In article ,
Radium wrote:
(Richard D Pierce) wrote in message
...
For example, if you're talking about such miniscule sound
pressure level variations, you're talking about detecting
displacements that are far smaller than the constituents of the
atomic nucleus. Describing such phenomenon in the context of
sound, which is a manifestation at the macro level, is
essentially meaningless. Further, the very techniques you are
wanting to use to measure these things, lasers and such, are
GROSSLY inadequate to the task.
Even when digital?
The "digital" issue is irrelevantm,: digital is simply a
notation of convenience or lack thereof for the data. The
problem is, no matter how you represent the data, you CAN'T GET
the data to the desired precision to begin with: you are up
against the fundamental physical limitations imposed by
uncertainty. And we are not talking of the inability to measure
because of uncertainty, i.e., the inability to measure both the
position and energy of an object with perfect certainty, we are
talking about the fact that an object simply cannot have a
simultaneously precise position and energy, period.
Uncertainty itself prevents you from even getting there. You
want to measure phenomenon of VERY low energy over VERY small
distances: that means you want extremely high certainty of both
position and momentum, whicb is simply forbidden by uncertainty.
Tou measure things over small distances, uncertainty requires
very high uncertainty in momentum, which means very high energy,
and vice versa.
Another significant stumbling block: the simple thermal energy
of air alone generates a sound pressure whose broadband
equivalent noise level is not very much below the threshold of
hearing, so simple thermal agitation itself will TOTALLY
overwhelm anything at the levels your are contemplating. Assume
you are trying to see what's going on at one attobel, or -340
decibels: the thermal noise is somehwre in the realm of 320 dB
higher. Assume you want to divide, as you say, into many
individual channels (I assume you mean frequency bins), you are
bitten again by the uncertainty principle (this time the
time-frequency uncertainty).
No. Channels are the available different locations of the audio
signal.
That is:
1 channel = mono
2 channels = stereo
Divide the audio spectrum (20 kHz)
into a google channels (10^100): the response time of each
channel is now 10^100/20,000 or 5*10^95 seconds, much longer
than the age of the universe (estimated at about 10^18 seconds),
much longer than GUT estimates of the half life of protons
(10^28 seconds) and, if GUT theories are correct, much longer
than ordinary matter will exist and thus the projected age of
the universe.
So, by the time half of the mass of the universe had decayed,
you'd have NO signal coming out of your analyzer yet.
What would it sound like we COULD? Well, that much we know:
noise. Ordinary noise with gaussian distribution. We'd be
listening to the simple noise of air due to random impacts of
air molecules against the detector due to thermal agitation at a
level that is 340 dB higher than what you'r looking for.
Shouldn't digital audio with a sufficiently strong bit-resolution and
high sampling rate have natural protection against noise?
No, you don't understand, you are asking to determine the
property of a system precisely where the system DOES NOT and
CANNOT HAVE the precision you ask for. Even if I were to
hypothesize PERFECT A/D conversion of the needed resolution, the
very thing I am measuring wimply CANNOT HAVE the kind of
properties you desire them to.
Digital has NOTHING to do with it. Let's make a microphone
diaphragm out of a single proton, for example. The sound level
you are trying to measure causes changes in the proton's state.
You want to measure that state. The simple and inevtiable fact
is that you CAN NEVER measure, simultaneously, the protons
position and its energy to precise values because a proton
CANNOT HAVE simultaneously a precisely defined energy and a
precisely defined position. These are fundamental limitations
imposed by physics, not by practical implementations.
Here's where your experiment falls apart in a very strange way.
You may choose to ignore the energy portion, and simply measure
where the proton is from moment to moment. But, by definition,
since movement of the proton between two moments defines
implicitly the lower limit of the uncertainty of its energy,
(since the change in position in time is the proton's
velocity and, in the simple case, the energy is the proton's
mass times the square of its velocity), you simply will never be
able to measure the position itself to the level of precision
you desire.
It's not intuitive, and there's no reason for it to be
intuitive.
Once again, HOW you represent the numbers makes NO difference:
you are forbidden by the very nature of the problem from ever
getting the numbers you want.
--
| Dick Pierce |
| Professional Audio Development |
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