Intuitively, because,
\(\psi=-\cfrac{\partial\psi}{\partial\,x}\) --- (*)
and that \(\psi\) exist as discrete frequencies in the frequency domain (ie as Dirac Delta functions). With the Inverse Fourier Transform of such frequency \(\psi\), back to the space domain which is an integration of all frequencies with a subsequent substitution,
\(c.t=x\)
where \(c\) is light speed, spreads \(\psi\) over all space. This might suggest that \(\psi\) when non zero, would require an infinite amount of energy. When we integrate \(\psi\) over all space however, the differentiation of \(\psi\) in expression (*) cancels with the integral of \(\psi\) over all space and we are left with an finite expression in \(\psi\) which is also \(F_{\rho}\), as
\(F_{\rho}=\psi\)
\(F_{\rho}\) that spreads from \(+\infty\) to \(-\infty\) and is finite at each value of \(x\). In this way, the field around a particle extends to infinity in space but does not require an infinite amount of energy; \(\psi\) in the frequency domain exists as discrete frequencies.
Quantum mechanics do not blow up to infinity as the result of expression (*) and Fourier transform from the frequency domain. This however, also implies that negative space must exist! But, what is negative space?!
Note: Negative frequencies need not exist as \(\psi\) is zero elsewhere but the positive discrete frequency value. Since we do not count cycles in the negative, negative frequencies implies negative time.
One big fat zero is still finite.
