TITLE: Why do we talk of the "weakness of gravity" rather than "the surprising charge to mass ratio of particles"?
QUESTION [17 upvotes]: The relative strength of gravity and electromagnetic forces is obvious — stand on a sheet of paper, and even with the whole of Earth pulling, your motion is stopped by the electric fields inside that sheet of paper.
Great.
This is often phrased as "gravity is the weakest of all forces" or some variant thereof. This seems equivalent to saying "the mass-to-charge ratio of fundamental particles is such that charge dominates".
My problem with phrasing it as "gravity is the weakest" is that different particles have different mass-to-charge ratios: according to this chart on Wikipedia, mass-to-charge ratios vary by over 6 orders of magnitude, even if you exclude massive neutral particles like the neutrinos where gravity is infinitely stronger.
With such a wide range of mass-to-charge ratios, why is the question usually phrased as being about the strength of forces? Why invoke extra dimensions for gravity to leak into (for example) when one also needs to explain an extra factor of -5.588×10^6 between top quarks and electrons? (I'm assuming that infinities would get explained away differently, but perhaps not?)
(Hope this isn't a duplicate, my searching mainly showed a lot of "why is gravity weak?" type questions, which isn't what I'm curious about — I want to know why phrasing it like that is seen as the best way of thinking about the problem).

REPLY [3 votes]: Comparing forces for particles brings us to the quantum mechanical framework, the underlying framework of nature.
Forces, quantum mechanically are represented as exchanges of particles in Feynman diagrams, and the probability of the interaction happening follows mathematically from that.
For example here is the Feynman diagram for same charge repulsion:

A  physics student  at graduate level, from this diagram follows a recipe that leads to  a computable integral, and the calculation  will show the repulsion of  like charges.
The strength of the interaction enters at the two vertices of the diagram and is given by the coupling constant.
Here are the coupling constants of the rest of the interactions.




It is in this sense that gravity is compared as the weakest of all forces.
The diagram of the two electrons could represent the exchange of a graviton, but when compared to the electromagnetic exchange of a photon , the probability of the gravitational interaction is  tiny :  in the integral the coupling constants enter multiplicatively and the calculational recipe raises them to the  fourth power .
This is the framework where all known forces are compared. Of course gravity is not yet quantized rigorously, only effective theories exist, but it is within this theory that the statement of gravity being weakest is clearly evident.
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