This question is my extension to this one. Please excuse if it sounds too naive, as I am not a physicist by trade.
From the above linked question and answers to it I understand no physical phenomena or properties in classical mechanics or thermodynamics can be "truly" negative, but only relative to some arbitrary reference point. I'm unsure about electrostatics, though. Electric charge occurs naturally in two elementary forms of a same "size", but opposite "sign". This "sign" is more than just a mathematical fiction; it is physically observable, as attraction resp. repulsion of other charges, depending on their sign. The question for me is whether opposite charges make these entities completely different by nature, or are they simply properties of one and the same entity.
For example, can we say that positron and electron are physically the same object, once carrying a "positive" and once a "negative" charge, or are they different kinds of objects that happen to have a same mass? Something along the lines: "If we flip the spin of an electron, it still remains an electron, but with an opposite spin". Can we make this analogy regarding electron/positron: If we flip the charge of a negatively charged "x-tron" (an electron), it still remains an "x-tron", but with a positive charge?
From my limited knowledge of quantum mechanics, I recon the answer to this last question is "No", implying that even in electrostatics negative numbers are just a mathematical trick we use to simplify descriptions of the nature, but I'd appreciate if someone could confirm that.
I acknowledge that my above reasoning is related to this question, but it is not the same IMO.
Best Answer
I think you are reading too much into the significance of negative numbers. We need to use numbers in physics to quantify things. Take distance, for example- if I walk from my desk I can qualify the extent of my movement by saying that I have walked 10 metres, say. If I walk another 10 metres to return to my desk, I have walked 20 metres in total, but my overall displacement is zero. You will see at once that the overall displacement is not the same as the sum of the lengths of the two legs of my short journey, but is equal to the difference between them because they were in reverse directions. We deal with this by adopting a convention that distance measured in one direction is positive and in another is negative. The negative sign is just a shorthand indication of the fact that we need to take one number away rather than adding it when we are calculating the total displacement.
The use of positive and negative charge is entirely analogous. We know from experiment that there are two types of charge- and that like charges repel while unlike charges attract. We also know that having equal numbers of unit charges cancel each other out, so if we have four of the first type and seven of the second type, their combined effect is the same as having three of the second type. Again we can use a negative charge just as a shorthand reminder that when we are quantifying the combined effect of multiple charges we need to subtract the number of one type from the number of the other.
Now, when you ask whether electrons and positrons are two different things, or whether they are the same thing with different charge attributes, the rhetorical answer is what difference does it make? You can describe them either way, but it doesn't make any difference to their physical properties.