In a sense you DO see the wave when you see the macroscopic object-say
a ball. So it's not that the wave amplitude is too small to allow any
effects to be seen.
What you don't see is any sort of obvious interference pattern. The
usual claim that any such interference pattern would not be observable
because the wavelengths are far too small makes sense.
There may be other complications preventing simple application of
the pure quantum mechanical wave-like time dependence to large objects,
but even if that turns out to be true, no new replacement equations are
It's hard to give a definite answer about 'deep physical meaning'.
The world must be made of something. So far as we can tell, it's made
of quantum things obeying quantum mechanical equations. Some of the
large scale behavior is describable as if it were made of classical
objects obeying classical equations.
Quantum behavior has been exhibited in the laboratory for extended
objects of the order of a few tens of atoms -- molecules have been
coaxed to produce interference patterns but the experiments are rather
difficult. Any perturbation of the internal degrees of freedom that's
different for different paths a molecule can take through a system (and
there are lots of ways big molecules can move, rotate, and jiggle)
spoils any possible interference.
On the flip side, though, large collections of atoms or of
electrons can be coaxed to coalesce into the same quantum state, which
can spread over a macroscopically observable range. Bose-Einstein
condensates can comprise macroscopically large numbers of atoms, and
long-range order in solids is often a manifestation of the underlying
wave mechanics of the constituent pieces.
(republished on 07/21/06)