*This post is a continuation of the previous one, which you should read first…*

Now, what exactly are these wormholes that certain physicists claim to be trying to make or, at least, simulate? In this post I’ll explain what the scientists did to bring the problem within reach of our still-crude quantum computers. *[I am indebted to Juan Maldacena, Daniel Jafferis and Brian Swingle for conversations that improved my understanding.]*

An important point from last post: a field theory with quarks and gluons, such as we find in the real world or such as we might find in all sorts of imaginary worlds, is related by the Maldacena conjecture to strings (including quantum gravity) moving around in more dimensions than the three we’re used to. One of these dimensions, the “radial dimension”, is particularly important. As in the previous post, it will play a central role here.

## Einstein-Rosen Bridge (ER) vs. Einstein-Podolsky-Rosen Entanglement (EPR)

It’s too bad that Einstein didn’t live long enough to learn that two of his famous but apparently unrelated papers actually describe the same thing, at least in the context of Maldacena’s conjecture. As Maldacena and Lenny Susskind explored in this paper, the Maldacena conjecture suggests that ER is the same as EPR, at least in some situations.

We begin with two identical black holes in the context of a string theory on the same curved space that appears in the Maldacena conjecture. These two black holes can be joined at the hip — well, at the horizon, really — in such a way as to form a bridge. It is not really a bridge in spacetime in the way you might imagine a wormhole to be, in the sense that you can’t cross the bridge; even if you move at the speed of light, the bridge will collapse before you get to the other side. Such is the simplest Einstein-Rosen bridge — a non-traversable wormhole.

What, according to the Maldacena conjecture, is this bridge from the point of view of an equivalent field theory setting? The answer is almost fixed by the symmetries of the problem. Take two identical field theories that would each, separately, be identical to one of the two black holes in the corresponding string theory. These two theories do not affect each other in any way; their particles move around in separate universes, never interacting. Despite this, we can link them together, forming a metaphorical bridge, in the most quantum sense you can imagine — we **entangle** them as much as we can. What does this mean?

## Entanglement

In quantum physics, we are no longer limited to things being one way or the other. They can be in between. Let’s take a famous example. A computer bit in an ordinary computer can be off (“0”) or on (“1”). Two such bits can have four possibilities: (0,0), (1,0), (0,1), or (1,1). But in a quantum context there are an infinity of possibilities. First, even one quantum bit (qubit) can be somewhere between on and off: cos θ (0) + sin θ (1), where θ is any real number between 0 and 2π. Two qubits can be in any combination of the form

- a (0,0) + b (0,1) + c (1,0) + d(1,1)

as long as |a|^{2} + |b|^{2} + |c|^{2} + |d|^{2} = 1. In fact a, b, c and d can be complex numbers, too. (In the following I’ll often drop a, b, c, d to keep expressions shorter.)

This has huge implications. If the bits are in the state [ (0,0) + (1,1) ] , what does this mean? One thing it means is that although we don’t know what we’ll get if we measure the first bit, we do know that **whatever the first bit is, the second bit will be the same.** That is: the first bit might be 1 or it might be 0, but if we measure it to be 1, then we can be sure we’ll find the second bit is 1 when we measure it.* (Naively, this is the same as saying that we don’t know what socks I’ll wear tomorrow, but we know that if I wear a red sock on the right foot, there will also be a red sock on my left foot. But that can’t be the whole story, because there’s a different state, [ (0,0) – (1,1) ], with the same naive feature but a minus sign, and that state is somehow be different. Maybe I’ll come back to the differences sometime; not today.)*

If instead the bits are in a state [ (0,1) + (1,0) ], then whatever the first bit is doing, the second is doing the opposite. In more complicated states, well… it’s complicated.

These are the kinds of entangled states that are used directly in Einstein, Podolsky and Rosen’s demonstration of quantum physics’ “spooky action at a distance”. What’s spooky? Even if the bits are far apart, even as far as Pluto,** in entangled states the measurement of one of the bits partially or completely determines what the other bit is doing**.

## The Thermofield Double State

Back to the ER bridge. To obtain the bridge in the field theory using Maldacena’s equivalence, we must entangle the two quark/gluon/etc field theories in the following precise way. Label every state in the quantum field theory by an integer n. *(This is a small cheat, because the number of states is uncountably infinite, but we will sidestep this subtlety.)* Now set up the “Thermofield Double State” (TFD) state of the two field theories, which is a sum over all of the states (n,n) weighted by a factor exp[- E_{n} / (2 k_{B} T)]. Here E_{n} is the energy of the state n; the temperature of either one of the black holes (remember they are identical) is T; and k_B is a famous constant of Nature, named after Ludwig Boltzmann. (The exponential of energy divided by temperature is a famous expression, due to Boltzmann, that always arises in the physics of temperature.) The TFD state can be written more explicitly in the math of quantum physics:

where L and R stand for the two field theories and β = 1/ ( k_{B}T). *[“Z” is just there to get the probabilities to come out to one, and the asterisk in “n*” indicates that really we should use the conjugate of the state n in one of the field theories.]*

In short, we perfectly correlate the two field theories — if one is measured to be in a state n, then other will also be in that same state *[actually its conjugate n*]* — and we weight the correlated states by a factor which is 1 for low energy states and exponentially small for high-energy states, so that it’s more probable to find the two field theories in states with energy below k_{B}T than above.

Importantly, these two quark/gluon/etc theories otherwise do not interact at all! They may as well live in different, disconnected universes. None of their particles ever meet. **Only the state in which they are placed relates them to each other.** This is the spookiest of actions — arranged for non-interacting field theories that have nothing to do with each other. Not only are they at a distance, that distance is effectively infinite — or better, not even meaningful.

Thus, the Maldacena equivalence implies that an Einstein-Podolsky-Rosen entangled state of two quark/gluon/etc field theories without gravity, suitably chosen, is physically equivalent to an Einstein-Rosen bridge joining two suitable black holes in a string theory on an appropriately curved space; remember this space has more space dimensions than the field theories have. [See the figure at the end of this post for an illustration.] As I emphasized before, nothing can travel from one end of the bridge to the other. But you can still do many interesting things with this bridge. For example, two objects that enter the bridge from opposite sides can meet in the middle, even if they can’t cross the bridge or return to their origins. In the equivalent field theories, this is described as producing two small disturbances, one in each field theory, which can engage with each other **even though the two field theories do not interact**. The entanglement between them produces effects that no pre-quantum physicist could ever have imagined.

I will soon have to write about **traversable** wormholes — ones where something actually ** can** cross from one side to the other. That’s part of the current hullabaloo. Because that story is a bit intricate, I will come back to it in a later post. For the moment, suffice it to say that in order to have something cross the bridge, we must allow communication between the outsides of the two black holes — not through the ER bridge but

**around**it. From the point of view of the equivalent field theories, we must arrange for them to interact, in a simple, prescribed way. No longer can they really be an infinite distance apart; otherwise the needed communication would take forever.

## Simulate?

With this in mind, let’s ask a simple question. Can’t we just check and study this conjectured relation between ER and EPR — between a physical spacetime bridge and a metaphorical, almost-metaphysical quantum bridge — just by putting the field theories on a computer, setting up the thermofield double state we want, and seeing how they behave?

Yes, in principle. No, in practice; it’s too hard. Modern computers can’t do it.

So we should ask — is there a simpler version of this problem where, perhaps, it might not be quite so difficult to simulate how this all works?

## Simplify…

The answer is yes, to a degree. Although black holes and wormholes in three or more spatial dimensions are too difficult, there is a sort of analogy — a cartoon of a wormhole — in just one spatial dimension (along with the usual time dimension). ONE SPATIAL DIMENSION.

That seems awfully limiting. In fact, gravity in one spatial dimension has barely any content at all; there’s no gravitational force, no gravitational waves, not much remnant of anything we’d call gravity at all. One dimension is a line that stretches from one point at left-infinity to another at right-infinity, so in a sense there’s always a bridge between one end and the other. [See the figure at the end of this post.] What does it mean to make a spacetime bridge in this context? Well, the trick is not to use the standard version of Einstein’s gravity. If we add a spinless field to gravity, we get something called “JT gravity” (named for its inventors, Jackiw and Teitelboim) and this theory has something that resembles, in cartoon form, a wormhole.

*In what sense is this a good cartoon? I’m not the expert here, so I’m giving you my impression; maybe I can give a better answer when I learn more. There are imaginable wormholes in three or more spatial dimensions that would connect black holes that are particularly stretched out along the radial direction — that’s the one that points toward the black hole’s horizon. In such cases it can sometimes be shown that the most important physics involves only that radial direction, and that certain physical questions can be answered by focusing only on that one dimension. In that context, even though the full theory in Maldacena’s conjecture has nine spatial dimensions (of which typically three or four are large, depending on context), only one of them actually matters for certain physical questions. The description of the physics involving that dimension, in an appropriate limit, reduces to JT gravity.*

Great! It’s a cartoon, but sometimes one can learn general lessons from cartoons. All we have to do, then, is perform the equivalent of this operation on the quark/gluon field theories that lie on the other side of Maldacena’s equivalence, reducing them down in dimensions — to zero space dimensions, so that the particles do not move in space, and experience only time — and we’ll find the exact description of this wormhole.

Unfortunately, that’s not practical.

But nevertheless it turns out there is a theory of quark-like objects in zero spatial dimensions and one time which seems to capture much of the physics of this cartoon wormhole. (A field theory in zero spatial dimensions is called “quantum mechanics”, studied by every college physics major.) This is called the Sachdev-Ye/Kitaev (or SYK) model. Caution: unlike the Maldacena conjecture, which proposes an **exact** relationship between field theories of quarks/gluons/etc and certain string theories, we have now moved to **a relationship which is no longer exact**. [In the figure at the end of this post, this is indicated by replacing an “=” sign with a “~” sign.] Instead, one obtains some kind of relationship with JT gravity only in a special regime of the SYK physics. It is hoped that that this regime captures something universal — i.e., independent of details — about the wormhole. That is, we may hope/pray that what we learn from the SYK model teaches us about the JT gravity wormhole, and that this in turn might teach us some lessons about more realistic wormholes.

This is somewhat analogous to the way, as I described in the previous post, that real-world quarks and gluons seem to capture some of the physics of string theories to which they are not precisely equivalent. It seems that there is something universal about hadron formation, because similar physics (Regge trajectories and something resembling KK towers) appears both (a) in string theories that don’t match the real world but in which calculations are easy, and (b) in the string theory that does match the real world but which can only be studied in experiments on hadrons — in natural simulations in the lab.

So here, too, we can hope and pray for the best. All we have to do is **artificially** simulate two copies of the SYK models, put them in the appropriate entangled state — the TFD state — and, if desired, add the required interactions to change the cartoon non-traversable wormhole into a cartoon traversable one.

## Simulate?

How might we do that? Well, classical computers are still more powerful than quantum computers, so clearly that’s the best way to proceed. Use a standard computer to calculate the physics of the SYK models; if you put that computer into your lab, then, well, I suppose you’ve simulated/made/studied a cartoon wormhole in a lab. However, don’t get confused; it’s still a computer simulation.

But it sounds more exciting to do the computation using a quantum computer (oooh, cool!) because then you really do need a lab just to make the computer in the first place. So now, if you succeed in doing a simulation, you can say more seriously that you did it in a lab. Note, however, that **the lab was needed for the quantum computer, not the wormhole.** And it’s still a computer simulation, just a less powerful one than you could do with an ordinary computer.

There’s just one more problem. You can’t do the desired simulation with existing quantum computers. Quantum computers aren’t that good yet. This problem is just too hard for them.

## Simplify…

So what do you do? You simplify the problem **again**, and you use classical computers (which, being more powerful, can handle this problem) to help you figure out how best to do it. This leads you to a simpler cartoon of the SYK model, called a “Sparsified SYK model.” Again, you can hope (and there are reasons to expect it) that a Sparsified SYK model, if sufficiently rich, can capture the most important physics of the SYK model in the required regime.

Let’s summarize where we are at. [See the figure at the end of this post.]

- The basic idea is to do build a quantum computer so it can do a simulation of two cartoons of SYK models, entangled and perhaps interacting.
- That in turn hopefully tells us about the behavior of two real SYK models, entangled and perhaps interacting.
- This in turn hopefully tells us about the behavior of cartoon non-traversable and traversable wormholes in JT gravity.
- (Notice we now have a cartoon-squared, and no precise equivalence as we had in the original Maldacena conjecture.)

- This in turn hopefully captures the physics of particular effects in very special classes of wormholes in certain string theories.
- This in turn hopefully captures the physics of wormholes in more general contexts in string theory.
- This in turn hopefully captures the physics of wormholes in the real world (assuming wormholes can actually exist.)

Got that? In the first two stages, one could have used a classical computer, and perhaps skipped the first step. But both because quantum computers are cool and because someday they will be more powerful than classical computers, it’s a nice exercise to see that it’s possible to use a quantum machine to carry out this set of calculations.

Extremely Important Caveat [similar to one as in the last post]: Notice that the gravity of the simulated cartoon wormhole has **absolutely nothing** to do with the gravity that holds you and me to the floor. First of all, it’s gravity in one spatial dimension, not three! Second, just as in yesterday’s post, the string theory (from which we ostensibly obtained the JT gravity) is equivalent to a theory of quarks/gluons/etc (from which we might imagine obtaining the SYK model) with no gravity at all. There is no connection between the string theory’s gravity (i.e. between that which makes the wormhole, real or cartoonish) and our own real-world gravity. Worst of all, this is an artificial simulation, not the natural simulation of the previous post; our ordinary gravity does interact with quarks and gluons, but it does not interact with the artificially simulated SYK particles. So the wormholes in question, no matter whether you simulate them with classical or quantum computers, are not ones that actually pull on you or me; these are not wormholes into which a pencil or a cat or a researcher can actually fall. In other words, no safety review is needed for this research program; nothing is being made that could suck up the planet, or Los Angeles, or even a graduate student.

## Simulate!

Finally, the path is set. The artificial simulation is carried out using a quantum computer; it passes a couple of important consistency checks; a paper is sent for publication in a famous journal; and when it’s published, someone calls the New York Times.

In my next post I’ll tell you more about what was actually done in this quantum computer experiment, and what was achieved scientifically, by this group and by others who’ve tried similar things.

## 32 Responses

“Core of the unification (AdS/CFT conjecture)”, connection between gravity-starved Holographic Universes at Regge trajectories: “If P-conservation were true, a mirrored version of the world (where left is right and right is left) would behave as the mirror image of the current world. If P-conservation were violated, then it would be possible to distinguish between a mirrored version of the world and the mirror image of the current world.”- Chien-Shiung Wu experiment provided a way to operationally define left and right without reference to the human body.

Both are correct is the “non-localized Equivalence principle”?, a “localized Quantum superposition”, beyond the extra spatial dimension or “radial” dimension, the..

Einstein-Rosen Bridge (ER) = Einstein-Podolsky-Rosen Entanglement (EPR), which appears in a Kantian way and Quantum decoherence at experiment (measurement problem), the bridge will still collapse between two black holes.

“Yukawa potential trajectories” are the emission of “Zero spin Pion-mediated (=> 👀) Nonradiative relaxation”, a Zeta connection (Penrose stairs) of “Non-abelian”, two small disturbances, one in each field theory,..

can be viewed as a natural quantum computer simulation of this equivalent string theory, like the “encryption algorithms (Time is Money)” – a strongly correlated models at finite temperature and teleportation protocols inspired by black hole physics.?

Ah, previously reading popular articles about the symbolic equation ER=EPR, I never realized the = sign is linking together one universe with a dual universe. Which really shows how much I’ve failed to understand.

Well, that’s typical — the popular articles simplify it down for you with sweet analogies, sometimes only half-understood by the writers if they’re not experts themselves — and the result is that the physics is mangled to the point that you can’t understand it at all.

It is certainly true that the statement ER=EPR strictly refers to ER in a world with gravity and EPR in a world without it. That’s important to understand first.

However, there is a way to bring them together into one universe. To see that you have to go back to the Randall-Sundrum and Verlinde papers of ’99/’00 (these were cited in my previous post, one with names mentioned explicitly and the other in the red warning paragraph toward the end of the post.) In that context, they show that you can glue an extra-dimensional region onto a standard string-theory compactified universe, and thereby do the ER=EPR setup within a single universe — as long as gravity is ordinarily weak enough compared to the forces that hold the EPR systems together. The precise relation between the gravity in the ordinary setting and the gravity inside the wormhole, when you insist they join into a single form of gravity, is a longer discussion than I can fit into this comment. It’s not even easy to explain in a blog post, so I’ll need to think about how to do that.

But in my previous post, I sort of did, quietly. I told you that doing studies of real world hadrons is equivalent to studying a weird string theory with (admittedly very small) extra dimensions. There is a gravity in that string theory, and because our hadrons do couple to ordinary gravity, the string theory’s gravity matches on to ours. It’s not obvious, but it is true.

This does not apply to the wormhole studies in question here, because they are simulations of the SYK model, not an actual realization with real-world particles of the SYK model. The former is not subject to ordinary gravity. The latter would be.

Thank you for bringing our attention to https://arxiv.org/abs/hep-th/9906182, the paper by Herman Verlinde!

I’d also like to point out https://arxiv.org/abs/1308.3695, as an indication of what the geometry corresponding to a single EPR pair might be like.

Dear prof. Strassler,

I seem to understand that the SYK model uses/considers/contemplates *Majorana* fermions. My question is: (if my understanding is correct) are there interesting implications of this fact?

Well, remember that the SYK model is being simulated, so these Majorana fermions are just being represented on a computer — in the recent paper the computer is quantum, but they’ve been represented on classical computers many times before. Majorana fermions have certainly be simulated previously in other contexts. Also, in SYK these are Majorana fermions in quantum mechanics, with just time but no space to move around in… not very exciting as fermions go. So I’m not aware of anything notable here.

If do not opposes, I would like to indicate to laity’s a little knowledge about this new and complicated quantum computing, just as was mentioned here:

https://en.wikipedia.org/wiki/Quantum_computing

https://en.wikipedia.org/wiki/Qubit

https://en.wikipedia.org/wiki/Quantum_supremacy

“Paldosky” and (twice) “Padolsky” should be “Podolsky”.

oops.. thanks!

excellent article, from what can be deduced we still have a series of matryoshka dolls full of hope to open !!

Thank professor !!

Excellent as always, more equations would be better. Regards Patrick Orlando

>… “real-world quarks and gluons seem to capture some of the physics of string theories to which they are not precisely equivalent”

Matt, I’m sorry, but this is just rewriting history. Superstrings do not “capture some of the physics” of hadronic strings. They were a point-blank, in-your-face attempt to generalize hadronic strings, done at a time when the math (S-matrix) interpretation still dominated over the emerging quark interpretation.

Below is a link to a beautiful description from that time period. It’s a Google Books link, but if you open the pop-up you can read the full page. I love the enthusiasm and sincere hope — I recall sharing it the first time I read it — that this 20-orders-of-magnitude (!) generalization of one of the best-established mass relationships in well-proven hadronic physics might just be the key to full unification of the forces. Those were heady, delightful times.

Anyone interested in the very human, highly speculative sequence of events by which modern math-only superstring theory first came about should find this page deeply interesting:

N. G. Cooper and G. B. West, editors , Particle Physics: A Los Alamos Primer (Cambridge University Press, 1988).

https://www.google.com/books/edition/Particle_Physics/55M4AAAAIAAJ?gbpv=1&bsq=rising%20Regge

Terry, I am not going to argue with you about something in which I am one of the world’s leading experts. Either you listen to me or you don’t.

https://arxiv.org/abs/hep-th/0003136

https://arxiv.org/abs/hep-th/0007191

https://arxiv.org/abs/hep-th/0109174

https://arxiv.org/abs/hep-th/0209211

https://arxiv.org/abs/hep-th/0309122

https://arxiv.org/abs/hep-ph/0501197

https://arxiv.org/abs/hep-th/0603115

https://arxiv.org/abs/0801.0629

/A field theory in zero spatial dimensions is called “quantum mechanics”.

It’s a cartoon, but sometimes one can learn general lessons from cartoons. All we have to do, then, is perform the equivalent of this operation on the quark/gluon field theories that lie on the other side of Maldacena’s equivalence, reducing them down in dimensions — to zero space dimensions, so that the particles do not move in space, and experience only TIME (encryption algorithms?) — and we’ll find the exact description of this wormhole./

The only way to peep at the Gravity is the ontological (kantian) way?. But human thinking is controlled by Money (encryption algorithms).?

>… “Such is the simplest Einstein-Rosen bridge — a non-traversable wormhole”

Might you have a reference on how the two-nearby-parallel-universes, particle-model-only ER bridges of the original 1935 ER paper were reinterpreted as space-traversing wormholes within a single universe? I realize this must have happened at some point, but I’ve never seen the paper that did it. It seems like a rather extraordinarily generalization.

This is a matter of causality; there is no way to distinguish two very distant regions of one universe and two disconnected universes without waiting an extremely long time. The details of proving this is outside my expertise but I would consider it physically obvious. The wormhole in question will drift over time and so its lifetime will change, but only on extremely long time scales of no direct interest.

There is a difference, as a matter of principle, because two strictly different asymptotically flat regions ( as in the Schwarzschild eternal vacuum solution ) are causally isolated for ever. This is not the same with the other case ( where the “mouths” of the wormhole can be connected by an external timelike worldline ). At least this is the case in GR.

Traversable wormholes ( again in GR ) are associated with some serious issues ( that I mentioned briefly in a previous post’s comment): Violation of energy conditions, existence of Cauchy horizons ( that implies unpredictability and instability that causes the collapse of the wormhole, especially if the mouths are close enough to allow for “feedback”), and potential violation of causality.

And change of topology if they are not pre-existed for ever.

These are examples of classical wormholes, though.

Not surprisingly, traversable wormholes are considered, semi- classically at least, physically problematic.

Interestingly, some of the striking characteristics of the classical , non traversable wormholes ( and black holes) like the volume growth of the internal ” trapped region” have been incorporated in conjectures ( like Susskind’s correspondence between computational complexity and the internal expansion of the volume).

As I understand it, the point of the work of Gao, Jafferis and Wall, https://arxiv.org/abs/1608.05687, is that traversable wormholes *do* exist in some quantum theories. They are no more difficult (and no less difficult) to implement than a quantum teleportation protocol. Causality is respected and the only violations of the energy conditions are those that are seen in ordinary quantum field theories. So while your point of view was widely held in the community until 2016, this has substantially changed.

The paper that you linked was really interesting ( thank you!).

I was already quite familiar with one of Aaron Wall’s papers that was concerned with GSL and Cauchy horizons in various configurations ( another very interesting, related subject).

From this first look, as I understand it:

– Violation of energy condition ( NEC) in this particular case is not problematic.

– This wormhole is rendered traversable only briefly ( according to the proper time of an internal observer that passes through) and it’s not, actually, a “shortcut”, i.e. it does not allow for signal propagation through the throat of the wormhole faster than it could have been through the exterior ambient spacetime.

– On this toy model, only test particles are considered as observers that can enter the wormhole ( this is usually the case with most papers, otherwise the calculations would have been intractable…) , but the authors give an argument that actual observers ( with non negligible mass, size and backreaction on the spacetime geometry ) might pass the briefly traversable wormhole ( although they consider only perturbations at a linearized level, as I understood it, so a fully non linear investigation might give different, less optimistic result).

– So it’s still open if Alice and Bob could meet in the interior, actually, or at least they leave this question open for a future paper…

– Another concern that I didn’t notice being addressed is that as the interior of the wormhole is rendered briefly traversable, an inner horizon could have been , at least temporarily, there. And inner horizons are infamously unstable, even to small perturbations.

Anyway, a second, more careful look is needed, along with further reading ( there are other related papers in the references and elsewhere).

Most of these issues aren’t open anymore. See for instance “Humanly traversable wormholes” https://arxiv.org/abs/2008.06618.

But yes, it seems sensible wormholes are never shortcuts.

I’m sorry but I don’t agree that Maldecena and Milekin are working in “a world not so different from ours.” They admit that they are using a different world. They are using a custom universe imagined by Lisa Randall not much related to ours. And even in that universe they can only say that some solutions may be suggesting traversable wormholes. To me this paper looks like an academic drill on the theme of wormholes.

It takes only one new force, one that we simply haven’t discovered yet, to show our world is that of Randall and Sundrum. I don’t think you understand what Randall and Sundrum actually did, in the context of the Maldacena conjecture. By the same token, you have not understood what I was telling you in https://profmattstrassler.com/2022/12/05/physicists-discover-string-theory-and-extra-dimensions-in-a-laboratory/ ; essentially what I was telling you is that the strong nuclear force itself is far closer to Randall and Sundrum than you realize. One more force similar to the strong nuclear force but infrared-conformal, and acting not on Standard Model particles but only on its own particles, would be enough to show that we live in a Randall-Sundrum world. [I showed this in an explicit example with Igor Klebanov — indeed, if Randall and Sundrum hadn’t been so smart and figured this out in 1999, we would have stumbled on their discovery in early 2000.]

A correction to my above comment:

The open question is if actual observers or finite size objects ( non test particles) could *pass* the traversable wormhole, not if they could meet in the interior…

They can pass. Even in an ER bridge, observers can meet in the middle. A traversable wormhole is one where a single observer can cross the bridge; and this is what Gao, Jafferis and Wall showed is possible, as have many others since in other contexts. Maldacena and Milekhin are pointing out that humans could cross a wormhole in an a world not so different from ours — though because of exponential redshift, the traveler would experience a short time but the outside would see the crossing time as exponentially long. They emphasize, though, that they have no idea how such a large wormhole could be created in the first place — but these solutions exist and make sense, apparently. I have not gone through the details of their mathematics to see how it works.

Yes, I don’t disagree that it’s principle possible for “Alice and Bob” to meet in the interior ( given some suitable assumptions). Each of them could see the other coming from the opposite “outgoing” direction and also, they could see a distorted image of the “other” spacetime region after they have crossed the horizon.

I corrected my comment only because it was kind of misleading, not what I wanted to say.

I’m reading now the Maldacena/ Milekhin paper. Thanks again for the posts and the paper recommendations.

Thank you for taking the time to do such a deep dive on this!

« in entangled states the measurement of one of the bits partially or completely determines what the other bit is doing.»

Not sure I understand, but you seem to be talking about pure numbers when you say “bit” but then as in the above sentence you are talking about one bit knowing what the other bit is doing. How can can two mathematical abstraction we call number have knowledge of each other? Maybe you can clarify.

Good question: no, although a “bit” is an abstract idea, I am really referring to a physical system that realizes that bit. For instance, a bit might be realized by an electron, forced to be stationary, but whose spin can be up or down. It could be an entire spin-1/2 atom stuck in a crystal. It could be a more stable on-off switch, as in a transistor. Any physical system with two states that can be described as an isolated, stable system for a sufficiently long time will do. To be a quantum bit, it has to be a lot more isolated and stable than a classical bit, because quantum objects more easily become entangled with objects around them than do classical objects… that’s why it’s hard to build quantum computers.

in quantum computers there is a high rate of qubit corruption, and finding an error-correcting code is desirable.

There is a “subtlety” in the description of an EPR experiment. If Alice and Bob are spacelike separated and do their measurements in two entangled particles , we can’t specify which measurement comes first, so there’s not an absolute temporal order between them.

From the point of view of Alice, it’s her measurement that affects the other ( Bob’s) bit and for Bob, it’s his measurement that

“collapses the wavefunction”. That’s the peculiar ” holistic” aspect of entanglement ( non separability: both particles are described by the same wavefunction.

This QM non locality respects special relativity and does not violate causality ( no-signaling).