An Introduction to String Theory

Slide 18 of 37
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A bigger failure comes when we try to put gravity and quantum field theory together: it's basically a train wreck. Because QFT must sum over every possible state, those states must include cases where the energy of one leg of a "loop" gets infinitely large. In QFTs that work, there are well-defined ways to make sense of those infinite sums. But in gravity, the strength of the interaction (corresponding to e in QED) is proportional to the energy of the particles. Thus, when the energy gets large, the sum over histories can't converge, and the theory breaks down.

In short, our understanding of nature is clearly incomplete, because the theory describing gravity simply cannot coexist with the theory describing everything else. That doesn't tell us what form the solution will take, of course! But there is no doubt that something more is needed.