Theories of the Universe: Famous Equations and Pools of Jell-O
Famous Equations and Pools of Jell-O
In the last section, you discovered that space and time were relative and that the only constant in the universe was the speed of light. After showing that these once thought absolutes were relative, Einstein extended that concept to show that energy and matter were not absolutes either. His most famous equation, E = mc2, revealed the interrelationship between these two quantities.
The two main kinds of radioactive decay associated with atomic nuclei are alpha decay and beta decay. Remember those two particles from “The Dual Nature of Light”? They have the effect of transforming a radioactive original nucleus (called the parent) into a nucleus of another element (called the daughter), which may or may not be radioactive itself. Simply put, it's a process in which an unstable nucleus or particle (like a neutron) spits out one or more particles and transforms into a stable nucleus or particle. Decay can involve the release of energy in the form of electromagnetic radiation as we noted in the discussion of Einstein's experiment.
We often hear reference to Einstein's theory of relativity. Well, in case you didn't know, there are really two theories. The first, the special theory of relativity, you've already read about in the last section and are about to finish up soon. The second, the general theory of relativity, deals with universal gravity. We'll be covering that in this section, too.
The Conversion of Energy
The conversion of matter into energy is an everyday occurrence. Every time you light a fire or burn coal, you are turning the energy of matter into the energy of heat. Imagine that before you built a fire you could weigh all of the molecules of air and wood that make the fire and, after the wood burned, you weighed the remaining air and the ashes. You would find that it weighed less. No, the missing weight didn't go up in smoke. It was transformed into heat energy, a precisely measurable amount of energy.
Einstein did a similar experiment only he used the radioactive decay (I discussed radioactivity in connection to carbon-14 in The Relative Nature of Space and Time of the element radium instead of a fire. With radium, an alpha particle (or helium nucleus) is emitted during the decay process, and the loss of this particle converts radium into the element polonium. Having weighed the original amount of radium, he compared that to the total weight of the emitted alpha particle and the weight of the polonium. And as we knew he would find out, weight was lost. Let's put this into terms of Einstein's famous equation.
E = mc2
Albert knew the total energy released, designated by the letter E, and the missing weight (mass), represented by the letter m.
If your mass is around 150 pounds, you contain enough energy of mass to power a small city for a week—that's if you could convert it. And this is one of the reasons why no one discovered that mass was convertible into energy before Einstein. It just didn't seem available. But finally, about 40 years after Einstein developed his famous equation, the first nuclear bomb converted the mass of a small amount of uranium into energy and revealed that it was, in fact, possible to do so.
The key to putting it all together was the speed of light, c, times itself, or c2. This is a huge number—34,596,000,000. These three things put together gives us his famous equation, E = mc2. This translates as energy is equal to mass times the speed of light squared. This can be rewritten two other ways, m = E ÷ c2 or m ÷ E = c2. Notice that no matter which way it's written, regardless of the amount of mass and because the speed of light squared is such a big number, the amount of energy released is huge. That's why you get so much energy at the expense of so little mass and why nuclear explosions are so immense.
The interesting thing about mass is the degree to which it changes the faster it is accelerated. As you already know, as objects approach the speed of light, time slows down, length shortens, but mass increases. The conversion of energy into mass is not as familiar to us as the conversion of mass into energy is, but it happens just as often. Every time you run, you put on a little extra mass. (And here you thought that all that running would help you lose weight!) A tightly coiled spring has more mass than the same spring relaxed because there is extra mass due to the energy coiling puts into it. In other words, the faster an object moves the more mass it gains.
There's an interesting distinction that should be made regarding weight and mass. In physics, the term usually used to denote the stuff that matter is composed of is mass. This is the sum total of all of the protons, electrons, and neutrons in the object. It's also defined by the quantity of matter in an object as measured in its relation to inertia, or the tendency to remain at rest, or if moving to keep moving. While weight is defined by the force of gravity acting on an object and is equal to the mass of the object times the acceleration of gravity, it can vary in different gravitational fields. You weigh less on the moon than on earth. Mass is normally expressed in metric terms, such as grams or kilograms. There are also different terms for mass depending on how it's used. There is gravitational mass, inertial mass, relativistic mass, and rest mass.
Well then, what about photons? They must weigh tons if they are traveling at the speed of light, right? Nope, photons are mass-less. They contain all of their mass in the form of motion energy. It is very similar to our discussion at the end of the last section. Let's look at the similarity.
Remember that the photon had diverted all of its motion through time to attain the maximum speed of motion through space. This is sort of the same scenario only instead of time it's mass. The photon has no mass and experiences no time because all of its energy of motion, the maximum speed that any object can travel through space, has been diverted away from the energy required to move through time and contained in its mass. The photon is pure energy, having no mass and experiencing no passage of time.
This energy/matter relationship is the reason behind the observable fact that light speed is the speed limit of the universe. No energy or information can travel faster than light because as anything begins to approach the speed, it gains an ever-increasing amount of mass. As previously mentioned, mass is a measure of inertia—a resistance to change in motion. So the more speed or motion something has, the harder it is to make it go faster, because it also has become more massive. Eventually, the object gets infinitely massive, which means that it would take an infinite amount of force to make it go any faster. So even inertia is not absolute. Inertia increases the faster you go.
In giant subatomic particle accelerators, electrons pushed to 99.999 percent of the speed of light gain 40,000 times their original mass. And just to show the change in a few decimal places, a muon (a particle identical to an electron except it's 200 times heavier) taken to 99.99999999 percent becomes 70,000 times heavier than its original mass. These particles pushed to nearly light speed don't gain velocity as much as they gain another form of energy—mass. So in reality, these particle accelerators aren't in the business of accelerating particles to high speeds as they are in the business of building them up to more remarkable masses.
Excerpted from The Complete Idiot's Guide to Theories of the Universe © 2001 by Gary F. Moring. All rights reserved including the right of reproduction in whole or in part in any form. Used by arrangement with Alpha Books, a member of Penguin Group (USA) Inc.
Here are the facts and trivia that people are buzzing about.