http://farside.ph.utexas.edu/teaching/em/lectures/node94.html states:
So, in the optimum case half of the power absorbed by the antenna is immediately re-radiated. Clearly, an antenna which is receiving electromagnetic radiation is also emitting it.
Suppose I have an ideal isotropic radiator radiating $P_x$ into empty space. Now every closed surface integral over the Poynting flux enclosing the radiator should give me the $P_x$. Take radii $r_1 < r_2 < r_3$, all much larger than the wavelength.
Now I place an ideal absorber (a material with wave impedance of $Z_0=377\Omega$ converting the incoming radiation into heat??) at $r_2$. The closed surface integral at $r_3$ should now give less than $P_x$ (because a fraction of the energy was absorbed inside). But to my understanding, the closed surface integral at $r_1$ should still be $P_x$.
Neglecting heat radiation, can anything at $r_1$ detect that radiation was absorbed at $r_2$?
Now I replace this ideal absorber with an ideal antenna. According to the text above, this antenna would re-radiate half of this power in most ideal conditions.
If I place another antenna at $r_1$, this antenna should be able to receive $\frac{P_x}{L_1} + \frac{P_x}{2 L_2}\frac{1}{L_2-L_1}$, where $L_n$ denotes the ideal free space path loss at radius $r_n$. The first term is from the ideal radiator and the second one the re-radiated power from the antenna at $r_2$. This implies that the mere presence of a receiving antenna with a perfect match can indeed be detected.
What is the difference between an ideal antenna and an ideal absorber? Why does an antenna re-radiate half of its power? Why can there be an ideal absorber but we cannot use it to detect signals? Why are we instead relying on something that throws away half of the power?
My vague explanation is that the electric field in the wave excites electrons in the conductor which accelerate. This acceleration not only generates the current/voltage (which is detected by the circuit) but also generates electromagnetic radiation. However, with a black-body, it is certainly possible to have something that absorbes 100% of radiation. (I have to note that the most efficient solar cell 47.1%, i.e. nearly half. Is this the same fundamental limit?)
From a wave propagation perspective, an electromagnetic wave can only be reflected if there is a change of impedance. If we assume the load perfectly matched with the antenna, where is this impedance change that causes half of the wave to be reflected? Is this somehow related with a change from $Z_0=377\Omega$ to the radiation resistance of the antenna? (mathematically this could make sense for a Hertz dipole where the radiation resistance represents a short as compared to $Z_0$ but not so much for a walf-wavelength dipole).
Similarly, assume the antenna is not terminated (open circuit). In this case, only 50% of the incoming power would be reflected by the open circuit?
PS: This question is inspired by https://electronics.stackexchange.com/questions/187681/can-a-radio-transmitter-somehow-detect-the-number-of-receivers-in-its-area, which leaves the actual answer controversial/open.
Any elaborate explanation is much appreciated.