Why Does E=mc2_ - Brian Cox [87]
When we first derived the distance equation in spacetime, it seemed that we had no flexibility to change it from place to place. Indeed we argued that the precise form of the distance equation was forced upon us by the constraints of causality. But we did make a very big assumption. We assumed that spacetime is the same everywhere. It is true enough to say that this turns out to be an assumption that works remarkably well and the experimental evidence is largely in its favor, for this assumption was a crucial one on the road to E = mc2. But maybe we have not looked carefully enough. Might spacetime not be the same everywhere, and might this lead to consequences that we can observe? The answer is emphatically yes. To arrive at this conclusion, let us follow Einstein on one last journey. It was a journey that caused him ten years of hard struggle before he finally arrived at yet another majestic destination: the theory of general relativity.
Einstein’s journey to special relativity was triggered by a simple question—what would it mean if the speed of light were the same for all observers? His rather more tortuous journey to general relativity began with an equally simple observation that impressed him so much that he could not rest until he had recognized its true significance. The fact is this: All things fall to the ground with the same acceleration. That’s it . . . that is what excited Einstein so much! It takes a mind like Einstein’s to recognize that such an apparently benign fact could be of very deep significance.
Actually, this is a famous result in physics, known long before Einstein came along. Galileo is credited with being the first to recognize it. Legend has it that he climbed up the Leaning Tower of Pisa, dropped two balls of different masses off the top, and observed that they hit the ground at the same time. Whether he actually carried out the experiment does not really matter; what is important is that he correctly recognized what the outcome would be. We do know for sure that the experiment was eventually performed, not in Pisa but on the moon in 1971 by Apollo 15 commander David Scott. He dropped a feather and a hammer and both hit the ground at the same time. We can’t do that experiment on earth because a feather gets caught by the wind and slows down, but it is quite spectacular when performed in the high vacuum of the lunar surface. There isn’t much need to go all the way to the moon to check that Galileo was right, of course, but that doesn’t detract from the drama of the Apollo 15 demonstration, and the video is well worth watching. The important fact is that everything falls at the same rate, if complicating factors such as air resistance can be removed. The obvious question is why? Why do they fall at the same rate, and why are we making it out to be such a big deal?
Imagine you are standing in a stationary elevator. Your feet press firmly on the ground and your head pushes down on your shoulders. Your stomach rests in place inside your body. Now imagine you have the misfortune to be inside an elevator that is plummeting toward the ground because the cables have been cut. Since everything falls at the same rate, your feet no longer push onto the floor of the lift, your head no longer pushes onto your shoulders, and your stomach floats freely inside your body. In short, you are weightless. This is a big deal because it is exactly as if someone had turned off gravity. An astronaut floating freely in outer space would feel just the same. To be a little more precise, as the lift falls there are no experiments that you can do inside the lift that are able to distinguish between the possibilities that you are plummeting toward earth or floating in outer space. Of course you know the answer because you walked into the elevator, and perhaps the floor counter is whizzing toward “ground” at an alarming rate, but that is not the point. The point is that the laws of physics are identical in the two cases. That is what affected Einstein so deeply.