Randall D. Peters

Physics Department, Mercer University

Macon, Georgia

Copyright 3 July 2006

The first observation of dissipation, in which values of energy loss or
gain were found to be near-multiples of
E_{h} = 1.1 ×10^{-11} J, involved the free-decay of a long-period
compound pendulum [1].
Similar tantalizing evidence for a `hysteron' of internal friction
quantization at the Compton-energy scale E_{h} was noted in
the hysteresis that was observed in length fluctuations of metal wires
as a function of temperature [2].

For the two experiments just mentioned, the friction responsible for the phenomena observed is thought to be of `internal' type rather than the result of sliding friction (tribology). A recent experiment suggesting the possibility that even sliding friction might be quantized, is one that involved `rolling friction' [3].

In addition to the references already cited, a summary of some of the author's mesodynamics research is found in a review article [4]. Section 5.1 of this article tells how the hysteron energy was observed to relate to fundamental constants as follows:

| (1) |

where a = 1/137 is the fine structure constant, m is the mass of the electron, and c is the speed of light.

Recently the author came to recognize an intimate direct
connection of
E_{h} with the Compton wavelength for the electron [l = h/(mc)
where
h is Planck's constant]; i.e.,

| (2) |

It is thus natural to refer to E_{h} as the Compton-energy scale of friction
quantization.

From Eq.(2) it is seen that E_{h} corresponds to
the energy of a photon whose wavelength is smaller than that of the
Compton wavelength by a factor of 137; i.e.,

| (3) |

where r_{e} is the classical electron radius.

That the value of l_{eff} = 1.8 ×10^{-14} m
is closer to nuclear than to atomic dimensions, could be important as
now explained.

When a metal is strained anelastically, there is an alteration in the configuration of defect structures; which must involve significant displacement of groups of atomic nuclei. This process is very unlike atomic theory cases in which the Born-Oppenheimer approximation is reasonable; i.e., adiabatic approximation in which a nucleus remains at rest. A meaningful description of the `jerky' (discontinuous) strains that are characteristic of many materials [5], is hard to realize on the basis of quantization at the electron-volt level. The eV is roughly seventy million times too small to be a natural energy-decrement for the description of such jerky alterations.

**Fine structure constant `mystery'**

The fine structure constant a is the fundamental physical
constant characterizing the strength of the electromagnetic interaction.
First considered by Arnold Sommerfeld in 1916, it can be thought of as
the ratio of two energies: (i) the energy needed to bring two electrons
from infinity to an arbitrary distance s against their electrostatic repulsion,
and (ii) the energy of a single photon of wavenumber k = 2p/l = 1/s where l is the photon's wavelength. Richard Feynman
said of this constant, ``It has been a mystery ever since it was
discovered more than fifty years ago, and all good theoretical
physicists put this number up on their wall and worry about it.
... It's one of the *greatest* damn mysteries of physics:
a *magic number* that comes to us with no understanding by man.
You might say the ``hand of God'' wrote that number, and ``we don't know
how He pushed His pencil''. We know what kind of a dance to do experimentally
to measure this number very accurately, but we don't know what kind of a
dance to do on a computer to make this number come out-without putting
it in secretly! '' [6].

A well-known trio of related fundamental-units of length `revolve around' the fine structure constant:

| (4) |

Since 2p a_{0} is a (deBroglie) wavelength that characterizes
`individual' electron interactions
with stationary nuclei, it is
postulated that
l_{eff} = 2p r_{e} = 2pa^{2} a_{0} = 1.8×10^{-14} m is a
(photon) wavelength that
characterizes `many-electron' interactions with non-stationary
nuclei. No first principles description of the mechanisms for such
interactions presently exists.

The following statement appears in one of the author's two recent contributions to the McGraw Hill Encyclopedia of Science and Technology [7]: ``It is possible that one of the last frontiers of physics actually lies in one of the most accessible parts of our world''. Considering its ubiquity, it is remarkable that so little is known about friction from first principles.

**Bibliography**

[1] R. Peters, ``Metastable states of a low-frequency mesodynamic
pendulum'', Appl. Phys. Lett. 57, 1825 (1990).

[2] R. Peters, ``Fluctuations in the length of wires'', Phys. Lett.
A, Vol 174, no. 3, 216 (1993).

[3] R. Peters, ``Mesoscale Quantization and Self-Organized Stability'',
online at http://arxiv.org/abs/physics/0506143

[4] R. Peters, ``Friction at the mesoscale'', Contemporary Phys, Vol.
45, No. 6, 475-490 (2004).

[5] A. Portevin & M. Le Chatelier, ``Tensile tests of alloys undergoing
transformation'', Comptes Rendus Acad. Sci. 176, 507 (1923).

[6] *QED-The strange theory of light and matter*,
Princeton University Press 1985, Ch. 4, Loose Ends, p. 129;
useful associated information in Wikipedia,
online at http://en.wikipedia.org/wiki/Fine_structure_constant

[7] topic titled ``Anhamonic Oscillator'', to be published in
the 10th edition.

File translated from T

On 3 Jul 2006, 12:12.