How many photons are received per bit transmitted from Voyager 1?

There's another major factor. I suppose it falls under the encoding. Frequency stability. In a certain sense, having an extremely precise oscillator at both the receiver and the transmitter, is the same thing as just having a better more frequency-stable antenna, or less noise in the channel (because you know what the signal you're listening for should look like).

I'm no physicist here so take this with a major grain of salt. I think the limit might ultimately arise from the uncertainty principle? Eventually the signal becomes so weak that measuring it, overwhelms the signal. This is why the receiver of space telescopes is cooled down with liquid helium. The thermally-generated background RF noise (black bodies radiate right down into the radio spectrum) would drown everything else out otherwise.

Along those lines, while I'm still not quite sure where the limit is, things become discrete at the micro level, and the smallest possible physical state change appears to be discrete in nature: https://en.wikipedia.org/wiki/Landauer%27s_principle Enough work physically must occur to induce a state change of some kind at the receiver, or no communication can occur. (But this interpretation is disputed!)

The resilience of the signal part...

https://www.allaboutcircuits.com/news/voyager-mission-annive...

> The uplink carrier frequency of Voyager 1 is 2114.676697 MHz and 2113.312500 MHz for Voyager 2. The uplink carrier can be modulated with command and/or ranging data. Commands are 16-bps, Manchester-encoded, biphase-modulated onto a 512 HZ square wave subcarrier.

The "Manchester encoding" brings us to https://www.allaboutcircuits.com/technical-articles/manchest...

https://en.wikipedia.org/wiki/Manchester_code

Note that "16 bps" while the system runs at 160 bps. This suggests that the data is repeated ten times and xor'ed with a clock running at 10 HZ.

While there's no VOY set up now, https://eyes.nasa.gov/dsn/dsn.html will occasionally show it. When that happens, you will likely see two set up for it. I've not seen them set up across multiple facilities - the facilities are 120° apart and only one has a spacecraft above the horizon for any given length of time.

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In the "sensitivity to photons" category, I'll also mention https://en.wikipedia.org/wiki/Lunar_Laser_Ranging_experiment...

At the Moon's surface, the beam is about 6.5 kilometers (4.0 mi) wide[24][i] and scientists liken the task of aiming the beam to using a rifle to hit a moving dime 3 kilometers (1.9 mi) away. The reflected light is too weak to see with the human eye. Out of a pulse of 3×10^17 photons aimed at the reflector, only about 1–5 are received back on Earth, even under good conditions. They can be identified as originating from the laser because the laser is highly monochromatic.

While there's no signal there, we're still looking at very sensitive equipment.

Coding counters the uncertainty principle by allowing multiple measurements, which can then be averaged. Thant counters the contribution of random noise.

There are practical signals we use every day that are "below the noise floor" before we decode them.

So while there is an ultimate limit of the maximum coding rate for a given signal-to-noise ratio, this is expressed in terms of a data rate (i.e. bits per second). If you're fine with lowering your data rate, there is no fundamental theoretical limit, as far as I understand.

Nope. It's one of those things that can take a bit to get used to, but everything on the electromagnetic spectrum is just light in the general sense. The only difference between radio-waves, x-rays, infra-red and (human) visible light is the frequency/wavelength.

If the frequency is high enough then the waves of light can be detected by things as small as cells in the back of your eye, or the pixels in a camera sensor. If it is too low then you need much larger detectors.

Other animals have detectors for different frequencies/wavelengths, allowing them to see either infra-red (mosquitos) or ultraviolet (bees, butterflies etc).

What we call "visible light" is just the particular range that our eyes can detect (about 400 to 800THz). If we were the size of a planet, and our eye cells were the size of a radio-telescope dish we would be able to "see" in those wavelengths. In fact, when we see images taken by radio telescopes, those have been essentially pitch-shifted up to something we can see, like the reverse of what we do when listening for bat clicks (where the pitch is downshifted to our hearing range).

The wikipedia article has a nice little diagram putting the wavelengths into perspective. https://en.wikipedia.org/wiki/Electromagnetic_spectrum