Fried Chicken: unfortunately, this thread has diverged from your quite reasonable beginner's questions about antenna theory, into an argument between experts seeking to demonstrate who among them is the bigger expert. Perhaps said experts could take their dispute elsewhere?
Let's come back to your questions.
I still want to know what's going on with the dipole antenna length. If I have a dipole antenna at full wavelength, wouldn't it pick up exactly nothing in a theoretical perfect world? Would it cancel out? If that guy's video is to be believed this is exactly the case....
That video is, quite simply, wrong.
The argument it presents is that in a full wavelength dipole, you would need to have currents travelling in opposite directions within each element, and that those opposing currents would have to cancel each other out, resulting in nothing being radiated from or received in the antenna.
But the whole idea of those opposite currents cancelling out is false in the first place. The narrator seems to think that either you can't have two currents flowing in opposite directions within the same piece of wire, or that if you do, their effect will somehow cancel out such that there is no radiation from the antenna.
But when talking about AC, it is perfectly normal to have different currents flowing at different points along a wire. In fact it's impossible not to. Whenever you have an AC current flowing in a wire, then the current in that wire will vary, all the way from one direction to the other and back again, at intervals of one wavelength all the way along the length of the wire.
Those "opposite" currents at different points do not cancel out, because they are not in the same places. In fact, they are all part of the same AC current. An AC current does not just vary over time: it also varies over space.
And their conclusion, that a full-wave dipole could not radiate, is also false. In reality a full wave dipole will radiate or receive just fine.
The reasons that half-wave dipoles are preferred are practical, rather than fundamental:
- A resonant antenna acts as a filter that preferentially receives or transmits a particular frequency.
- A half-wave dipole is the shortest resonant antenna for a given frequency, and therefore the smallest and cheapest to build.
- The impedance at the centre of a half-wave dipole is one that is easy to work with.
These properties are of great concern when e.g. building a transmitting station at long wavelengths, but in your case, none of them are critical:
- Your receiver is very capable of selecting what frequency to listen to and filtering out others; a resonant antenna can help, but isn't essential.
- In the case of your rabbit-ears antenna, you're free to vary its length to whatever works best within its range; there's no cost to extend it fully.
- Your receiver has more than enough variable gain to compensate for loss due to the antenna impedance not matching that of the radio.
As such, you're quite likely to find that a different configuration - e.g. extending the rabbit ears fully to get a larger antenna which can collect more of the available signal - will get you better results than trying to achieve a half-wave dipole configuration.
But is a radio measuring across the two sides of the dipole, or is it measuring across the two sides of the dipole and then the ground? Maybe I should ask this in a physics forum. I really want an ideal theoretical answer, not a practical one. I believe it's a simple question and there should thus be a simple answer no?
Simple answer: it is measuring across the two sides of the dipole. There doesn't need to be any "ground" involved. A dipole antenna works just fine floating in space. Having a planet nearby is a complication, rather than a requirement, for this type of antenna.
More correct answer: it is not really measuring across the two "sides", but rather measuring
at the feed point. By the feed point, I mean the point in the middle where the antenna has been split. Usually for a half-wave dipole this is in the middle, but you can place the feed point anywhere. The position of the feed point will determine the impedance seen by a radio connected at that point.