light from making it all the way through. Or at least, stops there from being any meaningful information encoded in the light. It occurs to me that this may be exactly what Hawking had in mind with his Chronology Protection Conjecture.

The only somewhat serious possibility I've left out here is if somehow, Kip Thorne's original conclusion that traversable wormholes necessarily imply the ability to build time machines is flawed. If that's the case, then I will admit there is a real possibility for faster than light communication in the future; and then the armor of computational complexity, or the chronology protection conjecture, or whatever you want to call it, would only come into play when you tried to make the wormhole into a time machine. This seems far fetched to me, but less far fetched than the idea that P=NP, perpetual motion machines are possible, and the 2nd law of thermodynamics is wrong, all of which I think would need to be true in order to have an actual microscopic wormhole that could be made into a closed timelike curve.

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