I'm going to attempt to make a Christmas light control system using an Arduino (either my existing Uno or I might go buy a Mega 2560, that's not important though) and a few of SainSmart's solid state relay boards.
I was thinking about trying to incorporate dimming into the light sequence, and I was wondering how I should go about that. (I haven't bought anything yet, this is purely a plan on paper) I know the Arduino can adjust LED brightness using PWM, but I wasn't sure if the SSRs could switch fast enough to deal with that. Is there a better way to do this than Arduino + relays? I want to keep this relatively cheap, and add to it over time, which is why I liked the idea of a mega 2560 and some relay boards (I could add relay boards as time/money permits, since the Mega supports 50-something outputs).
TL;DR: Can I use PWM to dim an incandescent bulb with solid-state relays?