[Paleopsych] SW: On Conservation of Mass
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Theoretical Physics: On Conservation of Mass
http://scienceweek.com/2005/sa050107-1.htm
The following points are made by Frank Wilczek (Physics Today 2004
December):
1) Is the conservation of mass as used in classical mechanics a
consequence of the conservation of energy in special relativity?
Superficially, the case might appear straightforward. In special
relativity we learn that the mass of a body is its energy at rest
divided by the speed of light squared [m = E/c^(2)]; and for slowly
moving bodies, it is approximately that. Since energy is a conserved
quantity, this equation appears to supply an adequate candidate,
E/c^(2), to fill the role of mass in the "culture of force".
2) However, that reasoning will not withstand scrutiny. The gap in its
logic becomes evident when we consider how we routinely treat
reactions or decays involving elementary particles. To determine the
possible motions, we must explicitly specify the mass of each particle
coming in and of each particle going out. Mass is a property of
isolated particles, whose masses are intrinsic properties -- that is,
all protons have one mass, all electrons have another, and so on. (For
experts: "Mass" labels irreducible representations of the Poincare
group.) There is no separate principle of mass conservation. Rather,
the energies and momenta of such particles are given in terms of their
masses and velocities, by well-known formulas, and we constrain the
motion by imposing conservation of energy and momentum. In general, it
is simply not true that the sum of the masses of what goes in is the
same as the sum of the masses of what goes out.
3) Of course when everything is slowly moving, then mass does reduce
to approximately E/c^(2). It might therefore appear as if the problem,
that mass as such is not conserved, can be swept under the rug, for
only inconspicuous (small and slowly moving) bulges betray it. The
trouble is that as we develop mechanics, we want to focus on those
bulges. That is, we want to use conservation of energy again,
subtracting off the mass-energy exactly (or rather, in practice,
ignoring it) and keeping only the kinetic part E - mc^(2) ~= mv^(2)/2.
But you can't squeeze two conservation laws (for mass and
nonrelativistic energy) out of one (for relativistic energy) honestly.
Ascribing conservation of mass to its approximate equality with
E/c^(2) begs an essential question: Why, in a wide variety of
circumstances, is mass-energy accurately walled off, and not
convertible into other forms of energy?
4) To explain why most of the energy of ordinary matter is accurately
locked up as mass, we must first appeal to some basic properties of
nuclei, where almost all the mass resides. The crucial properties of
nuclei are persistence and dynamical isolation. The persistence of
individual nuclei is a consequence of baryon number and electric
charge conservation, and the properties of nuclear forces, which
result in a spectrum of quasi-stable isotopes. The physical separation
of nuclei and their mutual electrostatic repulsion -- Coulomb barriers
--guarantee their approximate dynamical isolation. That approximate
dynamical isolation is rendered completely effective by the
substantial energy gaps between the ground state of a nucleus and its
excited states. Since the internal energy of a nucleus cannot change
by a little bit, in response to small perturbations it does not change
at all.
5) Because the overwhelming bulk of the mass-energy of ordinary matter
is concentrated in nuclei, the isolation and integrity of
nuclei--their persistence and lack of effective internal structure--go
most of the way toward justifying the zeroth law (the law of the
conservation of mass). But note that to get this far, we needed to
appeal to quantum theory and special aspects of nuclear phenomenology.
For it is quantum theory that makes the concept of energy gaps
available, and it is only particular aspects of nuclear forces that
insure substantial gaps above the ground state. If it were possible
for nuclei to be very much larger and less structured -- like blobs of
liquid or gas -- the gaps would be small, and the mass-energy would
not be locked up so completely.
Physics Today http://www.physicstoday.org
--------------------------------
Related Material:
THEORETICAL PHYSICS: ON THE CONCEPT OF FORCE
The following points are made by Frank Wilczek (Physics Today 2004
October):
1) Newton's second law of motion, F = ma, is the soul of classical
mechanics. Like other souls, it is insubstantial. The right-hand side
is the product of two terms with profound meanings. Acceleration is a
purely kinematical concept, defined in terms of space and time. Mass
quite directly reflects basic measurable properties of bodies
(weights, recoil velocities). The left-hand side, on the other hand,
has no independent meaning. Yet clearly Newton's second law is full of
meaning, by the highest standard: It proves itself useful in demanding
situations. Splendid, unlikely looking bridges, like the Erasmus
Bridge (known as the Swan of Rotterdam), do bear their loads;
spacecraft do reach Saturn.
2) The paradox deepens when we consider force from the perspective of
modern physics. In fact, the concept of force is conspicuously absent
from our most advanced formulations of the basic laws. It doesn't
appear in Schroedinger's equation, or in any reasonable formulation of
quantum field theory, or in the foundations of general relativity.
Astute observers commented on this trend to eliminate force even
before the emergence of relativity and quantum mechanics.
3) In his 1895 Dynamics, the prominent physicist Peter G. Tait, who
was a close friend and collaborator of Lord Kelvin (1824-1907) and
James Clerk Maxwell (1831-1879), wrote
"In all methods and systems which involve the idea of force there is a
leaven of artificiality.... there is no necessity for the introduction
of the word "force" nor of the sense-suggested ideas on which it was
originally based."(1)
4) Particularly striking, since it is so characteristic and so
over-the-top, is what Bertrand Russell (1872=1970) had to say in his
1925 popularization of relativity for serious intellectuals, /The ABC
of Relativity/:
"If people were to learn to conceive the world in the new way, without
the old notion of "force," it would alter not only their physical
imagination, but probably also their morals and politics.... In the
Newtonian theory of the solar system, the sun seems like a monarch
whose behests the planets have to obey. In the Einsteinian world there
is more individualism and less government than in the Newtonian."(2)
The 14th chapter of Russell's book is entitled "The Abolition of
Force." (3,4)
References (abridged):
1. P. G. Tait, Dynamics, Adam & Charles Black, London (1895)
2. B. Russell, The ABC of Relativity, 5th rev. ed., Routledge, London
(1997)
3. I. Newton, The Principia, I. B. Cohen, A. Whitman, trans., U. of
Calif. Press, Berkeley (1999)
4. S. Vogel, Prime Mover: A Natural History of Muscle, Norton, New
York (2001), p. 79
Physics Today http://www.physicstoday.org
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