[sdiy] Is everything digital?

[Richard Wentk]

At 18:54 14/05/2005, Magnus Danielson wrote:

>About the quantum steps on voltages, I tend to say a distinct no. If you take
>the metal plates again, but up a charge of one electron, check out the 
>range of
>voltages you can get by varying the distance between the plates. These
>distances needs to be quantized in order for the voltages to be quantized, but
>if the distance is continous, so will the voltage. Only certain very specific
>cases have quantized distances, such as "orbit radius" (a falacy name at the
>best) of electrons in an atom, but I have yeat to see a proof for quantized
>distanced in a general sense.

Casimir effect. Ultimately you're up against the Planck length, which *is* 
quantised, although it tends to disappear into a haze of probabilistic 
noise, so the extent to which it's quantised in any familiar sense is 
debatable. The way in which quantum processes are both discrete and 
probabilistic is one of the paradoxes about them. This means they're *not* 
in any sense digital, because digital circuitry should be 100% 
determnistic. You can have pseudo-randomness at the symbolic level in a 
digital circuit, but each individual digital switch will still be either on 
or off depending on input levels.

So if the input levels are set, you know absolutely what the output should 
be for a properly designed circuit. This is *completely different* 
behaviour to a quantum process like individual electron flow in a wire, 
where you know what the output *may* be, but you don't know what it is for 
sure until you measure it. 'Analogue' just means the probabilistic 
variations inherent in this are too small to be relevant for your 
particular design goal.

The real point is that you use the model most suited to your problem.

Digital design -> boolean model.
Parasitics control for internal chip modelling -> analogue and RF models.
Quantum devices -> quantum model.
Audio design -> analogue model.

Reality itself is none of these, although the quantum model seems to be the 
best one so far for sub-atomic processes. For all anyone knows reality is 
actually only made of shifting probability density fields. The various 
quantum models actually work perfectly well without any physical 'stuff' 
around  at all. As long as you have probabilities and some kind of 
measurement process to take a snap shot, that's all you need. (Of course 
that begs a lot of questions, but going too far in that direction only 
causes frothing and madness...)

Meanwhile *what defines a system as digital isn't discrete voltage 
distributions, but the use of formally defined symbolic logics and coding 
systems.*

  So I wouldn't consider sending eight voltage levels down to a wire to be 
digital - unless you have some kind of eight-level logic system at the 
other end performing symbolic operations. Similarly a trinary system is 
only digital if it uses some variant of trinary logic. If it does none of 
these things, it's quantised, not digital.

Likewise reality (probably) isn't digital, because there's nothing like 
Boolean logic happening at the quantum level.

It may yet turn out to be true that the quantum level really does work like 
a symbolic engine, in which case it will be more true to say that reality 
is digital. Until then it's more like a casino where you can't leave the 
table, your bets are fixed for you, and the house always wins.

Richard