Archive for the 'Physics' Category

Physical Attraction

Published
by
Steve Landsburg
on February 8, 2010
in Physics
. 28 Comments

sticksThis will be old news to the physics geeks, but I still remember what a revelation it was, back in grad school, when the physicist Gary Horowitz told me why an electric current exerts a magnetic force on a moving charged particle. (This is the source of all magnetism; those magnets on your refrigerator have little electric currents flowing through them all the time.)

So imagine a wire, made of protons that stay still and electrons that drift rightward; that drift is what we call a current. And imagine a nearby charged particle—call it Fred—also traveling rightward.

Now relativity tells us that Fred is allowed to think of himself as stationary, and the protons (along with you and me) as drifting off to the left. Relativity also tells us that if passengers on a moving train say the cars are 100 feet apart, then an observer at the station will say they’re closer than that. In this case (according to Fred) you and I are the passengers moving with the train of protons, and if we say they’re an angstrom apart, then Fred says they’re closer. That means Fred sees more positive charge per inch of wire than we do. If Fred himself happens to be negatively charged, he’ll be drawn toward the wire.

As far as Fred is concerned, that’s a purely electrical force, but it’s a force that you and I can’t account for on electrical grounds. So you and I call it magnetism.

At the same time, Fred sees the electrons in the wire as slower-moving, and therefore farther apart, than you and I do, so he sees less negative charge per inch of wire than you and I do. According to Fred, then, the gap between positive and negative charge in the wire is even greater, which means he’s pulled in even harder, which you and I call even more magnetism.

If you’re geeky enough to care, it’s a nice exercise in relativity theory to show that the magnetic force is proportional both to the current (that is, the number of electrons per inch, times the speed of the electrons, as measured by you and me) and to Fred’s velocity. It just now took me three tries to get this right, but it’s very nice when it finally works.

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The Big Answers

Published
by
Steve Landsburg
on January 25, 2010
in Physics and Puzzles
. 93 Comments

trainLast week, I posed some brain teasers and a riddle about special relativity.

The brain teasers were all solved by multiple commenters; I’ll summarize their answers at the end of this post. The special relativity problem proved trickier; here it is again:

A circular train (front of the locomotive attached to the rear of the caboose) sits on a circular track. At some point, the train accelerates and starts traveling around the track. Because the train is moving, I (an observer stationary relative to the track) should see it shrink. But the track doesn’t shrink. So the train can’t stay on the track, and gets pulled inward, ending up inside the track. On the other hand, the passengers say the track has shrunk, so they should expect to get pushed outside the track. How can everyone be right?

Now to the answer.

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Geek or Dork?

Published
by
Steve Landsburg
on January 22, 2010
in Physics and Puzzles
. 17 Comments

There are a bazillion alleged “paradoxes” in special relativity, all based on exactly the same fallacy, but I might have just invented a brand-new one—-where “invented” is shorthand for “confused the hell out of myself for a while”. When I finally got up and drew a picture (as opposed to lying in bed with my eyes closed doing something that felt like thinking), it became clear that, sure enough, it was the same old fallacy again (how could it not have been?), but in a new enough guise that someone reading this might find it amusing.

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Life, the Universes and Everything

Published
by
Steve Landsburg
on December 2, 2009
in Ontology, Philosophy, Physics and Religion
. 17 Comments

As I mentioned the other day, I’ve recently (at the direction of my old friend Deirdre McCloskey) been reading some of the work of John Polkinghorne, the physicist-turned-theologian who seems to write about a book a week attempting to reconcile his twin faiths in orthodox science and orthodox Christianity.

Although Belief in God in an Age of Science is a very short book, it is too long to review in a single blog post. Fortunately, though, much of the non-lunatic content is concentrated in roughly the first ten pages, so I’ll comment here only on those.

Polkinghorne begins in awe. He is awestruck by the extent to which our Universe seems to have been fine-tuned to support life; this is the subject matter of the much-discussed anthropic cosmological principle. To take just one example (which Polkinghorne does not mention): The very existence of elements other than hydrogen and helium depends on the fact that it’s possible, in the interior of a star, to smoosh three helum atoms together and make a carbon atom; everything else is built from there. But it’s not enough to make that carbon atom; you’ve also got to make it stick together long enough for a series of other complicated reactions to occur. Ordinarily, that doesn’t happen, but now and then it does. And the reason it happens even occasionally is that the carbon atom happens to have an energy level of exactly 7.82 million electron volts. In fact, this energy level was predicted (by Fred Hoyle and Edwin Salpeter) before it was observed, precisely on the basis that without this energy level, there could be no stable carbon, no higher elements, and no you or me.

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What Are You Surest Of?

Published
by
Steve Landsburg
on November 4, 2009
in Evolution, Math, Ontology and Physics
. 39 Comments

Among the things you’re sure of, which are you surest of? For Richard Dawkins, writing in the Wall Street Journal, it’s the theory of evolution:

We know, as certainly as we know anything in science, that [evolution] is the process that has generated life on our own planet.

Now, I would be thunderstruck if the theory of evolution turned out to be fundamentally wrong, but not nearly so thunderstruck as if arithmetic turned out to be inconsistent. In fact, I can think of quite a few things I’m more sure about than evolution. For example:

1. The consistency of arithmetic. (This amounts to saying that a single arithmetic problem can’t have two different correct answers.)

2. The existence of conscious beings other than myself.

3. The fact that the North won the American Civil War. (That is, historians are not universally mistaken about this. I am not interested in quibbling about what constitutes a “win”; I mean to assert that the North won in the everyday sense of the word, as reported in all the history texts.)
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The Unreasonable Effectiveness of Physics

Published
by
Steve Landsburg
on November 2, 2009
in Math and Physics
. 5 Comments

In The Big Questions (pages 18-19) I talk (channeling the physicist Eugene Wigner) about the apparently unreasonable effectiveness of mathematics in revealing truths about the physical world. In Wigner’s words, “It is difficult to avoid the impression that a miracle confronts us here.”

But the physicist Peter Landsberg (no relation!) observes that sometimes the miracle runs in the opposite direction, and offers a curious use of physical reasoning to reveal a purely mathematical truth!

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