Why Does E=mc2_ - Brian Cox [22]
Here is where the mathematics we did earlier in this chapter becomes very valuable. We have made a precise prediction for the amount by which a little clock traveling at speed actually slows down relative to a clock standing still. We can therefore use our equation to predict by how much time should slow down when traveling at 99.94 percent of the speed of light, and therefore by how much a muon’s lifetime should be extended. Einstein predicts that the muons in Brookhaven should have their time stretched by a factor ofwith υ/c = 0.9994. If you have a calculator handy, then type the numbers in and see what happens. Einstein’s formula gives 29, exactly as the Brookhaven experimenters found.
It’s worth taking a brief pause here to ponder what has happened. Using only Pythagoras’ theorem and Einstein’s assumption about the speed of light being the same for everyone, we derived a mathematical formula that allowed us to predict the lengthening of the lifetime of a subatomic particle called a muon when that muon is accelerated around a particle accelerator in Brookhaven to 99.94 percent of the speed of light. Our prediction was that it should live 29 times longer than a muon standing still, and this prediction agrees exactly with what was seen by the scientists at Brookhaven. The more you think about this, the more wonderful it is. Welcome to the world of physics! Of course, Einstein’s theory was already well established in the late 1990s. The scientists at Brookhaven were interested in studying other properties of their muons—the life-enhancing effects of Einstein’s theory provided a bonus, which meant that they got to observe them for longer.
We must therefore conclude, because experiment tells us so, that time is malleable. Its rate of passage varies from person to person (or muon to muon) depending upon how they move about.
As if this rather unsettling behavior of time isn’t enough, something else is lurking, and the alert reader may have spotted it. Think back to those muons whizzing around the AGS. Let’s put a little finish line in the ring and count how many times the muons cross it as they circulate before they die. For the person watching the muons, they cross 400 times because their lifetimes have been extended. How many times would you cross the finish line if you could speed around the ring with the muons? It has to be 400 as well, of course; otherwise the world would make no sense at all. The problem is that according to your watch, as you fly around the ring with the muons, they live for only 2.2 microseconds, because the muon is standing still relative to you and muons live for 2.2 microseconds when they stand still. Nevertheless, you and the muon must still manage to make 400 or so laps of the ring before the muon finally expires. What has happened? Four hundred laps in 2.2 microseconds doesn’t seem possible. Fortunately, there is a way out of this dilemma. The circumference of the ring could be reduced from the viewpoint of the muon. To be entirely consistent, the length of the ring, as determined by you and the muon, must shrink by exactly the same amount that the muon’s lifetime increases. So space must be malleable too! As with the stretching of time, this is a real effect. Real objects do shrink when they move. As a bizarre example, imagine a 4-meter-long car trying to fit into a 3.9-meter-long garage. Einstein predicts that if the car is traveling faster than 22 percent of the speed of light, then it will just about squeeze into the garage, at least for a split second before it crashes through the back wall. Again, if you have been following the maths, then you can