How would we distinguish them

In this golden age of atomic physics an obvious question was given serious scientific thought, atoms are small fast and hard to see. There is a fundamental rule in physics that you cannot absolutely pin down the location of an electron at any given time, this comes from the Heisenberg uncertainty principle stated below.

$$\Delta x \Delta p \ge {\hbar \over 2}$$

This formula states that there must be uncertainty in either the wavelength or the location of an electron. Due to the fact that we cannot pin down the location of any one wavelength or location together we have no way to 'prove' that any electron is separate than the one next to it at a given second. The formula above has been verified again and again in double slit experiments. As the commonly seen interference pattern in the experiment is a direct result of the the uncertainty in momentum. Image courtesy of

Another thing to note is that every electron is identical in both charge and mass. This part is actually been known for a long time. The fact that the charge is uniform is how you are reading this computer. Electrons being uniform in mass is actually a key factor in how basic wiring operates. Electricity basically works by pushing electrons through a wire, electron charge over time is how we define current. If electrons weren't uniform in charge current would be unpredictable and difficult, possible dangerous to harness. The mass of an electron can be determined by shooting it at atoms, measuring where it goes and applying kinematic equations among other ways. These ideas have been known for a while and have been tested thousands of times. As far as we can tell every electron is exactly uniform.