Chapter Excerpt

Chapter 14
Allegro (Ma Non Troppo)
Passage for Strings

I’ve got the world on a string.
—Frank Sinatra

Quantum mechanics and general relativity peacefully coexist over a wide range of distances, including all those that are accessible to experiments. Although both theories should apply on all length scales, the two theories have a mutual understanding about which of them dominates at measurably long and short distances. Quantum mechanics
and general relativity can peacefully share territory because each respects the other’s authority in its designated domain. General relativity is important for massive extended objects, such as stars or the galaxy. But gravity’s influence on an atom is negligible, so you can safely study an atom ignoring general relativity. Quantum mechanics,
on the other hand, is critical at atomic distances because its predictions for an atom are substantial and differ significantly from those of classical physics.

However, quantum mechanics and relativity do not have an entirely harmonious relationship. These two very different theories never adequately negotiated the extremely tiny distance known as the Planck scale length, 10−33 cm. From Newton’s gravitational force law, we know that the strength of gravity is proportional to masses and inversely proportional to distance squared. Even though on atomic scales, gravity is weak, the gravitational force law tells us that on even tinier scales, the force of gravity is enormous. Gravity is important not only for very massive extended objects, but also for objects that are in extremely close proximity, separated by the minuscule Planck scale length. If we try to make predictions about this unmeasurably small distance, both quantum mechanics and general relativity would contribute significantly, and the two theories’ contributions would be incompatible. Neither quantum mechanics nor gravity can be neglected in this contested territory, where quantum mechanical and general relativity calculations fail to cooperate, and predictions are bound to fail.

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