Cecil, W5DXP wrote:
"Until someone can explain exactly how a lumped inductor causes a
45-degree phase shift in the current, I`m going to assume that a lumped
inductor is incapable of that feat."

There are base loading coils in shielded boxes which don`t radiate but
do have significant inductance which make too-short antennas seem long
enough for impedance matching purposes.

How to get 45-degrees? Make te reactance equal to the total resistance
in the circuit. Pythagoras showed how about 2500 years ago. You have a
1:1 ratio between resistance and reactance which are at right-angles to
each other. Thus, the resultant impedance is the vector sum which is the
square root of 2 times the resistance or reactance which are equal.
Pythagoras said: c sq = a sq + b sq.

c = impedance
a = resistance
b = reactance

Resistance and reactance are at right angles to each other. When they
are equal, their resultant impedance bisects the right-angle of
90-degrees, so the impedance is at 45-degrees.

In a resistance, the voltage drop is instantaneous with the current
through the resistance. In a pure inductance, current lags the voltage
by 90-degrees. In a circuit containing both resistance and inductive
reactance, the current lag is somewhere between 0 and 90-degrees. In
fact, the current makes the same angle with the applied voltage as
impedance in the circuit makes with the resistance because volts and
amps are in-phase in the resistance.

An inductor which radiates brings an extra to the impedance calculation,
its radiation resistance.

Best regards, Richard Harrison, KB5WZI