Edit: my question is not directly about Feynman diagram, but instead about the nature of off shell objects, were they as common as the on shell ones. I am trying to suggest that if an electron goes off shell in a suitable way, then it will be impossible to tell it apart from muon. Again, i have no intention to directly refer to internal lines in Feynman diagram.
A particle is said to be moving off shell if $E^2-p^2\neq m^2$, where $m$ is the known rest mass of the particle.
But how do we measure the rest mass of a particle for the first time?
We measure it by using the formula $E^2-p^2= m^2$. (We accelerate the particle in a known electric field, measure the acquired velocity and then calculate the mass using the equations of Special relativity.)
Now, thankfully, in everyday life, when we repeat this experiment, we get the same value for the mass, making us believe that the rest mass is a constant.
But in QFT, we come across the idea of off shell motion, in which, $E^2-p^2= (m+a)^2$, where $m$ is the 'known' rest mass and $a$ is an arbitrary number.
So, basically, a particle moving off shell will appear as a normal particle with a slightly different mass. So, for a person who is unaware of its known rest mass, a particle moving off shell would appear as a completely normal relativistic particle.
In other words, according to my argument, muon can be considered as an electron moving off shell.
Is this interpretation correct?