Ideas from Teachers
I use NOVA's "Time Travel"
program to supplement my introduction to the time travel theme of my Science Fiction course. (I also show "Understanding: Uncertainty," a program from The Learning Channel).
I introduce the mathematical/logical time/space Paradoxes of Zeno, as well as the ideas of both Immanuel Kant and Henri Bergson, who radically redefined the concept of time. I show the movie of HG Wells' "The Time Machine" and read stories by P.K. Dick, Ray Bradbury, Robert Heinlein, William Tenn, Robert Silverberg, and John Varley. I also use other visual media such as "12 Monkies," "StarGate:SG1," and "The X-Files Movie."
Each is a variation on the theme of the Paradoxes of Time Travel, or, why time travel is but an interesting fantasy besotted with internal contradictions, localized white holes notwithstanding.
Sent in by
Lucius M. Nelligan Sorrentino
Eastport High School
This activity could be used with NOVA's "Time Travel"
program. The concept of time travel is bound up in a mathematical anomaly that surfaces when we investigate the nature of mass as it nears the speed of light. Here are two thought experiments:
Einstein As Traffic Cop
The mass of any object is subject to its velocity, as all matter is in motion, with "resting mass" being an artificial concept. To calculate the mass of a moving object, one uses an equation created by Einstein.
Let's assume for a moment that our mass at this moment is our "resting mass," as though we are motionless. Now, let's accelerate toward the speed of light. What happens? Try the following formula to answer that queston.
New Mass = Your Resting Mass / Square Root (1 - (Your velocity squared / speed of light squared))
A little algebraic simplification will tell you that unless you begin traveling very fast (at least 60 percent the speed of light), we wouldn't see much of a change in your mass. So, move a little faster, say 95 percent the speed of light.
Here's a hint on shortcutting the problem: Normally we think of the speed of light as 299,792,458 mps. However, that number, or a number equal to 95 percent of it are pretty unwieldy. Therefore, assume that the speed of light = 1, and that 95% = .95.
Now we can begin seeing how Einstein becomes a traffic cop. What will happen when your velocity (v) becomes equal to the speed of light?
So now you are dividing your resting mass by 0. I don't know about you, but I've always been told that you can't divide by zero. However, now is the time to do so. In terms of relativity, as you approach the speed of light, your mass continues to increase, until it becomes infinite. The only way that will happen in Einstein's equation is if 0 = 1/infinity.
Want to see it happen another way?
Substitute the formula for your new mass into the familiar E = mc2 and simplify.
We are left with the inevitability that the speed of light is the absolute limit for matter as we know it. There is no supply of an infinite amount of energy required to accelerate to the speed of light. But, is that all there is to the story?
An Imaginary Einstein
It doesn't take much time before you begin to realize that if you try to travel faster than the speed of light, a serious mathematical problem arises. If v > c, you end up with the square root of a negative number, which we call "imaginary." Calculators don't like them. Does that mean that they are of no consequence. Many might pass them off as mere abstractions worthy only of a passing notice in a math book. Wrong again!
Consider this: If the speed of light is the absolute limit for matter because of the energy costs to travel that fast, could it be that there are particles that would require an infinite amount of energy just to slow down to the speed of light? Is there such a creature?
Yes, as experimentation has demonstrated. Beginning in the 1960's, physicists began debating the existence of so-called tachyons (from "tachys," speedy). These particles were postulated to travel faster than the speed of light, and that slowing to the speed of light was energy-consuming for them. Recent work has confirmed a quasi-particle with such characteristics.
This discussion is abstracted from "The Zero Seminars." Please e-mail me for information on this unit.
Sent in by
Lewiston High School