Confusion on metrological terminologies in physics I had came across many physicists or engineers use words like Measurable, Detectable, Observable and Quantifiable.
Are those words synonymous in physics in general, in the field of metrology or in engineering?
 A: No, these are not synonyms, although some if these terms can be - depending on the context.
Quantifiable means that it can be described numerically and compared using greater/lesser/equal operators. E.g., length is quantifiable, but symmetry or presence/absence of a property are not.
Observable often appears in the context of quantum mechanics to distinguish from the methematical quantities, which are used to describe a phenomenon, but which cannot be themselves observed/measured - they exist only in human minds.
Measurable can be synonymous with observable in QM context, but it may also be synonymous with detectable in a more mundane setting, meaning that our devices are sufficiently sensitive to detect something. The quantity might be present, quantifiable and observable, but too weak, and hence below the detection threshold of our measuring devices.
Another important example is the electric and magnetic fields in electromagnetic waves - these are real physical fields, which are too difficult to measure - what is usually detected is the field intensity (roughly its amplitudes squared and averaged over detector response time.)
The exact meaning of the terms may vary among different fields, but the examples above show that they are not the same thing.
