Okay, so I don't sum over them like I would a repeated index. However, I am still unsure how to proceed from here. Another comment says that this should work like matrix multiplication, but that would mean i'm adding terms for corresponding alphas and nus

So I should iterate through nu and alpha at the same time like 0,0 1,1 ... etc? But if it's like matrix multiplication wouldn't I still have to add each of those terms?

@Mr.Wayne, oops thank you I misread your question.

Is this for Z_total? If so shouldn't there be a factor of 1/N! In front?

@A.V.S. ohh interesting! I was under the impression that the CFT side was supposed to correspond with our universe more directly. I also found a similar question since I posted, but I can't vote to close since the question is in answered - physics.stackexchange.com/questions/708864/…

I realize now there were some glaring holes in my understanding of SR, and solving this problem really helped me iron out the kinks. This ends up just being a variation of Einstein's Train, so I dont know why this appeared to be so complicated to me before, but I want to say thank you to @Marco Ocram, for pointing out my mistakes and helping me in the right direction.

@WillO Right, thankfully Thomas and Marco helped me realize that I was not accounting for simultaneity.

So is this why Thomas commented above to use the t = γ(t+vx/c^2) equation?

@WillO I'm not sure what you mean - its just space between the two. But that should also be dilated in this instance.