Take the 2-minute tour ×  A few weeks ago at a conference a
speaker I was listening to made a comment to the effect that a
function (let's say scalar) cannot be analytic because otherwise
it would violate causality. He didn't make this precise as it
was a side comment, and although it intrigued me (I had never
heard that said before) I didn't give it much thought until this
morning.  Now that I think about it, it actually seems quite
obvious. Just look in $1+1$ Minkowski space: suppose $f$ is
analytic around some point $(t_0, x_0)$, then I can find some
ball about this point such that at another point $(t,x)$ in the
ball but outside the light cone of $(t_0,x_0)$ we have that
$f(t,x)$ is completely determined by the value of the function
and its derivatives at $(t_0,x_0)$. This seems to be against the
spirit of causality.  If the above is correct, does anyone know
when this was first discussed? I imagine that it would have been
quite a long time ago. It's interesting because until this
conference I had never h