variable pwm output to a ssr to christmas lights. How to smooth the blinking.

Hey, let me first start by saying im new to arduino's and electric projects, so bear with me. Basically I have the arduino hooked up to a pot so I can vary the output voltage of a pwm pin. This pin is connected to a solid state relay which controles christmas tree lights. But when I change the power coming out of the pin, it affects the strobe frequency of the lights, not their brightness. For example, when the pot is at its minimum, the lights are off, then when I begin to turn it up, the lights begin to flash faster and faster until the pot is at max and the lights are fully on. This is not what I want, I need them to dim or glow brighter just like an led would if I connected an led to the pwm output.

I was thinking maybe a capacitor might help smooth this out and change the frequency of flashes into brightness? Kinda like when you smooth dc after rectifying it from ac. Or is there another way to do this?

Essentially all I want is a light dimmer for my led christmas lights controled by the arduino.

Sorry, SSRs cannot be used as AC dimmers unless they are of the "random" (-R) type. Most out there are the zero-cross type, they can only be turned on/off, but there's no phase control possibility. Even if you have (however unlikely) a random trigger SSR, dimming cannot be done by simply PWM'ing the SSR input.

Do a Search for "AC Phase Control".