Experiments to measure it:
Given the view of the Standard Model where the electron and quarks are just completely separate matter fields, there is at first sight no clear theoretical requirement for that.
As mentioned e.g. at QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga by Silvan Schweber (1994) chapter 1.6 "Hole theory", Dirac initially wanted to think of the holes in his hole theory as the protons, as a way to not have to postulate a new particle, the positron, and as a way to "explain" the proton in similar terms. Others however soon proposed arguments why the positron would need to have the same mass, and this idea had to be discarded.
Clear experiment diagram which explains that the droplet mass determined with Stoke's law:
Video 1.
Quantum Mechanics 4a - Atoms I by ViaScience (2013)
. Source.
American Scientific, LLC sells a ready made educational kit for this: www.youtube.com/watch?v=EV3BtoMGA9c
Here's some actual footage of a droplet on a well described more one-off setup:
Video 2.
Millikan's Experiment, Part 2: The Experiment by Phil Furneaux (2017)
. Source. From Lancaster University
This American video likely from the 60's shows it with amazing contrast: www.youtube.com/watch?v=_UDT2FcyeA4

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