# What is a charge? [duplicate]

If mass is the measure of the inertia of a body, then what is a charge?

Everyone tells that it is a fundamental property but i believe it must have a unique definition. Anyone know in this regard?

• What's wrong with the definition of Wikipedia: "Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field.". What about it doesn't work? Mar 15, 2016 at 3:23
• rather than a property is it possible to relate it to another meaningful measure?like mass in the example
– user111211
Mar 15, 2016 at 3:27
• Mass is also a property, but it is an unrelated one. Well, it is related in the sense that a charged body has to have rest-mass and that the lightest body that can hold a charge of one electron charge has the rest-mass of an electron, but other than that there is no fixed ratio. Mar 15, 2016 at 3:29
• To be very clear inertia is the property of matter whereby it resists changes in the vector velocity (or more properly momentum, but you have to go around a couple of times before that version is clear), and mass is a measure how much of that property a object has. Mar 15, 2016 at 3:40

Mass is slightly more complicated than you've stated: mass is a measure of both an object's inertia and its tendency to interact with other objects via gravity. It's the case in general relativity that an object's gravitational mass and its inertial mass are exactly the same, because inertia and gravity are both properties of the interaction between matter and spacetime. Vigorous searches for violations of this equivalence principle have turned up no evidence to the contrary.

In that second sense, mass is a sort of "gravitational charge": two objects with masses $m_1, m_2$ at rest and separated by a distance $r$ have a gravitational interaction energy $$U_\text{grav} = -G \frac{m_1 m_2}r$$ which is proportional to the product of the masses.

It turns out that gravity is not the only way that objects can interact with each other. Objects at rest separated by a distance $r$ also have an interaction energy $$U_\text{elec} = \alpha \hbar c \frac{q_1 q_2}r$$ where the dimensionless "fine structure constant" is given by $\alpha \approx 10^{-2}$, the constant $\hbar c \approx \rm 200\,MeV\,fm$ corresponds to a tiny amount of energy even at tiny distances, and we have a funny empirical fact that every observed value of $q_i$ is an integer. For historical reasons (there was no reason to suspect $q$ was always an integer) we define "electric charge" of an object as $qe$ rather than $q$, with $e^2 = 4\pi\epsilon_0\alpha\hbar c$ having some other historically-interesting constants involved and an annoyingly small value in macroscopic units.

We can actually re-write the gravitational interaction the same way, $$U_\text{grav} = -\frac{\hbar c}{M_P^2} \frac{ m_1 m_2 }r.$$ However the ratio between the mass of a typical lump of matter --- a proton --- and the "scale mass" for gravity, $M_P = \sqrt{\hbar c/G}$, is about $10^{-19}$, which suggests this is not a useful direction to go in. There is no evidence that the masses $m$ of common particles are small integer multiples of anything, so that isn't a simplifying approximation in the same way. We find ourselves living in a world where there are a fairly small number of building blocks for ordinary matter, each with a different ratio of charge to mass $q/m$, and no obvious pattern among them.

There are two other interactions that we know about which are governed the same sort of way. One is a "strong" interaction with $\alpha_S \approx 0.1$ and charge that comes in integer lumps --- three types of "color" charges for matter, and anti-colors for the antimatter, with the possibility of making "uncharged" objects by combining all the colors. Another is a "weak" interaction with $\alpha_W \approx 10^{-4}$ and approximately integer lumps of charge, for a complicated and beautiful reason which is too much for your question. (Experts: the weak charge of the neutron is 1, and the weak charge of the proton is $1-4\sin^2\theta_W$.)

So there's a long-winded definition with some examples for you: a "charge" is a property of matter which describes the strength of its interaction with other matter via different features of the vacuum. So far as anyone knows there are four of these interactions.

Assuming by charge, you mean electric charge,

According to Quantum Electrodynamics, (which is the most successful theory of Nature,) the fundamentality nature of the electric charge, (as a quantum number,) is due to the fact that it represents the coupling 'constant' between matter field and electromagnetic field.

A charge has a lot more properties than only the one you mentioned.

The distinctive feature is the electric field by which a charged particle is surrounded. It is a convention that electrons negativ charged and protons positive charged. Charged particles could be separated into negativ and positive charged particles. In rigid bodies it is possible only to move a more or a less of electrons inside one body. So a capacitor has two foils (plates), separated by an isolating gap or material. Between the plates the separated charges produce a common electric field. Using a capacitor with extended distances it is possible to use them as a measurement instrument. Putting a particle between the charged plates, one will observe a movement to one of the plates (in one direction for negative charged particles and the other direction for positive charged particles) or nothing for uncharged particles. The charge of electrons and protons as well as of their anti-particles are intrinsic properties. This means that we believe that they are exist without any influence by external fileds.

Charges have the property of mass, of magnetic dipole moment and of intrinsic spin. The last two properties are a unit. Moving a charged particle (electron, positron, proton, ...) through a magnetic field leads to the deflection of the particle from its straight path. This happens if the direction of the magnetic field is not parallel to the movement of the charges or if the magnetic field is moving in space (again non-parallel to the moving charge) or the magnetic field is varying in strength.

This bring us to the last property of charges. They able to absorb and re-emit photons. During straight and positive accelerations due to an observer they absorb the energy of photons (but re-emissioning photons of lower energy). During acceleration in circle or spirals and during breaks above all they emit photons.

• Did you mean to make accelerating in the same direction as velocity and accelerating in the opposite direction of velocity sound physically different? Because that's a frame dependent notion. And your answer combines quantum things like spin and classical things like a trajectory in the same direction as a classical field at the point of the trajectory. Very confusing. Mar 15, 2016 at 15:41
• @Timaeus I was not sure that XB Overlord knows that braking is an acceleration too. And what confuses you? Mar 15, 2016 at 16:16
• You claim that accelerating in the direction of velocity absorbs photons and emit photons. Then you make it sound like when you accelerate in the opposite direction as velocity that you merely emit photons (but do not absorb). But different observers disagree about whether the acceleration in the direction of velocity or in the opposite direction as velocity. So did you really intend to make it sound like these are physically distinct things? Mar 15, 2016 at 16:21
• @Timaeus I added "due to an observer". Would it be clearer? Mar 15, 2016 at 17:08
• I guess its more clearly wrong. My questions were not rhetorical. You really are trying to claim that switching frames changes whether photons are absorbed? Mar 15, 2016 at 17:59