MadSci Network: Physics

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

     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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