### Re: Is thermal noise 'truly' random?

Date: Wed Sep 9 14:22:03 1998
Posted By: Tye Morancy, Grad student, Physics, UMASS Lowell
Area of science: Physics
ID: 903680105.Ph
Message:
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Well, that's an interesting question because there are different ways
of looking at it.  "Random heat motion", as you put it, is a fundamental
principle of thermodynamics and is based on a macroscopic scale.  This is
so because thermodynamics deals only with macroscopic variables, such as
pressure, temperature, and volume.  Its basic laws are expressed in terms
of these quantities mentioning no such existence of atoms making up matter.
However, statistical mechanics, which deals with many of the topics of
thermodynamics, does suggest the existence of atoms.
Now, applying the laws of mechanics statistically, one can express all
the thermodynamic variables as certain averages of atomic properties.  For
a given macroscopic system, the number of atoms is typically so large that
the averages would be very sharply defined quantities.  The theory under
which all this is covered is a sub-branch of the "kinetic theory of gases"
called statistical mechanics, which was developed by J. Willard Gibbs
(1839-1903) and by Ludwig Boltzmann (1844-1906).
Thus, agitation of atoms, is not so much random, but statistical in
nature.  Things like probability and statistics govern how and how often
atoms collide and transfer energy.  Between successive collissions, a
molecule in a gas will move with a constant speed along a straight line.
The term "mean free path", is the average distance between these successive
collisions.  This mean free path is related to the density of the molecules
for a given volume and to their size.  Let's say we have a gas made of
atoms approximated to spheres which have a diameter d.  The cross section
(the area of the atom presented as a target) for a collision is pi*d^2.  In
other words, a collision will occur when the centers of the two atoms (or
molecules) are within a distance d of one another.  The probability comes
in when considering how often and when these collisions will occur.  The
reason that the word random probably comes to mind is because that so many
collisions can be occuring with probabilstic results that the outcome or
endpoint of any given atom/molecule at a given time for this system will be
alomst impossible to predict, let alone calculate.  We could follow a
particulaer atom in the gas to see how hard this is to predict.  The atom
is travelling with a constant velocity and collides with another atom, by
which an energy transfer occurs depending on the angle and initial
energies.  The two then fly off in their two respective directions to
repeat the whole cycle.  Now envision that there are several of these
situations occuring and all of them interacting/overlapping at various
points.  The whole thing is occurring probabilistically on top of it all
and would seem very easy just to label it random or chaotic.  I agree with
that whole-heartedly.
So to summarize, I would say that the situation is chaotic, but
deterministic by the laws of probability and statistics.  The largest
growth of statistical mechanics uses the statistical application of the
laws of quantum mechanics to many-atom systems, which is called quantum
statistics, rather than the application classical mechanics as is the case
for statistical mechanics.
In terms of pointing you to some resources or perhaps further
discussion, you need only look in most physics texts (undergrad. level and
up) under the heading of "kinetic theory of gases" or statistical
mechanics.  I performed a wide search on the WWW and had a very difficult
time of locating educational materials on the subject.  Perhaps some of
these keywords and/or explanations will provide you with a little more
insight or a new direction to take.  I wish you luck and keep the questions
coming if things are a little unclear.

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