Tag Archives: science communication

If That Measures the Quantum Vacuum, Anything Does

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Sabine Hossenfelder has gradually transitioned from critical written content about physics to YouTube videos, mostly short science news clips with the occasional longer piece. Luckily for us in the unable-to-listen-to-podcasts demographic, the transcripts of these videos are occasionally published on her organization’s Substack.

Unluckily, it feels like the short news format is leading to some lazy metaphors. There are stories science journalists sometimes tell because they’re easy and familiar, even if they don’t really make sense. Scientists often tell them too, for the same reason. But the more careful voices avoid them.

Hossenfelder has been that careful before, but one of her recent pieces falls short. The piece is titled “This Experiment Will Measure Nothing, But Very Precisely”.

The “nothing” in the title is the oft-mythologized quantum vacuum. The story goes that in quantum theory, empty space isn’t really empty. It’s full of “virtual” particles, that pop in and out of existence, jostling things around.

This…is not a good way to think about it. Really, it’s not. If you want to understand what’s going on physically, it’s best to think about measurements, and measurements involve particles: you can’t measure anything in pure empty space, you don’t have anything to measure with. Instead, every story you can tell about the “quantum vacuum” and virtual particles, you can tell about interactions between particles that actually exist.

(That post I link above, by the way, was partially inspired by a more careful post by Hossenfelder. She does know this stuff. She just doesn’t always use it.)

Let me tell the story Hossenfelder’s piece is telling, in a less silly way:

In the earliest physics classes, you learn that light does not affect other light. Shine two flashlight beams across each other, and they’ll pass right through. You can trace the rays of each source, independently, keeping track of how they travel and bounce around the room.

In quantum theory, that’s not quite true. Light can interact with light, through subtle quantum effects. This effect is tiny, so tiny it hasn’t been measured before. But with ingenious tricks involving tuning three different lasers in exactly the right way, a team of physicists in Dresden has figured out how it could be done.

And see, that’s already cool, right? It’s cool when people figure out how to see things that have never been seen before, full stop.

But the way Hossenfelder presents it, the cool thing about this is that they are “measuring nothing”. That they’re measuring “the quantum vacuum”, really precisely.

And I mean, you can say that, I guess. But it’s equally true of every subtle quantum effect.

In classical physics, electrons should have a very specific behavior in a magnetic field, called their magnetic moment. Quantum theory changes this: electrons have a slightly different magnetic moment, an anomalous magnetic moment. And people have measured this subtle effect: it’s famously the most precisely confirmed prediction in all of science.

That effect can equally well be described as an effect of the quantum vacuum. You can draw the same pictures, if you really want to, with virtual particles popping in and out of the vacuum. One effect (light bouncing off light) doesn’t exist at all in classical physics, while the other (electrons moving in a magnetic field) exists, but is subtly different. But both, in exactly the same sense, are “measurements of nothing”.

So if you really want to stick on the idea that, whenever you measure any subtle quantum effect, you measure “the quantum vacuum”…then we’re already doing that, all the time. Using it to popularize some stuff (say, this experiment) and not other stuff (the LHC is also measuring the quantum vacuum) is just inconsistent.

Better, in my view, to skip the silly talk about nothing. Talk about what we actually measure. It’s cool enough that way.

Cause and Effect and Stories

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You can think of cause and effect as the ultimate story. The world is filled with one damn thing happening after another, but to make sense of it we organize it into a narrative: this happened first, and it caused that, which caused that. We tie this to “what if” stories, stories about things that didn’t happen: if this hadn’t happened, then it wouldn’t have caused that, so that wouldn’t have happened.

We also tell stories about cause and effect. Physicists use cause and effect as a tool, a criterion to make sense of new theories: does this theory respect cause and effect, or not? And just like everything else in science, there is more than one story they tell about it.

As a physicist, how would you think about cause and effect?

The simplest, and most obvious requirement, is that effects should follow their causes. Cause and effect shouldn’t go backwards in time, the cause should come before the effect.

This all sounds sensible, until you remember that in physics “before” and “after” are relative. If you try to describe the order of two distant events, your description will be different than someone moving with a different velocity. You might think two things happened at the same time, while they think one happened first, and someone else thinks the other happened first.

You’d think this makes a total mess of cause and effect, but actually everything remains fine, as long nothing goes faster than the speed of light. If someone could travel between two events slower than the speed of light, then everybody will agree on their order, and so everyone can agree on which one caused the other. Cause and effect only get screwed up if they can happen faster than light.

(If the two events are two different times you observed something, then cause and effect will always be fine, since you yourself can’t go faster than the speed of light. So nobody will contradict what you observe, they just might interpret it differently.)

So if you want to make sure that your theory respects cause and effect, you’d better be sure that nothing goes faster than light. It turns out, this is not automatic! In general relativity, an effect called Shapiro time delay makes light take longer to pass a heavy object than to go through empty space. If you modify general relativity, you can accidentally get a theory with a Shapiro time advance, where light arrives sooner than it would through empty space. In such a theory, at least some observers will see effects happen before their causes!

Once you know how to check this, as a physicist, there are two kinds of stories you can tell. I’ve heard different people in the field tell both.

First, you can say that cause and effect should be a basic physical principle. Using this principle, you can derive other restrictions, demands on what properties matter and energy can have. You can carve away theories that violate these rules, making sure that we’re testing for theories that actually make sense.

On the other hand, there are a lot of stories about time travel. Time travel screws up cause and effect in a very direct way. When Harry Potter and Hermione travel back in time at the end of Harry Potter and the Prisoner of Azkaban, they cause the event that saves Harry’s life earlier in the book. Science fiction and fantasy are full of stories like this, and many of them are perfectly consistent. How can we be so sure that we don’t live in such a world?

The other type of story positions the physics of cause and effect as a search for evidence. We’re looking for physics that violates cause and effect, because if it exists, then on some small level it should be possible to travel back in time. By writing down the consequences of cause and effect, we get to describe what evidence we’d need to see it breaking down, and if we see it whole new possibilities open up.

These are both good stories! And like all other stories in science, they only capture part of what the scientists are up to. Some people stick to one or the other, some go between them, driven by the actual research, not the story itself. Like cause and effect itself, the story is just one way to describe the world around us.

Stories Backwards and Forwards

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You can always start with “once upon a time”…

I come up with tricks to make calculations in particle physics easier. That’s my one-sentence story, or my most common one. If I want to tell a longer story, I have more options.

Here’s one longer story:

I want to figure out what Nature is telling us. I want to take all the data we have access to that has anything to say about fundamental physics, every collider and gravitational wave telescope and ripple in the overall structure of the universe, and squeeze it as hard as I can until something comes out. I want to make sure we understand the implications of our current best theories as well as we can, to as high precision as we can, because I want to know whether they match what we see.

To do that, I am starting with a type of calculation I know how to do best. That’s both because I can make progress with it, and because it will be important for making these inferences, for testing our theories. I am following a hint in a theory that definitely does not describe the real world, one that is both simpler to work with and surprisingly complex, one that has a good track record, both for me and others, for advancing these calculations. And at the end of the day, I’ll make our ability to infer things from Nature that much better.

Here’s another:

Physicists, unknowing, proposed a kind of toy model, one often simpler to work with but not necessarily simpler to describe. Using this model, they pursued increasingly elaborate calculations, and time and time again, those calculations surprised them. The results were not random, not a disorderly mess of everything they could plausibly have gotten. Instead, they had structure, symmetries and patterns and mathematical properties that the physicists can’t seem to explain. If we can explain them, we will advance our knowledge of models and theories and ideas, geometry and combinatorics, learning more about the unexpected consequences of the rules we invent.

We can also help the physicists advance physics, of course. That’s a happy accident, but one that justifies the money and time, showing the rest of the world that understanding consequences of rules is still important and valuable.

These seem like very different stories, but they’re not so different. They change in order, physics then math or math then physics, backwards and forwards. By doing that, they change in emphasis, in where they’re putting glory and how they’re catching your attention. But at the end of the day, I’m investigating mathematical mysteries, and I’m advancing our ability to do precision physics.

(Maybe you think that my motivation must lie with one of these stories and not the other. One is “what I’m really doing”, the other is a lie made up for grant agencies.
Increasingly, I don’t think people work like that. If we are at heart stories, we’re retroactive stories. Our motivation day to day doesn’t follow one neat story or another. We move forward, we maybe have deep values underneath, but our accounts of “why” can and will change depending on context. We’re human, and thus as messy as that word should entail.)

I can tell more than two stories if I want to. I won’t here. But this is largely what I’m working on at the moment. In applying for grants, I need to get the details right, to sprinkle the right references and the right scientific arguments, but the broad story is equally important. I keep shuffling that story, a pile of not-quite-literal index cards, finding different orders and seeing how they sound, imagining my audience and thinking about what stories would work for them.

Small Shifts for Specificity

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Cosmologists are annoyed at a recent spate of news articles claiming the universe is 26.7 billion years old (rather than 13.8 billion as based on the current best measurements). To some of the science-reading public, the news sounds like a confirmation of hints they’d already heard: about an ancient “Methuselah” star that seemed to be older than the universe (later estimates put it younger), and recent observations from the James Webb Space Telescope of early galaxies that look older than they ought.

“The news doesn’t come from a telescope, though, or a new observation of the sky. Instead, it comes from this press release from the University of Ottawa: “Reinventing cosmology: uOttawa research puts age of universe at 26.7 — not 13.7 — billion years”.

(If you look, you’ll find many websites copying this press release almost word-for-word. This is pretty common in science news, where some websites simply aggregate press releases and others base most of their science news on them rather than paying enough for actual journalism.)

The press release, in turn, is talking about a theory, not an observation. The theorist, Rajendra Gupta, was motivated by examples like the early galaxies observed by JWST and the Methuselah star. Since the 13.8 billion year age of the universe is based on a mathematical model, he tried to find a different mathematical model that led to an older universe. Eventually, by hypothesizing what seems like every unproven physics effect he could think of, he found one that gives a different estimate, 26.7 billion. He probably wasn’t the first person to do this, because coming up with different models to explain odd observations is a standard thing cosmologists do all the time, and until one of the models is shown to explain a wider range of observations (because our best theories explain a lot, so they’re hard to replace), they’re just treated as speculation, not newsworthy science.

This is a pretty clear case of hype, and as such most of the discussion has been about what went wrong. Should we blame the theorist? The university? The journalists? Elon Musk?

Rather than blame, I think it’s more productive to offer advice. And in this situation, the person I think could use some advice is the person who wrote the press release.

So suppose you work for a university, writing their press releases. One day, you hear that one of your professors has done something very cool, something worthy of a press release: they’ve found a new estimate for the age of the universe. What do you do?

One thing you absolutely shouldn’t do is question the science. That just isn’t your job, and even if it were you don’t have the expertise to do that. Anyone who’s hoping that you will only write articles about good science and not bad science is being unrealistic, that’s just not an option.

If you can’t be more accurate, though, you can still be more precise. You can write your article, and in particular your headline, so that you express what you do know as clearly and specifically as possible.

(I’m assuming here you write your own headlines. This is not normal in journalism, where most headlines are written by an editor, not by the writer of a piece. But university press offices are small enough that I’m assuming, perhaps incorrectly, that you can choose how to title your piece.)

Let’s take a look at the title, “Reinventing cosmology: uOttawa research puts age of universe at 26.7 — not 13.7 — billion years”, and see if we can make some small changes to improve it.

One very general word in that title is “research”. Lots of people do research: astronomers do research when they collect observations, theorists do research when they make new models. If you say “research”, some people will think you’re reporting a new observation, a new measurement that gives a radically different age for the universe.

But you know that’s not true, it’s not what the scientist you’re talking to is telling you. So to avoid the misunderstanding, you can get a bit more specific, and replace the word “research” with a more precise one: “Reinventing cosmology: uOttawa theory puts age of universe at 26.7 — not 13.7 — billion years”.

“Theory” is just as familiar a word as “research”. You won’t lose clicks, you won’t confuse people. But now, you’ve closed off a big potential misunderstanding. By a small shift, you’ve gotten a lot clearer. And you didn’t need to question the science to do it!

You can do more small shifts, if you understand a bit more of the science. “Puts” is kind of ambiguous: a theory could put an age somewhere because it computes it from first principles, or because it dialed some parameter to get there. Here, the theory was intentionally chosen to give an older universe, so the title should hint at this in some way. Instead of “puts”, then, you can use “allows”: “Reinventing cosmology: uOttawa theory allows age of universe to be 26.7 — not 13.7 — billion years”.

These kinds of little tricks can be very helpful. If you’re trying to avoid being misunderstood, then it’s good to be as specific as you can, given what you understand. If you do it carefully, you don’t have to question your scientists’ ideas or downplay their contributions. You can do your job, promote your scientists, and still contribute to responsible journalism.

Solutions and Solutions

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The best misunderstandings are detective stories. You can notice when someone is confused, but digging up why can take some work. If you manage, though, you learn much more than just how to correct the misunderstanding. You learn something about the words you use, and the assumptions you make when using them.

Recently, someone was telling me about a book they’d read on Karl Schwarzschild. Schwarzschild is famous for discovering the equations that describe black holes, based on Einstein’s theory of gravitation. To make the story more dramatic, he did so only shortly before dying from a disease he caught fighting in the first World War. But this person had the impression that Schwarzschild had done even more. According to this person, the book said that Schwarzschild had done something to prove Einstein’s theory, or to complete it.

Another Schwarzschild accomplishment: that mustache

At first, I thought the book this person had read was wrong. But after some investigation, I figured out what happened.

The book said that Schwarzschild had found the first exact solution to Einstein’s equations. That’s true, and as a physicist I know precisely what it means. But I now realize that the average person does not.

In school, the first equations you solve are algebraic, x+y=z. Some equations, like x^2=4, have solutions. Others, like x^2=-4, seem not to, until you learn about new types of numbers that solve them. Either way, you get used to equations being like a kind of puzzle, a question for which you need to find an answer.

If you’re thinking of equations like that, then it probably sounds like Schwarzschild “solved the puzzle”. If Schwarzschild found the first solution to Einstein’s equation, that means that Einstein did not. That makes it sound like Einstein’s work was incomplete, that he had asked the right question but didn’t yet know the right answer.

Einstein’s equations aren’t algebraic equations, though. They’re differential equations. Instead of equations for a variable, they’re equations for a mathematical function, a formula that, in this case, describes the curvature of space and time.

Scientists in many fields use differential equations, but they use them in different ways. If you’re a chemist or a biologist, it might be that you’re most used to differential equations with simple solutions, like sines, cosines, or exponentials. You learn how to solve these equations, and they feel a bit like the algebraic ones: you have a puzzle, and then you solve the puzzle.

Other fields, though, have tougher differential equations. If you’re a physicist or an engineer, you’ve likely met differential equations that you can’t treat in this way. If you’re dealing with fluid mechanics, or general relativity, or even just Newtonian gravity in an odd situation, you can’t usually solve the problem by writing down known functions like sines and cosines.

That doesn’t mean you can’t solve the problem at all, though!

Even if you can’t write down a solution to a differential equation with sines and cosines, a solution can still exist. (In some cases, we can even prove a solution exists!) It just won’t be written in terms of sines and cosines, or other functions you’ve learned in school. Instead, the solution will involve some strange functions, functions no-one has heard of before.

If you want, you can make up names for those functions. But unless you’re going to classify them in a useful way, there’s not much point. Instead, you work with these functions by approximation. You calculate them in a way that doesn’t give you the full answer, but that does let you estimate how close you are. That’s good enough to give you numbers, which in turn is good enough to compare to experiments. With just an approximate solution, like this, Einstein could check if his equations described the orbit of Mercury.

Once you know you can find these approximate solutions, you have a different perspective on equations. An equation isn’t just a mysterious puzzle. If you can approximate the solution, then you already know how to solve that puzzle. So we wouldn’t think of Einstein’s theory as incomplete because he was only able to find approximate solutions: for a theory as complicated as Einstein’s, that’s perfectly normal. Most of the time, that’s all we need.

But it’s still pretty cool when you don’t have to do this. Sometimes, we can not just approximate, but actually “write down” the solution, either using known functions or well-classified new ones. We call a solution like that an analytic solution, or an exact solution.

That’s what Schwarzschild managed. These kinds of exact solutions often only work in special situations, and Schwarzschild’s is no exception. His Schwarzschild solution works for matter in a special situation, arranged in a perfect sphere. If matter happened to be arranged in that way, then the shape of space and time would be exactly as Schwarzschild described it.

That’s actually pretty cool! Einstein’s equations are complicated enough that no-one was sure that there were any solutions like that, even in very special situations. Einstein expected it would be a long time until they could do anything except approximate solutions.

(If Schwarzschild’s solution only describes matter arranged in a perfect sphere, why do we think it describes real black holes? This took later work, by people like Roger Penrose, who figured out that matter compressed far enough will always find a solution like Schwarzschild’s.)

Schwarzschild intended to describe stars with his solution, or at least a kind of imaginary perfect star. What he found was indeed a good approximation to real stars, but also the possibility that a star shoved into a sufficiently small space would become something weird and new, something we would come to describe as a black hole. That’s a pretty impressive accomplishment, especially for someone on the front lines of World War One. And if you know the difference between an exact solution and an approximate one, you have some idea of what kind of accomplishment that is.

Traveling This Week

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I’m traveling this week, so this will just be a short post. This isn’t a scientific trip exactly: I’m in Poland, at an event connected to the 550th anniversary of the birth of Copernicus.

Not this one, but they do have nice posters!

Part of this event involved visiting the Copernicus Science Center, the local children’s science museum. The place was sold out completely. For any tired science communicators, I recommend going to a sold-out science museum: the sheer enthusiasm you’ll find there is balm for the most jaded soul.

Whatever Happened to the Nonsense Merchants?

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I was recently reminded that Michio Kaku exists.

In the past, Michio Kaku made important contributions to string theory, but he’s best known for what could charitably be called science popularization. He’s an excited promoter of physics and technology, but that excitement often strays into inaccuracy. Pretty much every time I’ve heard him mentioned, it’s for some wildly overenthusiastic statement about physics that, rather than just being simplified for a general audience, is generally flat-out wrong, conflating a bunch of different developments in a way that makes zero actual sense.

Michio Kaku isn’t unique in this. There’s a whole industry in making nonsense statements about science, overenthusiastic books and videos hinting at science fiction or mysticism. Deepak Chopra is a famous figure from deeper on this spectrum, known for peddling loosely quantum-flavored spirituality.

There was a time I was worried about this kind of thing. Super-popular misinformation is the bogeyman of the science popularizer, the worry that for every nice, careful explanation we give, someone else will give a hundred explanations that are way more exciting and total baloney. Somehow, though, I hear less and less from these people over time, and thus worry less and less about them.

Should I be worried more? I’m not sure.

Are these people less popular than they used to be? Is that why I’m hearing less about them? Possibly, but I’d guess not. Michio Kaku has eight hundred thousand twitter followers. Deepak Chopra has three million. On the other hand, the usually-careful Brian Greene has a million followers, and Neil deGrasse Tyson, where the worst I’ve heard is that he can be superficial, has fourteen million.

(But then in practice, I’m more likely to reflect on content with even smaller audiences.)

If misinformation is this popular, shouldn’t I be doing more to combat it?

Popular misinformation is also going to be popular among critics. For every big-time nonsense merchant, there are dozens of people breaking down and debunking every false statement they say, every piece of hype they release. Often, these people will end up saying the same kinds of things over and over again.

If I can be useful, I don’t think it will be by saying the same thing over and over again. I come up with new metaphors, new descriptions, new explanations. I clarify things others haven’t clarified, I clear up misinformation others haven’t addressed. That feels more useful to me, especially in a world where others are already countering the big problems. I write, and writing lasts, and can be used again and again when needed. I don’t need to keep up with the Kakus and Chopras of the world to do that.

(Which doesn’t imply I’ll never address anything one of those people says…but if I do, it will be because I have something new to say back!)

Talking and Teaching

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Someone recently shared with me an article written by David Mermin in 1992 about physics talks. Some aspects are dated (our slides are no longer sheets of plastic, and I don’t think anyone writing an article like that today would feel the need to put it in the mouth of a fictional professor (which is a shame honestly)), but most of it still holds true. I particularly recognized the self-doubt of being a young physicist sitting in a talk and thinking “I’m supposed to enjoy this?”

Mermin’s basic point is to keep things as light as possible. You want to convey motivation more than content, and background more than your own contributions. Slides should be sparse, both because people won’t be able to see everything but also because people can get frustrated “reading ahead” of what you say.

Mermin’s suggestion that people read from a prepared text was probably good advice for him, but maybe not for others. It can be good if you can write like he does, but I don’t think most people’s writing is that much better than what they say in talks (you can judge this by reading peoples’ papers!) Some are much clearer speaking impromptu. I agree with him that in practice people end up just reading from their slides, which indeed is bad, but reading from a normal physics paper isn’t any better.

I also don’t completely agree with him about the value of speech over text. Yes, putting text on your slides means people can read ahead (unless you hide some of the text, which is easier to do these days than in the days of overhead transparencies). But just saying things means that if someone’s attention lapses for just a moment, they’ll be lost. Unless you repeat yourself a lot (good practice in any case), you should avoid just saying anything you need your audience to remember, and make sure they can read it somewhere if they need it as well.

That said, “if they need it” is doing a lot of work here, and this is where I agree again with Mermin. Fundamentally, you don’t need to convey everything you think you do. (I don’t usually need to convey everything I think I do!) It’s a lesson I’ve been learning this year from pedagogy courses, a message they try to instill in everyone who teaches at the university. If you want to really convey something well, then you just can’t convey that much. You need to focus, pick a few things and try to get them across, and structure the rest of what you say to reinforce those things. When teaching, or when speaking, less is more.

The Temptation of Spinoffs

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Read an argument for a big scientific project, and you’ll inevitably hear mention of spinoffs. Whether it’s NASA bringing up velcro or CERN and the World-Wide Web, scientists love to bring up times when a project led to some unrelated technology that improved peoples’ lives.

Just as inevitably as they show up, though, these arguments face criticism. Advocates of the projects argue that promoting spinoffs misses the point, training the public to think about science in terms of unrelated near-term gadgets rather than the actual point of the experiments. They think promoters should focus on the scientific end-goals, justifying them either in terms of benefit to humanity or as a broader, “it makes the country worth defending” human goal. It’s a perspective that shows up in education too, where even when students ask “when will I ever use this in real life?” it’s not clear that’s really what they mean.

On the other side, opponents of the projects will point out that the spinoffs aren’t good enough to justify the science. Some, like velcro, weren’t actually spinoffs to begin with. Others seem like tiny benefits compared to the vast cost of the scientific projects, or like things that would have been much easier to get with funding that was actually dedicated to achieving the spinoff.

With all these downsides, why do people keep bringing spinoffs up? Are they just a cynical attempt to confuse people?

I think there’s something less cynical going on here. Things make a bit more sense when you listen to what the scientists say, not to the public, but when talking to scientists in other disciplines.

Scientists speaking to fellow scientists still mention spinoffs, but they mention scientific spinoffs. The speaker in a talk I saw recently pointed out that the LHC doesn’t just help with particle physics: by exploring the behavior of collisions of high-energy atomic nuclei it provides essential information for astrophysicists understanding neutron stars and cosmologists studying the early universe. When these experiments study situations we can’t model well, they improve the approximations we use to describe those situations in other contexts. By knowing more, we know more. Knowledge builds on knowledge, and the more we know about the world the more we can do, often in surprising and un-planned ways.

I think that when scientists promote spinoffs to the public, they’re trying to convey this same logic. Like promoting an improved understanding of stars to astrophysicists, they’re modeling the public as “consumer goods scientists” and trying to pick out applications they’d find interesting.

Knowing more does help us know more, that much is true. And eventually that knowledge can translate to improving people’s lives. But in a public debate, people aren’t looking for these kinds of principles, let alone a scientific “I’ll scratch your back if you’ll scratch mine”. They’re looking for something like a cost-benefit analysis, “why are we doing this when we could do that?”

(This is not to say that most public debates involve especially good cost-benefit analysis. Just that it is, in the end, what people are trying to do.)

Simply listing spinoffs doesn’t really get at this. The spinoffs tend to be either small enough that they don’t really argue the point (velcro, even if NASA had invented it, could probably have been more cheaply found without a space program), or big but extremely unpredictable (it’s not like we’re going to invent another world-wide web).

Focusing on the actual end-products of the science should do a bit better. That can include “scientific spinoffs”, if not the “consumer goods spinoffs”. Those collisions of heavy nuclei change our understanding of how we model complex systems. That has applications in many areas of science, from how we model stars to materials to populations, and those applications in turn could radically improve people’s lives.

Or, well, they could not. Basic science is very hard to do cost-benefit analyses with. It’s the fabled explore/exploit dilemma, whether to keep trying to learn more or focus on building on what you have. If you don’t know what’s out there, if you don’t know what you don’t know, then you can’t really solve that dilemma.

So I get the temptation of reaching to spinoffs, of pointing to something concrete in everyday life and saying “science did that!” Science does radically improve people’s lives, but it doesn’t always do it especially quickly. You want to teach people that knowledge leads to knowledge, and you try to communicate it the way you would to other scientists, by saying how your knowledge and theirs intersect. But if you want to justify science to the public, you want something with at least the flavor of cost-benefit analysis. And you’ll get more mileage out of that if you think about where the science itself can go, than if you focus on the consumer goods it accidentally spins off along the way.

The Problem of Quantum Gravity Is the Problem of High-Energy (Density) Quantum Gravity

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I’ve said something like this before, but here’s another way to say it.

The problem of quantum gravity is one of the most famous problems in physics. You’ve probably heard someone say that quantum mechanics and general relativity are fundamentally incompatible. Most likely, this was narrated over pictures of a foaming, fluctuating grid of space-time. Based on that, you might think that all we have to do to solve this problem is to measure some quantum property of gravity. Maybe we could make a superposition of two different gravitational fields, see what happens, and solve the problem that way.

I mean, we could do that, some people are trying to. But it won’t solve the problem. That’s because the problem of quantum gravity isn’t just the problem of quantum gravity. It’s the problem of high-energy quantum gravity.

Merging quantum mechanics and general relativity is actually pretty easy. General relativity is a big conceptual leap, certainly, a theory in which gravity is really just the shape of space-time. At the same time, though, it’s also a field theory, the same general type of theory as electromagnetism. It’s a weirder field theory than electromagnetism, to be sure, one with deeper implications. But if we want to describe low energies, and weak gravitational fields, then we can treat it just like any other field theory. We know how to write down some pretty reasonable-looking equations, we know how to do some basic calculations with them. This part is just not that scary.

The scary part happens later. The theory we get from these reasonable-looking equations continues to look reasonable for a while. It gives formulas for the probability of things happening: things like gravitational waves bouncing off each other, as they travel through space. The problem comes when those waves have very high energy, and the nice reasonable probability formula now says that the probability is greater than one.

For those of you who haven’t taken a math class in a while, probabilities greater than one don’t make sense. A probability of one is a certainty, something guaranteed to happen. A probability greater than one isn’t more certain than certain, it’s just nonsense.

So we know something needs to change, we know we need a new theory. But we only know we need that theory when the energy is very high: when it’s the Planck energy. Before then, we might still have a different theory, but we might not: it’s not a “problem” yet.

Now, a few of you understand this part, but still have a misunderstanding. The Planck energy seems high for particle physics, but it isn’t high in an absolute sense: it’s about the energy in a tank of gasoline. Does that mean that all we have to do to measure quantum gravity is to make a quantum state out of your car?

Again, no. That’s because the problem of quantum gravity isn’t just the problem of high-energy quantum gravity either.

Energy seems objective, but it’s not. It’s subjective, or more specifically, relative. Due to special relativity, observers moving at different speeds observe different energies. Because of that, high energy alone can’t be the requirement: it isn’t something either general relativity or quantum field theory can “care about” by itself.

Instead, the real thing that matters is something that’s invariant under special relativity. This is hard to define in general terms, but it’s best to think of it as a requirement for not energy, but energy density.

(For the experts: I’m justifying this phrasing in part because of how you can interpret the quantity appearing in energy conditions as the energy density measured by an observer. This still isn’t the correct way to put it, but I can’t think of a better way that would be understandable to a non-technical reader. If you have one, let me know!)

Why do we need quantum gravity to fully understand black holes? Not just because they have a lot of mass, but because they have a lot of mass concentrated in a small area, a high energy density. Ditto for the Big Bang, when the whole universe had a very large energy density. Particle colliders are useful not just because they give particles high energy, but because they give particles high energy and put them close together, creating a situation with very high energy density.

Once you understand this, you can use it to think about whether some experiment or observation will help with the problem of quantum gravity. Does the experiment involve very high energy density, much higher than anything we can do in a particle collider right now? Is that telescope looking at something created in conditions of very high energy density, or just something nearby?

It’s not impossible for an experiment that doesn’t meet these conditions to find something. Whatever the correct quantum gravity theory is, it might be different from our current theories in a more dramatic way, one that’s easier to measure. But the only guarantee, the only situation where we know we need a new theory, is for very high energy density.