Why Does E=mc2_ - Brian Cox [26]
Glance out your window. You may be faced with the distorted reflections of a city, as the afternoon light scatters off sheets of steel and glass, or black and white cattle grazing in neatly fenced green fields. But whether cityscape or farmland, the most astonishing thing about practically every window view in the world is the evidence of human intervention. Our civilization is all-pervasive, and yet twenty-first-century physics tells us that, at its heart, it is all a mathematical dance involving a handful of subatomic particles, organized by only four forces of nature over 13.7 billion years. The complexity of human brains and the products of the powerful synthesis between consciousness and dexterous skill that we glimpse outside our windows mask the underlying simplicity and elegance of nature. The scientist’s task is to hunt for those properties that act as a Rosetta stone, to allow us to decipher the language of nature and reveal its beauty.
The tool that allows us to search for and exploit these properties of nature is mathematics. In itself, this is a sentence that throws up deep questions, and entire books have been written attempting to advance plausible reasons as to why it may be so. Quoting Eugene Wigner again: “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.” Perhaps we will never understand the true nature of the relationship between mathematics and nature, but history has shown that mathematics allows us to organize our thinking in a way that proves to be a reliable guide to a deeper understanding.
As we have been at pains to emphasize, to proceed in this spirit, physicists write down equations, and equations do nothing more than express relationships between different real-world “things.” An example of an equation is speed = distance/time, which we met in the last chapter when we were discussing light clocks: in symbols υ = x/t, where υ is the speed, x is the distance traveled, and t is the time taken to travel the distance x. Very simply, recall that if you travel 60 miles in 1 hour, then you have traveled at a speed of 60 miles per hour. Now, the most interesting equations will be those that are capable of furnishing a description of nature that is agreed upon by everyone. That is, they should deal only in invariant quantities. We could all then agree on what we are measuring, irrespective of our perspective in the universe. According to common sense, the distance between any two points in space is such an invariant quantity, and pre-Einstein it was. But we saw in the previous chapter that it is no such thing. Remember: Common sense is not always reliable. Similarly, the passage of time has become a subjective thing and it varies depending on how fast clocks are moving relative to each other. Einstein has upset the order of things, and we cannot even rely on distance and time to build a reliable picture of the universe. From the point of view of a physicist looking for the deep laws of nature, the equation υ = x/t is therefore of no fundamental use, because it does not express a relationship between invariant quantities. By undermining space and time, we have shaken the very foundations of physics. What, then, are we to do?
One option is to try and reestablish order by making a conjecture. Conjecture is a fancy word for “guess,” and scientists do it all the time—there are no prizes for how smart we are in figuring out the underlying theory; a successful educated guess will do just fine so long as it agrees with experiment. The conjecture is radical: Space and time can be merged into a single entity that we call “spacetime,” and distances in spacetime are invariant. This is a bold assertion