[escepticos] inercia

[Carlos Ungil <Carlos.Ungil@...>]

Hola, hola.

[Accipiter]
> A decir verdad, de lo poco que he leído al respecto siempre había extraído la
> misma conclusión: que de una u otra manera, la inercia es consecuencia de la
> fuerza gravitatoria, y que la masa del universo tiene, por tanto, mucho que
> ver en ello.

[Eloy Anguiano]
> No, la inercia no es consecuencia de tal cosa. Lo que sí está claro es 
> que la masa gravitatoria y la masa inercial son la misma masa. Eso no 
> quiere decir que la inercia tenga nada que ver con la gravedad. Sólo son 
> dos manifestaciones físicas de una propiedad inherente de la materia: la 
> masa.

Algo tendrán que ver gravedad e inercia si Ciufolini y Wheeler han
escrito un libro de 500 páginas llamado ´Gravitation and Inertia'
(Princeton University Press, 1995).

Del prólogo:

The local equivalence of "gravitation" and "inertia," or the local
"cancellation" of the gravitational field by local inertial frames,
inspired Einstein to the theory of general relativity. This
equivalence is realized through the geometrodynamical structure of
spacetime. A gravitational field is affected by mass-energy
distributions and currents, as are the local inertial
frames. Gravitational field and local inertial frames are both
characterized by the spacetime metric, which is determined by
mass-energy distributions and currents.

The precise way by which the spacetime metric is determined by
mass-energy and mass-energy currents is clarified by the initial value
formulation of general relativity. Central to the understanding of the
origin of inertia in Einstein theory are: (a) the geometrodynamical
formulation of the initial-value problem on a spacelike three-manifold
and the Cauchy problem, (b) cosmological considerations on the
compactness of space of some model universes and on hypothetical
rotations of the cosmological fluid with respect to the local inertial
observer, that is, with respect to the local gyroscopes; and (c) the
theory and the measurement of the "gravitomagnetic field" and
"dragging of inertial frames" by mass-energy currents. Some emphasis
is given in the book to these topics.

De la sección 7.1 [Some Highlights of the Past]:

Einstein found Mach´s words to be a guide to the theory of general
relativity. What does general relativity say about the mechanism
through which faraway stars influence the local frame of reference in
the here and the now? Briefly put, it says (1) there is such an
influence, (2) it is not some mysterious new natural phenomenon, and
(3) instead it is a manifestation, in the subtle sense, of the very
mechanism which transmits gravitation itself.

Ultimos párrafos del libro (sección 7.2 [Geometrodynamics and Inertia]):

We conclude by recalling our distinction (chaps. 4 and 5) among three
possible interpretations, more or less strong, of the *origin of
inertia in Einstein general relativity*, clarified by the formulation
of the initial-value problem.

(1) The spacetime geometry and therefore the _local inertial frames_
    along the world line of every test particle are influenced and at
    least _in part determined by the energy density and the energy
    density currents_ throughout the hypersurface [SIGMA].

(2) The spacetime geometry is _completely determined by the energy
    density and the energy density currents_ on [SIGMA].
 
(3) The interpretation (2) is satisfied, and, _in addition_, some
    _cosmologial requirements_ are satisfied: the closure in time of
    the universe and the average global nonrotation of the mass-energy
    in the universe relative to local gyroscopes.

We have discussed these interpretations of inertia in geometrodynamics
in chapters 4 and 5. We expect that the experimental verification of
the weaker interpretation (1), always satisfied in general relativity,
that is, the nonexistence of an absolute inertial frame and in
particular the influence of mass-currents on (local) inertial frames,
should eventually directly come from one of the experiments described
in chapter 6 for the measurement of the ¨"dragging of inertial
frames." We further observe that according to the interpretation (2),
one requires the absence of any part of the space geometry that is
unaffected by the mass-energy content in the universe, such as an
asymptotically flat metric, *[eta]*, as a part of *g*; one may then
require the _space_ [SIGMA] to be _compact_ (see chaps. 4 and 5). The
cosmological conditions of the stronger interpretation (3) are
discussed in chapter 4.

In conclusion we may summarize: *mass-energy "tells" spacetime how to
curve and spacetime "tells" mass-energy how to move.* From here the
step is small in concept, if long in mathematics, to the influence of
mass-energy there on inertia here: Mass-energy there (and here) curves
the "space" there (and here), and "space" there has to join on
smoothly to "space" elsewhere and "space" elsewhere to "space"
here. "Space" and mass-energy there and here determine spacetime. But
spacetime here "tells" matter here, and gyroscopes here, how to
move. Therefore: *mass-energy there rules inertia (local inertial
frames) here.*

De las posibles interpretaciones enumeradas por Ciufolini y Wheeler
del origen de la inercia en la teoría de la relatividad general de
Einstein, la (2) era la preferida por el propio Einstein (al menos en
"The Meaning of Relativity"). Uno de los argumentos a favor de un
universo espacialmente limitado es el siguiente (en la traducción de
Espasa Calpe):

2. La idea expresada por Mach de que la inercia depende de la acción
   mutua de los cuerpos esta contenida, en primera aproximación, en
   las ecuaciones de la teoría de la relatividad. De estas ecuaciones
   se infiere que la inercia depende, por lo menos en parte, de la
   acción recíproca de las masas. Como no es satisfactoria la
   suposición de que la inercia depende en parte de acciones mutuas y
   en parte de una propiedad independiente del espacio, la idea de
   Mach resulta apoyada por esta falta de consistencia. Pero esta idea
   de Mach sólo es válida en un universo finito, espacialmente
   limitado, pero no en un universo infinito cuasi euclidiano. Desde
   el punto de vista epistemológico es más satisfactorio tener las
   propiedades mecánicas del espacio completamente determinadas por la
   materia y esto sólo sucede en un universo espacialmente limitado.

Chau,
	Carlitos