Once Before Time - Martin Bojowald [15]
With this astonishing trick, Einstein was able to extend Newton’s theory and erase its flaw. In Einstein’s gravity there are no spooky interactions between distant objects in a direct way. By incorporating space and time—not as a rigid and given stage as Newton had assumed, but as a changing object with an inherent structure subject to physical laws—this action at a distance is forever banned from physics. Masses cause their directly surrounding space-time region to curve, upon which other masses experience a gravitational force as a result of the curvature. That this does not constitute action at a distance can be seen when the first mass is moving, causing the gravitational force on other masses to change. As shown by general relativity, this change does not occur instantaneously: The change in curvature has to propagate sufficiently far in space-time before it can reach distant masses. Physical interactions happen only locally, and what haunted Newton is resolved; a consistent theoretical underpinning has been gained. But perhaps the most impressive consequence of curved space-time can be experienced in cosmology, in which general relativity determines the temporal evolution of the universe itself.
LIMITS OF SPACE AND TIME: THE END OF A THEORY
Beware of asking for more time: no ill fate ever grants it.
—MIRABEAU
Promoting space-time from a mere stage, serving only to support the change of matter, to a physical object in the theory of relativity is a revolution (figure 2). The complicated interplay—matter curves space, and its own motion is influenced by curvature—leads to a mathematical description of unprecedented difficulty, keeping not only physicists but also mathematicians busy up to the present day. Fortunately, the theory is now sufficiently well understood to reveal many fundamental implications for our understanding of physical behavior, in particular that of the universe. The role of space-time, now seen as a physical object, is often compared to a novel in which one of the characters is the book itself. Consequences of such a novel would surely be surprising, though hard to imagine. Independently of imagination, consequences of the physical role of space-time can reliably be computed by means of the underlying mathematics. As we will see, this has even more ominous consequences in general relativity than are suggested by the example of the novel.
Before entering this dark chapter of so-called singularities, we will once more have a look at the relationship between gravity and the transformability of space and time. The division between space and time is influenced not only by velocity, but also gravity as caused by matter. For instance, time proceeds faster at higher altitudes, where the distance to the center of the earth is larger.7 As before, such changes are usually imperceptibly small, but they do by now have technological relevance. The most precise atomic clocks experience a significant change in their rate when they are raised by just ten meters! As already mentioned, these effects, in addition to those due to velocities, must be taken into account if relativity is to be tested by means of atomic clocks on airplanes. (In this case, the gravitational effect is even larger than the velocity effect, and both are opposite to each other: At high velocities, clocks should be slower, but in an actual experiment with the typical altitudes and velocities of airplanes they are faster as a result of gravity.)