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Conservation laws of dynamics and gravito-inertial fields
Volume
28A,
number
7
PHYSICS
CONSERVATION
LAWS
OF
DYNAMICS
13 January 1969
LETTERS
AND
GRAVITO-INERTIAL
FIELDS
H. G. L. COSTER and J. R. SHEPANSKI School
of Physics.
The University
of New South Wales!
Sydney,
Australia
Received 6 December 1968
The theory of gravito-inertial fields is shown to lead directly to the basic conservation laws of dynamics.
The recently developed theory of gravito-inertial fields [ 1,2] is based on the following (freespace) field equations: (i): I7X (5 = 6,al/at
(iii): V-G = - p /a
,
(ii): I7 X 1 = ig - a,3 G/at
g
,
(iv) : v-1 = 0 .
0’
g = V x I + cola G/at .
(2)
In the previous work, which was concerned with the process of setting up the formalism and foundations of the theory, it was shown that: (i): Equations (1) imply propagating gravito-inertial fields, their speed of propagation being ((~~6~)-$= = c. (ii): All relativistic dynamical effects emerge solely as direct consequences of field equations (1). (iii): The theory is fully consistent with the principle of equivalence. (iv): The field energy and the field momentum associated with a moving massive object completely account for the energy and momentum of the object. (v): A clue as to what may constitute a (neutral) fundamental particle is found by way of a special (limiting) form for the mass distribution within it. It can be shown that, for such a particle, the whole restmass is distributed in the field. In the present communication we examine the gravito-inertial interpretation of, and the rationale behind, the conservation laws of dynamics. To deal with the problem of conservation of linear momentum, we define a closed system, intuitively, as one in which the overall measure 512
$;/pgdv
=
0*
(1)
Here G and Iare the gravitic and inertial field strengths and pg and jg constitute the gravitational mass and mass-current density, while oo, 6, are, respectively, the gravitic permittivity and the inertial permeability of free space. The momentum density, rr, associated with the mass distribution of the fields is then identified with the gravitational current density jg, so that: 7c=j
of the field-source strength (i.e. mass) within its volume (V), must be independent of time. Thus:
This clearly constitutes [2] a statement of the overall mass-energy conservation for such a system. Now, in view of the definition (2), the net momentum flux through the surface S bounding the volume is: J&dS= [l%rdV= o. j+dV, S V V which, for a closed system, in view of equations (l(iii)) and (3), gives: n*dS=
0.
(4)
Hence, for a close d system, the net flux of momentum through the enclosing surface is zero. This is equivalent to the conservation of the total linear momentum in such a system. The requirement for pg and ig to satisfy a continuity equation had been initially used [l] to set up the field equations (1). The latter, however, together with the definition (2), now constitute the very foundation of the dynamical theory and hence are its basic postulates. The relativistically correct form for the particle momentum derives directly from the field equations (1) and is not the result of an assumed law of momentum conservation. Further, the concept of angular momentum on this field theory is intimately linked with that of the inertial dipole moment of a circulating mass (analagous to the magnetic dipole produced by a circulating charge). The conservation of angular momentum, intuitively, follows from the conser-
Volume
28A, number
PHYSICS
7
LETTERS
vative nature of the inertial field (cf. eq. (l(iv))). Thus the thebry provides a further, field based, insight into the nature of the dynamical conservation
laws.
ETATS
LIES
DANS
L’OXYDE
13 January 1969
1. H. G. L. Coster and J. R. Shepanski, J. Phys. A. (Proc. Phys. Sot.), to be published. 2. H. G. L. Coster and J. R. Shepanski, submitted for publication to J. Phys. A. (Proc. Phys. Sot.).
CUIVREUX
A BASSE
TEMPERATURE
M. ZOUAGHI et A. CORET Laboratoire
de Spectroscopic
et d’Optique du Corps Solide (associS au Centre National de la Recherche Znstitut de Physique, Universit6 de Strasbourg, France Requ le 4 d6cembre
Scientifique)
1968
Photocurrent minima which correspond to absorption maxima are observed with Cu20 samples at 1lOoK in the infrared region. These experimental results are interpreted in terms of creation of bound levels in CugO.
Le spectre d’absorption de Cu20 a 77oK dans le domaine infrarouge se caracterise par un grand nombre de bandes dont l’origine n’a pas encore et& elucidee [l]. Ces bandes, qui apparaissent surtout dans les cristaux recuits a llOOoC, sous une forte’pression d’oxyg&e (250 a 300 mm Hg), ont des intensites differentes. La plus intense se trouve a 1.28 cc. D’autres, moins intenses, se trouvent a 0.64 CL,0.77 p, 0.93 ).L, 1.00 ~1, 1.37 p, 1.45 p et 1.63 p. Les bandes situ&es entre 1.28 p et 0.93 p ont et& attribuees a la creation d’etats lies dans Cu2G [2]. Les etudes de la photoconductivite a haute temperature [3] et de l’influence du preeclairement a temperature ordinaire sur la photoconductivite infrarouge a llO°K de Cu20 [4] ont abouti a la conclusion suivante: l’existence dans Cu20 de lacunes d’ions cuivre (V&) avec des trous pi&g&, c’est-l&-dire de centres V. Ces centres V peuvent etre trees, soit par addition d’oxygene, soit par injection de trous P l’aide d’un Bclairement adequat. Nous presentons, dans cet article, les resultats experimentaux obtenus a partir de l’etude de
plusieurs Bchantillons de Cu20 prepares dans des conditions differentes (voir tableau). L’btude a 6% effect&e al 1lOoK en gardant constamment les Bchantillons sous vide. La figure montre les spectres de photoconductivite des echantillons de types B18 et Cl8 dont les caracteristiques se trouvent sur le tableau. Les deux spectres se caracterisent par un minimum de photocourant P 1.28 g. Un autre minimum a 0.66 p a 6% observe. 11est tres prononce dans le cas de B18. A 1.64 J.Iun minimum de photocourant appara?t, bien marque seulement pour C18. On note enfin l’apparition, dans le spectre de photoconductivite de B18, de structures amour de 1.0 ,u et de 2.2 p. La comparaison des spectres d’absorption obtenus a 7’7OKet ceux de photoconductivite obtenus a llO°K est possible, &ant don& les t&s leger deplacement des bandes observe par Schwab et al. [2] entre 77oK et 290°K. Nous constatons qu’au maximum d’absorption a 1.28 p correspond un minimum de photocourant. Le minimum de photocourant P 1.64 p correspond P un maximum d’absorption. La bande d’ab-
Table 1. Echantillon
Pression d’oxygene de recuit
B18
non recuit
Cl8
recutt
Temperature du recuit
Duree du recuit
Mode de refroidissement Lent (48 h)
300 mm Hg
1100
96
Trempe
s/vide
513
28A,
number
7
PHYSICS
CONSERVATION
LAWS
OF
DYNAMICS
13 January 1969
LETTERS
AND
GRAVITO-INERTIAL
FIELDS
H. G. L. COSTER and J. R. SHEPANSKI School
of Physics.
The University
of New South Wales!
Sydney,
Australia
Received 6 December 1968
The theory of gravito-inertial fields is shown to lead directly to the basic conservation laws of dynamics.
The recently developed theory of gravito-inertial fields [ 1,2] is based on the following (freespace) field equations: (i): I7X (5 = 6,al/at
(iii): V-G = - p /a
,
(ii): I7 X 1 = ig - a,3 G/at
g
,
(iv) : v-1 = 0 .
0’
g = V x I + cola G/at .
(2)
In the previous work, which was concerned with the process of setting up the formalism and foundations of the theory, it was shown that: (i): Equations (1) imply propagating gravito-inertial fields, their speed of propagation being ((~~6~)-$= = c. (ii): All relativistic dynamical effects emerge solely as direct consequences of field equations (1). (iii): The theory is fully consistent with the principle of equivalence. (iv): The field energy and the field momentum associated with a moving massive object completely account for the energy and momentum of the object. (v): A clue as to what may constitute a (neutral) fundamental particle is found by way of a special (limiting) form for the mass distribution within it. It can be shown that, for such a particle, the whole restmass is distributed in the field. In the present communication we examine the gravito-inertial interpretation of, and the rationale behind, the conservation laws of dynamics. To deal with the problem of conservation of linear momentum, we define a closed system, intuitively, as one in which the overall measure 512
$;/pgdv
=
0*
(1)
Here G and Iare the gravitic and inertial field strengths and pg and jg constitute the gravitational mass and mass-current density, while oo, 6, are, respectively, the gravitic permittivity and the inertial permeability of free space. The momentum density, rr, associated with the mass distribution of the fields is then identified with the gravitational current density jg, so that: 7c=j
of the field-source strength (i.e. mass) within its volume (V), must be independent of time. Thus:
This clearly constitutes [2] a statement of the overall mass-energy conservation for such a system. Now, in view of the definition (2), the net momentum flux through the surface S bounding the volume is: J&dS= [l%rdV= o. j+dV, S V V which, for a closed system, in view of equations (l(iii)) and (3), gives: n*dS=
0.
(4)
Hence, for a close d system, the net flux of momentum through the enclosing surface is zero. This is equivalent to the conservation of the total linear momentum in such a system. The requirement for pg and ig to satisfy a continuity equation had been initially used [l] to set up the field equations (1). The latter, however, together with the definition (2), now constitute the very foundation of the dynamical theory and hence are its basic postulates. The relativistically correct form for the particle momentum derives directly from the field equations (1) and is not the result of an assumed law of momentum conservation. Further, the concept of angular momentum on this field theory is intimately linked with that of the inertial dipole moment of a circulating mass (analagous to the magnetic dipole produced by a circulating charge). The conservation of angular momentum, intuitively, follows from the conser-
Volume
28A, number
PHYSICS
7
LETTERS
vative nature of the inertial field (cf. eq. (l(iv))). Thus the thebry provides a further, field based, insight into the nature of the dynamical conservation
laws.
ETATS
LIES
DANS
L’OXYDE
13 January 1969
1. H. G. L. Coster and J. R. Shepanski, J. Phys. A. (Proc. Phys. Sot.), to be published. 2. H. G. L. Coster and J. R. Shepanski, submitted for publication to J. Phys. A. (Proc. Phys. Sot.).
CUIVREUX
A BASSE
TEMPERATURE
M. ZOUAGHI et A. CORET Laboratoire
de Spectroscopic
et d’Optique du Corps Solide (associS au Centre National de la Recherche Znstitut de Physique, Universit6 de Strasbourg, France Requ le 4 d6cembre
Scientifique)
1968
Photocurrent minima which correspond to absorption maxima are observed with Cu20 samples at 1lOoK in the infrared region. These experimental results are interpreted in terms of creation of bound levels in CugO.
Le spectre d’absorption de Cu20 a 77oK dans le domaine infrarouge se caracterise par un grand nombre de bandes dont l’origine n’a pas encore et& elucidee [l]. Ces bandes, qui apparaissent surtout dans les cristaux recuits a llOOoC, sous une forte’pression d’oxyg&e (250 a 300 mm Hg), ont des intensites differentes. La plus intense se trouve a 1.28 cc. D’autres, moins intenses, se trouvent a 0.64 CL,0.77 p, 0.93 ).L, 1.00 ~1, 1.37 p, 1.45 p et 1.63 p. Les bandes situ&es entre 1.28 p et 0.93 p ont et& attribuees a la creation d’etats lies dans Cu2G [2]. Les etudes de la photoconductivite a haute temperature [3] et de l’influence du preeclairement a temperature ordinaire sur la photoconductivite infrarouge a llO°K de Cu20 [4] ont abouti a la conclusion suivante: l’existence dans Cu20 de lacunes d’ions cuivre (V&) avec des trous pi&g&, c’est-l&-dire de centres V. Ces centres V peuvent etre trees, soit par addition d’oxygene, soit par injection de trous P l’aide d’un Bclairement adequat. Nous presentons, dans cet article, les resultats experimentaux obtenus a partir de l’etude de
plusieurs Bchantillons de Cu20 prepares dans des conditions differentes (voir tableau). L’btude a 6% effect&e al 1lOoK en gardant constamment les Bchantillons sous vide. La figure montre les spectres de photoconductivite des echantillons de types B18 et Cl8 dont les caracteristiques se trouvent sur le tableau. Les deux spectres se caracterisent par un minimum de photocourant P 1.28 g. Un autre minimum a 0.66 p a 6% observe. 11est tres prononce dans le cas de B18. A 1.64 J.Iun minimum de photocourant appara?t, bien marque seulement pour C18. On note enfin l’apparition, dans le spectre de photoconductivite de B18, de structures amour de 1.0 ,u et de 2.2 p. La comparaison des spectres d’absorption obtenus a 7’7OKet ceux de photoconductivite obtenus a llO°K est possible, &ant don& les t&s leger deplacement des bandes observe par Schwab et al. [2] entre 77oK et 290°K. Nous constatons qu’au maximum d’absorption a 1.28 p correspond un minimum de photocourant. Le minimum de photocourant P 1.64 p correspond P un maximum d’absorption. La bande d’ab-
Table 1. Echantillon
Pression d’oxygene de recuit
B18
non recuit
Cl8
recutt
Temperature du recuit
Duree du recuit
Mode de refroidissement Lent (48 h)
300 mm Hg
1100
96
Trempe
s/vide
513