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How is the speed of light measured by the most current method i.e. using lasers and atomic clocks? Alternatively, is there a better method?

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The speed of light can't be measured anymore (in SI units) because it has had a defined value since 1983. See Why do universal constants have the values they do?

Before 1983, the meter was defined in terms of the wavelength of a certain emission line of krypton 86. The second is also defined in terms of an atomic standard (the frequency of a transition in cesium 133). Therefore before 1983 it was possible to measure the speed of light, and such a measurement would have consisted of comparing these two atomic standards.

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