An airplane (particle) traveling at the speed of sound
causes shock waves in the air which, if passed through
double slits, would no doubt cause interference.

How about: A photon (particle) traveling at the speed
of light causes shock waves in the aether which, when
passed through double slits, causes interference?

Impossible for empty space - but we now know that space
is not empty. :-) Quoting "Alpha and Omega", by Seife,
"Empty space is an incredibly complex substance, and
scientists are just beginning to understand its properties."
--
73, Cecil http://www.w5dxp.com