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You use units to make it convenient to talk about numbers. It's easy to do mental arithmetic with small numbers and hard to do mental arithmetic with scientific notation. So we tend to choose units where values of interest have numerical values between one-tenth and ten thousand (with a lot of give and take). For instance, we use the non-SI "astronomical ...

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is there any requirement to measure whether the durations of 9 192 631 770 periods of different primary frequency standards and/or of the same primary frequency standard in different trials, had been and remained equal to each other, by (presumably) unambiguous means (such as the "ideal clocks" described in MTW §16.4) ? There's no explicit mentioning of ...

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is there any requirement to determine (and possibly correct for) the perturbation, or "shift", of any and all primary frequency standards, besides the described "shift due to ambient radiation"? Yes. These are called "systematic errors" and they are the order of business pretty much all day, every day, at the metrology labs that implement frequency ...

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I'm not going to talk about the misunderstanding you have, but about the actual question you asked.The mass energy equivalence equation is $$E^2=(mc^2)^2 + (pc)^2$$ ($p$ is the momentum of the body). If we use specialized units such that $c$ (the speed of light) becomes dimensionless, we can have the same units for mass and energy. (This can be done, for ...

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Is there any rationale from the standpoint of physics to choose candela as a base SI unit? That's still the wrong question. The right question: Why do these standards (any of them) exist? The answer is commerce and industry. The SI doesn't exist to support the sciences; that it does support the sciences is a nice side benefit. It exists to support ...

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Wikipedia gives the origin of the unit, with references, starting from the previous definition of 'candlepower' (based on an actual candle), through the redefinition in terms of a perfect blackbody emitter at the melting temperature of platinum, to the modern definition which may more easily be realised experimentally.

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That definition is for calibration. Luminosity is based on a standardized model of human eye and takes into account sensitivity of human eye to different wavelengths. Two source with the same intensity but different frequency have different luminosity. Luminosity is related to intensity and frequency by the luminosity function.

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