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Peter Shor's total misunderstanding of ER=EPR is deeply disappointing

He probably believes that hundreds of people with the IQ above 160 have the IQ below the dog's IQ

As an undergrad, I learned about Peter Shor's name for the first time – in the context of his work on quantum computers and, in the middle of my grad school years, in the context of his quantum algorithm for the factorization of large integers. He had to be extremely brilliant when it came to the analysis of the manipulation with the quantum information, I concluded.

Well, that conclusion was probably too fast.

For many years, I have seen pieces of evidence that Peter Shor was a de facto member of the community that frantically, almost religiously, fights against modern theoretical physics. Almost all the members of that community know basically nothing about modern theoretical physics as studied by the professionals – e.g. about Chapter 1-3 of textbooks of string theory, supersymmetry, and similar topics. For all practical purposes and almost all impractical purposes, they're just a bunch of laymen-haters who love to hate something they don't know at all. Many of them are motivated by their ego that was hurt when they learned that they were not smart enough to become real theoretical physicists.



Peter Shor appeared to be interested in fundamental physics so you could think he should know much more than that. He must have spent hundreds of hours with theoretical physics. Shouldn't he have learned something about it? He's Shor – that Shor. Why shouldn't he be equally informed as another guy in quantum information, e.g. John Preskill? Preskill has a high-energy physics background but for many years, he's been doing similar things as Peter Shor – quantum information. They have written a paper together, too. Why aren't they similar?



Even after 2000, Preskill was present in the high-energy theoretical physics literature. 1800+ citations in HEP include one paper above 500 cits (with Kitaev), one above 250 (with Hayden), and 26 other papers. Lots of the papers are about quantum error correction in quantum gravity which is, in some sense, an interdisciplinary topic where the experts have to know something about quantum gravity as well as the quantum information.

Peter Shor has also tried to publish papers that appear in the INSPIRE database, more precisely one paper with one citation. The output differs by three orders of magnitude. Where does this huge difference come from?

I think that the difference boils down to some Shor's predetermined, almost religious plan to be a hater of physics. At an infamous anti-physics blog at Columbia University, Shor recently described his skepticism concerning ER=EPR and other things. One shouldn't be surprised when other members of that community – who have no reason to understand anything about physics – are totally confused. But Shor? He wrote, among other things:

Clayton: I am extremely skeptical of ER=EPR. Susskind says:

“ER=EPR tells us that the immensely complicated network of entangled subsystems that comprises the universe is also an immensely complicated (and technically complex) network of Einstein-Rosen bridges.”

I don’t see how you can say that entanglement is the same thing as ER bridges unless you mean something completely different by either “entanglement” or “ER bridges” than Schrödinger meant, or Einstein and Rosen meant. Entanglement is a property of quantum mechanics, ER bridges are a property of general relativity, and as far as we know quantum field theory works fine without general relativity, and vice versa.

And Google Scholar says that this paper has 745 citations, which is two thirds as many as the AMPS (Black Holes: Complementarity or Firewalls) paper, which actually contains real, potentially correct, ideas.
Let me simplify it. He is extremely skeptical of the ER-EPR correspondence because the wormholes belong to general relativity, entanglement belong to quantum mechanics, these are different theories, so the objects must be different, too! Ingenious. ER=EPR was disproven. End of story. Or is it?

As he observes, Google Scholar lists that the paper by Maldacena and Susskind has 745 citations. There is a hundred or hundreds of authors of these followup papers – these papers have tens of thousands of pages and their authors have written the combined of a million of pages of other papers.

Don't you think, Dr Shor, that if it were possible to disprove ER=EPR by your simple observation, these hundreds of people who have written a million of pages about physics would have been capable of figuring this fact out? Do you really believe that all these people who have gotten not only PhDs but also jobs at some very prestigious places – usually after a job contest where they had to beat lots of competitors – are complete idiots? Do you really need to question that the "entanglement" and the "Einstein-Rosen bridge" are unambiguous, well-defined notions in theoretical physics? Why should they and how could they mean something "completely different" than what they mean?

Even before you study the ER=EPR paper itself, Dr Shor, don't you think that it is a much more likely explanation that your knowledge is utterly insufficient to meaningfully evaluate questions such as "is the ER-EPR correspondence correct"? And that you would have a better chance to know at least epsilon about theoretical physics if you actually spent some hours by studying it, instead of inventing slogans to impress those laymen who are totally clueless? Slogans that are nothing else than lame excuses explaining why it's OK for you to understand nothing about contemporary physics? It's not OK.

The "debunking" by Shor is ludicrously wrong, of course. The ER-EPR correspondence says that wormholes are equivalent to entanglement in the real world around us or, which is more specific and well-defined from a theorist's viewpoint (and also more general because in theory, there are other vacua than ours), in every consistent theory of gravity. We may actually say "in every consistent theory of relativistic gravity" as well because even classical GR isn't quite consistent because it doesn't know what to do in the presence of naked singularities which may emerge (among other problems).

Maldacena and Susskind don't even have to explicitly say that "they are working (or assuming to be) within quantum gravity" because 1) all the people who meaningfully read the hep-th arXiv know that all gravity on that arXiv is "quantum gravity", 2) the fact that they're making statements within quantum gravity is obvious from the very fact that the paper talks both about wormholes and about the quantum entanglement! Because of the second point, Shor's complaint is exactly as silly as someone's complaint against the sentence "Apple just surpassed Microsoft by its capitalization." – "How could an apple surpass Microsoft if the apple is a fruit and Microsoft is a company? Microsoft isn't even an orange so it's even worse than comparing apples and oranges." Nice. But a sane person knows from the context that "Apple" means a company, too. Similarly, "a wormhole" in the Maldacena-Susskind paper means "a wormhole in a consistent world with gravity" or "a wormhole theoretically embedded in a theory of quantum gravity".

While Maldacena and Susskind surely propose a statement about any situation involving quantum gravity, they particularly focus on the tests of the conjecture within Maldacena's holographic AdS/CFT correspondence. That pair of dual descriptions is known to reproduce the laws of general relativity (in an AdS space) in the long-distance limit. Consequently, the creation of Einstein-Rosen bridges in the bulk should be allowed there, too. So they have to have some description of the wormhole in terms of the boundary CFT degrees of freedom. And they decide that the entangled state created out of the microstates of the black hole pair is the only possible option. So assuming that AdS/CFT works – users of the hep-th arXiv generally agree – and the possibility of an Einstein-Rosen bridge within these AdS/CFT vacua, one may almost rigorously prove ER=EPR.

In quantum gravity, there may be Einstein-Rosen bridges (non-traversable wormholes) and when they're there, Maldacena and Susskind determined, they have the exact same effect on all observers and couples of observers as entangled black hole pairs. When they walk like a duck (an entangled black hole pair), quack like one, and so on, they are a duck. More concretely, the consistent Hilbert space of the quantum gravity theory really requires that there's no "other" representation of the wormhole than the entangled black hole pair.

This hypothesis passes all the basic tests that you may invent and all the fast conceivable paradoxes may be explained not to exist when you're careful enough – which they had to be. It's not shocking that ER=EPR is true. When two objects are perfectly entangled, it means that all measurements done by 2 observers on these 2 objects will end up with the same (or easily translatable) results. So the 2 observers will think that they're basically probing the same thing.

In particular, two infalling observers into 2 black holes are making some measurements. So the perfect entanglement says something about their correlated measurements. They will really experience one black hole interior. It's harder to see (the reasons are analogous to those in the quantum teleportation) but they will also see one another – for a while before they die in the singularity.

The perfect entanglement is just a "metric tensor" on a subspace of the Hilbert space, a way to translate two kinds of indices. And just like in the Penrose notation for tensors (I wanted to pick a nice graphic example of a completeness relation but others exist, too), such a conversion of two types of indices may be represented by a line that connects the two pins for the indices. Here the indices describe a microstate of a black hole, something that describes the complete state of the black hole interior whose macroscopic properties were fixed. So if you connect two such indices, it really says that the two black hole interiors are logically connected with each other. It's a small step to propose that it is an actual wormhole that connects the two black hole interiors and it indeed is one. By extension, ER=EPR at least morally implies that even small systems – and elementary particles are tiny, sub-Planckian black holes, if you wish – develop super-thin wormholes that connect them when they are entangled. Quantum gravity allows geometry and topology to fluctuate and indeed, as Maldacena and Susskind taught us, the modified, wormhole-like topology linked to any entanglement is an aspect of these "quantum foam" fluctuations. When the wormhole is super-thin and therefore "very quantum", you can't really trust the classical GR intuition involving smooth wormholes, however, so without a full definition of the theory of quantum gravity, ER=EPR may be said to be "vacuous" for small entangled systems.

Many laymen in Shor's community were trained to parrot and indefinitely repeat some completely wrong slogans such as "string theory is not even wrong because it's not falsifiable". These are people whose vast majority just doesn't have a clue about the later-years graduate school-level or higher-level theoretical physics – so the wrongness of their statements is no more shocking than the "bow-wow" frequently emphasized by your dog (or "haf haf" if your dog is Czech).

But when someone whose name is as famous as Peter Shor's also makes these far-reaching statements that are only justified by ludicrously incorrect slogans, it's just embarrassing. When I was an undergrad, instructors were generally teaching us that when a famous scientist associates himself with some extremely wrong statements, he loses his good name, image, credibility, and often his job, too. I think that the times have changed and the expectations of the institutionalized science have dramatically weakened. If this blog post weren't written, people wouldn't even know that Peter Shor has incredibly embarrassed himself.

His comparison with the AMPS firewall paper is bizarre, too. At the end, there are no firewalls and the conclusion of AMPS is wrong – so Shor criticizes a correct paper while he praises a wrong one. But AMPS were really and carefully enough proving a sophisticated theorem that has some assumptions – and one assumption is basically the perfect locality (tensor factorization of the degrees of freedom inside and outside a black hole), which they prove to be incompatible with the information preservation and other facts generally believed about the dynamics of quantum black hole (this incompatiblity had really been obvious for decades before the AMPS paper so in the big picture, they found nothing new). So while they're wrong, AMPS surely did nothing like a one-sentence sophistry based on naive slogans such as Shor's observation that "wormholes and entanglement are different because they're from different theories".

I am really amazed by the conspiracy theorist's thinking by someone who is eager to fool himself into believing that the physicists – some of whom have collectively discovered a substantial part of the 20th century theoretical physics even outside quantum gravity or string theory – would be unable to notice that two concepts belong to "different theories" and therefore any claim about their equivalence had to be wrong. If this reasoning were possible, wouldn't every person with the IQ above 60 be capable of noticing? It would be as easy as noticing that you shouldn't compare fruits with Microsoft. Why would someone assume that 100+ people whose individual IQ is uniformly above 160 have the IQ that is uniformly below 60? It's crazy.

The ER-EPR correspondence was just a specific example. There are dozens of similarly important concepts and insights in theoretical physics that Peter Shor – and others in that community – are skeptical about for similarly silly reasons. Theirs is really a cult of a sort, a cult where you affirm your presence by maximally ludicrous statements. And Peter Shor probably thinks that the uninformed Internet users at those obscure websites where everyone dislikes physics – users who are eager to praise him for ludicrous statements – are the only ones who read his embarrassing pronouncements. But that assumption is incorrect.

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