Momentum and Teleportation

Teleportation in Homecoming requires that energy, momentum, angular momentum and mass be conserved—all basic laws of physics. We’ll skip mass and angular momentum for right now, and just look at the situation where something is moving in a straight line.

Anything that is moving has both kinetic energy (energy of motion) and momentum, but the two are not the same. The difference is usually expressed mathematically: energy is half the mass times the square of the velocity and momentum is the mass times the vector velocity, but for many that just makes if more confusing. Let’s try this, instead. (If you don’t understand mass, think weight.)

Consider a car. Let it be a big, heavy car, say an SUV. Suppose it is coasting at a steady speed, say, 30 miles an hour to the west. Can a mosquito stop it by hitting the windshield? Not likely! The car’s resistance to having its steady motion changed is due to its momentum. This momentum has a direction—the direction the car is moving. Friction will slow it down, eventually, by transferring its momentum to the earth, but for the moment we’ll ignore that.

It also has kinetic energy. If the speed is doubled, the momentum will also double—but the kinetic energy will increase by a factor of four.

Remember momentum has a direction. Suppose we have another SUV moving 30 miles an hour to the east. Speed to the east and speed to the west cancel, so the momentum of the two-car system is zero. Their kinetic energy does not cancel, as can be seen if the two cars meet head-on—when the dust settles, they will be stationary at the point where they met. But the energy will have gone into crumpling metal (and whatever else makes up the cars) and ultimately into heat.

It is possible for two objects to bounce off of each other in such a way that energy, as well as momentum, is conserved. But if the momentum adds up to zero before the impact, it must also add up to zero after the impact. This is a common problem in billiards, though in this case the balls are most often moving at angles to each other so the vector sum of the momentum is not zero—but it will still be the same after the collision as it was before.

The conservation of momentum, in fact, nicely encapsulates Newton’s laws of motion.

Now consider Roi’s problem in teleporting to a very different location. He is moving with the planet under his feet. For illustration, let’s assume he is on the equator, at sea level, at sunrise, and wants to go to the opposite hemisphere, also on the equator at sea level, but at sunset.

Assuming he is on a planet like the Earth, he is moving toward the sun at around a thousand miles an hour, and the area he wants to teleport to is moving away from the sun at the same speed. No change in kinetic energy, but if he doesn’t do something about momentum, he’ll arrive moving about two thousand miles an hour relative to his surroundings—not a very survivable teleport!

My solution is strictly science fiction—I assume it is possible for a person (or a machine) to transfer or “swap” momentum from one mass to another. But they’d better remember to do it!

Eighth Day

On the Eighth day of Christmas my true-love gave to me,
Eight cars polluting,
Seven blizzards raging,
Six aurorae swirling,
Five solar flares.
Three mammoths
Two ptarmigan
And a spruce hen in a spruce tree.

The Greenhouse Carol

(to the tune of “Auld Lang Syne”)

Should present climate be forgot,
And ne’er again be seen?
Should glaciers melt and oceans rise
Just because our house is green?
Because our house is green my friends,
Because our house is green,
We’ll sit and swelter in the sun
Because our house is green.

Should deserts spread across the land
While hurricanes grow cruel
From cows and swamps and growing rice,
And from burning fossil fuel?
From burning fossil fuel, my friends,
From burning fossil fuel,
We’ll all dehydrate in the sun
From burning fossil fuel.

Should the I T C Z go away,
And the savannahs return?
Should glaciers melt and cities drown
Because the jungles burn?
Because the jungles burn, my friends,
Because the jungles burn,
We’ll parboil in the tropic sun
Because the jungles burn.