In particular, how can you have both positrons and electrons if there is no "bit" to set or unset?
I hope this is not a stupid question, but if a particle has no internal structure, where can the difference between the electron and its antiparticle exist?
If it is due to something "external", like spin (if indeed spin is external), how do we know we can't change this by applying some external influence -- change then an electron into a positron somehow?
The full information about all properties of (free) electrons and positrons is "stored" in the (quantum) field operator $$\psi(x) =\sum\limits_s \int d\mu(p) \left[ b(p,s) u(p,s) e^{-ip\cdot x}+ d(p,s) v(p,s) e^{i p\cdot x} \right], \tag{1} \label{1}$$ being always "present" at any time-space point $x=(t, \vec{x})$ and independently of the actual state of the system (e.g. vacuum = no particle present, one electron present, one positron present, 153 electrons and 2 positrons present, and infinitely more possibilities).
Although the fermion field operator \eqref{1} is not directly observable, the operators representing the measurable quantities of the system (observables) are obtained from \eqref{1} by building (bosonic) functionals like $$Q= -e\int d^3x\, : \psi^\dagger(x) \psi(x): \tag{2} \label{2}$$ for the charge or $$P^\mu =\int d^3x : \psi^\dagger(x) i \partial^\mu \psi(x): \tag{3} \label{3}$$ for the total energy $P^0$ and the total momentum $\vec{P}$.
If a certain (pure) state $| \chi\rangle$ (out of the infinitely many possible ones) of the system is realized, the expectation value of an observable $A$ is obtained by computing $\langle \chi |A|\chi \rangle$. Let us take the most general one-electron state $$|\chi\rangle = \sum\limits_s \int d\mu(p) f(p,s) b^\dagger (p,s) |0\rangle \tag{4} \label{4}$$ as an example. In this case, we have $\langle \chi |Q |\chi \rangle =-e$ and $\langle \chi |P^\mu |\chi \rangle = \sum\limits_s \int d\mu(p) |f(p,s)|^2 p^\mu$, and analogously for other observables.
I dont think that information have size.When we say that e.g a latch stores a bit we are refering to the output voltage level.How does the latch store the voltage level?The transistors inside the gate conduct or not current and by voltage division we get the output value.But the information itself isnt something you can hold on.Information is not a physical thing.
if a particle has no internal structure, where can the difference between the electron and its antiparticle exist?
Your premise does not seem correct: a physical electron does have internal structure, as evidenced by vacuum polarization and electron's Coulomb field, which field carries at least a part of the mass of the physical electron. I wrote elsewhere:
My understanding is: when people say that elementary particles, such as electrons, are point particles, they mean that they are described by the Dirac equation / QED with great accuracy. The Nobel prize winner Dehmelt, who established strong experimental limitations on the size of the electron, wrote (Physica Scripta. Vol. T22, 102-110, 1988): "an elementary Dirac particle, such as the electron, is the closest laboratory approximation of a point particle."
And the Dirac particle is subject to uncertainty principle. Moreover, if the coordinate of the Dirac particle is measured better than the Compton wavelength, we cannot be sure we have just one particle because of possible pair production.
If it is due to something "external", like spin (if indeed spin is external), how do we know we can't change this by applying some external influence -- change then an electron into a positron somehow?
I would say, because of experimental evidence of charge conservation.
