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Literatur
See W. Isard, “Spatial Interaction Analysis: Some Suggestive Thoughts from General Relativity Physics,”Papers of the Regional Science Association, XXVII (1971); see also Isard, “Preliminary Notes on Relativistic Concepts and the Dynamics of Multi-Nation Interaction,”Papers of the Peace Research Society (International), XVII (1971).
These feedbacks of (3) may be considered to be “post-Newtonian” corrections.
It is recognized that the feedback framework of this section is only one of several possible frameworks that might be utilized. Our framework ignores crossterms in stating the feedback effect.
This was the historical case for several areas in England.
The dimensions of the constantG are $ × mile/tons2.
W. Isard and P. Liossatos, “On Location Analysis for Urban and Regional Growth Situations,”The Annals of Regional Science, VII (June, 1972), pp. 1–27.
For the cost to be relevant in this particular context, we must also assume that the anticipated tax or social cost pertains to a particular technology, where technology may be taken to vary from location to location. Such technology for any given location might be the “best” technology which is economically feasible, or some “reasonable” technology. We also must assume that deviation from that technology, when it involves the use of technology which is technically still better, incurs such sharply rising costs that it is not considered feasible by any plant manager. Similarly, any deviation from that technology in the direction of worse technology incurs such sharply increased taxes or social costs that it too is not considered economically feasible. This assumption in essence fixes technology for any possible location and precludes substitution between the tax outlays or social costs represented byGm 0 m 1/r at any location and other outlays.
Strictly speaking, for such a system additional mass is associated with all real masses because of their mutual interaction.
For more refined analysis, we should add other forces to the lower part of the diagram to reflect the “additional” mass to be associated with massm i because of the energy field.
These bodies would include the steel fabricators and other diverse activities as well as population which come in time (not instantaneously) to locate around the steel plant, or the new financial and other professional service activities that come to locate at the center of the metropolitan region. etc.
Thus, numerous restaurant, automobile service stations, and other activities are pulled or repelled with greater force to (from) these locations.
And this is so in any other system of coordinates which moves at a constant velocity with respect to either. This property stems from the assumption that space is Eulidean and time is homogeneous. Frames in which these assumptions are manifested are designated inertial coordinates. If there exists one inertial system, such as the one for which equations (21) and (22) pertain, then any other system moving at constant velocity with respect to this system is also an inertial system. In short, if an inertial system exists, then there is an infinity of them—the Galilean principle of relativity—and each inertial system is equally suitable for studying the laws of mechanics.
See standard books on mechanics such as L. D. Landau and E. M. Lifshitz,Mechanics (London: Pergamon Press, 1960), p. 30.
Just as all individuals who are rotating on the earth view the Empire State Building as fixed even though it too is rotating.
See W. Isard and P. Liossatos, “Social Energy: A Relevant New Concept for Regional Science,”London Studies in Regional Science, III (1972).
Ibed.See W. Isard and P. Liossatos, “Social Energy: A Relevant New Concept for Regional Science,”London Studies in Regional Science, III (1972).
L. Infeld and J. Plebanski,Motion and Relativity (New York: Pergamon Press, 1960).
V. Fock,The Theory of Space, Time and Gravitation (New York: Macmillan Company, 1964).
See Fock,ibid.. pp. 311–317, among others, for this derivation. Also see Appendix A of this paper.
Alternatively, we can say that this correction comes about because the masses involved are to be corrected due to the presence of an energy field, or more precisely, due to the presence of the gravitational field which carries energy.
It should be noted that the Fock approach adheres strictly to the Lagrangian expression (63) and views the class of coordinate systems in which (63) is valid as those best suited for physical measurements and for an objective description of events—that is, for expressing the laws of motion in terms of the space-time of everyday life, i.e., of Newtonian mechanics. This class of coordinate systems is the harmonic class. However, Infeld would insist that we should not restrict the class of coordinate systems to the harmonic class as Fock does; rather every coordinate system which becomes Cartesian at infinity should be permissible for analysis. Therefore, since each of these systems becomes Cartesian at infinity, and since the motions of each of these systems can be mirrored unambiguously as a Cartesian system at infinity, it is convenient to find one coordinate system in which all motions are the same as would be described by an observer at infinity within experimental error. (Infeld and Plebanski,op. cit., pp. 60–63, 141–144, 153–155.) In short, Infeld does not find equation (63) convenient for use, and thus transforms it to (64).
See Appendix C.
For further discussion see W. Isard, “Spatial Interaction Analysis ...,” and references cited therein.
See A. Papapetrou, “Equations of Motion in General Relativity,”Proceedings of the Physiocal Society of London, A. 64, LVII (1951).
L. Brillouin,Relativity Reesxamined (New York: Academic Press, 1970), p. 51.
For a thorough discussion of this problem, seeibid.
Note that the second term is always positive sincem */M≤1/4. This can be seen if we letm * take its maximum value, namely, a value equal toM/2.
See Appendix C for a similar derivation.
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Research supported by Grant A. P. 00842-02, Environmental Protection Agency.
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Isard, W., Liossatos, P. Industrial location: Agglomeration and feedback analysis. Papers of the Regional Science Association 28, 5–36 (1972). https://doi.org/10.1007/BF01961451
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DOI: https://doi.org/10.1007/BF01961451