Warped Passages - Lisa Randall [56]
Furthermore, physicists were able to use Einstein’s equations to explore other types of gravitational field. With general relativity, scientists could describe and study black holes. These fascinating, enigmatic objects form when matter is highly concentrated within a very small volume. In black holes the geometry of spacetime is extremely distorted, so much so that anything entering a black hole gets trapped inside. Even light cannot escape. Although the German astronomer Karl Schwarzschild discovered that black holes were a consequence of Einstein’s equations almost immediately after general relativity’s development,* it was not until the 1960s that physicists took seriously the idea that they could be real things in our universe. Today, black holes are well accepted in the astrophysical community. In fact, it looks as though there is a supermassive black hole at the center of every galaxy, including our own. Moreover, if there are hidden dimensions then there exist higher-dimensional black holes which, when big, look like the four-dimensional black holes that astronomers have observed.
Coda
To conclude the story of the GPS system, it turns out that to calculate position to within a meter, we must measure time to better than one part in 1013. The only possible way to get this accuracy is with atomic clocks.
But even if we had perfect clocks, time dilation would slow them down by about one part in 1010. This error, if not corrected, would be a thousand times too big for our desired GPS system. We also have to account for the gravitational blueshift, a general relativity effect associated with a photon traveling in a changing gravitational field, which gives an error at least this great. This and other general relativity deviations would give errors that, if ignored, would build up at a rate greater than 10 km per day.† Ike (and current GPS systems) must correct for these relativistic effects.
Although by now relativity has been well tested and even gives rise to effects that need to be accounted for in practical devices, I do find it fairly remarkable that anyone listened to Einstein at first. He was completely unknown, working in the Bern patent office because he couldn’t get a better job. From this unlikely location he proposed a theory that went against the beliefs of all other physicists of his time.
Gerald Holton, a Harvard historian of science, tells me that the German physicist Max Planck was Einstein’s first champion. Without Planck, who immediately recognized the brilliance of Einstein’s work, it might have taken much longer for it to be recognized and accepted. Following Planck, a few other notable physicists knew enough to listen and pay attention. And shortly afterwards, so did the world.
What to Remember
The speed of light is constant. It is independent of the speed of an observer.
Relativity modifies our notions of space and time and tells us that we can treat them together as a single spacetime fabric.
Special relativity relates the values of energy, momentum (which tells how an object responds to a force), and mass. For example, E = mc2, where E is energy, m is mass, and c is the speed of light.
Mass and energy make spacetime curve, and you can think of that curved spacetime as the origin of the gravitational field.
6
Quantum Mechanics: Principled Uncertainty, the Principal