Entanglement and wormholes: Are they the same?

Question

Some "recent" studies (e.g., http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.211603) popularized in the news (e.g., http://news.mit.edu/2013/you-cant-get-entangled-without-a-wormhole-1205 or https://www.ias.edu/ideas/2013/maldacena-entanglement) argue that quantum entanglement results from the creation of a wormhole. I am not a quantum whisperer so I was not able to determine the validity of these reports.

Is there any merit to this idea or is this a cute mathematical idea without any testable hypotheses? It is a cute idea and could get around some pesky issues with our understanding of entanglement but are there any serious flaws/holes in this idea (pun was not intended but can be for humor's sake)? To be clear, I am not looking for a philosophical discussion of this idea. I am curious if the arguments hold water.

If they do, then does that mean we can estimate wormhole lifetimes based upon the distribution of entangled vs. non-entangled particles after time $\tau$?

Answer 1

First off, the article is available on arXiv if you really desire to read it and can't access it. As for its relevance to the real world, that's where I first have to confess my biases: I earned my M.Sc. in Applied Physics working for a theory group in a condensed-matter-heavy university, that means that (1) I am not really qualified enough to interpret this paper's full significance; (2) I am more skeptical, since my applied-theory background makes me approach theory as "how can I optimize my chance of seeing something interesting in an experiment" or "how can we find a perfect balance between these two effects?" which is not the goal of this sort of theory work; and (3) my condensed-matter background puts me a little at odds with high-energy physics in general and string theory in particular. So please keep those in mind and interpret me as a bit unreliable of a source.

The first thing I can tell you is that this research is not outright crank material. It's not just that PRL is a standard magazine with respected peer review processes, but also that the author belongs to a respectable institution and most of the paper is an incremental result on an incremental result on a speculation from some of the more famous theorists in string theory, which is kind of how science really goes in practice. (At some level this is also indirectly incentivized as universities are now very interested in publication counts and citation counts, which benefits small incremental publications moreso than anything large or revolutionary.) If people are telling you "Julian Sonner doesn't know what he's talking about!" you need to be very cautious to make sure first that you judge whether those people know what they're talking about!

The second thing I can tell you is that this research involves an AdS/CFT duality, so the wormholes that it's describing are not wormholes in the real world. So this is a bit difficult to describe, but basically the idea is that you can pretend that our nice spacetime is wrapped around some other geometrical space; our "Minkowski spacetime" is the boundary of this "anti-de-Sitter space," (hence AdS) often called the "bulk." Then a conformal quantum field theory (CFT) on our boundary can be understood as a string theory inside the bulk. This particular approach concerns itself with the most famously known AdS/CFT duality, called 4SYM, which stands for "supersymmetric Yang-Mills theory with 4 supersymmetries", and it explicitly does not include gravity in its modeling, which is kind of a clue that you will not get real wormholes out of this theory.

You might wonder "why the heck would you want to do this?" and the answer is basically that it turns out that sometimes you don't have a closed form for a sum, for example if you did not know that $1 + x + x^2 + x^3 + x^4 + \dots$ converges to $1/(1 - x)$ for $-1 < x < 1.$ You might not even be able to figure out the pattern for all of the coefficients; in this case it's trivially all 1 but maybe you have to basically analyze all possible diagrams that have $m$ nodes with their edges colored a certain way so that the nodes connect in certain rules; and the only way you can think to do this is just "I am going to draw out these graphs by hand and/or ask a computer to help me:" and then you don't have a nice closed form, you just have a big complicated series. Well, you can roughly state that only the first 5 or 10 or 20 matter, as long as $x$ is small, so let's just add them all up and see what we come up with! In quantum field theories this problem happens a lot and $x$ is a measure of how strongly two things "couple" to each other. It basically turns out that the stronger the coupling in the CFT realm, the weaker the interaction is in the AdS realm, so you can get very good results from summing the series in the bulk for field theories that were intractable because they coupled too strongly to be analyzed.

In fact the claim in this paper is that you can look at a pair-production event in the CFT side (our world) and it must be described by a complementary wormhole production in the AdS side (the theory world). Curiously, just like how you cannot transmit real information across the quantum entanglement, this wormhole is a special sort of wormhole which does not allow matter transfer across it. This sort of wormhole that appears in the AdS space is analogous to two black-holes which are connected across spacetime such that if two people decide to pilot their spaceships into the black holes they can meet each other at some time before being crushed by the gravitational singularity.

And the third thing I can tell you is that this theoretical approach to "let's use this explicit construction to understand entanglements like wormholes" is likely to be of some theoretical importance but less experimental importance. I'm a little hesitant to say this because AdS/CFT is kind of the best wrench that I've seen come out of string theory; it takes this "let's pretend that the world really is 10-dimensional with 5 of those dimensions wrapped up into a compact representation" cosmological attitude, which seems to me like a bunch of speculation founded on the "this model is so pretty that it must be accurate" idea that has never worked out very well for me in the past, and upends it: "hey, give me this field theory that you have, and I will tell you a few interesting things about it that you probably never suspected!" But it seems to have one huge limitation which is that, to the limited extent that I understand this stuff, it seems like you have to start with a sufficiently nice string theory in the AdS space and then determine what it looks like in the CFT space, and hope that the resulting Lagrangian matches someone's physical model somewhere. That is even though there is some conjectured "duality" in general, everything I have ever seen has been some sort of explicit coincidence. So like real-life wrenches they come in certain particular sizes and shapes and if your bolt doesn't happen to fit inside the wrenches we know about, "we conjecture that there is another wrench that fits your bolt!" but we don't actually have it available to use.

In these respects it is probably much closer to a cute mathematical idea with no real testable consequences.

Answer 2

I wrote an stack exchange post on whether wormholes exist. So I will leave some of the answer to this question there.

Susskind has argued that entanglements and nontraversable wormholes have a type of equivalency. This equivalency is with respect to black holes, where in the Penrose diagram the regions I and II are connected to the same interior of a black hole. The Penrose diagram in effect is telling these two regions have black holes that are entangled with each other.

In a sense a black hole is a nontraversable black hole. I refer to the diagram above which is the Penrose conformal diagram for a black hole. In the regions I and II are hyperbolas that represent the constant radial position of an observer. The red circle is the virtual fluctuation of a particle which an observer on a constant radial path would observe to emerge from the past or white hole horizon and then approach the black hole horizon. The circle determines the $e^{2\pi iH/g}$ for the quantum field with $g~=~c^2/\rho$ on a constant radial path with $\rho$. The black hole with the split horizon represents two entangled blackholes in the region I and II. The emission of Hawking radiation, here diagrammed as the two dots connected by a red segment, transfers some of this entanglement to the two regions. The new event horizon is seen as the two hyperbolic paths in blue. The two black holes are then no longer completely entangled.

This is another illustration of how spacetime is built up from entanglements. Raamsdonk illustrated this in a paper http://arxiv.org/abs/1005.3035. This presentation does not give a dynamics for how the big bang produces spacetime, but it does illustrate how spacetime is an emergent epiphenomenology of quantum mechanics. I am using the black hole as a sort of theoretical laboratory, which might in some way become more of an experimental object.

Now let us suppose I am in region I and I have the particle emitted by Hawking radiation (red dot on my side region I), and this particle is in the state $\psi~=~\sum_n\chi_n$. I then open up a wormhole into region II, which by the horizons is not accessible by ordinary means, and I grab the other particle and bring it to region I. I now have two particles that because of their entanglement are indistinguishable and are thus duplicates. I have closed the state on my side region I.

The cloning theorem says that if I have a state $\psi$ cloning it so $\psi~\rightarrow~\psi\psi$ results in an inconsistency. Let me write $\psi~=~a|a\rangle~+~b|b\rangle$. For simplicity I am considering it with two basis elements. My duplication then means $$ \psi~\rightarrow~\psi\psi~=~aa|aa\rangle~+~ab|ab\rangle~+~ba|ba\rangle~+~bb|bb\rangle. $$ However the duplication can also just mean $a|a\rangle~\rightarrow~aa|aa\rangle$ and $b|b\rangle~\rightarrow~bb|bb\rangle$ and I have no “ab and ba terms.” So there is no consistent way to clone or Xerox states. It would also mean that I can find a hidden variable underlying an entanglement. So it appears that wormholes run into some trouble with quantum physics. In addition the prospect that spacetime is woven together by quantum entanglements appears to suggest that changing spatial topology and cloning a quantum state by unitary means is the same thing.

However we can come up with “close clones” of quantum states. There has been some interest in this. The spacetime correspondence would then be some quantum superposed topology deformation on the base topology. The transition probably can't be complete, but there could be some quantum fluctuations or coherent effects that mean the topology of space can have some small quantum amplitude for a different topology. Changing the topology completely or classically is potentially the same as a perfect clone of a quantum state. This is in a sense a “quantum logical” reason for why the speed of light is a sort of absolute limit.

The wormhole then does not communicate information from region I and II, just as entanglements do not signal faster than light. The black hole or nontraversable wormhole with the Einstein-Rosen bridge does not then create a multiply connected causal path across space. This is similar to the noncloning theorem of quantum mechanics.

Answer 3

No the article is wrong about entanglement; entanglement involves no communication.

A (traversable) wormhole allows you to send stuff through it.

Suppose Alice and Bob meet up and share an entangled Bell pair. They then separate by light years and keep thier particles. Those particles are still entangled (if they don't get disturbed "too much" over the years of spaceflight, which is an engineering challange to achieve but not physically impossible).

Does a wormhole connect Alice and Bob? Not one that can be used to sand any mass-energy or information, because of the pesky no communication theorem. So what does entanglement mean? They can still use it to help coordinate their actions without communication, which uses the entanglement up in the process. Because of the lack of communication, it doesn't matter whether Alice or Bob is first in measuring their particle; if they are space-like seperated it's undefined who is even first!

The popsci articles, of course, reliably get it wrong:

But what enables particles to communicate instantaneously — and seemingly faster than the speed of light — over such vast distances?

The above quote is wrong and does not capture the fascinating "coordination without communication" subtlety of entanglement.

It is thought to be impossible to create a wormhole in real-life because it would need special repulsive negative mass. The best candidate to do so is the casmir effect, which creates tiny pockets of negative energy. However, the requirement of a much greater quantity of nearby positive energy probably ruins any wormhole attempt.

Answer 4

Non-locality of entanglement is not experimentally yet fully proven beyond doubts/loopholes. It must have been proven mathematically though. Non-locality of Entanglement correlations has not been sufficiently scrutinized yet. All efforts are geared towards proving non-locality via Bell's inequality. Bell's inequality is not sufficient to prove non-locality. All it can prove is that static hidden variables (within entangled pair) are not capable of producing different kind of correlations.

Taking example of perfect anti correlated Bell's state, the correlations are -

1) 100 % anti correlation

2) 50/50 outcome when measured a particle in any one angle over and over.

3) Same spin (both up or both down) SQ(sin(A/2)) times, when measured at relative angle of A over and over.

So comparison (even if the worm hole do exist), can not give any real outcome.