Tag Archives: newton

Merry Newtonmas!

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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!

Perimeter and Patronage

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I’m visiting the Perimeter Institute this week. For the non-physicists in the audience, Perimeter is a very prestigious institute of theoretical physics, founded by the founder of BlackBerry. It’s quite swanky. Some first impressions:

  • This occurred to me several times: this place is what the Simons Center wants to be when it grows up.
  • You’d think that the building is impossible to navigate because it was designed by a theoretical physicist, but Freddy Cachazo assured us that he actually had to get the architect to tone down the impossibly ridiculous architecture. Looks like the only person crazier than a physicist is an artist.
  • Having table service at an institute café feels very swanky at first, but it’s actually a lot less practical than cafeteria-style dining. I think the Simons Center Café has it right on this one, even if they don’t quite understand the concept of hurricane relief (don’t have a link for that joke, but I can explain if you’re curious).
  • Perimeter has some government money, but much of its funding comes from private companies and foundations, particularly Research in Motion (or RIM, now BlackBerry). Incidentally, I’m told that PeRIMeter is supposed to be a reference to RIM.

What interests me is that you don’t see this sort of thing (private support) very often in other fields. Private donors will found efforts to solve some real-world problem, like autism or income inequality. They rarely fund basic research*. When they do fund basic research, it’s usually at a particular university. Something like Perimeter, a private institute for basic research, is rather unusual. Perimeter itself describes its motivation as something akin to a long-range strategic investment, but I think this also ties back to the concept of patronage.

Like art, physics has a history of being a fashionable thing for wealthy patrons to support, usually when the research topic is in line with their wider interests. Newton, for example, re-cast his research in terms of its implications for an understanding of the tides to interest the nautically-minded King James II, despite the fact that he couldn’t predict the tides any better than anyone else in his day. Much like supporting art, supporting physics can allow someone’s name to linger on through history, while not running a risk of competing with others’ business interests like research in biology or chemistry might.

A man who liked his sailors

*basic research is a term scientists use to refer to research that isn’t made with a particular application in mind. In terms of theoretical physics, this often means theories that aren’t “true”.

There’s something about Symmetry…

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Physicists talk a lot about symmetry. Listen to an article about string theory and you might get the idea that symmetry is some sort of mysterious, mystical principle of beauty, inexplicable to the common man or woman.

Well, if it was inexplicable, I wouldn’t be blogging about it, now would I?

Symmetry in physics is dead simple. At the same time, it’s a bit misleading.

When you think of symmetry, you probably think of objects: symmetric faces, symmetric snowflakes, symmetric sculptures. Symmetry in physics can be about objects, but it can also be about places: symmetry is the idea that if you do an experiment from a different point of view, you should get the same results. In a way, this is what makes all of physics possible: two people in two different parts of the world can do the same experiment, but because of symmetry they can compare results and agree on how the world works.

Of course, if that was all there was to symmetry then it would hardly have the mystical reputation it does. The exciting, beautiful, and above all useful thing about symmetry is that, whenever there is a symmetry, there is a conservation law.

A conservation law is a law of physics that states that some quantity is conserved, that is, cannot be created or destroyed, but merely changed from one form to another. Energy is the classic example: you can’t create energy out of nothing, but you can turn the potential energy of gravity on top of a hill into the kinetic energy of a rolling ball, or the chemical energy of coal into the electrical energy in your power lines.

The fact that every symmetry creates a conservation law is not obvious. Proving it in general and describing how it works required a major breakthrough in mathematics. It was worked out by Emmy Noether, one of the greatest minds of her time, which given that her time included Einstein says rather a lot. Noether struggled for most of her life with the male-dominated establishment of academia, and spent many years teaching unpaid and under the names of male faculty, forbidden from being a professor because of her gender.

Why must women always be banished to the Noether regions of physics?

Noether’s proof is remarkable, but if you’re not familiar with the mathematics it won’t mean much to you. If you want to get a feel for the connection between symmetries and conservation laws, you need to go back a bit further. For the best example, we need to go all the way back to the dawn of physics.

Christiaan Huygens was a contemporary of Isaac Newton, and like Noether he was arguably as smart as if not smarter than his more famous colleague. Huygens could be described as the first theoretical physicist. Long before Newton first wrote his three laws of motion, Huygens used thought experiments to prove deep facts about physics, and he did it using symmetry.

In one of Huygens’ thought experiments, two men face each other, one standing on a boat and the other on the bank of a river. The men grab onto each other’s hands, and dangle a ball on a string from each pair of hands. In this way, it is impossible to tell which man is moving each ball.

Stop hitting yourself!

From the man on the bank’s perspective, he moves the two balls together at the same speed, which happens to be the same speed as the river. The balls are the same size, so as far as he can see they should have the same speed afterwards as well.

On the other hand, the man in the boat thinks that he’s only moving one ball. Since the man on the bank is moving one of the balls along at the same speed as the river, from the man on the boat’s perspective that ball is just staying still, while the other ball is moving with twice the speed of the river. If the man on the bank sees the balls bounce off of each other at equal speed, then the man on the boat will see the moving ball stop, and the ball that was staying still start to move with the same speed as the original ball. From what he could see, a moving ball hit a ball at rest, and transferred its entire momentum to the new ball.

Using arguments like these, Huygens developed the idea of conservation of momentum, the idea of a number related to an object’s mass and speed that can never be created or destroyed, only transferred from one object to another. And he did it using symmetry. At heart, his arguments showed that momentum, the mysterious “quantity of motion”, was merely a natural consequence of the fact that two people can look at a situation in two different ways. And it is that fact, and the power that fact has to explain the world, that makes physicists so obsessed with symmetry.