That's a big if. I haven't done the math yet, but I'll bet that the outside rim of at least one of the gears would have to be started moving faster than the speed of light. I'm not sure how you would do that.
The gear just before the first gear at light speed would have the outside rim moving at about 100th of the speed of light. It would take quite a bit of energy to do that.
(Others have pointed out that at speeds well before the speed of light, some of the gears would melt. I'm ignoring that.)
That's a big if. I haven't done the math yet, but I'll bet that the outside rim of at least one of the gears would have to be started moving faster than the speed of light. I'm not sure how you would do that.
The gear just before the first gear at light speed would have the outside rim moving at about 100th of the speed of light. It would take quite a bit of energy to do that.
(Others have pointed out that at speeds well before the speed of light, some of the gears would melt. I'm ignoring that.)