A small follow-up to this answer: if you cast Witch Bolt + Twinned Spell, when you use your action to deal WB damage on your next turn, do you deal damage to both targets or to one? I lean towards the latter, following the answer above (that it's one spell with two effects/targets), but wanted to check.
1 Answer
You're targeting a second creature with the same spell. I think that for all intents and purposes all of the effects, even the use your action to damage them effect from Witch Bolt should continue.
This thread from the WOTC forums seems to agree with this interpretation. Particularly this post by Plaguescarred.
If twinned spell is going to be possible it basically turns the target line of Witch Bolt into "you target 2 creatures" and then the action on following turns would damage both creatures.
Mike Mearls confirms this on twitter (HT CTWind)
One spell instance, two targets.