## Relativity and quantum mechanics

There was just one problematic feature in the emerging quantum mechanics: it did not encompass the laws of relativity. We will meet Einstein's theory of relativity in Chapters 15 and 16; it had been put forward at the beginning of the century, and was by now well established. If relativity and quantum mechanics are both correct representations of the laws of nature, then they must fit together, and yet there appeared to be serious inconsistencies between the two. For example, Schrodinger's equations dealt with space and time in separate ways, but according to relativity the two must be treated on the same footing.

The dilemma appeared to be resolved by Oskar Klein (1894-1977) and Walter Gordon, but not to Dirac's satisfaction, since their methods did not fit in with his generalised quantum theory. The Klein-Gordon method was based on the relativistic relation between energy and momentum, which involves the squares of these quantities. Dirac's theory dealt only with linear mathematical relations, and quadratic relations had no place in it. While this might be considered a technicality, it presented a serious difficulty to Dirac. Such a major flaw in his generalised quantum mechanics was simply unacceptable.

The solution to the problem came in 1927 — in Dirac's own words, 'by accident, just by playing with the mathematics'.

He found that he could express the relativistic relations in a linear way, by using matrices instead of ordinary algebraic quantities. The principles of relativity now fitted neatly into his generalised quantum mechanics, and the two basic laws of nature seemed to be represented correctly in the scheme.

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