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String theory has, even among theoretical physicists, the reputation of being mathematically intimidating. But many of its essential elements can actually be described simply. This article aims to answer a few basic questions. How does string theory generalize standard quantum field theory? Why does string theory force us to unify general relativity with the other forces of nature, while standard quantum field theory makes it so difficult to incorporate general relativity? Why are there no ultraviolet divergences in string theory? And what happens to Albert Einstein’s conception of spacetime? Anyone who has studied physics is aware that although physics—like history—does not precisely repeat itself, it does rhyme, with similar structures appearing in different areas. For example, Einstein’s gravitational waves are analogous to electromagnetic waves or to the water waves at the surface of a pond. I will begin with one of nature’s rhymes: an analogy between quantum gravity and the theory of a single particle. Even though we do not really understand it, quantum gravity is supposed to be some sort of theory in which, at least from a macroscopic point of view, we average, in a quantum mechanical sense, over all possible spacetime geometries. (We do not know to what extent that description is valid microscopically.) The averaging is performed, in the simplest case, with a weight factor exp(iI/ℏ), where I is the Einstein–Hilbert action: I=116πG∫d4xg‾√(R−2Λ). Here G is Newton’s constant, g is the determinant of the metric tensor, R is the curvature scalar, Λ is a cosmological constant, and d4x is the spacetime volume element. We could add matter fields, but we do not seem to need them. Let us try to make such a theory with one spacetime dimension instead of four. The choices for a one-manifold are quite limited: Moreover, the curvature scalar is identically zero in one dimension, and all that’s left of the Einstein–Hilbert action is the cosmological constant. However, Einstein’s fundamental insights were not tied to the specific Einstein–Hilbert action. Rather, they were in the broader ideas that the spacetime geometry can vary dynamically and that the laws of nature are generally covariant, or invariant under arbitrary diffeomorphisms (coordinate transformations) of spacetime. (See the article by Michel Janssen and Jürgen Renn on page 30.) By applying those insights, we can make a nontrivial quantum gravity theory in one dimension provided we include matter fields.

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弦理論は、理論物理学者の間でさえ、数学的に威圧的であるという評判を持っています。しかし、その重要な要素の多くは、実際には簡単に説明できます。この記事は、いくつかの基本的な質問に答えることを目的としています。弦理論は標準量子場理論をどのように一般化するのか？弦理論はなぜ一般相対論を統一することを強いるのか

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String theory has a reputation that it is mathematically intimidating even among theoretical physicists. However, many of its important elements can be explained briefly in practice. This article is intended to answer some basic questions. String theory is based on standard quantum field theory

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弦理論は、理論物理学者の間でさえ数学的に脅迫的であるという評判を持っています。ただし、その重要な要素の多くは実際には簡単に説明できます。この記事はいくつかの基本的な質問に答えることを意図しています。弦理論は標準的な場の量子論に基づいています

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String theory has a reputation that it is mathematically threatening even between theoretical physicists. However, many of its important elements can be explained briefly in practice. This article is meant to answer some basic questions. String theory is based on the standard field quantum theory

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弦理論は、理論物理学者の間でさえ数学的に脅威を与えているという評判を持っています。ただし、その重要な要素の多くは実際には簡単に説明できます。この記事はいくつかの基本的な質問に答えることを意図しています。弦理論は標準場の量子論に基づいています

BACK INTO ENGLISH

String theory has a reputation that it poses a mathematical threat even among theoretical physicists. However, many of its important elements can be explained briefly in practice. This article is meant to answer some basic questions. String theory is based on standard field quantum theory

INTO JAPANESE

弦理論は理論物理学者の間でさえ数学的脅威をもたらすという評判を持っています。ただし、その重要な要素の多くは実際には簡単に説明できます。この記事はいくつかの基本的な質問に答えることを意図しています。弦理論は標準場の量子論に基づいています

BACK INTO ENGLISH

String theory has a reputation that it brings mathematical threat even among theoretical physicists. However, many of its important elements can be explained briefly in practice. This article is meant to answer some basic questions. String theory is based on the standard field quantum theory

INTO JAPANESE

弦理論は理論物理学者の間でさえ数学的脅威をもたらすという評判を持っています。ただし、その重要な要素の多くは実際には簡単に説明できます。この記事はいくつかの基本的な質問に答えることを意図しています。弦理論は標準場の量子論に基づいています

BACK INTO ENGLISH

String theory has a reputation that it brings mathematical threat even among theoretical physicists. However, many of its important elements can be explained briefly in practice. This article is meant to answer some basic questions. String theory is based on the standard field quantum theory