Quote: . . . the Higgs field exhibits the most inelegant of the known laws governing fields and particles. There’s an amusing tendency for those who tout beauty to ignore this, as though it were an inconvenient family member, and to focus instead on Einstein’s elegant theory of gravity. Yet even that theory has its issues.
Endnote: Einstein’s theory of gravity is amazingly elegant as long as one ignores the puzzle of “dark energy,” which would have been easier to do had it been exactly zero, and as long as gravity is a very weak force, as its weakness leads to extremely simple equations. In string theory, Einstein’s equations become much more complex, and the elegant simplicity of the math shifts to the level of the strings themselves . . . perhaps.
I’ll expound below upon the second bullet point, hoping to draw attention to general questions concerning aesthetics in theoretical physics.
More about tidal forces today (see also yesterday’s post) and the conceptual point underlying Earth’s ocean tides.
(Quote) Because gravity dwindles at greater distances, the Moon’s pull is stronger on the near side of the Earth and weaker on the far side than it is on the Earth’s center. This uneven pull stretches our planet’s oceans slightly, resulting in a small bulge of water, not much taller than a human, both on the Earth’s side facing the Moon and on the opposite side, too.
(Endnote) To explain why gravity leads to a water bulge on both sides of the Earth is too complex for a footnote, and I’d rather not repeat the most commonly heard explanations, which are misleading. One can see a hint of the cause as follows: if one drops a water balloon in constant gravity, it will fall as a sphere, whereas if it is pulled more strongly at the bottom than at the top, it will stretch into an oval as it falls.
Here I’ll explain this last observation more carefully.
[This is a tricky one… it’s easy to make confusing statements about Einstein’s theory of gravity (general relativity), and so I am especially hopeful of getting readers’ feedback on this subtle issue, to make sure what follows is 100% clear and correctly stated.]
(Quote) On Earth’s surface, we are roughly 4,000 miles from Earth’s center. But if you ascended another 22,000 miles, where you’d find the GOES weather satellites that monitor Earth’s weather patterns, you’d find your weight (but not your mass!) reduced to one-fortieth of what it is on Earth… And if you traveled out into deep space, far from any large object, you’d weigh virtually nothing. Yet all the while, your body’s mass—the difficulty I would face if I tried to speed you up or slow you down—would never change.
(Endnote) Confusingly, astronauts orbiting Earth inside nearby space stations appear to float as though weightless. From Newton’s perspective, they are not truly weightless; if they were, they’d coast, leaving the Earth’s vicinity and moving rapidly into deep space. Instead, they and their spaceship are pulled by gravity into a common orbit around the Earth. Since they travel on the same path as their container and as the camera which films them, they seem and feel weightless. (This subtle issue is turned on its head in Einstein’s view of gravity.)
Astronauts in a space station seem to float, as though they are weightless. Are they truly weightless? Or are they only apparently weightless?
The same issues arise for people in a freely falling elevator, accelerating downward with ever greater speed. They will feel weightless, too. But are they?
Newton would have said they are apparently weightless, subject to gravity but all falling together along with their vehicle. A naive (but instructive!) reading of Einstein might lead us to say that they are truly weightless… that the gravity that Newton claims is present is a pure illusion, a fictitious force. But a precise Einsteinian would say they are almost but not quite weightless — and the lack of perfect weightlessness is a clue, a smoking gun in fact, that they are indeed subject to gravity.
The press is full of excitement today at the news that anti-matter — hydrogen anti-atoms, specifically, made from positrons and anti-protons instead of electrons and protons — falls down rather than rising up. This has been shown in the ALPHA experiment at CERN. But no theoretical physicist is surprised. Today I’ll explain one of many reasons that no one in the halls of theoretical physics even blinked.
One basic point is that “anti-particle” is not a category but a relationship. We do not say “electrons are particles” and “positrons are anti-particles”, nor do we say “quarks are particles” and “anti-quarks are anti-particles.” Such statements would be inconsistent. Instead we say “quarks and anti-quarks are each others’ anti-particles.” (It’s like the term “opponent” in a football match.) That’s because some particles are their own anti-particles, including photons. If we tried to divide all the types of particles into two categories, it wouldn’t be clear where photons would go; we couldn’t say either that they are particles or that they are anti-particles.
“Anti-particle” is a relationship, exchanging electrons with positrons and leaving photons unchanged. It is not a category; there are no objects that can be said to be “antiparticles”. (If there were, would photons be particles or would they be anti-particles?)
Because of this, we can’t hope that all the types of particles separate into two groups, particles which fall and anti-particle which rise. At best, we would have to guess what would happen to particles that are their own anti-particles. Fortunately, this is easy. There is such a thing as a positronium atom, an exotic atom made from an electron and positron co-orbiting one other. A positronium atom is its own anti-particle; if we flip every particle for its anti-particle, the positronium atom’s electron and positron simply switch places. If indeed gravity pulls down on electrons and pushes up by the same amount on positrons, then gravity’s pull on a positronium atom would cancel. This atom would neither rise nor fall; it would float, feeling no net gravity.
This example would then lead us to expect that particles that are their own anti-particles will float. The logic would apply to photons; they would feel no gravity.
Electrons and quarks make up atoms and are known to fall. If the positrons and anti-quarks that make up anti-atoms were to rise instead, then positronium atoms would float. This would imply that photons float too. But experiments have shown for a century that photons fall.
This would be a consistent picture. But experimentally, it is false: photons do feel gravity. The Sun bends the path of light, a fact that made Einstein famous in 1919, and an object’s strong gravity can create a gravitational lens that completely distorts the appearances of objects behind it. Photons can even orbit black holes. So experiment would force us to accept the picture shown below, if we want positrons to rise. Unfortunately, it is logically inconsistent.
Since photons fall too, we would have to believe either that positronium floats even though photons fall, or that positrons rise even though positronium falls. Neither makes any sense either conceptually or mathematically.
The only consistent picture, then, is that everything falls. Are there any loopholes in this argument? Sure; perhaps the gravity of the Earth, made of atoms, causes electrons and quarks to fall rapidly and causes positrons and anti-quarks to rise slowly, so that positronium still falls, just more gently than ordinary atoms do. (The reverse would be true around a planet made of anti-atoms.) This gives us many more possibilities to consider, and we have to get into more complex questions of what experiment has and hasn’t excluded.
But we would still face another serious problem, because there are anti-quarks inside of protons. (One line of evidence for this is shown here.) If quarks and anti-quarks, which have the same inertial mass (the type of mass that determines how they change speed when pushed) had different gravitational mass (which determines how gravity affects them), then protons and neutrons, too, would not have equal inertial and gravitational mass. [The many gluons inside the protons and neutrons could make this even worse.] Since electrons do have equal inertial and gravitational mass, protons and neutrons would then fall at a different rate than electrons do. The consequence would be that different atoms would fall at slightly different rates. High precision experiments clearly say otherwise. This poses additional obstructions to the idea that anti-quarks (and the anti-protons and anti-neutrons that contain them) could rise in Earth’s gravity.
At best, when it comes to mass and gravity, existing experiments only allow for minor differences between atoms and anti-atoms. To look for subtle effects of any such differences is one of the real, long-term goals of the ALPHA experiment. What they’ve done so far is a neat experimental coup, but despite the headlines, it does not change our basic knowledge of anti-particles in general or of anti-atoms in particular. For that, we have a few years to wait.
Today a reader asked me “Out of the quantum fields which have mass, do any of them also have weight?” I thought other readers would be interested in my answer, so I’m putting it here. (Some of what is discussed below is covered in greater detail in my upcoming book.)
Before we start, we need to rephrase the question, because fields do not have mass.
Once we clear away the hype (see the previous posts 1, 2, 3, 4), and realize that no one is doing anything as potentially dangerous as making real wormholes (ones you could actually fall into) in a lab, or studying how to send dogs across the galaxy, we are left with a question. Why bother to do wormhole research at all?
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.
How Do We Study Black Holes, and Why?
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.
Why Wormholes?
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.
The Power of Duality: A Rosetta Stone for Quantum Gravity
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.
An conceptual illustration of the proposal that two perfectly entangled quantum systems (EPR) are equivalent to a wormhole connecting the locations of those systems (ER), and represent two languages for describing exactly the same thing. The wormhole is empty; the slabs shown merely indicate how distances are shrinking as one proceeds to the wormhole’s midpoint. Not shown is that the wormhole changes shape over time; for the situation in this picture, this wormhole is “non-traversable”, because there’s insufficient time to cross from one side of the bridge to the other before it shrinks down to nothing.
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.
From ER=EPR to Traversable Wormholes
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!
The Dream of Simulating Quantum Gravity
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! [Worse, we don’t have an exact duality in that case; the auxiliary quantum system we need isn’t really the same “text” as the wormhole. These are two systems, not one, with a limited but useful overlap.]
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.
A wormhole! What an amazing concept — a secret tunnel that connects two different regions of space! Could real ones exist? Could we — or our dogs — travel through them, and visit other galaxies billions of light years away, and come back to tell everyone all about it?
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!
I’ve been trying to train our dog, Phoebe, to fetch a ball through a wormhole. She seems eager but nervous.
What’s the problem?
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!
This post is a continuation of the previous one, which you should read first…
Now, what exactly are these wormholes that certain physicists claim to be trying to make or, at least, simulate? In this post I’ll explain what the scientists did to bring the problem within reach of our still-crude quantum computers. [I am indebted to Juan Maldacena, Daniel Jafferis and Brian Swingle for conversations that improved my understanding.]
An important point from last post: a field theory with quarks and gluons, such as we find in the real world or such as we might find in all sorts of imaginary worlds, is related by the Maldacena conjecture to strings (including quantum gravity) moving around in more dimensions than the three we’re used to. One of these dimensions, the “radial dimension”, is particularly important. As in the previous post, it will play a central role here.
Einstein-Rosen Bridge (ER) vs. Einstein-Podolsky-Rosen Entanglement (EPR)
It’s too bad that Einstein didn’t live long enough to learn that two of his famous but apparently unrelated papers actually describe the same thing, at least in the context of Maldacena’s conjecture. As Maldacena and Lenny Susskind explored in this paper, the Maldacena conjecture suggests that ER is the same as EPR, at least in some situations.
We begin with two identical black holes in the context of a string theory on the same curved space that appears in the Maldacena conjecture. These two black holes can be joined at the hip — well, at the horizon, really — in such a way as to form a bridge. It is not really a bridge in spacetime in the way you might imagine a wormhole to be, in the sense that you can’t cross the bridge; even if you move at the speed of light, the bridge will collapse before you get to the other side. Such is the simplest Einstein-Rosen bridge — a non-traversable wormhole.
What, according to the Maldacena conjecture, is this bridge from the point of view of an equivalent field theory setting? The answer is almost fixed by the symmetries of the problem. Take two identical field theories that would each, separately, be identical to one of the two black holes in the corresponding string theory. These two theories do not affect each other in any way; their particles move around in separate universes, never interacting. Despite this, we can link them together, forming a metaphorical bridge, in the most quantum sense you can imagine — we entangle them as much as we can. What does this mean?
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.
Einstein’s relativity. Everybody’s heard of it, many have read about it, a few have learned some of it. Journalists love to write about it. It’s part of our culture; it’s always in the air, and has been for over a century.
Most of what’s in the air, though, is in the form of sound bites, partly true but often misleading. Since Einstein’s view of relativity (even more than Galileo’s earlier one) is inherently confusing, the sound bites turn a maze into a muddled morass.
For example, take the famous quip: “Nothing can go faster than the speed of light.” (The speed of light is denoted “c“, and is better described as the “cosmic speed limit”.) This quip is true, and it is false, because the word “nothing” is ambiguous, and so is the phrase “go faster”.
