I wanted to make a smart switch with a dimmer using an arduino and a solid state relay. I was wondering if this would be possible and if their would be any problems if I tried to do so. Also, the switch would be controlling 6 light bulbs.
You need a random, not zero-crossing, switching SSR and you will need to get the zero crossings into your Arduino through something like an optoisolator, so you can time the delays to triggering on each half-cycle.
The latter would look something like this:
Everything to the left of the optoisolator on the above schematic and the output terminals of the SSR are at mains potential, and proper precautions must be taken for safety. Best to have someone local have a look at it to make sure it's safe before applying mains power- you could hurt yourself or permanently damage your computer or other property.