# In Pilot wave theory how far does the wave stretch?

The one thing I find difficult to understand is how far does the Pilot Wave extend. Does the Pilot Wave permeate through the entire universe?

• If you consider a real and physical explanation for the pilot wave, like photons emitted from an accelerated electron then yes. Photons travel across the whole universe as far as we know. – Bill Alsept Jan 13 '18 at 4:09

$$\psi(r, \theta, \phi) \propto e^{-a_0 r}$$
In this case the electron, perhaps counterintuitively, shows no motion, because this is a "stationary state" with $\nabla \psi = 0$. Instead it hangs at some, unknown before a measuring experiment, fixed position that is almost certainly near the nucleus.
But the situation is identical to standard QM other than that there is now an added element of a hidden well-defined particle position underneath: the wave is very localized near the atom, filling up approximately its observed volume. In exact mathematical terms it is infinite because the exponential does not actually reach zero, but it becomes completely insignificant more than a few Bohr radii $a_0$ from the nucleus.