[dotancohen]

You don't have to know the sign, you could tell which way the electrons are going.

We tell the aliens: you take all sorts of organics with liquid inside (on earth we typically use a lemon, but other organics will do), and put a stake of element 29 in one side and a stake of element 30 in the other. You then connect them with a length of element 29. Keep trying different organics until you find one that works. They might not have lemons, but there is a good chance that something will eventually work.

You'd need to predefine what the atomic numbers mean and some other things, but we're already assuming some level of communication already being established so this aspect is not far-fetched.

[ko27]

Congrats, you devised an experiment to determine left and right. The only issue? You need to know what's left and right when placing those elements.

[pgalvin]

Okay, I’ve got elements 29 and 30. Which side do I put each on?

See the problem? :)

[dotancohen]

No, it really doesn't matter. Have you never made a lemon or potato battery before?

[immibis]

The electrons are flowing towards the element 29 side. Is that left or right?

[dotancohen]

Now arrange the apparatus such that the element 29 side is near you, and the element 30 side is far from you. Additionally, ensure that the wire is up (further from the locally dominant gravitational mass). Now place an election between the "lemon" and the wire. See which way the election moved? That was right (or left, I don't remember).

[immibis]

The electron doesn't move.

Edit: if you make the electron move, it will move towards or away from the wire, depending whether it's moving in the same or opposite direction as the electrons in the wire.

[griffzhowl]

Set up whatever apparatus you like, you can always set up its mirror image, and then the electrons are going in the opposite direction. So which is right and which is left?

Remember you haven't yet established with the alien what you mean by right and left, so you won't be able to instruct it to set up your apparatus rather than its mirror image, and of course you can't appeal to the right-hand rule.

This problem has no solution because electromagnetism is right-left symmetric. You would need to use the weak decay (and assume that your alien is made of matter rather than antimatter)

[raincole]

I'd suggest you to re-read your parent comment. They already explained it concisely but you seem to be a bit to caught up in this lemon battary idea.

[dotancohen]

I addressed that. We know which way the electrons flow from the anode to the cathode. I specifically chose this example because of the right-hand rule.