Something that's going to be a bit tricky here is that electrons are really, really slow when we're talking about electricity through a wire. The electrons will bounce around very quickly at random, but the average flow caused by a current is slow. Really, really slow.

https://en.wikipedia.org/wiki/Drift_velocity

For a specific but not unreasonable example:

> Therefore in this wire the electrons are flowing at the rate of −0.000023 m/s. At 60 Hz alternating current, this means that within half a cycle the electrons drift less than 0.2 μm. In other words, electrons flowing across the contact point in a switch will never actually leave the switch.

That kind of speed means that any messages sent over a copper wire are not going to be sending electrons all the way for that message. The electrons that 'carry' the message "I AM A VIRTUAL SWORD" will not go from my machine to yours as a rushing block. Instead all I'll be doing is tapping the end of a very long pole connecting our two properties, so you can read the message by the patterns of the end of the pole in your house moving ever-so-slightly.

So, I guess I am transferring mass, but nothing that comes from me goes to you.

This also assumes a very particular direction. There's nothing, as far as I'd understand, that requires me to be pushing electrons at you. I could be pulling on the pole slightly rather than pushing.

I'd love any corrections or additions to this, purely my lay understanding of the topic.