[Paleopsych] SW: On Conservation of Mass

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Theoretical Physics: On Conservation of Mass

    The following points are made by Frank Wilczek (Physics Today 2004
    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:
    The following points are made by Frank Wilczek (Physics Today 2004
    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
    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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