Why Does E=mc2_ - Brian Cox [7]
This may all seem rather philosophical, but in fact such musings lead to a profound conclusion about the nature of space itself, and they allow us to take the first step along the path to Einstein’s theories of relativity. So what conclusion about space can be drawn from Galileo’s reasoning? The conclusion is this: If it is in principle impossible to detect absolute motion, it follows that there is no value in the concept of a special grid that defines “at rest,” and therefore no value in the concept of absolute space.
This is important, so let us investigate it in more detail. We have already established that if it were possible to define a special Aristotelian grid covering the whole universe, then motion relative to that grid could be defined as absolute. We have also argued that since it is not possible to design an experiment that can tell us whether we are in motion, we should jettison the idea of that grid, simply because we can never work out to what it should be fixed. But how then should we define the absolute position of an object? In other words, where are we in the universe? Without the notion of Aristotle’s special grid, these questions have no scientific meaning. All we can speak of are the relative positions of objects. There is therefore no way of specifying absolute positions in space, and that is what we mean when we assert that the notion of absolute space itself has no meaning. Thinking of the universe as a giant box, within which things move around, is a concept that is not required by experiment. We can’t overemphasize how important this piece of reasoning is. The great physicist Richard Feynman once said that no matter how beautiful your theory, no matter how clever you are or what your name is, if it disagrees with experiment, it’s wrong. In this statement is the key to science. Turning this statement around, if a concept is not testable by experiment, then we have no way of telling whether it’s right or wrong, and it simply doesn’t matter either way. Of course, that means we could still assume that an idea holds true, even if it isn’t testable, but the danger is that in so doing we run the risk of hindering future progress because we are holding on to an unnecessary prejudice. So, without any possible means to identify a special grid, we are freed from the notion of absolute space, just as we have been freed from the concept of absolute motion. So what?! Well, being freed from the millstone of absolute space played a crucial role in allowing Einstein to develop his theory of space and time, but this will have to wait until the next chapter. For now, we have established our freedom, but we haven’t acted as liberated scientists just yet. To whet the appetite, let us merely state that if there is no absolute space, then there is no reason why two observers should necessarily agree on the size of an object. That really should strike you as bizarre—surely if a ball has a diameter of 4 centimeters that is the end of the matter, but without absolute space it need not be.
So far we have discussed in some detail the connection between motion and space. What, then, of time? Motion is expressed as speed, and speed can be measured in miles per hour—that is, the distance traveled through space in a particular interval of time. In this way, the notion of time has in fact already entered into our thinking. Is there anything to be said of time? Is there some experiment we can do to prove that time is absolute, or should we also jettison this even more deeply held concept? Although Galileo dispensed with the notion of absolute space, his reasoning has nothing at all to teach us about absolute time. Time is immutable, according to Galileo. Immutable time means that it is possible to imagine perfect little clocks, all synchronized to show the same time, ticking away at every point in the universe. One clock could be on a plane, one on the ground, one