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By Root 1009 0

of shorter distances could be a true restriction imposed by the laws of physics. As we will see in the following chapter, quantum mechanics tells us that small probes require high energies. But once the energy trapped in a small region is too big, matter collapses into a black hole. At this point, gravity takes over. More energy then makes the black holes bigger—not smaller—much as we are accustomed to from more familiar macroscopic situations where quantum mechanics plays only a limited role. We just don’t know how to explore any distance tinier than the Planck length. More energy doesn’t help. Very likely, traditional ideas about space no longer apply at this tiny size.

I recently gave a lecture where, after explaining the current state of particle physics and our suggestions for the possible nature of extra dimensions, someone quoted back to me a statement I had forgotten I’d made about the possible limitations of our notion of spacetime. I was asked how I could reconcile speculations about extra dimensions with the idea of spacetime breaking down.

The speculations for the breakdown of space and possibly time apply only at the unobservably small Planck length. Since no one has observed scales smaller than 10-17 cm, the requirement of a nice smooth geometry at measurable distances is not violated. Even if the notion of space itself breaks down at the Planck scale, this is still much smaller than the lengths we explore. There is no inconsistency so long as a smooth recognizable structure emerges when we average over larger, observable scales. After all, different scales often exhibit very different behaviors. Einstein can talk about smooth geometries of space on large scales. But his ideas might break down at smaller scales—so long as they’re so tiny and yield such negligible effects on measurable scales that the new more fundamental ingredients have no discernible impact we can observe.

Independently of whether or not spacetime breaks down, a critical feature of the Planck length that our equations certainly tell us would be true is that at this distance, gravity, whose strength is minuscule when acting on fundamental particles at the distances we can measure, would become a strong force—comparable in strength to the other forces we know. At the Planck length, our standard formulation of gravity according to Einstein’s theory of relativity would cease to apply. Unlike larger distances where we know how to make predictions that agree well with measurements, quantum mechanics and relativity are inconsistent when we apply the theories we generally use in this tiny regime. We don’t even know how to try to make predictions. General relativity is based on smooth classical spatial geometry. At the Planck length, quantum fluctuations can make a spacetime foam with too much structure for our conventional formulation of gravity to apply.

To address physical predictions at the Planck scale, we need a new conceptual framework that combines quantum mechanics and gravity into a single more comprehensive theory known as quantum gravity. The physical laws that work most effectively at the Planck scale must be very different from the ones that have proven successful on observable scales. The understanding of this scale could conceivably involve a paradigm shift as fundamental as the transition from classical to quantum mechanics. Even if we can’t make measurements at the tiniest distances, we have a chance of learning about the fundamental theory of gravity, space, and time through increasingly advanced theoretical speculations.

The most popular candidate for such a theory is known as string theory. Originally string theory was formulated as a theory that replaces fundamental particles with fundamental strings. We now know that string theory also involves fundamental objects other than strings (which we’ll learn a little more about in Chapter 17), and the name is sometimes replaced with a broader (but less well-defined) term, M-theory. This theory is currently the most promising suggestion for addressing the problem of quantum gravity.