A good cartoon is that a form factor is the function that describes how an object deforms when exposed to an outside influence with a particular momentum. The form factor is a function of momentum.
There are many different kinds of outside influence. They can be scalar (think: just increasing the pressure uniformly), vector (put in an electric field), tensor (zap with a gravitational wave), pseudovector (magnetic field), pseudoscalar (zap with a pion).
Of course, you can apply a scalar outside influence and a vector at once. But the scalar, vector, tensor, pseudovector, and pseudoscalar labels denote different representations of the Lorentz group [lorentz].
What's more: the Wigner-Eckhart theorem [wigner] basically says [cheat] that the response can be factored into three pieces: the strength of the external influence, a factor that depends only on the representation of the external influence, and a factor that depends only on the property of the thing you're talking about (a proton, in this instance).
So people call it the gravitational form factor because if you exposed the proton to a gravitational wave, it's the thing you need to know about the proton to know how it deforms.
Note that because of the factorization you don't actually have to zap the proton with a gravitational wave! You can measure it by zapping the proton with other stuff, as long as you can get that stuff to have the right rotational properties or measure the response to many different perturbations and sum the responses the right way to mock up a tensor operator. The experiment at JLab doesn't use gravitational waves, it uses these latter approaches.
Roughly speaking at zero momentum the form factor is the charge of the object you measure if it's just sitting there. So the electric form factor evaluated at zero momentum is the electric charge, the gravitational form factor evaluated at zero momentum is the mass.
What are radii? Express the form factor as a function of momentum^2 [possible]. In units that physicists like to work in (where c=1, hbar=1), the units of momentum are 1/length. Expand the form factor as a Taylor series in momentum^2 and you will get
form factor(p) = charge + # radius^2 p^2 + ...
where # is a known dimensionless number.
The above story is a cartoon but can be made more-or-less precise depending on how much quantum field theory you learn.
cheat: this is a little bit of a cheat, it's only true to leading order in a taylor series in the strength of the external influence.
possible: it's always possible to arrange this, or at least to separate the momentum dependence into a factor dictated by the rotational symmetry properties and another factor dictated by the object, just like in the Wigner-Eckhart theorem.
There are many different kinds of outside influence. They can be scalar (think: just increasing the pressure uniformly), vector (put in an electric field), tensor (zap with a gravitational wave), pseudovector (magnetic field), pseudoscalar (zap with a pion).
Of course, you can apply a scalar outside influence and a vector at once. But the scalar, vector, tensor, pseudovector, and pseudoscalar labels denote different representations of the Lorentz group [lorentz].
What's more: the Wigner-Eckhart theorem [wigner] basically says [cheat] that the response can be factored into three pieces: the strength of the external influence, a factor that depends only on the representation of the external influence, and a factor that depends only on the property of the thing you're talking about (a proton, in this instance).
So people call it the gravitational form factor because if you exposed the proton to a gravitational wave, it's the thing you need to know about the proton to know how it deforms.
Note that because of the factorization you don't actually have to zap the proton with a gravitational wave! You can measure it by zapping the proton with other stuff, as long as you can get that stuff to have the right rotational properties or measure the response to many different perturbations and sum the responses the right way to mock up a tensor operator. The experiment at JLab doesn't use gravitational waves, it uses these latter approaches.
Roughly speaking at zero momentum the form factor is the charge of the object you measure if it's just sitting there. So the electric form factor evaluated at zero momentum is the electric charge, the gravitational form factor evaluated at zero momentum is the mass.
What are radii? Express the form factor as a function of momentum^2 [possible]. In units that physicists like to work in (where c=1, hbar=1), the units of momentum are 1/length. Expand the form factor as a Taylor series in momentum^2 and you will get
where # is a known dimensionless number.The above story is a cartoon but can be made more-or-less precise depending on how much quantum field theory you learn.
lorentz: https://en.wikipedia.org/wiki/Representation_theory_of_the_L...
wigner: https://en.wikipedia.org/wiki/Wigner%E2%80%93Eckart_theorem
cheat: this is a little bit of a cheat, it's only true to leading order in a taylor series in the strength of the external influence.
possible: it's always possible to arrange this, or at least to separate the momentum dependence into a factor dictated by the rotational symmetry properties and another factor dictated by the object, just like in the Wigner-Eckhart theorem.