I bring up dogs because of a comment, quoted in the Guardian and elsewhere, by my friend and colleague, experimentalist Maria Spiropulu. Spiropulu is a senior author on the wormhole-related paper that has gotten so much attention in the past week, and she was explaining what it was all about.

*“People come to me and they ask me, ‘Can you put your dog in the wormhole?’ So, no,” Spiropulu told reporters during a video briefing. “… That’s a huge leap.”*

For this, I can’t resist teasing Spiropulu a little. She’s done many years of important work at the Large Hadron Collider and previously at the Tevatron, before taking on quantum computing and the simulation of wormholes. But, oh my! The idea that this kind of research could ever lead to a wormhole that a dog could traverse… that’s more than a huge leap of imagination. It’s a huge leap straight out of reality!

Decades ago there was a famous comedian by the name of Henny Youngman. He told the following joke — which, being no comedian myself, I will paraphrase.

*I know a guy who wanted to set a mousetrap but had no cheese in his fridge. So he cut a picture of a piece of cheese from a magazine, and used that instead. Just before bed, he heard the trap snap shut, so he went to look. In the trap was a picture of a mouse.*

Well, with that in mind, consider this:

- Imaginary cheese can’t catch a real mouse, and
**an imaginary wormhole can’t transport a real dog!**

As I explained in my last post, the recent wormhole-related paper is about **an artificial simulation of a wormhole**… hence the title, *“Traversable wormhole dynamics on a quantum processor”*, rather than *“First creation of a wormhole.”* Actually, they’re not even simulating the wormhole directly. As I described, the simulation is of some stationary particles — not **actual** particles, just simulated ones, represented in a computer — and the (simulated) interactions of those particles create a special effect which acts, in some ways, like a (simulated) wormhole. *[The math of this is called the SYK model, or a simplified version of it.]*

This is a very cool trick for artificially simulating a wormhole, one that can be crossed from one side to the other before it collapses. The trick was invented by theorists in this paper (see also this one), following on this pioneering idea. But it is not a trick for making a real wormhole. Moreover, this is a simulated wormhole in **one spatial dimension**, not the three we live in. In this sense, it is a cartoon of a wormhole, like a stick figure, with no flesh and blood.

Even if this were a real one-dimensional wormhole, you cannot hope to send a three-dimensional dog through it. You could not even send a three-dimensional **atom** through a one-dimensional wormhole. Dimensions don’t work that way.

Remember, this wormhole does not exist in the real world; it is being represented by the bits of the computer. In a sense, it is being **thought** — represented in the computer’s crude memory. Try it: imagine a wormhole (it doesn’t matter how accurate.) Imagine a dog now going through it. Ok, you have just done a simulation of a dog going through a wormhole… an imagined dog moving through an imagined wormhole. Naturally, your brain didn’t do a very accurate simulation. It lacks all the fancy math. Armed with that math, the computer can do a professional-quality artificial simulation.

But just as you cannot take your real dog, the one you pet and play fetch with, and have it travel through the wormhole you imagined in your brain, you cannot take a real dog and pass it through a computer simulation of a wormhole. That would be true even if that wormhole were three-dimensional, rather than the one-dimensional cartoon. Nor can you take a real atom, or even a real photon *[a particle of light]*, and send it through an imaginary, artificially simulated wormhole. Only an artificially simulated photon, atom or dog can pass through an artificially simulated wormhole.

Wormholes in nature are about **real** gravity. Wormholes in a computer are about **mathematically simulated** gravity. Real gravity pulls real things and might or might not make real wormholes; it has to obey the laws of nature of our universe. Imaginary gravity pulls imaginary things and can create imaginary wormholes; it is far less constrained, because the person doing the simulation can have the computer consider all sorts of imaginary universes in which the laws of nature might be very different from ours. Imaginary wormholes might behave in all sorts of ways that are impossible in the real world. For instance, the real world has (at least) three dimensions of space, but on a computer there’s no problem to simulate a universe with just one dimension of space… and that’s effectively what was done by Spiropulu and her colleagues, following the proposals of this paper and others by quantum gravity experts.

So let’s not confuse what’s real with what’s artificially simulated. And by the way, just because a quantum computer was used instead of an ordinary one doesn’t change what’s real with what is not. Real dogs are quantum; quantum computers are real; both have to obey the laws of the real world. But anything **simulated** on a quantum computer is not real, and need not obey those laws.

Setting aside these simulated wormholes — could real wormholes exist, and could you send your dog through one?

Until recently there was a lot of debate as to whether wormholes actually make sense; maybe, it was thought, they violate some deep principles and are forbidden in nature. But in the last few years this debate has subsided. I’ll discuss this in more detail in my next post. But here are a few things to keep in mind:

It has been shown (most directly here, by Maldacena and Milekhin) that in some imaginary universes that are not so different from our own, it is possible for wormholes to exist that are large enough for dogs and humans to travel through. **BUT:**

- A person in that universe could not use them to travel faster than light from point A to point B — i.e., there is no chance that these wormholes could be used to go instantly halfway across the universe, and thus communicate faster than a message sent by radio waves outside the wormhole from A to B. Nor could they be used for time travel to the past.
- To avoid travelers being torn apart by tidal forces, the openings to these wormholes must be immense — far, far larger than a human. They’re not like the round doorways you see in science fiction movies.
- Although the wormhole traveler would feel the trip to be short, the travel time from the point of view of those outside the wormhole would be spectacularly long. If you did a round trip through the wormhole and back, your friends and family would all be long dead when you returned.
- The region inside the wormhole could easily become very dangerous; any photons that leak in from the other side will become extreme gamma rays bombarding the traveler passing through. To avoid this and other similar problems, the wormhole’s huge openings must be kept isolated and absolutely pristine.
- It’s hard to understand how to produce stable wormholes like this in a universe whose temperature is as high as ours (2.7 Kelvin about absolute zero).
- It is hard to imagine how such a wormhole could be created through any natural or artificial process. (I wrote here about why real wormholes, even if they can exist in our universe, are extremely difficult to create or manage; and that’s true not only for macroscopic ones large enough for a dog but for microscopic ones as well. The same is true for black holes, which definitely do exist in our universe.)
- For these and/or other reasons, large traversable wormholes of this sort may not be possible in our universe; the specific laws of nature we live in may not allow wormholes worthy of the name, or at least not large ones. This is an open question and may depend on facts about our universe that we don’t yet know.

So you will not be sending your dog on any such journey. It’s wildly unrealistic.

One final note — if it becomes possible, decades or centuries from now, to attempt the fabrication of real, microscopic wormholes in an Earth-bound lab, it should not be attempted without a thorough safety review. Real black holes and wormholes aren’t easily handled and can potentially be very dangerous if anything goes wrong. It would be a terrible thing if one got away from you and ate your dog.

It’s not terribly unusual for the Moon to pass in front of a planet and block it, from the point of view of some of us on Earth. This time it is Mars’ turn. You’ll be able to see the Moon eclipsing Mars (a “lunar occultation” of Mars), weather permitting, in the region shown below. This map is taken from in-the-sky.org, where you can enter your location and find out exactly when you’ll see Mars disappear behind the Moon and then reappear.

This should be fun even with the naked eye — Mars won’t disappear in an instant but will do so gradually — but it will be better with binoculars, and great in a small telescope. It will give you a chance to see that yes, the Moon is in slow, steady motion in the sky relative to the planets, which (being further) seem to move more slowly. Lunar and solar eclipses provide a similar opportunity to observe this motion, but I think occultations provide the clearest sense of it.

The Full Moon can be seen from south to north across the Earth. Why isn’t the occultation visible everywhere? It is because the Moon is smaller than the Earth, as I explained here as part of my series on “Do It Yourself Astronomy”. In a sense, the light of Mars effectively (though not literally) casts the Moon’s shadow onto the Earth, and the shadow’s width — the width of the region over which the occultation is visible — would be the same as the diameter of the Moon, were the occultation visible close to the Earth’s equator. (As I pointed out, you can use this fact to measure the Moon’s size without ever leaving the Earth.) Because tonight’s occultation is visible closer to the poles, the region of visibility on the Earth’s surface is distorted by the Earth’s curvature, making it larger than the Moon by about 50% — about 3000 miles (5000 km) or so. (That’s yet more evidence that the Earth’s not flat, in case you needed some.)

Finally, there’s something quite remarkable about this occultation. It occurs close to two special moments:

- almost at full Moon (within a few hours);
- almost at “Mars opposition” (within a few hours) — when Mars is (nearly) closest, brightest and highest in the midnight sky, as brilliant as it gets over its cycle.

Since (1) happens once a month, and (2) happens once every two years, and occultations don’t occur all the time, this seems like quite a coincidence!

Only… it’s not as big a coincidence as it looks. A puzzler for you: why isn’t it a coincidence that (1) and (2) happen at the same time? That is, if there’s an lunar occultation of Mars at full Moon, why must Mars be nearly at opposition? [Hint: it’s just geometry.]

]]>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.

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?

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**.

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

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?

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.

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.

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.

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.

That said, there are profound problems with this headline. But the headlines we’ve seen this week, along the lines that “Physicists create a baby wormhole in the laboratory”, are actually WORSE than this one. ** **

**It is more accurate to say that “string theory and extra dimensions were discovered experimentally in the 1960s” than to say that “a baby wormhole was created in a lab in the early 2020s.”**

And now I’m going to show you why. As you’ll see in this post and the next, the two claims are related.

In the 1960s, a wide variety of “hadrons” (particles containing quarks, gluons and anti-quarks) were discovered — not just the protons and neutrons from which we’re made, or the pions and their cousins found in the 1940s and 1950s, but a whole host of them, with an alphabet-Greek-salad of names. Study of these hadrons led to the proposal, prior to the discovery of quarks, that **maybe hadrons are little strings**. There was quite a bit of experimental evidence for this idea! But to make a long story short, the proposal eventually failed when quarks were discovered and confirmed in the 1970s. (Meanwhile string theory was repurposed for a theory of quantum gravity etc. [a “Theory of Everything”], and the rest is history/not even wrong/lost in math/not even close.)

But actually, string theory didn’t fail. It was just string theory in flat four dimensions that failed.

Bear with me. This takes a few steps.

In 1997, Juan Maldacena, following on old ideas of Gerard ‘t Hooft and Alexander Polyakov, among others, and hinted at by works by many other string theory/black hole researchers (such as Igor Klebanov, Andy Strominger, etc.), uncovered strong evidence for a radical conjecture:

*There are quantum field theories**(theories of gluons, quark-like particles, and some additional friends,***but with no gravity***, in a world with***three**space dimensions and one time dimension)*that are*exactly equivalent*to supersymmetric string theory (**a theory with***nine***space dimensions and one time dimension, with an infinite set of particles and fields, and***with***quantum gravity)**where the strings are moving on a uniformly 9+1 dimensional curved space.*

[[If you don’t know what “supersymmetric” means, don’t worry about it; it won’t be relevant here.]]

This sounds crazy at first. How can a theory with quantum gravity be equivalent to one without quantum gravity? and how can two theories with different numbers of space-dimensions be equivalent? Nevertheless, the conjecture is almost certainly correct. In this post I won’t go into the mountains of evidence here in favor of this “AdS/CFT” or “gauge/string duality” conjecture. [A figure illustrating this relation, and some of the others mentioned below, is located at the end of this post.]

Within a short time, Maldacena’s conjecture was extended to theories that are more similar to the real world — gluon/quark/etc. theories that exhibit remarkably real-world-like behavior. This includes formation of hadrons out of gluons and quark-like particles, for instance, along with many extra hadrons not found in the real world. The conjecture implies that these theories (not necessarily supersymmetric themselves) are also exactly equivalent to a supersymmetric string theory, with quantum gravity, but now on a more complicated curved space.

What makes this equivalence possible? The point is that even though the string theory exists in nine spatial dimensions (plus one time), only three spatial dimensions extend out to infinity and are visible macroscopically. The rest are somewhat curled up microscopically, but in a very clever way that assures that one of those dimensions is particularly long and important. [See the figure at the end of this post for a rough illustration.] That long but finite fifth dimension — let me call it the “radial” dimension (the one that stars in the famous work of Lisa Randall and Raman Sundrum, which came soon after Maldacena’s conjecture) — is the one that assures this string theory has properties similar to the real world. What are they?

- Unlike the string theory first considered in the 1960s, in which the strings moved on flat spatial dimensions, the curved nature of the space on which these strings move assures that
**none of the hadrons predicted by this new string theory arrangement should be massless***[except possibly some pion-like particles.]* - For each hadron of low mass (M) and low “spin” (angular momentum J) there should be an associated set of hadrons of ever-increasing angular momentum and mass, with M growing roughly like the square root of J. [[These sets of hadrons are called
**Regge trajectories**.]] - For each particle of low M and low J, there should be a “tower” of hadrons of increasing M but the same J. [[These sets of hadrons are called
**Kaluza-Klein (KK) towers.**]]

The precise details depend on the particular theory. But these general properties — no massless hadrons, and hadrons organized into Regge trajectories and KK towers — are the basic predictions that are almost independent of any details.

Well, long before this, when people discovered the hadrons of the real world, they learned that **the quark-antiquark hadrons (the “mesons”) of the real world do indeed satisfy all of these criteria.** (The baryons — hadrons like protons and neutrons — do too, but their story is more complicated and I won’t cover it now; there’s a little discussion here.) The real world has hadrons in Regge trajectories and KK towers, none of them massless. Nowadays we understand that this is the signature of a string theory with an extra finite radial dimension of space. The details of the hadrons teach us, in principle, the details of this string theory and the space on which the strings move.

And so it’s completely clear, in hindsight, that** the particle physicists of the 1960s discovered string theory and at least one extra spatial dimension**, though they didn’t know it at the time. (It’s even clear what quarks and gluons are — they are spikes on a string that nearly reach one edge of the radial dimension.) It was only after Maldacena’s breakthrough that this became self-evident.

**In short, as physicists at the Large Hadron Collider and its many predecessors have been studying the physics of quarks and gluons and the details of hadrons, they have secretly been studying string theory, extra dimensions, and even (to a more limited extent) quantum gravity.**

Now, many of you will be ** screaming bloody murder** at the spectacular claims made in the two previous paragraphs. And well you should be!… just as you should be screaming

The thing is, though, ** I’m not joking.** The claims made in the previous paragraphs are both

- factually true
**if**Maldacena’s original conjecture is correct, and - morally/ethically outrageous for having left out all sorts of crucial fine print.

By comparison, the claims made about the “lab baby wormholes”, which also rely on Maldacena’s conjecture, are suggestive rather than factually true, and the fine print is more extensive.

So let’s look at the fine print for the hadrons representing a string theory. I’ll need it when I come to wormholes next time.

I have to emphasize that it is absolutely true — **if Maldacena’s conjecture is correct** — that a theory of quarks and gluons found in the real world is exactly equivalent to a string theory in extra dimensions. Take the real world and ignore its gravity (that would greatly complicate the story.) Though it would be hard to carry out in practice, you could take one of Maldacena’s examples where the equivalence is well-established, add a few things to it (including the weak nuclear and electromagnetic forces and the Higgs field and electrons etc.) which maintain the equivalence, and then start stripping things away *[via mass terms and expectation values]* until you are left with the quarks and gluons of the Standard Model, and no remnants from supersymmetry or anything else the real world doesn’t have. None of this messes up the equivalence. There *is* a string theory in extra dimensions that is exactly equivalent to the real world.

Finding exactly the best way to construct this string theory, beginning to end, would be tedious and hard. To my knowledge, no one has even bothered to try. Why not?

The problem is that stripping out all that extra stuff, to move the theory toward the real world, is guaranteed to dramatically and qualitatively change the space in which the string theory travels. It will become so tightly wound up and complex that it’s barely a space at all. We don’t know any details of what this space looks like, except that, for sure, the long finite radial dimension in the cases described earlier becomes **a very short radial dimension**. [See the Figure at the end of this post.] No one has any idea how to calculate anything about string theory on such a space *[especially with “Ramond-Ramond background fields”, which make things infinitely worse]*, and so, no one can be sure how it actually behaves. It’s not even obvious there should be any objects in the theory that intuitively resemble strings at all!

In fact, the only reason to be confident that this string theory actually has the characteristically stringy and extra dimensional features listed in (1), (2) and (3) above is that **we have simulated this theory in a laboratory**! In many laboratories, in fact. That’s what our particle physics accelerators that make hadrons have been doing for sixty years. You see, from this perspective, **the real world’s quarks and gluons**, as observed in real-world particle physics experiments, **can be viewed as a natural quantum computer simulation of this equivalent string theory**, about which we otherwise know very little.

If theorists knew in the 1960s what we know today, the string theory interpretation of the data wouldn’t have been dropped so quickly. It would have lived on, well into the 1970s and 1980s and beyond. The competing views — quarks/gluons vs strings-in-curved-extra-dimensions — would have been seen as complementary, as they are today. But the required string theory is a heck of complicated beast, while the mathematics of quarks and gluons is, by comparison, very simple. Quarks and gluons are a much better intuitive basis for understanding the world, and allow us to make precise calculations for experiments, while the string theory, though it is of intuitive value in numerous contexts, is useless for precise calculations. * (Admittedly, this is a technical problem, not a conceptual one. It’s conceivable that someday a mathematical breakthrough, perhaps one that would allow us to simulate string theories on an artificial computer, will make the string theory viewpoint more practically useful.)*

[** Extremely Important Caution**: none of what I’ve said here implies that the string theory I’m referring to is a “Theory of Everything”. The string theory in question has nothing to do with the quantum physics of the gravity that holds you and me to the floor. Remember, this string theory is equivalent to quarks and gluons

Where does this leave us? We have learned from natural simulation that, for some reason we don’t understand deeply, the very complicated quantum string theory that’s equivalent to the real world’s quarks, gluon and hadrons has some remarkable, surprising, qualitative, but experimentally relevant similarities with the string theories that show up in the context of Maldacena’s conjecture, which aren’t the real world but whose properties can be calculated. Because of that, one can hope to learn some **qualitative lessons** about the real world using this equivalence *(as many authors have done, including myself here and here.)* This is a classic technique: consider a universe similar to ours in which you can draw a clear conclusion, and then hope/pray that you can draw a similar qualitative conclusion about our own universe. It works sometimes, but by no means always. You need more evidence, often from experiment, before you can be sure that your conclusion is valid in the real world. But still, even when you’re not sure of it, a plausible conjecture can occasionally point you to even better ideas.

Now, what about those wormholes? They rely on the same Maldacena equivalence, and they suffer from the same fine print, plus a lot more. *(For instance, the wormhole that’s been quasi-simulated exists in only one spatial dimension, not three.)* I’ll start to tell you their story in my next post.

In the meantime, let me reiterate: **it is less true that wormholes **(even baby ones)** have been made **(or even simulated)** in a lab than it is that particle experimentalists of the 1960s discovered string theory and extra dimensions. **Theorists in this subject have all known about the string theory viewpoint for the last twenty years or so, and we use it often, but we didn’t make a big deal out of it to the world’s journalists. Why not? Because the quarks/gluons viewpoint on the real world is both intuitive and practically useful, while Maldacena’s equivalent theory of strings on a tightly curved space is often neither, not to mention imprecisely known.

But hey, if physicists and journalists are all collectively going to lower the bar and make an international spectacle about a quasi-simulation of a cartoon of a wormhole, then, well, by that standard, I guess we ought to let everyone know that string theory and extra dimensions are absolutely real and have long been the subject of 20th- and 21st-century particle physics experiments. That’s no parody, no joke, no kidding. But don’t misread it for something more than it is. READING THE FINE PRINT ISN’T OPTIONAL!

- Did physicists create a wormhole in a lab? No.
- Did physicists create a baby wormhole in a lab? No.
- Did physicists manage to study quantum gravity in a lab? No.
- Did physicists simulate a wormhole in a lab? No.
- Did physicists make a baby step toward simulating a wormhole in a lab? No.
- Did physicists make a itty-bitty baby step toward
**simulating an analogue of a wormhole**— a “toy model” of a wormhole — in a lab? Maybe.

Don’t get me wrong. What they did is pretty cool! I’d be pretty proud of it, too, had I been involved. Congratulations to the authors of this paper; the methods and the results are novel and thought-provoking.

But the hype in the press? **Wildly, spectacularly overblown!**

I’ll try, if I have time next week, to explain what they actually did; it’s really quite intricate and complicated to explain all the steps, so it may take a while. But at best, what they did is analogous to trying to learn about the origin of life through some nifty computer simulations of simple biochemistry, or to learning about the fundamental origin of consciousness by running a new type of neural network. *It’s not the real thing; it’s not even close to the real thing; it’s barely even a simulation of something-not-close-to-the-real-thing. *

Could this method lead to a simulation of a real wormhole someday? Maybe in the distant future. Could it lead to making a real wormhole? Never.

I find it hard to understand why physicists sometimes think it is a good idea to claim more than what they’ve actually done. I don’t know anyone who has ever really benefited from that.

]]>In fact at least four and perhaps five of the ten CubeSats launched along with NASA’s Artemis mission have apparently failed in one way or another. This includes the **Near-Earth Asteroid Scout** and **Team Miles**, both of which were intended to test and use new technologies for space travel but with whom communication has not been established, and **OMOTENASHI**, which is intended to study the particle physics environment around the Moon and land a mini-craft on the surface, but which has had communication issues and will not be able to deploy its lander. It’s not clear what’s happening with **Lunar-IR** either.

One has to wonder whether this very high failure rate is due to the long delays suffered by the Artemis mission. The original launch date was at the end of August; batteries do degrade, and even satellites designed for the rigors of outer space can suffer in Florida’s heat and moisture.

]]>The recent launch of NASA’s new moon mission, Artemis 1, is mostly intended to demonstrate that NASA’s incredibly expensive new rocket system will actually work and be safe for humans to travel in. But along the way, a little science will be done. The Orion spacecraft at the top of the giant rocket, which will actually make the trip to the Moon and back and will carry astronauts in future missions, has a few scientific instruments of its own. Not surprisingly, though, most are aimed at monitoring the environment that future astronauts will encounter. But meanwhile the mission is delivering ten shoe-box-sized satellites (“CubeSats“) which will carry out various other scientific and/or technological investigations. A number of these involve physics, and a few directly employ particle physics.

The use of particle physics detectors for the purpose of studying the not-so-empty space around the Moon and Earth is no surprise. Near any star like the Sun, what we think of as the vacuum of space *(and biologically speaking, it is vacuum: no air and hardly any atoms, making it unsurvivable as well as silent)* is actually swarming with subatomic particles. Well, perhaps “swarming” is an overstatement. But nevertheless, if you want to understand the challenges to humans and equipment in the areas beyond the Earth, you’ll inevitably be doing particle physics. That’s what a couple of the CubeSats will be studying, entirely or in part.

What’s more of a surprise is that one of the best ways* to find water on the Moon *without actually landing on it involves putting particle physics to use. Although the technique is not new, it’s not so obvious or widely known, so I thought I’d draw your attention to it.

Designed at Arizona State University, the LunaH-Map CubeSat will look for water on the Moon, using a tried and true technique known as “neutron spectroscopy”. The strategy relies from the start on particle physics, taking advantage of the existence of “cosmic rays”, which are (mainly) protons and atomic nuclei traveling at near the speed of light across the universe. These particles are accelerated to extreme speeds by natural particle accelerators found in supernovas and perhaps elsewhere. They may travel for many thousands of years across the galaxy, or even longer from outside our galaxy, before reaching our vicinity. The Sun and its planets and moons are all constantly being peppered by these particles.

On Earth, most cosmic rays strike an atom in the atmosphere before they reach the ground. *(The debris from these collisions allowed scientists to discover a number of subatomic particles, such as the positron and the muon, and they play a role in many modern experiments, such as this one.)* Since the Moon has no atmosphere to speak of, cosmic rays instead slam straight into the lunar dirt.

What ensues is a “hadronic shower”, a natural particle physics process similar to that found at the Large Hadron Collider, within the “hadron calorimeters” of the ATLAS or CMS experiments. (*These portions of the ATLAS and CMS detectors measure the energies of hadrons, particles containing quarks, antiquarks and gluons.)* A computer simulation of a hadron shower is shown at left. How does a shower arise?

When a high-energy proton hits an atomic nucleus (typically within a meter of the lunar surface), it breaks the nucleus apart into protons, neutrons and smaller atomic nuclei. Typically some of the remnants now have enough energy themselves to break apart nearby atomic nuclei, whose remnants break apart further nuclei, etc. The result is that the cosmic ray’s large amount of energy is transformed into a shower of protons, neutrons and other nuclear fragments. Whereas the original cosmic ray was moving at nearly the cosmic speed limit (a.k.a. the speed of light, 300,000 kilometers per second), the particles in the shower are typically moving much more slowly, perhaps 10 to 1,000 kilometers per second — still fast by human standards, but far below light speed.

Not surprisingly, since the cosmic ray comes from above, most of the particles in this shower move downward into the lunar soil. They collide with other atomic nuclei and eventually slow to a stop. But there are always a few protons and neutrons that by chance have a collision that knocks them upwards. Consequently, even a downward-directed cosmic ray shower will produce some particles that make their way out of the ground and back into space. Once they get out, there’s nothing to stop them, since there’s no air around the Moon. A spacecraft going by just overhead can hope to detect them as they head out into empty space.

The basic trick of LunaH-Map, which I’ll explain in a moment, is that **if the ground that the cosmic ray struck contains hydrogen, any upward-going particles will be slower on average than if there’s no hydrogen there.** Most lunar soil has no hydrogen, as determined by various missions to the moon. But lunar soil that contains water ice in it will have plenty of hydrogen, since water is hydrogen and oxygen (H_{2}O). So if you can detect particles of certain speeds as you pass over a certain part of the Moon, you can tell whether there’s water ice embedded in the soil.

To explain all this, I need to tell you why particle speeds are sensitive to the presence of hydrogen, and which types of particles are best to measure.

The effect of hydrogen on particle speed involves something you probably understand intuitively, even if you were not taught it in a first-year physics class. It’s illustrated in the figure below.

- If you bounce a ping-pong ball off a heavy, stationary rock, the rock won’t budge, and the ping-pong ball will bounce off it in a new direction but without losing any of its speed.
- If you bounce a ping-pong ball off a second, stationary ping-pong ball, both ping-pong balls will be moving after the collision, and the speed of both balls will be
**less**than the initial speed of the first ball.

*(For those who’ve had a little physics: these facts are required by conservation of energy and momentum. In the first case the rock absorbs almost none of the ping-pong ball’s kinetic energy, so the ball retains what it had before, as for a tennis ball bouncing off a wall; in the second case, the first ping-pong ball loses a significant fraction of its kinetic energy to the second one.)*

Imagine, then, a proton or a neutron that emerges from the shower of particles that follows a cosmic ray impact. Much slower than the original cosmic ray, it is still moving at many kilometers per second. What happens as it repeatedly strikes atoms in the soil?

Protons and neutrons have about the same mass. Typical atomic nuclei in the Moon, such as oxygen or silicon, contain more than ten protons and neutrons, and so, with much larger masses than a single proton or neutron, they act like a heavy rock. Our speedy neutron or proton will bounce off such a nucleus without slowing down. *(A minor detail: It may not always simply bounce; other things may happen which can slow it down somewhat, but not enough to affect what I’m about to tell you.) *

But because hydrogen’s nucleus is itself just a single proton, **the collision of a proton or neutron with a hydrogen nucleus is like the collision of two ping-pong balls** — two objects of equal or nearly equal mass. The result: the one that’s moving will lose on average half its energy, or about 30% of its speed, relative to the lunar surface. If there’s a lot of hydrogen in the soil, then this process may happen repeatedly to most protons and neutrons in the cosmic ray shower. And so **protons and neutrons emerging from soil rich in hydrogen are on average much slower compared to those emerging from soil that’s poor in hydrogen.**

The LunaH-MAP cubesat, like many spacecraft before it, is looking for this effect on **neutrons**. Why on neutrons and not on protons? Because there are protons everywhere around the Moon, streaming in from the Sun and from elsewhere. Neutrons, by contrast, only can exist on their own (as opposed to inside a stable atomic nucleus) for about 15 minutes. Consequently, any neutrons from the Sun or other distant source won’t make it to the Moon. So any neutrons near the Moon, even some distance overhead, are much more likely to have come from the Moon than from anywhere else.

LunaH-MAP comes quite close to the Moon’s surface (just a few kilometers above it), which allows it to examine the Moon in considerable detail. All it does, as it flies over the surface, is count how many neutrons it encounters. What’s crucial is that ** it is only sensitive to neutrons of moderate to high speed, and it can’t detect the slow ones** (slower than about 7 kilometers per second.) Above most regions of the Moon, where the heat of the Sun quickly vaporizes any water ice and releases it to space, the spacecraft will find many neutrons of moderate speed, dislodged by cosmic rays and leaking out from the surface. But in craters near the poles, where there are regions mostly or always in shadow, ice deposited by comets still remains; and there, as the spacecraft passes overhead, many of the neutrons will have been slowed down so much that LunaH-MAP can’t detect them.

That’s how, without ever landing there, LunaH-MAP can give us a detailed map as to where hydrogen, and likely water ice, is to be found on the Moon. Similar techniques can and have been used on planets such as Mars and asteroids such as Ceres. Pretty cool, right? Just another great example of how seemingly exotic and esoteric discoveries of one century — cosmic rays were first observed in 1911, and the neutron was identified in 1932 — turn out to be essential tools in the next.

]]>- the claim by the CDF experiment that the W boson mass is higher than predicted in the Standard Model (discussed on this blog here and here), and
- the claim by a group of theorists known as the “NNPDF collaboration” that there are (in a sense that I have briefly discussed here) unexpectedly many charm quark/anti-quark pairs “in” (or “intrinsic to”) the proton,

both depend crucially on our understanding of the fine details of the proton, as established to high precision by the NNPDF collaboration itself. This large group of first-rate scientists starts with lots of data, collected over many years and in many experiments, which can give insight into the proton’s contents. Then, with a careful statistical analysis, they try to extract from the data a precision picture of the proton’s internal makeup (encoded in what is known as “Parton Distribution Functions” — that’s the PDF in NNPDF).

NNPDF are by no means the first group to do this; it’s been a scientific task for decades, and without it, data from proton colliders like the Large Hadron Collider couldn’t be interpreted. Crucially, the NNPDF group argues they have the best and most modern methods for the job — NN stands for “neural network”, so it has to be good, right? — and that they carry it out at higher precision than anyone has ever done before.

But what if they’re wrong? Or at least, what if the uncertainties on their picture of the proton are larger than they say? If the uncertainties were double what NNPDF believes they are, then the claim of excess charm quark/anti-quark pairs in the proton — just barely above detection at 3 standard deviations — would be nullified, at least for now. And even the claim of the W boson mass being different from the theoretical prediction, which was argued to be a 7 standard deviation detection, far above “discovery” level, is in some question. In that mass measurement, **the largest single source of systematic uncertainty is from the parton distribution functions**. A mere doubling of this uncertainty would reduce the discrepancy to 5 standard deviations, still quite large. But given the thorny difficulty of the W mass measurement, any backing off from the result would certainly make people more nervous about it… and they are already nervous as it stands. (Some related discussion of these worries appeared in print here, with an additional concern here.)

In short, a great deal, both current and future, rides on whether the NNPDF group’s uncertainties are as small as they think they are. How confident can we be?

The problem is that there are very few people who have the technical expertise to check whether NNPDF’s analysis is correct, and the numbers are shrinking. NNPDF is a well-funded European group of more than a dozen people. But in the United States, the efforts to study the proton’s details are poorly funded, and smaller than ever. I don’t agree with Sabine Hossenfelder’s bludgeoning of high-energy physics, much of which seems to arise from a conflation of real problems with imaginary ones — but she’s not wrong when she argues that basic science is under-funded compared to more fancy-sounding stuff. After all, the US has spent a billionish dollars helping to build and run a proton collider. How is it that we can’t spend a couple of million per year to properly support the US-based PDF experts, so that they can help us make full use of this collider’s treasure trove of data? Where are our priorities?

A US-based group which calls itself CTEQ-TEA, which has been around for decades and was long a leader in the field, is disputing NNPDF’s uncertainties, and suggesting they are closer to the uncertainties that CTEQ-TEA itself finds in its own PDFs. (Essentially, if I understand correctly, they are suggesting that NNPDF’s methods fail to account for all possible functional forms [i.e. shapes] of the parton distribution functions, and that this leads the NNPDF group to conclude they know more than they actually do.) I’m in no position, currently, to evaluate this claim; it’s statistically subtle. Nor have I spoken to any NNPDF experts yet to understand their counter-arguments. And of course the CTEQ-TEA group is inevitably at risk of seeming self-serving, since their PDFs have larger uncertainties than those obtained by NNPDF.

But frankly, it doesn’t matter what NNPDF says or how good their arguments are. With such basic questions about nature riding on their uncertainties, we need a second and ideally a third group that has the personnel to carry out a similar analysis, with different assumptions, to see if they all come to the same conclusion. We cannot abide a situation where we depend on one and only one group of scientists to tell us how the proton works at the most precise level; we cannot simply assume that they did it right, no matter how careful their arguments might seem. Mistakes at the forefront of science happen all the time; the forefront is a difficult place, which is why we revere those who achieve something there. We cannot have claims of major discoveries (or lack thereof!) reliant on a single group of people. And so — **we need funding for other groups**. Otherwise it will be a very long time before we know whether or not the W boson’s mass * is* actually above the Standard Model prediction, or whether there really

Prizes worth millions of dollars a year, funded by the ultra-wealthy, are given to famous theoretical physicists whose best work is already in the past. At many well-known universities, the string theory and formal quantum field theory efforts are well-funded, thanks in part to gifts from very rich people. That’s great and all, but progress in science depends not only on the fancy-sounding stuff that makes the headlines, but also on the hard, basic work that makes the headline-generating results possible. Somebody needs to be funding those foundational efforts, or we’ll end up with huge piles of experimental data that we can’t interpret, and huge piles of theory papers that sound exciting but whose relation to nature can’t be established.

I doubt this message will get through to anyone important who can do something about it — it’s a message I’ve been trying to deliver for over 20 years — but in an ideal world I’d like it to be heard by to two groups of people: (1) the funders of particle physics at the National Science Foundation and the Department of Energy, who ought to fund string theory/supersymmetry a little less and proton fundamentals a little more; and (2) Elon Musk, Mark Zuckerberg, Jeff Bezos, Yuri Milner, and other gazillionaires who could solve this problem with a flick of their fingers.

]]>