[sdiy] Is everything digital?

[Magnus Danielson]

From: Glen <mclilith at charter.net>
Subject: [sdiy] Is everything digital?
Date: Sat, 14 May 2005 11:19:11 -0400
Message-ID: <4.1.20050514110840.0323bf08 at mail.charter.net>

Glen,

> I know that lots of the elder engineers like to remind the young digital
> whipersnappers that "it's all analog", just to see that puzzled look on
> their faces.  :)
> 
> On a certain level, the elder engineers are totally correct, and it's not
> my point to argue that.
> 
> However, if voltage is caused by an imbalance of electrons between two
> physical locations, and if electrons are discrete units which can be
> counted, then wouldn't it be reasonable to say there should be a discrete
> number of steps between let's say 1 volt and 2 volts? To go from 1 volt, to
> 2 volts, aren't we simply increasing the imbalance of electrons by a
> certain discrete number of electrons? If so, then there are only so many
> different unique voltage levels between 1 and 2 volts. This would make
> voltage purely a digital property.

Not quite. The voltage is a "constructed" unit which in itself is a
rationalisation rather than anything else, it's not a very fundamental unit at
all, but it is a _very_ handy unit to use in engineering. Let's say we have two
metal plates with some distance a between these plates. We charge them up with
say 100V. Now, one of the plates has N (a very large integer number) excess
electrons where as the other plate lacks N electrons. The charge Q of the
plates is simply the excess number of electrons (N) times the unit charge q.
However, this doesn't indicate the amount energy we have bound in this system.
If we recall that a positive charge and a negative charge attracts each other,
we also recall that there is a force pulling them together. However, if we keep
these plates at a fixed distance (a) we have some form of mechanical structure
that ensures that they are not pulled together (heavy objects with no other
force will also attract each other, but the time until they touch each other
can be very long). This constant force indicate the energy potential we have
built into the system. If we now move the plates to a further distance, we have
pulled the spring and inserted more energy to the system. If we would measure
the voltage we would have seen that the voltage have gone up. Voltage is a
normalized energy in relation to the charge, we have E=Q*U, so U=E/Q or energy
per charge. We can change the energy and thus voltage with totally linear
methods, but the charge we can only change in steps of unit charge (that of an
electron). Given a fixed plate situation, the voltage will change by each
electron, and Milikens famous oil-drop experiment was really using this fact to
measure the charge of the electron, crude but effective!

However, the unit charge is VERY tiny, about 1,6022*10^-19 Coulomb, so for
most electronics that one encounters, the number of electrons is so huge that
it behaves like an analogue number in reality. Often, we care about current,
which is nothing else than a measure of how much charge is transfered per unit
time, i.e. Q=I*t where I is Ampere and t is time in seconds.

A team at Chalmers university have made a device in which they have made an
extreme form of Field Effect Transistor (FET) in which _each_ electron comming
in on the Gate creates a bump in the Source-Drain voltage and it now becomes a
simple thing to measure the current on the Gate by using a frequency counter.
The current through the gate is simply the measured frequency (1/s) times the
unity charge of 1,6022*10^-19, that is I=q/t. It challenges the existing
definition for the SI base unit of Ampere and eventually we can remove it as
a derived base unit from the base unit of second. BTW is also the kilogram
being converted into a derived form, but no decission is made yeat.

> This brings another disturbing concept:  Can we have things such as a 1/3
> electron? What about a 3.1416.... electron? Aren't they all the same, as
> far as our human minds have been able to differentiate? Can we know for
> certain that "all electrons are created equal"?

Electrons comes only at unity charge.

However, there *do* exists such ugly things as fractional unity charge, and as
it so happends, it is in steps of 1/3. These exists among the quarks, but since
these is tied together by gluons, we can't observe them as separate particles
but rather in bunches of 2 or 3. Now we are into the Quantum Electro Dynamics
(QED - another little Feynman "joke"). As it happends, you can't combine the
quarks into combinations giving anything other than unity-charge multiples like
0, +1, -1 etc. So, unity charge properties are maintained.

In the end, we can observe many forms of quantum behaviours, but usually they
are obscured and muddled out by the high temperature we live in, so what we see
is a mixture of real linear ("analogue") behaviours and statistical behvarous
of quantum behaviours. This statistical muddeling have created a huge
difficulty in figuring out the underlying mechanisms. The work towards a GUT
(Grand Unified Theory) such as the famous string theory/theories is deeply into
discrete math in many dimensions (10-11 needed, but more have been used too).

So, when I grunt a little and say "It's all analogue anyway" it is to indicate
that we must many times analyse things from an analogue perspective. We have
not yeat started to utilize the quantum properties to store binary digits. We
can make such things in the lab, but nothing has reached the mass-market. So I
still think mu grunting is motivated. The quantized levels and quantized time
of digital electroncis is a gross oversimplification, but it allows usefull
and efficient methods which I would not like to be without, but it is a model
which is never completely fullfilled and thus will it not be accurate. Unless
you understand the analogue limits and make them better, your digital models
will break and you will not understand why, so for all practical reasons, the
grunt is very well motivated.

Cheers,
Magnus - one of those grunters