Quantum Theory Cannot Hurt You_ A Guide to the Universe - Marcus Chown [49]
What would happen, however, if you were to push a mass closer and closer to the speed of light? Well, since the ultimate speed is unattainable, the body would have to become harder and harder to push as you get it closer and closer to the ultimate speed.
Being hard to push is the same as having a big mass. In fact, the mass of a body is defined by precisely this property—how hard it is to push it. A loaded refrigerator which is difficult to budge, is said to have a large mass, whereas a toaster, which is easy to budge, is said to have a small mass. It follows therefore that, if a body gets harder to push as it approaches the speed of light, it must get more massive. In fact, if a material body was ever to attain the speed of light itself, it would acquire an infinite mass, which is just another way of saying its acceleration would take an infinite amount of energy. Whatever way you look at it, it’s an impossibility.
Now, it is a fundamental law of nature that energy can neither be created or destroyed, only transformed from one guise into another. For instance, electrical energy changes into light energy in a lightbulb; sound energy changes into the energy of motion of a vibrating diaphragm in a microphone. What, then, happens to the energy put into pushing a body that is moving close to the speed of light? Hardly any of the energy can go into increasing the body’s speed since a body moving at close to the speed of light is already travelling within a whisker of the ultimate speed limit.
The only thing that increases as the body is pushed harder and harder is its mass. This, then, must be where all the energy goes. But, recall, energy can only be changed from one form into another. The inescapable conclusion, discovered by Einstein, is therefore that mass itself is a form of energy. The formula for the energy locked up in a chunk of matter of mass, m, is given by perhaps the most famous equation in all of science: E = mc2, where c is the scientists’ shorthand for the speed of light.
The connection between energy and mass is perhaps the most remarkable of all the consequences of Einstein’s special theory of relativity. And like the connection between space and time, it is a two-way thing. Not only is mass a form of energy, but energy has an effective mass. Put crudely, energy weighs something.
Sound energy, light energy, electrical energy—any form of energy you can think of—they all weigh something. When you warm up a pot of coffee, you add heat-energy to it. But heat-energy weighs something. Consequently, a cup of coffee weighs slightly more when hot than when cold. The operative word here is slightly. The difference in weight is far too small to measure. In fact, it is far from obvious that energy has a weight, which is of course why it took the genius of Einstein to first notice it. Nevertheless, one form of energy at least—the energy of sunlight—does reveal its mass when it interacts with a comet.
Light can push the tail of a comet because light energy weighs something. Photons have an effective mass by virtue of their energy. Another familiar form of energy is energy of motion. If you step into the path of a speeding cyclist, you will be left in no doubt that such a thing exists. Energy of motion, like all other forms of energy, weighs something. So you weigh marginally more when you are running than when you are walking.
It is energy of motion that explains why the photons of sunlight can push a comet tail. An explanation is needed because they actually have no intrinsic mass. If they did, after all, they would be unable to travel at the speed of light, a speed that is forbidden to all bodies with mass. What light has instead is an effective mass—a mass by virtue of