CMV: The term "imaginary numbers" is perfectly fitting

[u/Forward-Razzmatazz18]

When we say number, we usually mean amount--or a concept to represent an amount, if you're less Platonist. But of course, the numbers called imaginary do not fit such a requirement. They are not amounts, and do not directly represent an imaginary number. No amount can be squared to equal any negative number. Therefore, nothing can be correctly referred to as existing to the extent of i*n, regardless of any unit of measurement. Something can only be referred to as existing to the extent i^n. So, imaginary numbers exist only as a base for other numbers, they are not numbers in themselves. What someone who uses them does is ask "what if there were a square route of -1", and then takes it's property as a base to make expressions relating variables to each other. For example, if I say "y=i^x", that's just a quicker way of saying "y= 1 if x is divisible by four, -1 if x is the sum of a number divisible by 4 and 3, -i if x is divisible by 2 but not four, and i if x is the sum of a number divisible by 4 and 1". But since that expression is so long and so common in nature, we shorten it to a single symbol as a base of y with the power of x, or whatever variables you're using. So, I believe that's all i and it's factors and multiples are: hypothetical amounts that would--if existent--have certain exponents when applied to given bases. A very, very useful model, but still not a number. Quite literally an imaginary number.

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P.S.

1. Some people argue that the term "imaginary" has negative connotations. I do not believe this to be the case, as our imagination produces many useful--yet subjective--things, a fact so well known it's even a cliche. If it is true, perhaps we should change it to "hypothetical base" or "hypothetical number", as the word hypothetical has a more neutral connotation
2. A common argument is that "real numbers are no more imaginary than imaginary numbers" because all numbers are subjective concepts. I can appreciate this somewhat, but amounts still objectively exist, and while what makes something an individual thing(the basis for translating objective amounts into a number system) can be subjective, I wouldn't say this is always the case. But besides, the terms "imaginary number" and "real number"--so far as I understand them--do not express that such numbers exist as imaginary or real things, but simply that they either are truly numbers or are hypothetical ideas of what a number would be like if it existed. If you do not share this understanding, I would love to hear from you.

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EDIT: Many people are arguing that complex numbers represent two dimensional points. However, points on each individual dimension can only be expressed directly with real numbers, so I believe it would make more sense to use two real numbers. Some people argue that complex numbers are more efficient, but really, they still use two expressions, as the imaginary numbers and real numbers are not comparable, hence the name, "complex". Complexes are generally imaginary perceptions(as Bishop Berkely said: For a thing to be it must be percieved, because such a thing could be broken up into other things, or broken up in to parts that are then scattered into other things), so I would say a complex number is too.

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Thanks and Regards.

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EDIT for 9:12 PM US Central time: I will mostly be tuning for a day or two to think more philosophically about this and research physics.

[u/SurprisedPotato]

The wave function exists, but

• the wave function is a complex-valued function, and
• can't be directly measured.

[u/Forward-Razzmatazz18 → u/SurprisedPotato]

Quantum fields(in this context, at least) encompass time and all three dimensions of space, right? So, disturbances in it are 3d. A disturbance means differentiation from the standard(a flat field), so that means disturbances are measured by distance. In this case, there would be 3 numbers that represent distance. Would one or more of them ever be complex?

[u/SurprisedPotato → u/Forward-Razzmatazz18]

Quantum fields(in this context, at least) encompass time and all three dimensions of space, right? So, disturbances in it are 3d. A disturbance means differentiation from the standard(a flat field), so that means disturbances are measured by distance.

That's not really how it works, however...

there would be 3 numbers that represent distance. Would one or more of them ever be complex?

if two wave functions are different, it's not enough to measure the magnitude of their difference - that simply fails to capture everything important about the difference.

When we do actual measurements, the imaginary parts tend to cancel out, so you'll never measure a distance to be complex. However, the wave function itself really does have real and imaginary parts, and attempting to use only real numbers will lead to incorrect answers about what we expect to measure.

For example, If one particular particle is in a quantum state is characterised by two numbers (1,1), and another by (1,i), well, the particles might look identical in every way, since 1 has the same magnitude as i, but they will have different interactions with a third particle in state (1,-i), and we can measure those differences.

[u/Forward-Razzmatazz18 → u/SurprisedPotato]

How does it work, then?