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Are there any known (measurable continuous) physical quantities, which are neither base quantities of SI, nor are derivable from the base quantities?

In other words, are there any quantities which require units not part of SI?

I am not including in this question quantities that are dimensionless (such as angles), or that have an inherent unit (such as discrete quantities, e.g. 1 bit).

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  • $\begingroup$ Related. $\endgroup$ – rob Aug 2 '18 at 20:21
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    $\begingroup$ Electrical charge is a discrete quantity, so be careful there. However, at the scale of the macroscopic human interactions (which is what the SI is all about), charge appears to be continuous. Since the SI exists primarily for commerce, things that appear only at the quantum scale are a bit irrelevant to the SI. In particular, quantum chromodynamics. There is no SI unit for color charge. $\endgroup$ – David Hammen Aug 2 '18 at 21:12
  • $\begingroup$ @DavidHammen I made a point of excluding discrete quantities like color charge since no standard unit is required in such cases, and would therefore not be missed even if SI endeavoured to cover all of the quantities of modern physics. A good answer to the question would be a continuous quantity only relevant at quantum scale, and therefore not included in SI, but that does seem rather a contradiction in terms. Does such a quantity exist? $\endgroup$ – Heisenbugs Aug 2 '18 at 21:35
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As you get farther and farther from electro-mechanical physics, you'll pick up more and more non-SI units that are arguably still "physical".

For example, the CIE system of color has measurable continuous values that aren't, strictly speaking, derivable from SI base units.

enter image description here

(WikiCommons, see above link). The axes are "X and Y chromaticity".

Further away, getting into the social sciences, you'll find things like Gross Domestic Product that are measurable and continuous (at least in the sense the electrical charge is), but not directly related to SI units.

Are those physical? Yes, in the same sense that potential energy is: They are caused by, and can in turn make stuff happen in, the physical world.

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No.

Information is not a quantity which has a unit given in the SI that is arguably of fundamental physical importance and a universal quantity (i.e. is applicable across the entire Universe, as far as we can understand). Granted, it could be considered dimensionless, but then again, so could plane angle and the SI provides the radian to measure that. The units bit (or "shannons" when referring to information had, not information storage capacity), byte (= 8 bits), nat (~1.44 b), hartley (~3.32 b), etc. are not SI units.

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