Again, I understand this. My question is meant to generate discussion with others who may be attempting to use the new Apple TV with a converter, so that we may all learn from one another's experiences and identify a compatible solution.
And, yes, HDMI is the only supported means of communicating with an Apple TV, and the many converters that are on the market for communicating with HD TVs that lack a HDMI port are, in fact, HDMI devices. HDMI is nothing more than an interface that supports a well-defined signaling protocol. Lots of devices support HDMI — televisions, of course, but also AV receivers, DVRs, computers, test equipment, and... converter boxes. Each of these devices must understand the signaling protocol of connected devices. You TV, for example, has to pull in the signals traveling via HDMI and turn those signals into images and sound — just as an AV receiver will turn the signal into 5:1 audio, or a piece of test equipment may analyze the protocol. Similarly, a converter will receive the HDMI signal and turn it into images and sound.
It it important to note that there are older televisions that provide HDMI ports that don't work with various other HDMI devices, whether that's a Apple TV, a Blu-Ray player, or an AV receiver.
It's all about devices understanding the signaling — especially handshake signaling that might say:
"Hi! I'm a 4th generation Apple TV and I support this, that, an this other thing! Who are you?"
"Hi! I'm a brand new spiffy TV, and I support all of that too!"
"Yay!"
"Yay!"
"Let's play!"
In my case, n perhaps others, the exchange is going something like this:
"Hi! I'm a 4th generation Apple TV and I support this, that, an this other thing! Who are you?"
"Hi! I'm a converter box, and I support this and that... but I've never heard of the other thing."
"Oh... I but the other thing is really important to me..."
"Aw, that's okay... Why don't you go ahead and start giving me all of your picture and sound signals, okay?
"..."
"Hello?"
"..."
"Hello?"
"..."
<tap> <tap> <tap> "Is this thing on?"
"..."