Monthly Archives: December 2014

Merry Newtonmas!

Yesterday, people around the globe celebrated the birth of someone whose new perspective and radical ideas changed history, perhaps more than any other.

I’m referring, of course, to Isaac Newton.

Ho ho ho!

Born on December 25, 1642, Newton is justly famed as one of history’s greatest scientists. By relating gravity on Earth to the force that holds the planets in orbit, Newton arguably created physics as we know it.

However, like many prominent scientists, Newton’s greatness was not so much in what he discovered as how he discovered it. Others had already had similar ideas about gravity. Robert Hooke in particular had written to Newton mentioning a law much like the one Newton eventually wrote down, leading Hooke to accuse Newton of plagiarism.

Newton’s great accomplishment was not merely proposing his law of gravitation, but justifying it, in a way that no-one had ever done before. When others (Hooke for example) had proposed similar laws, they were looking for a law that perfectly described the motion of the planets. Kepler had already proposed ellipse-shaped orbits, but it was clear by Newton and Hooke’s time that such orbits did not fully describe the motion of the planets. Hooke and others hoped that if some sufficiently skilled mathematician started with the correct laws, they could predict the planets’ motions with complete accuracy.

The genius of Newton was in attacking this problem from a different direction. In particular, Newton showed that his laws of gravitation do result in (incorrect) ellipses…provided that there was only one planet.

With multiple planets, things become much more complicated. Even just two planets orbiting a single star is so difficult a problem that it’s impossible to write down an exact solution.

Sensibly, Newton didn’t try to write down an exact solution. Instead, he figured out an approximation: since the Sun is much bigger than the planets, he could simplify the problem and arrive at a partial solution. While he couldn’t perfectly predict the motions of the planets, he knew more than that they were just “approximately” ellipses: he had a prediction for how different from ellipses they should be.

That step was Newton’s great contribution. That insight, that science was able not just to provide exact answers to simpler problems but to guess how far those answers might be off, was something no-one else had really thought about before. It led to error analysis in experiments, and perturbation methods in theory. More generally, it led to the idea that scientists have to be responsible, not just for getting things “almost right”, but for explaining how their results are still wrong.

So this holiday season, let’s give thanks to the man whose ideas created science as we know it. Merry Newtonmas everyone!

Sorry Science Fiction, Quantum Gravity Doesn’t Do What You Think It Does

I saw Interstellar this week. There’s been a lot of buzz among physicists about it, owing in part to the involvement of black hole expert Kip Thorne in the film’s development. I’d just like to comment on one aspect of the film that bugged me, a problem that shows up pretty frequently in science fiction.

In the film, Michael Caine plays a theoretical physicist working for NASA. His dream is to save humanity from an Earth plagued by a blight that is killing off the world’s food supply. To do this, he plans to build giant anti-gravity spaceships capable of taking as many people as possible away from the dying Earth to find a new planet capable of supporting human life. And in order to do that, apparently, he needs a theory of quantum gravity.

The thing is, quantum gravity has nothing to do with making giant anti-gravity spaceships.

Michael Caine lied to us?

This mistake isn’t unique to Interstellar. Lots of science fiction works assume that once we understand quantum gravity then everything else will follow: faster than light travel, wormholes, anti-gravity…pretty much every sci-fi staple.

It’s not just present in science fiction, either. Plenty of science popularizers like to mention all of the marvelous technology that’s going to come out of quantum gravity, including people who really should know better. A good example comes from a recent piece by quantum gravity researcher Sabine Hossenfelder:

But especially in high energy physics and quantum gravity, progress has basically stalled since the development of the standard model in the mid 70s. […] it is a frustrating situation and this makes you wonder if not there are other reasons for lack of progress, reasons that we can do something about. Especially in a time when we really need a game changer, some breakthrough technology, clean energy, that warp drive, a transporter!

None of these are things we’re likely to get from quantum gravity, and the reason is rather basic. It boils down to one central issue: if we can’t control the classical physics, we can’t control the quantum physics.

When science fiction authors speculate about the benefits of quantum gravity, they’re thinking about the benefits of quantum mechanics. Understanding the quantum world has allowed some of the greatest breakthroughs of the 20th century, from miniaturizing circuits to developing novel materials.

The assumption writers make is that the same will be true for quantum gravity: understand it, and gravity technology will flow. But this assumption forgets that quantum mechanics was so successful because it let us understand things we were already working with.

In order to miniaturize circuits, you have to know how to build a circuit in the first place. Only then, when you try to make the circuit smaller and don’t understand why it stops working, does quantum mechanics step in to tell you what you’re missing. Quantum mechanics helps us develop new materials because it helps us understand how existing materials work.

We don’t have any gravity circuits to shrink down, or gravity materials to understand. When gravity limits our current technology, it does so on a macro level (such as the effect of the Earth’s gravity on GPS satellites) not on a quantum level. If there isn’t a way to build anti-gravity technology using classical physics, there probably isn’t a way using quantum physics.

Scientists and popularizers generally argue that we can’t know what the future will bring. This is true, up to a point. When Maxwell wrote down equations to unify electricity and magnetism he could not have imagined the wealth of technology we have today. And often, technologies come from unexpected places. The spinoff technologies of the space race are the most popular example, another is that CERN (the facility that houses the Large Hadron Collider) was instrumental in developing the world wide web.

While it’s great to emphasize the open-ended promise of scientific advances (especially on grant applications!), in this context it’s misleading because it erases the very real progress people are making on these issues without quantum gravity.

Want to invest in clean energy? There are a huge number of scientists working on it, with projects ranging from creating materials that can split water using solar energy to nuclear fusion. Quantum gravity is just about the last science likely to give us clean energy, and I’m including the social sciences in that assessment.

How about a warp drive?

Indeed, how about one?

That’s not obviously related to quantum gravity either. There has actually been some research into warp drives, but they’re based on a solution to Einstein’s equations without quantum mechanics. It’s not clear whether quantum gravity has something meaningful to say about them…while there are points to be made, from what I’ve been able to gather they’re more related to talking about how other quantum systems interact with gravity than the quantum properties of gravity itself. The same seems to apply to the difficulties involved in wormholes, another sci-fi concept that comes straight out of Einstein’s theory.

As for teleportation, that’s an entirely different field, and it probably doesn’t work how you think it does.

So what is quantum gravity actually good for?

Quantum gravity becomes relevant when gravity becomes very strong, places where Einstein’s theory would predict infinitely dense singularities. That means the inside of black holes, and the Big Bang. Quantum gravity smooths out these singularities, which means it can tell you about the universe’s beginnings (by smoothing out the big bang and showing what could cause it), or its long-term future (for example, problems with the long-term evolution of black holes).

These are important questions! They tell us about where we come from and where we’re going: in short, about our ultimate place in the universe. Almost every religion in history has tried to answer these questions. They’re very important to us as a species, even if they don’t directly impact our daily lives.

What they are not, however, is a source of technology.

So please, science fiction, use some other field for your plot-technology. There are plenty of scientific advances to choose from, people who are really working on cutting-edge futuristic stuff. They don’t need to wait on a theory of quantum gravity to get their work done. Neither do you.

Where do you get all those mathematical toys?

I’m at a conference at Caltech this week, so it’s going to be a shorter post than usual.

The conference is on something call the Positive Grassmannian, a precursor to Nima Arkani-Hamed’s much-hyped Amplituhedron. Both are variants of a central idea: take complicated calculations in physics and express them in terms of clean, well-defined mathematical objects.

Because of this, this conference is attended not just by physicists, but by mathematicians as well, and it’s been interesting watching how the two groups interact.

From a physics perspective, mathematicians are great because they give us so many useful tools! Many significant advances in my field happened because a physicist talked to a mathematician and learned that a problem that had stymied the physics world had already been solved in the math community.

This tends to lead to certain expectations among physicists. If a mathematician gives a talk at a physics conference, we expect them to present something we can use. Our ideal math talk is like when Q presents the gadgets at the beginning of a Bond movie: a ton of new toys with just enough explanation for us to use them to save the day in the second act.

Pictured: Mathematicians, through Physicist eyes

You may see the beginning of a problem here, once you realize that physicists are the James Bond in this analogy.

Physicists like to see themselves as the protagonists of their own stories. That’s true of every field, though, to some degree or another. And it’s certainly true of mathematicians.

Mathematicians don’t go to physics conferences just to be someone’s supporting cast. They do it because physics problems are interesting to them: by hearing what physicists are working on they hope to get inspiration for new mathematical structures, concepts jury-rigged together by physicists that represent corners that mathematics hasn’t yet explored. Their goal is to take home an idea that they can turn into something productive, gaining glory among their fellow mathematicians. And if that sounds familiar…

Pictured: Physicists, through Mathematician eyes

While it’s amusing to watch the different expectations go head-to-head, the best collaborations between physicists and mathematicians are those where both sides respect that the other is the protagonist of their own story. Allow for give-and-take, paying attention not just to what you find interesting but to what the other person does, without assuming a tired old movie script, and it’s possible to make great progress.

Of course, that’s true of life in general as well.

The Three Things Everyone Gets Wrong about the Big Bang

Ah, the Big Bang, our most science-y of creation myths. Everyone knows the story of how the universe and all its physical laws emerged from nothing in a massive explosion, growing from a singularity to the size of a breadbox until, over billions of years, it became the size it is today.

bigbang

A hot dense state, if you know what I mean.

…actually, almost nothing in that paragraph is true. There are a lot of myths about the Big Bang, born from physicists giving sloppy explanations. Here are three things most people get wrong about the Big Bang:

1. A Massive Explosion:

When you picture the big bang, don’t you imagine that something went, well, bang?

In movies and TV shows, a time traveler visiting the big bang sees only an empty void. Suddenly, an explosion lights up the darkness, shooting out stars and galaxies until it has created the entire universe.

Astute readers might find this suspicious: if the entire universe was created by the big bang, then where does the “darkness” come from? What does the universe explode into?

The problem here is that, despite the name, the big bang was not actually an explosion.

In picturing the universe as an explosion, you’re imagining the universe as having finite size. But it’s quite likely that the universe is infinite. Even if it is finite, it’s finite like the surface of the Earth: as Columbus (and others) experienced, you can’t get to the “edge” of the Earth no matter how far you go: eventually, you’ll just end up where you started. If the universe is truly finite, the same is true of it.

Rather than an explosion in one place, the big bang was an explosion everywhere at once. Every point in space was “exploding” at the same time. Each point was moving farther apart from every other point, and the whole universe was, as the song goes, hot and dense.

So what do physicists mean when they say that the universe at some specific time was the size of a breadbox, or a grapefruit?

It’s just sloppy language. When these physicists say “the universe”, what they mean is just the part of the universe we can see today, the Hubble Volume. It is that (enormously vast) space that, once upon a time, was merely the size of a grapefruit. But it was still adjacent to infinitely many other grapefruits of space, each one also experiencing the big bang.

2. It began with a Singularity:

This one isn’t so much definitely wrong as probably wrong.

If the universe obeys Einstein’s Theory of General Relativity perfectly, then we can make an educated guess about how it began. By tracking back the expansion of the universe to its earliest stages, we can infer that the universe was once as small as it can get: a single, zero-dimensional point, or a singularity. The laws of general relativity work the same backwards and forwards in time, so just as we could see a star collapsing and know that it is destined to form a black hole, we can see the universe’s expansion and know that if we traced it back it must have come from a single point.

This is all well and good, but there’s a problem with how it begins: “If the universe obeys Einstein’s Theory of General Relativity perfectly”.

In this situation, general relativity predicts an infinitely small, infinitely dense point. As I’ve talked about before, in physics an infinite result is almost never correct. When we encounter infinity, almost always it means we’re ignoring something about the nature of the universe.

In this case, we’re ignoring Quantum Mechanics. Quantum Mechanics naturally makes physics somewhat “fuzzy”: the Uncertainty Principle means that a quantum state can never be exactly in one specific place.

Combining quantum mechanics and general relativity is famously tricky, and the difficulty boils down to getting rid of pesky infinite results. However, several approaches exist to solving this problem, the most prominent of them being String Theory.

If you ask someone to list string theory’s successes, one thing you’ll always hear mentioned is string theory’s ability to understand black holes. In general relativity, black holes are singularities: infinitely small, and infinitely dense. In string theory, black holes are made up of combinations of fundamental objects: strings and membranes, curled up tight, but crucially not infinitely small. String theory smooths out singularities and tamps down infinities, and the same story applies to the infinity of the big bang.

String theory isn’t alone in this, though. Less popular approaches to quantum gravity, like Loop Quantum Gravity, also tend to “fuzz” out singularities. Whichever approach you favor, it’s pretty clear at this point that the big bang didn’t really begin with a true singularity, just a very compressed universe.

3. It created the laws of physics:

Physicists will occasionally say that the big bang determined the laws of physics. Fans of Anthropic Reasoning in particular will talk about different big bangs in different places in a vast multi-verse, each producing different physical laws.

I’ve met several people who were very confused by this. If the big bang created the laws of physics, then what laws governed the big bang? Don’t you need physics to get a big bang in the first place?

The problem here is that “laws of physics” doesn’t have a precise definition. Physicists use it to mean different things.

In one (important) sense, each fundamental particle is its own law of physics. Each one represents something that is true across all of space and time, a fact about the universe that we can test and confirm.

However, these aren’t the most fundamental laws possible. In string theory, the particles that exist in our four dimensions (three space dimensions, and one of time) change depending on how six “extra” dimensions are curled up. Even in ordinary particle physics, the value of the Higgs field determines the mass of the particles in our universe, including things that might feel “fundamental” like the difference between electromagnetism and the weak nuclear force. If the Higgs field had a different value (as it may have early in the life of the universe), these laws of physics would have been different. These sorts of laws can be truly said to have been created by the big bang.

The real fundamental laws, though, don’t change. Relativity is here to stay, no matter what particles exist in the universe. So is quantum mechanics. The big bang didn’t create those laws, it was a natural consequence of them. Rather than springing physics into existence from nothing, the big bang came out of the most fundamental laws of physics, then proceeded to fix the more contingent ones.

In fact, the big bang might not have even been the beginning of time! As I mentioned earlier in this article, most approaches to quantum gravity make singularities “fuzzy”. One thing these “fuzzy” singularities can do is “bounce”, going from a collapsing universe to an expanding universe. In Cyclic Models of the universe, the big bang was just the latest in a cycle of collapses and expansions, extending back into the distant past. Other approaches, like Eternal Inflation, instead think of the big bang as just a local event: our part of the universe happened to be dense enough to form a big bang, while other regions were expanding even more rapidly.

So if you picture the big bang, don’t just imagine an explosion. Imagine the entire universe expanding at once, changing and settling and cooling until it became the universe as we know it today, starting from a world of tangled strings or possibly an entirely different previous universe.

Sounds a bit more interesting to visit in your TARDIS, no?