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By Kenneth Chang


Object Lessons

Bad physics in the movies may be worse than none at all.

AT YOUR NEIGHBORHOOD BOOKSTORE, you can now pick upEverything I Really Need to Know I Learned From Watching Star Trek. Within its pages, author Dave Marinaccio offers such nuggets of wisdom as the following: "If you mess up something, it's your responsibility to make things right again. (Say you disrupt history and cause the Nazis to win World War II. To correct matters, you have to let Joan Collins walk in front of a car even though you're in love with her.)"

But when Mr. Marinaccio runs across Goliath (he is Dave, after all), he'll pull out his slingshot, churn through his Star Trek physics to calculate the trajectory to the ogre's eye... and promptly send the rock sailing straight into the ground. Snap, crunch, bye, bye, Mr. Marinaccio. Sir Isaac Newton, father of calculus and physics, has been doornail dead since 1727. In the succeeding 268 years, physics moved on to curved space, quantum mechanics, quarks, black holes. Still Newton-ignorance bedevils the entertainment business -- and it could cost the lives of cavalier book writers such as Mr. Marinaccio.

Last weekend, I was watching old Star Trek, the episode titled "Damned If I Can Remember the Name, But It's the One Where Spock Cries, Sulu Runs Around Bare-chested with a Fencing Foil and The Enterprise Goes Back in Time." What makes Star Trek enjoyable is Star Trek moments. Every time McCoy scowls at Kirk, saying, "Damnit, Jim, I'm a doctor, not a (insert some other profession.)" qualifies as a Star Trek moment. This episode, with Spock crying, Sulu dashing and Enterprise time-travelling, is chockful of Star Trek moments.

The plot is pure Star Trek, too. A mysterious malady unhinges the crew's inhibitions. Sulu fancies himself a swashbuckler. Spock despairs; his Vulcan nature prevents him from ever showing love towards his mother. And a generic Irish character named O'Reilly locks himself in the engine room and, over the intercom, regales the ship with Irish drinking songs. All this while -- and this is very important -- the starship Enterprise is orbiting a planet.

Just minutes before the end of the episode, Captain Kirk and Scotty the Wonder Engineer finally break the door open and rush in. Scotty turns in horror to Kirk and says, "He's turned the engines off. It'll take 20 minutes to get them back on."

Kirk swivels around, shouts, "But you have to. We're going to burn up in the atmosphere in eight minutes!"

"That's impossible, captain!" Scotty protests.

"Youcan'tjustgoandchangethelawsofphysics." But it's Star Trek, and you know the Enterprise isn't going to become a flying shish-kebab (at least not until the third movie).

You might notice, too, that they have already gone and changed the laws of physics. Real objects don't move the way they do in Star Trek.


I FIRST MET NEWTON'S LAWS in high school physics. During one class, Mr. "Fizzix" Hicken rattled off the first half of Newton's Law. Objects at rest tend to remain at rest. Stare at a rock. That concept settled happily in some nook of neurons and rested.

By and large, a non-moving object doesn't start moving unless something happens: someone picks it up, a large wind gust blows it, an earthquake jostles it. Overcoming rest -- to thwart inertia, to a lug some piece of something from Point A to Point B -- requires effort. It's a concept obvious to everyone.

However, the Mr. Hicken's next sentence jarred me: "If the object is moving, it'll keep moving." Through the rest of class, I sat there thinking simply, He's wrong. It takes energy to keep moving. That's the lesson of experience. Running in circles is exhausting. Unpushed swings stop swinging. Rolling stones stop rolling, become resting stones, and gather moss. Rest, I believed, possessed a privileged place in the universe, and all things tend to rest.

Objects in motion tend to stay in motion.

Sir Isaac Newton devised the first theory of relativity. To illustrate this old style relativity, let's say we have a watermelon and a pane of glass. To avoid the complications of gravity(which has the annoying tendency to pull things down) and air resistance (which slows stuff down), let's say this pair of objects is hanging out in the middle of interstellar space. As far as physics is concerned -- even the classical Newtonian sort -- a watermelon zooming in on a resting pane of glass at 100 miles per hour is exactly the same as if the watermelon were sitting motionless and along comes this 100 mph piece of glass. It's just a different way of looking at the same problem, different "frames of reference" in the words of physicists. Where the watermelon and pane of glass end up depends only their relative speed and direction. (Einstein, for his theory of relativity, the one called special relativity, added the condition that the speed of light is the same no matter what. That one condition leads, for instance, to the paradox of twins aging at different rates if one goes cavorting about the universe on a spaceship while the other stays on Earth.)

Once you move the watermelon and glass pane from outer space to our everyday gravity-bound existence, the preceding example is no longer true. Gravity is an extra force that complicates the equations. But what really changes everything is friction, that stickiness when two things rub. Friction is the reason why the part Newton's First Law, having to do with moving objects, is so contrary to common sense.

On Earth, there is a special frame of reference: the one with all the resting rocks. The Earth is, obviously, much larger than the watermelon and the glass pane. Objects are constantly rubbing against the Earth and the layer of air it pulls along. When a baseball springs off a hitter's bat heading for the deep right field bleachers, molecules of oxygen, nitrogen and hydrogen BOIING off it and slow it down. The collisions between ball, air and Earth scatter the ball's motion until its direction and speed match that of the surrounding planet.

This is rest.


FORCE EQUALS mass times acceleration.

F = ma

That's the central lesson of high school physics: Newton's Second Law. The force on an object is equal to its mass multiplied by its acceleration. Winches and pulleys, blocks slipping down a slope, pendulums rocking back and forth. Almost every problem is a variation of Newton's Second Law.

A quiz: Dave Giantkiller is swinging his slingshot around in a circular motion. At the point indicated in the diagram below, he lets the rock fly. In what direction does the rock go?


I WISH TELEVISION and movie writers wouldn't mess up three-century-old physics. It's a hopeless wish. For instance, in the climactic scene of the movie Batman, Vickie Vale tumbles off a very tall steeple in the Gotham Cathedral. Batman jumps after her and catches her. Actually, I don't remember quite how they end up falling together, but anyway, there they are falling, destined to become sidewalk indentations, when the caped hero throws out his bat-hook which snags a convenient hook-snagging portion of the cathedral and brings them to swift stop in mid-air, well above the hard sidewalk.

F= ma.

You don't have to hit the ground to die. The force of breaking their fall would likely snap a couple of necks and rupture a host of internal organs. For the numbers-averse, skip to the next paragraph. For people who like numbers, here's a back-of-an-envelope calculation. Mass: about 300 pounds of Michael Keaton, Bat suit, and Kim Basinger. Acceleration: Assume the Bat rope stretches about 10 feet. Terminal velocity -- the speed at which the downward tug of gravity on a falling person is balanced out by the slowing effects of air resistance -- is about 150 miles per hour. Those assumptions lead to an deceleration of 1200 feet per second squared as the Bat rope snaps taut. Convert those numbers into metric (physicists always use metric, because it's simpler), insert them into F=ma, and here's the answer: some 50,000 Newtons. Most people will think it odd that falling out of cathedral will produce boxes and boxes of Fig Newton cookies, so here's a picture (albeit a rather contrived one) of what 50,000 Newtons would do to you: You're suspended horizontally above the ground. Three Toyota Corollas are snugly attached to your belt. The cars are dropped.

Here's a one-number description of an equivalent situation. Take a long rope. Tie one end securely to a building. Tie the other end around your waist. Jump onto a motorcycle. Speed away from the building at 150 miles per hour. Ride until rope runs out.

So, anyway, Batman should be dead, and a rather messy death at that. But isn't "suspension of disbelief" synonymous with "movies"? If I can accept for a couple of hours the idea of a millionaire running around in black latex, why should a little wrong physics bother me? After all, science fiction often revolves around fictional science. That isn't necessarily bad. For the sake of story, it's often necessary to go invent some notion like hyperspace to get the characters beyond the solar system and over to the next star.

Sometimes I don't even mind wrong science. Star Trek is built on wrong science. Despite all those time-travelling stories, the Star Trek universe is, at its core, one that obeys the laws of Newton, not his successors. Stardates flow at a steady rate, ignoring special relativity's expanding and shrinking time conundrums. The Enterprise crew, zipping about the galaxy at really, really fast speeds doesn't age any more slowly than the folks back on Earth. Light travels at infinite speed. (Otherwise they can't see what's behind them; the light would never catch up.)

It doesn't bother me that when Gene Roddenbery devised the Star Trek universe he threw out Einstein's relativity. I don't expect television writers to work through complex equations in order to write scripts. Scientific preciseness would merely befuddle.

When starships fall out of the sky because their engines sputter and die, however, that bothers me. Wrong science is no longer a storytelling convenience designed to avoid obtuse technical jargon, but a cornerstone of the plot.

An orbit is a continuous state of falling. Air is again troublesome, so for this explanation, let's go the moon (and ignore the slight atmosphere it has). If you throw a watermelon horizontally, it'll go so far before gravity tugs it back to the surface. Throw it faster and it'll go further before it splats. But the surface of the moon is curved so that the farther the ball travels, the farther it must drop before it hits the ground. Throw the melon fast enough and the rate of falling is the same rate as the surface curving away. The ball is in orbit.

Now remember Newton's First Law, the non-intuitive part of it. Objects in motion tend to stay in motion.

The watermelon around the moon doesn't need any engines to stay up. Neither did the Enterprise. Oh sure, some high-flying air molecules would bang into them and might eventually knock them down. Such was the fate of NASA's first space station, Skylab. But falling, the decaying inward spiral before the final flameful plunge, took months, not minutes, and one would think starships would hang out far outside the reach of the upper atmosphere anyway.


Answer to quiz: The rock is just like the watermelon around the moon, except there's no moon, so there's no gravity, thus no force to drag the rock down. So the moment it's let go, the rock zooms off in a straight line.

TO TEST THE PEOPLE'S KNOWLEDGE of physics, back in 1980, researchers at Johns Hopkins University gave the above problem plus and three others to undergraduate students there. A slim majority, 53 percent, answered the slingshot question correctly. The most common wrong answer was to envision the rock spirally outward (and into the ground). According to the researchers, the explanations of those who drew the curving paths, were "strikingly reminiscent of the medieval theory of impetus, which claimed that an object set in motion acquires an impetus that serves to maintain the motion." The students believed the rock somehow remembered that it was moving in a circular path and sought to continue in that spiral. In my physics class, Mr. Hicken gave us copies of the New York Times article that reported the study's results. We were lucky. The previous year, those four Johns Hopkins questions were the final exam in its entirety. If I recall correctly, the class did so wonderfully, he had to give them another final exam so as to not torpedo almost everyone's grades. Encouragingly, though, in the Johns Hopkins study, students who had taken physics did much better than those who had not. So it's a fixable deficiency. But the converse is that those who have not taken high school physics -- most people -- do not understand 300-year-old physics, to say nothing of physics today.

Science has moved beyond Newton. Society must soon make important decisions based on 20th century science: where to put nuclear waste, how to halt global warming, whether to dabble in the genetic code. Yet if we cannot figure out where a rock goes when it flies out of a slingshot, the likelihood of correctly answering more difficult questions is not promising.