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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.

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    $\begingroup$ I don't understand how the fact that flipping the charge of an electron turns it into a positron implies that "that even in electrostatics negative numbers are just a mathematical trick we use to simplify descriptions of the nature", and so I don't really get what you want as an answer to this question. $\endgroup$
    – ACuriousMind ♦
    Commented Nov 9, 2021 at 11:37
  • $\begingroup$ @ACuriousMind What I meant is that if positron and electron are the same "objects", where the charge is a property, like spin, then talking about "negative charge" makes physically sense. If they are not the same objects, then negative charge means simply an excess of electrons over positrons (or protons, or whatever positively charged particles). Like the "negative pressure" on a membrane simply means that there is an excess pressure on the other side. Can you confirm or deny that electric charge is a property that a particle can acquire and change, like the spin? $\endgroup$
    – Igor F.
    Commented Nov 9, 2021 at 11:45
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    $\begingroup$ I don't understand what it means for positron and electron to be "the same objects". It is a fact that they only differ in their electric charge. What does it mean for charge to be a "property like spin" as opposed to not being a "property like spin"? $\endgroup$
    – ACuriousMind ♦
    Commented Nov 9, 2021 at 11:48
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    $\begingroup$ there is a mathematical phenomena that time reversed matter would have the same effect as being the same with an opposite charge. e.g time reversed electron is mathematically identicle to a positron $\endgroup$
    – jensen paull
    Commented Nov 9, 2021 at 12:07
  • $\begingroup$ @ACuriousMind My confusion obviously stems from my lack of understanding of particle physics, and, perhaps, from ambiguities of the natural language. I understand that an electron can change its spin. It would still be called "electron". Is there a way to change its charge? For example, can I shoot an electron into a nucleus, turn two of its protons into neutrons and obtain a positron as a result? I've heard of $\beta^+$ and $\beta^-$ decays, but not of the above. Still, would any physical law speak against this possibility? $\endgroup$
    – Igor F.
    Commented Nov 9, 2021 at 12:39

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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.

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  • $\begingroup$ what I understand from electrostatics is that positive and negative charge are completely identical for our purposes, but beyond that on a more fundamental level: Is it that charge is a coin, with positive and negative being two opposite sides of it, with each having absolutely no precedence over the other; or is there any evidence supporting that 'the universe' shows any bias to one type of charge over the other in any way possible(in terms of appearance in natural processes, properties, etc.)? $\endgroup$
    – Reet Jaiswal
    Commented Nov 9, 2021 at 12:59
  • $\begingroup$ Thanks. After some thought, I believe my question was a philosophical one, concerning "identity". To get back to the spin analogy: When an electron interacts with a photon and, as a result, we obtain an electron with a different spin, the question whether the original electron changed its spin or whether it's a new electron makes no sense in physics. $\endgroup$
    – Igor F.
    Commented Nov 11, 2021 at 7:39

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