# Show that Fourier transform does not violate causality

1. Sep 2, 2010

### coushal

1. The problem statement, all variables and given/known data

Show that Fourier transform does not violate causality. In other words, let $$\hat{E}(\omega)$$ be Fourier transform of function $${E}(t)$$. Show that $$E(t_1)$$, as evaluated from inverse fourier transform formula using $$\hat{E}(\omega)$$, does not depend on $$E(t_2)$$ for
$$t_2>t_1$$

2. Relevant equations

3. The attempt at a solution
I don't quite get the meaning of does not depend''. Obviously, for sufficiently nice'' $$E(t)$$, the inverse fourier transform formula gives exactly $$E(t)$$ (if the transforms are appropriately normalized). So if one fixes the value $$E(t_1)$$ and perturbs $$E$$ for other $$t$$ (no matter in the past or in the future), the inverse fourier transform will still return the function which has value $$E(t_1)$$ at point $$t_1$$.

So, it looks like I don't understand the problem. Explanation is greatly appreciated.