How to denote a larger distance
Suppose I have some measurement with interferometer number 1, let's call the result A, and another measurement with interferometer number 2, let's call that one B. Suppose that always A>B (in some known, fixed coordinate system and units; the numbers can be negative). What the best way to describe this in words?
- Interferometer #1 measures a larger distance than #2.
- Interferometer #1 measures a higher distance than #2.
- Interferometer #1 measures a bigger distance than #2.
- Interferometer #1 measures more than #2.
- Interferometer #1 measures less negative than #2.
- Interferometer #1 measures a more positive number than #2.
- Interferometer #1 measures a less negative number than #2.
I would like to use "a larger distance" but I find that unclear when comparing A=-5 with B=-6.
Solution 1:
I don't think any of the seven alternatives sound correct.
First off, when dealing with distances, the comparators "longer" or "greater" work better than "larger," "higher," or "bigger." Larger would imply some kind of area or volume; higher implies height or altitude, and bigger is simply too vague, and doesn't sound sufficiently scientific.
However, all seven alternatives seem to imply that the measuring device #1 is capable of measuring a longer distance than measuring device #2, rather than comparing the two measurements themselves.
When A and B are both positive, simply say, "Measurement A is greater than Measurement B," or, "The measurement taken from Interferometer #1 was greater than the measurement taken from Interferometer #2."
When A and B are both negative, use, "Measurement B is less than Measurement A," or, "The measurement taken from Interferometer #2 was less than the measurement taken from Interferometer #1."
Moreover, this assumes that the magnitude is not as important as the real value, which isn't always the case in physics. One might need to say, "The magnitude of Measaurement B was greater than the magnitude of Measurement A," in the case where, say, A = 2, and B = -5.
If you're asking if there is a single set of words to use - irrespective of whether the values are positive or negative - I can't think of a good template to use.
Solution 2:
In English, a distance is always positive. Positive values can be compared using larger/higher/bigger. because there is a minimum (zero). Your measurements allow negatives, so they shouldn't be described with 'a larger/higher/bigger/greater distance'.
You can still compare values, saying 'less than' or 'greater than'. However, you've set up your sentence so that using less/greater will sound strange: "Thing A measures a value greater than Thing B", the infelicity being from the verb 'measures' which takes an object 'value'/'measurement' (it's perfectly grammatical, and it seems reasonable to try that, it just turns out to have all the unsatisfying ways that you listed).
Because of negative values, I'd suggest using 'X is greater than Y'. For example:
The measurement from interferometer #1 is greater than the measurement from #2.
or
Interferometer #1's measurement is greater than #2's.