The answer is that it has nothing to do with actually making wormholes… at least, not in the sense of science fiction portals that you and I could use to travel from here to some faraway place across the universe. It has to do with potentially gaining new insight into the quantum physics of gravity, space and time.

Why do scientists do research on black holes? There are at least two very different reasons.

- Large black holes can be observed in nature. These black holes, which astronomers and gravitational wave experimenters study, are well-described by non-quantum physics — “classical” physics, where the future is (in principle) truly predictable from the past.
- Small black holes are a window into quantum gravity — the unknown quantum physics of spacetime, where space itself is governed by the uncertainty principle, meaning that the very shape of spacetime can’t be precisely specified. This is relevant for black holes far too small for us to discover using astronomy, yet far too difficult for us to produce experimentally. They are important because they pose conceptual problems and puzzles for quantum gravity. Theoretical physicists think about black holes, and study their math, in hopes of uncovering quantum gravity’s secrets.

To gain more insight into their workings, scientists also simulate black holes on computers, and study analogues to black holes in laboratories.

In contrast to black holes, there may be no wormholes worthy of the name anywhere in our universe. Though recent research clearly shows that there’s no principle that forbids wormholes from existing, it also shows it’s unlikely that large wormholes can be produced or can endure in our universe. While black holes are a generic outcome of the collapse of a huge star, wormholes are relatively delicate, and difficult to create and maintain.

But wormholes may be even more interesting than black holes for the problems of quantum gravity. This was only appreciated, slowly at first, over the past 10 years.

It’s hard to define the quantum state of a black hole. *[In quantum physics, objects don’t just have locations and motions; roughly speaking, they have “states”, in which they have a combination of many locations and motions all at once.]* The basic obstacle is **entropy,** a measure of missing information. The air in your room has entropy, because although you may know its temperature and pressure, you do not know where every atom of air is; that’s missing information. It turns out that a black hole has entropy too, which means that our usual description of a black hole is intrinsically missing some crucial information. That prevents us from knowing precisely what its state is.

But surprisingly, in some circumstances **the quantum state of a wormhole can be sharply defined** — in which case its entropy is ** zero**. (Such a wormhole is not missing any information. But if you take either half of this wormhole and ignore the other half, you find a black hole. That black hole has entropy precisely because you’re ignoring all the information included in the other half of the wormhole!) To obtain and understand such a wormhole involves giving it two apparently different but actually interchangeable descriptions, one in terms of space-time and gravity, where the wormhole’s geometric shape is clear, and one in terms of what one might call a gravity-independent auxiliary quantum system, in which its quantum state is precisely defined.

One physical object, two quantum descriptions — one with gravity, one without; the first with more space dimensions than the latter. It’s like being able to read the same text in two completely different languages. It’s an example of what physicists often call “a duality.” (I’ve gone into more detail about this in recent posts here and here.)

This is the message of what goes by the mantra of “ER=EPR”, referring to two famous and apparently unrelated papers from 1935 by Einstein and Rosen, with the second having Podolsky as a co-author. ER=EPR asserts that two apparently different things,

- a tangible bridge across curved, extra-dimensional space between two regions, and
- a less tangible bridge, established with quantum entanglement between objects in the same two regions, without any use of gravity,

are **literally** the same thing.

Discovering that spacetime is related to quantum entanglement, and that ER and EPR involve the same issues, is somewhat like discovering that two poorly understood and partially readable texts in completely different languages are actually two translations of exactly the same document. It’s a Rosetta stone. Parts of the document can easily be read in one language, other parts in the second language; and putting them together, we find we can read more and more.

Similarly, the math of a wormhole (ER) looks completely different from the math of two quantum-entangled non-gravitational systems (EPR). But in particular cases, Juan Maldacena and Lenny Susskind argued, they are two languages describing the same object. We can combine these two partial views of this single object to learn more and more about it.

Moreover, because we’re using math, not text, we can go a step further. Even in regimes where we cannot “read the document” in either language, we can use computers to explore. Scientists can try to **simulate** the math of the entangled auxiliary quantum systems on a computer, ideally a quantum computer so that it keeps track of all quantum effects, to learn more about the wormhole’s behavior in regimes where we have no idea how it works — in regions where the quantum uncertainty principle affects space and time.

Even more remarkable would be to actually make — not merely simulate — this entangled pair of auxiliary quantum systems. **Then we would be closer to making a wormhole, with laws of nature different from ours and with its own gravity**, that connects on to our world. But that’s a long ways off, and not the story for the present.

A further breakthrough, beyond the original ER=EPR idea, came with the work of Gao, Jafferis and Wall (see also here and here) in which it was demonstrated for the first time that “traversable wormholes” — ones that can truly serve as bridges across which objects can be transported — do make physical sense. Astonishingly, they are related by duality to an important and exciting research area in quantum information, called “quantum teleportation.” That’s the process by which, using two entangled quantum systems, quantum information can be brought to one of the systems, destroyed in that system, and recreated in that second system some distance away. Again, don’t expect anyone to be teleporting your dog, but simple information and ultra-microscopic objects might be transportable.

Be warned though; **the teleportation only works if additional non-quantum information is traded between the two systems**. In the wormhole language, that means you can only get through the wormhole ** if information is also passed outside the wormhole** from the departure region to the arrival region. This makes it impossible to go someplace that you haven’t already been sending messages to, and to use any such wormhole as a shortcut — i.e., to get to your destination faster than could a near-light-speed spacecraft traveling outside the wormhole. Not only do portals to ultra-distant places remain science fiction, they now seem even more likely to stay that way.

Still, with these caveats, there’s still something amazing here: we can now imagine using the Rosetta stone of duality to simulate a traversable wormhole, and learn how it works in quantum gravity. That would be fantastic!

This is a dream, yet to be fulfilled. Computers are nowhere near being able to handle the questions we’d like to answer about the gravity we live with in our “four-dimensional space-time” (our familiar three space dimensions, plus one more for time). But by simplifying the problem in several steps (see the last figure of this post), we can at least hope to answer some early questions in a much simpler sort of wormhole in a simpler sort of gravity. This is what I’d prefer to call ** an artificially-simulated cartoon wormhole **— rather than a “baby” wormhole, because unlike a baby, it isn’t a small version of an adult, nor has it any hope of growing into one. It’s more like a stick figure. It’s in two-dimensional space-time — one space and one time. That’s a big simplification — there’s nothing like normal gravity there!

**But cartoons aren’t to be mocked.** Don’t underestimate them; cartoons are a powerful tool for educators everywhere, and subversive political cartoons have helped take down governments. For decades, famous physicists — Schwinger, ‘t Hooft, Gross and Neveu, Kogut and Susskind, and many more — have studied cartoon versions of real physics, especially ones in which our four space-time dimensions are replaced with just two. They’ve often learned interesting lessons from doing so, sometimes even profound ones.

*[Note: Stick figure physics also can be a very good description of real stick-figure systems, for example a one-dimensional chain of atoms inside a material.]*

I hasten to caution you that this technique does not **always** work. Not all of the lessons learned from stick-figure physics turn out to apply to the corresponding real-world problem. But this method has had enough success that we should take cartoon studies seriously.

This is why exploration of one-dimensional wormholes, and of some sort of auxiliary quantum problem to which they might be approximately related, may be worthwhile. And this is why it’s important to learn to simulate these auxiliary quantum systems on quantum computers, as was done in the paper that generated all the hype, based on proposals made in this paper and this one. Even if we can’t hope soon to understand how three-dimensional quantum space emerges from quantum entanglement, we can perhaps hope to learn more about one-dimensional quantum space, using quantum computer simulation. Maybe what we learn there would already teach us a deep and universal truth about quantum gravity, or at least suggest new ways to think about its subtleties.

The experiment done in the recent paper is a baby step in this direction. Others have attempted something along similar lines, but this is the first experiment that seems to have focused on the truly wormhole-like regime, and found some evidence for what was expected already of wormholes (from direct calculation and from classical computers…I’ll write about those details in a future post.) That seems like a real step forward. But let’s keep things in perspective. No new knowledge was created by this experiment; its achievements were technical and technological. It’s not a conceptual breakthrough. (I’m not alone in this view; Lenny Susskind, Dan Harlow and Scott Aaronson all expressed the same opinion in the New York Times and elsewhere.)

But nevertheless, this experiment represents a little arrow that points to a possible big future… not a future of a new Elon Musk, building wormholes for fun and profit, but one of a future Einstein, comprehending the quantum nature of spacetime itself.

]]>- -2 + 3 =
**+1**!!! Breakthrough!!!!!!!!!

whereas anyone who knew the details would have said

- -300 – 2 + 3 = -299 ? Cool bro, but…

In other words, it was a good day for fusion, but not nearly good enough.

To be fair to everyone, the scientists involved have made tremendous progress in the last few years; they weren’t even close to getting this much energy out until 2021. They’re 10 times ahead of where they were in 2019 and over 100 times ahead of where they were in 2010. If they can continue this progress and figure out how to get another 100 times as much fusion energy out **without requiring vastly more electricity**, then this all might start to be somewhat interesting.

But even then, it seems it’s going to be very tough to get anything resembling a power plant out of this fusion strategy. Experts seem to think the engineering challenges are immense. (Have any readers heard someone say otherwise?) Perhaps Tokomaks are still the way to go.

I’m annoyed, as I’m sure many of you are. I was myself too trusting, assuming that the politician-scientists who made the claims would be smart enough not to over-hype something that would get so much scrutiny. It’s the 21st century; you can’t come out and say something so undeservedly dramatic without the backlash being loud and swift. Instead they played the political spin game as though it was still the 1970s. I think they were hoping to convince Congress to keep their funding going (and because of an application of their work to nuclear weapons, they may succeed.) But when it comes to nuclear fusion as a solution to our energy/climate crisis — did they really think people wouldn’t quickly figure out they’d been duped? Seriously?

To quote one of the comments on my last post, from Blackstone, “It seems to me that this whole civilization desperately needs a reality check.” I completely agree. We’re so driven now by hype and click-bait that it’s almost impossible to separate the wheat from the chaff. Maybe at some point the people driving this international daily drama show will realize they’re doing serious harm. Clearly we’re not there yet.

But that’s what this blog is for, as are some others in a similar vein. Hopefully I won’t make too many mistakes like the one I made Tuesday, and when I make them, I’ll always fix them. Thank you to the many commenters who raised valid concerns; I know you’ll always keep me honest if I take a false step.

]]>Nuclear **fission** (the breaking of larger atomic nuclei into smaller pieces) was discovered in the 1930s, and used to generate energy in 1942. Work on fission in settings both uncontrolled (i.e. bombs) and controlled (ie. power plants) proceeded rapidly; bombs unfortunately were quickly designed and built during World War II, while useful power plants were already operating by 1951. Meanwhile work on fusion also proceeded rapidly; in the uncontrolled setting, the first bomb using fusion (triggered by a fission bomb!) was already made in 1951, and in a flash of a decade, huge numbers of hydrogen bombs filled the arsenals of superpowers large and small. But controlled fusion for power plants… Ah.

Had it been as easy to control fusion as it was to control fission, we’d have fusion plants everywhere; fossil fuels would be consigned only to certain forms of transportation, and the climate crisis would be far less serious than it is right now. But unfortunately, it has been 70 years of mostly bad news — tragic news, really, for the planet.

But finally we have a little glimmer of hope. On December 5th, somebody finally managed, without using a bomb, to get more fusion-generated energy out of an object than the energy they had to put into it.

[UPDATE: Not really. Though this was a success and a milestone, it wasn’t nearly as good as advertised. Yes, more energy came **out of the fusing material** than was put **into the fusing material**. But it took far more energy to make the necessary laser light in the first place — 300 megajoules of energy off the electricity grid, compared to a gain from the fusing material of about 1 megajoule. So overall it was still a big net loss, even though locally, at the fusing material, it was a net gain. See this link, in particular the third figure, which shows that the largest energy cost was electricity from the grid to run the lasers. In short, well, it’s still a good day for fusion, but we are even further from power plants than we were led to believe today.]

In the Sun and similar stars, fusion proceeds through several processes in which protons (the nuclei of the simplest form of hydrogen) are converted to neutrons and combine with other protons to form mainly helium nuclei (two protons and two neutrons). Other important nuclei are deuterium D (a version of hydrogen with a proton and neutron stuck together), tritium T (another version with a proton plus two neutrons — which is unstable, typically lasting about 12 years), and Helium-3 (two protons plus one neutron.)

Fusion is a fascinating process, because all four of the famous forces of nature are needed. *[The fifth, the Higgs force, plays no role, though as is so often the case, the Higgs field is secretly crucial.]* In a sense, it’s a poster child for our understanding of how the cosmos works. Consider sunshine:

- We need gravity to hold the Sun together, and to crush its center to the point that its temperature reaches well over ten million degrees.
- We need electromagnetism to produce the light that carries energy to the Sun’s surface and sunshine to Earth.
- We need the strong nuclear force to make protons and neutrons, and to combine them into other simple nuclei such as deuterium, tritium and helium.
- We need the weak nuclear force to convert the abundant protons into neutrons (along with a positron [i.e. an anti-electron] and a neutrino.)

How can we be sure this really happens inside the Sun? There are quite a few ways, but perhaps the most direct is that we observe the neutrinos, which (unlike everything else that’s made in the process) escape from the Sun’s core in vast numbers. Though very difficult to detect on Earth, they are occasionally observed. By now, studies of these neutrinos, as here by the Borexino experiment, are definitive. Everything checks out.

In the recent experiment on Earth, gravity’s role is a little more indirect — obviously we wouldn’t have a planet on which to live and laboratories in which to do experiments without it. But it’s electromagnetism which does the holding and crushing of the material. The role of the strong and weak nuclear forces is similar, though instead of starting with mostly protons, the method that made fusion this week uses the weak nuclear force long before the experiment to make the neutrons needed in deuterium and tritium. The actual moment of fusion involves the strong nuclear force, in which

- D + T –> He + n

i.e. one deuterium nucleus plus one tritium nucleus (a total of two protons and three neutrons) are recombined to make one helium nucleus and one neutron, which come out with more motion-energy than the initial D and T nuclei start with.

The breakthrough this week? Finally, after decades of promises and disappointments, workers at a US lab, Lawrence Livermore Laboratory in California, working at the National Ignition Facility, have gotten significantly more energy out of fusion than they put in. How this works is described by the lab here. The steps are: make a pellet stocked with D and T; fire up a set of lasers and amplify them to enormous power; aim them into a chamber containing the pellet, heating the chamber to millions of degrees and causing it to emit X-rays (high-energy photons); the blast of X-rays blows off the outer layer of the pellet, which *[action-reaction!]* causes the inner core of the pellet to greatly compress; in the high temperature and density of the pellet’s core, fusion spontaneously begins and heats the rest of the pellet, causing even more fusion.

Not as easy as it sounds. For a long time they’ve been getting a dud, or just a little fusion. But finally, the energy from fusion has exceeded the energy of the initial lasers by a substantial amount — 50%.

This one momentary success is far from a power plant. But you can’t make a power plant without first making power. So December 5th, eighty years and three days after fission’s first good day, was a good day for fusion on Earth, maybe the first one ever.

If this strategy for making fusion will ever lead to a power plant, this process will have to repeated over and over very rapidly, with the high-energy particles that are created along the way being directed somewhere where they can heat water and turn a steam turbine, from which electric current can be created as it is in many power plants. Leaving aside the major technical challenges, one should understand that this does not come without radioactive pollution; the walls of the container vessel in which the nuclear reactions take place, and other materials inside, will become radioactive over time, and will have to be disposed of with care, as with any radioactive waste. But it’s still vastly safer than a fission power plant, such as are widespread today. Why?

First, the waste from a fission plant is suitable for making nuclear weapons; it has to be not only buried safely but also guarded. Waste from a fusion plant, though still radioactive, is not useful for that purpose.

Second, if a fission plant malfunctions, its nuclear chain-reaction can start running away, getting hotter and hotter until the fuel melts, breaks through the vessel that contains it, and contaminates ground, air and water. By contrast, if a fusion plant malfunctions, its nuclear reactions just… stop.

And third, mining for uranium is bad for the environment (and uranium itself can be turned into a fuel for nuclear weapons.) Mining for hydrogen involves taking some water and passing electric current through it. Admittedly it’s a bit more complicated than that to get the deuterium and especially the tritium you need — the tritium be obtained from lithium, which does require mining — but still, less digging giant holes into mountains and contaminating groundwater with heavy metals.

Meanwhile, both forms of nuclear power have the advantage that they don’t dump loads of carbon into the atmosphere, and avoid the kind of oil spills we saw this week in Kansas.

So even though we are a long way from having nuclear fusion as a power source, and even though there will be some nuclear waste to deal with, there are good reasons to note this day. Someday we might look back on it as the beginning of a transformed economy, a cleaner atmosphere, and a saved planet.

]]>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!