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What are all the fields that we know so far that can be associated to charges of the kind "+" and "-" (not necessarily the electric +/- charges). I already know the EM field. Are there other examples? Will the disturbances in such a field propagate slower than the speed of light? (like for the EM field)

Example: not gravity because we haven't found anti-gravity (or "negative mass" particles that climb the gravitational field in the opposite direction).

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    $\begingroup$ Fields are mathematical constructs used to describe physical phenomena. They aren't physical things themselves. But to answer your last sentence any field describing something that has mass like sound, pressure, density, movement of gasses, movement of fluids, temperature, topographical height, deformation/strain etc. Fields need not be vectors. $\endgroup$
    – DKNguyen
    Apr 27, 2023 at 0:35
  • $\begingroup$ What about the gluon field of QCD and the electroweak field of EW? i.e. do you accept charges outside of the EM type? If you only want to talk about EM charges, then one has to point out that there should only be one theory governing one kind of physical phenomena in use at any one time. $\endgroup$ Apr 27, 2023 at 9:16

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I think pretty much any problem that is formulated as a continuity equation with a non-zero "source" term can be described in similar terms. In differential form the continuity equation is $$\frac{\partial\rho}{\partial t}+\vec\nabla\cdot\vec J = g$$ where $\rho$ is the spatial density of a quantity that is conserved in some sense (think number of particles per unit volume), $\vec J$ is the flow rate or "flux" of this quantity (particle current density, i.e. flow per unit time per unit area), and $g$ is the rate at which this quantity is generated or "sourced" per unit volume (how fast particles are created). To see how this fits with electrostatics, compare with Gauss' law: $$\vec\nabla\cdot\vec D = \rho.$$ We see that charge density "sources" the E-field, which serves as the "flow rate".

The classic analogy for electrostatics is the flow of an incompressible fluid that fills all space. In this analogy, charge ($\text C$) becomes the rate at which fluid is sourced into (positive) or sinked out of (negative) the space ($\text{kg/s}$), $\vec E$ ($\text{V/m}$) becomes fluid velocity ($\text{m/s}$), and $\epsilon$ ($\text{F/m}$) becomes the fluid density ($\text{kg/m}^3$). There are lots of other examples, here are just a few:

  • Heat flow: the field is heat flux, the charge is the rate at which heat is generated/absorbed.
  • Current flow: the field is current density, the charge is the rate at which electric charge is sourced/sinked.
  • Electromagnetic energy flow: the field is Poynting's vector, the charge is the rate of work done on electric charges.
  • Statistical description of the motion of a system of particles: the field is the flow of particles in phase space, the charge is the rate at which particles are "generated" via collisions.
  • Newtonian gravity: the field is the gravitational field, the charge is mass. There is only one type of charge (positive or negative).
  • Gravitoelectromagnetism is entirely analogous to electromagnetism, magnetic fields an all, where again the charge is mass.

If you are looking for "charges" that are conserved (i.e. the amount of total charge is constant), see the examples listed here, along with Noether's theorem.

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