Owen Duffy wrote:
Having regard for the sign of the traveling waves, the only solution
to those constraints / conditions is that the reflected travelling
wave must have zero amplitude.

Sorry Owen, that's not true. Assuming a 1/2WL dipole,
the reflected voltage has traveled 180 degrees. The
reflected current has traveled the same 180 degrees
plus experienced a 180 degree phase shift at the tip
of the dipole. Assuming 100 watts is being applied to
the antenna, the following conditions satisfy the
observed conditions on the dipole at the feedpoint.

Pfor = 500W, Vfor = 548V, Ifor = 0.91A

Pref = 400W, Vref = 490V, Iref = 0.81A

Pnet = 100W, Vnet = 58V, Inet = 1.72A

You talk of the "reflected wave" as if it has inertia, that it must
keep travelling when it reaches the junction of the feedline and the
antenna? You are not alone in speaking that way, but thinking that way
will get in the way of understanding what is happening.

It is well known that all EM waves contain energy and
momentum (inertia) so David is correct. The thing that
reverses the momentum of the reflected wave is destructive
interference at the Z0-match point. Anyone interested in
understanding how/why it happens is invited to peruse
my energy analysis article at: http://www.w5dxp.com/energy.htm
--
73, Cecil http://www.w5dxp.com