## Saturday, December 03, 2022

### The wormhole kerfuffle, ER=EPR, and all that

I was busy trying to finish off a grant proposal and paper revisions this week and didn't have the time to react in realtime to the PR onslaught surrounding the recent Nature paper by a team from Harvard, MIT, Fermilab, and Google.  There are many places to get caught up on this, but the short version:

• Using their Sycamore processor, the experimentalists implemented a small-scale version of the SYK model.  This is a model that has many interesting properties, including the fact that it is a testbed for holography, in which a bulk system may be understood by the degrees of freedom on its boundary.  For an infinitely large SYK system, there is a duality to a 2D gravitational system.  So, a protocol for moving entanglement in the qubits that make up the SYK system is equivalent to having a traversable wormhole in that 2D gravitational system.
• The actual experiment is very cool.
• The coverage in the press was extensive (Quanta, NY Times, e.g.).  There was a lot of controversy (see Peter Woit's blog for a summary, and Scott Aaronson for a good take) surrounding this, because there was some initial language usage that implied to a lay-person that the team had actually created a traversable wormhole.  Quanta revised their headline and qualified their language, to their credit.
Rather than dogpiling on the media coverage, there are two main points at issue here that I think are worthy of discussion:
1.  What do we mean when we say that we have experimentally implemented a model of a system?     When atomic physicists use ultracold fermionic atoms to make a 2D lattice governed by the Mott-Hubbard model (like here and here), we say that they have made a Mott insulator.  That same model is thought to be a good description of copper oxide superconductors.  However, no one would say that it actually is a copper oxide superconductor.  When is a model of a thing actually the thing itself?   This is at the heart of the whole topic of quantum simulation, but the issue comes up in classical systems as well.  My two cents:  If system A and system B are modeled extremely well by the same mathematics, that can give us real insights, but it doesn't mean that system A is system B.  Better language might be to say that system A is an analog to system B.  Physicists can be sloppy with language, and certainly it is much more attention-getting to editors of all stripes (be they journal editors or journalism editors) to have a short, punchy, bold description.  Still, it's better to be careful.
2. What do theorists like Lenny Susskind truly mean when they claim that entanglement is genuinely equivalent to wormholes?  This is summarized by the schematic equation ER = EPR, where ER = Einstein-Rosen wormhole and EPR = Einstein-Podolsky-Rosen entanglement.  I think I get the core intellectual idea that, in quantum gravity, spacetime itself may be emergent from underlying degrees of freedom that may be modeled as sorts of qubits; and that one can come up with fascinating thought experiments about what happens when dropping one member of an entangled pair of particles into the event horizon of a black hole.  That being said, as an experimentalist, the idea that any kind of quantum entanglement involves actual Planck-scale wormholes just seems bonkers.  That would imply that sending a photon through a nonlinear crystal and producing two lower energy entangled photons is actually creating a Planck-scale change in the topology of spacetime.  Perhaps someone in the comments can explain this to me.  Again, maybe this is me not understanding people who are being imprecise with their word choice.

Peter Armitage said...

Hi Doug, I haven't fully formed my own thoughts on this and other related examples of hype recently. I'm sympathetic to some of the pushback against this hype, but not all of it.

Sometimes these analogies from CM (or AMO... or qubit systems) to exotic fundamental physics phenomena are useful. Sometimes they aren't. I have only unorganized thoughts and questions on these matters. These include... What is the motivation for making the analogy? Is it just PR? Or is it better understanding? In this regard, is the analogy helpful? Does it help us understand either the CM phenomenon or fundamental particle phenomenon better? Or does the analogy only confuse? (this seems to be the biggest sin in the current brouhaha). Does the existence of an analogy point to some deeper level of commonality between the disparate phenomena. Why does nature appears to like to repeat itself? Of course "Nature" also likes to repeat itself, but that's a less interesting effect. :)

In the black hole on chip example, it was clear that the headline was constructed as click bait (or was effectively that). This is an obvious "no no". But some of this kind of analogy making is useful and even more frequently it is interesting. It was obviously useful in the analogies between Higgs and superconductivity. And it was useful in the notion for MBS in superconducting quantum wires and schemes for quantum computation. I had discussion with a PP colleague some years ago and he was insisting that the MBS of quantum wires was not $really$ a Majorana and I argued that it was. Perhaps it might win people over my colleague to say that a fundamental particle Majorana and a MBS are both examples of Majorana, although they are obviously not the same as each other. In the same sense we can say that a violin string and a swaying skyscraper are both examples of a mass on a spring, although they are obviously not the same as each other.

One could do the same for the SYK on a chip, and "real" wormhole. And of course nature likes to repeat itself.

Anonymous said...

EPR involves flat spacetime, not a wormhole in sight. Minkowski spacetime. ER is a section of a maximally extended vacuum solution of the Einsten equations that has existed eternally and cannot be brought into being by any known astrophysical process. Vacuum fluctuations are not spacetime fluctuations, insofar as they are in fact real fluctuations rather than mathcmatical accounting devices.

atyy said...

It seems that in this case, even if one were to accept that the duality allows one to say "create", the dual doesn't have a spacetime geometry, so it can't have been a wormhole in any plain sense.

Anonymous said...

I am confused even by the statement that "the actual experiment is very cool". It seems the use of a quantum computer for this demonstration was not particularly enlightening, the bulk of the work went into classical computations to simplify the calculation so that it could be run on less than 10 noisy qubits. Is there something cool we learned about quantum computation or the SYK model from this exercise? I'm not sure about the answer to that. I'm usually in the camp of loving condensed matter emergence and cold atom simulation, but I am not sure about this result being as enlightening.

Jacques Distler said...

I don't think you can make the slightest headway in understanding the slogan "ER=EPR" until you understand that AdS/CFT is a duality between a bulk gravitational theory (in an asymptotically-AdS spacetime) and a (non-gravitational) quantum field theory on the conformal boundary of that spacetime.

There's a limit (the "large-N" limit) in which the boundary QFT is quantum-mechanical, but the bulk theory is classical. We don't strictly need to be in that limit, but that's the easiest one to be in because, while classical GR is hard, quantum gravity is harder.

In any case, part of the correspondence involves a mapping between states of the QFT and bulk geometries (which is what a "state" is, in classical GR). Now you could ask, "What state of the QFT corresponds to having a wormhole geometry in the bulk?" And it's not terribly surprising that this is some entangled state in the QFT.

But there are lots of entangled states in a QFT, with varying degrees of entanglement. Famously, the vacuum state of a QFT is highly-entangled. But the vacuum state is dual to empty AdS; with not a wormhole in sight.

So, as a general statement, "ER=EPR" is too fuzzy to be useful. But there certainly are wormhole geometries and their boundary duals. That's what's being explored in this SYK/JT-gravity setup.