As for "twin EM signals, 90 degrees out of phase", the right-angle
relationship is spatial, in the plane of the wavefront, and it is not
between twin signals. It is between the lines of the E and M fields.

It appears that I am having difficulties explaining this
"out of phase" business. Let me try once mo

Take a snapshot of the dipole when the charges are crowded at
the ends of the dipole: all negative charges are at one end and
all positive charges are at the other end. At this very moment,
in the proximity of the antenna there is a maximum electric field
with vectors oriented from the "positive" half of the dipole to the
"negative" half. This electric field has just reached its peak. But
in the same time there is close to zero flow of charges in the
antenna, implying that the magnetic field is close to zero.

Indeed, the magnetic field is perpendicular to the electric field;
however, it is zero exactly when the electric field is maximal.
This is called a "90 degree out of (time-)phase".

However - in theory - an accelerated point of charge creates
an EM front with an electric field and a magnetic field in
(time-)phase, i.e. they peak and die together, perpendicular
on each other. Moreover, in free space a varying electric field
generates a magnetic field in (time-)phase with the originating
electric field (without the need of any charge).

So, the problem is that the dipole generates two fields (E&M)
out of (time-)phase; whereas EM propagation in free space
implies two fields in phase. The "contradiction" can not be more
clear than this.

In order to explain this wonder, I was suggesting the following
scenario:

The dipole give us these two ortogonal fields, E1 and M1 : an electric
field and a magnetic field out of time-phase. E1 is a time varying electric
field, hence it creates its own companion - say - M2 which is a magnetic
field in time-phase! with E1. In the same time, M1 is a time-varying
magnetic field, hence it creates its own companion - say - E2 which
is an electric field in time-phase with M1.

Doing the arithmetic, we conclude that we have four fields altogether,
which represent two separate EM emissions: E1&M2 is one emission,
and E2&M1 is the other one. These two emission are obviously out
of time-phase(they inherited from their originators), i.e. when
[E1 and M2] both peak, [E2 and M1] both die. This is like saying that
the two EM radiations are 90 degrees out of time-phase.

From here on, I do not know how to continue. One way may be that
these two EM radiations - as any behaving waves - sum up vectorially,
and lead to a unique EM radiation with an amplitude a bit higher that the
initial ones. The problem I am having with this explanation is that the
wavelength is also a bit shorter - which does not sound right.

So, I am looking for a better continuation - or for a better explanation
of the following : how comes that we start with two out of time-phase E
and M fields and end up with an EM propagation, i.e. with E and M
in time phase ?

Cordially,

Nic.