New Theory Of Gravitation Research Articles

Das makroskopische Gravitationsfeld in der einheitlichen Quantenfeldtheorie

AbstractA theory of the gravitation field is proposed in connection with a new spinorial formulation of EINSTEIN'S equivalence principle and HEISENBERG'S unified quantum theory of fields. In the gravitation theory the gravitational field is given by the coefficients hAi (xl) of the matrix of the anholonomic non‐Lorentzian transformations from the Lorentzian metric ηAB to the physical metric gik (xl) of the Riemannian space‐time V4. The field equations and the commutation rules for the hAi are working in the Lorentzian space. The metric of the Riemannian V4 is given by the average gik = 〈|hAi, hBk|〉ηAB. For all matter fields (and for HEISENBERG's “Urfeld”) the field equations are equations in this Riemannian V4. The interaction between the gravitational field hAi and the matter‐tensor is given by a potential‐like coupling‐term.We prove that this new theory of gravitation gives for makroscopic matter the same linear approximation equations like general relativity and that a perihel‐motion δφ ≈ 76 δφ EINSTEIN results in the second approximation. But, we are finding essential differences to general relativity for the theory of gravitation radiation and for the theory of interaction of matter with strong gravitation fields.

A conformal theory of gravitation

Certain aspects of the new theory of gravitation proposed in a recent paper are examined in greater detail. It is shown that in the smooth fluid approximation the familiar Einstein equations follow as a result of a specific conformal transformation. The equations of the the theory differ from those of Einstein in the neighbourhood of a particle, however. This is illustrated by means of an explicit solution. Criticisms of the theory by other authors are considered and discussed.

PHOTONS IN THE GRAVITATIONAL FIELD

In a previous paper, "The Gravitokinetic Field and the Orbit of Mercury," a new theory of gravitation was introduced, according to which space–time is always flat and the gravitational field is described by equations of Maxwellian form. In this paper it is shown that the theory correctly predicts the gravitational red shift and the gravitational deflection of a light ray. The interaction of photons with a gravitational field follows from the basic premises of quantum theory, that photon frequency is proportional to its energy and that photon wavelength is inversely proportional to its momentum. The photon velocity and proper mass depend on the gravitational potential, and the deflection of a light ray is due to gravitational refraction. The validity of the antisymmetric field equations for sources of variable rest mass is due to the divergence of the group velocity from the dynamical velocity.

Critique of a new theory of gravitation

Hoyle & Narlikar (1964 d ) have developed a new theory of gravitation, for which they claim that it is a direct interparticle action theory, that it ‘is equivalent to that of Einstein in the description of macroscopic phenomena, and hence the situation is the same so far as the classical tests of general relativity are concerned’, that the sign of the gravitational constant is correctly determined, and that it has other advantages over Einstein’s theory such as implying the absence of solutions representing an empty universe. In the present paper, it is shown that these claims are largely unsubstantiated.

On the Hoyle-Narlikar theory of gravitation

It is shown that the direct-particle action-principle from which Hoyle & Narlikar derive their new theory of gravitation not only yields the Einstein field-equations in the ‘smoothfluid’ approximation, but also implies that the ‘ m ’-field be given by the sum of half the retarded field and half the advanced field calculated from the world-lines of the particles. This is in effect a boundary condition for the Einstein equations, and it appears that it is incompatible with an expanding universe since the advanced field would be infinite. A possible way of overcoming this difficulty would be to allow the existence of negative mass.

On the New Theory of Gravitation of Hoyle and Narlikar

On the New Theory of Gravitation of Hoyle and Narlikar

A new theory of gravitation

A new theory of gravitation is developed. The theory is equivalent to that of Einstein in the description of macroscopic phenomena, and hence the situation is the same so far as the classical tests of general relativity are concerned. The new theory differs in its global implications, however. There are two main differences of principle. In the usual theory, the negative sign of the constant of proportionality –8 πG which appears in the field equations R ik – ½ g ik R = –8 πGT ik is chosen arbitrarily. In the present theory there is no such ambiguity; the sign must be minus. Further, the magnitude of G follows from a determination of the mean density of matter, thereby enabling the cosmologist to know how hard he will hit the ground if he is unfortunate enough to fall over a cliff. The second point of principle is that the equation R ik = 0 for an empty world in Einstein theory becomes meaningless; there is no such thing as an ‘empty’ world; in the present theory emptiness demands no world at all. Nor can there be a world containing a single particle, the least number of particles is two.

BOOK REVIEWS

Book reviewed in this article:Embryology of the Viviparous Insects, by Harold R. Hagan, Associate Professor of Biology, The City College of the College of the City of New York.The House of Life, by George A. Rubissow.Elementary Science Education in American Public Schools, by Harrington Wells, Associate Professor of Science Education, University of California, Santa Barbara College.Linear Computations, by Paul S. Dwyer, Professor of Mathematics, University of Michigan.The Calculus of Finite Differences, by L. M. Milne‐Thomson, Professor of Mathematics in the Royal Naval College, Greenwich Gresham Professor in Geometry.Analytic Geometry, Second Edition, by John W. Cell, Professor of Mathematics, North Carolina State College of Agriculture and Engineering, University of North Carolina.General Homogeneous Coordinates in Space of Three Dimensions, by E. A. Maxwell, Fellow of Queens', College, Cambridge.Science for Everyday Use, by Victor C. Smith, Department of General Science, Ramsey Junior High School, Minneapolis, and B. B. Vance, Chairman, Science Department, Kiser High School, Assistant Professor of Biology and Education, The University of Dayton.Climate in Everyday Life, by C. E. P. Brooks, I.S.O., D.Sc., F. R. Met. Soc.Vacuum‐Tube Voltmeters, by John F. Rider;A. New Theory of Gravitation, by Dr. Jakob Mandelker, Assistant Professor of Mechanics, Georgia Institute of Technology.

On Birkhoff's New Theory of Gravitation

It is pointed out in the first place: (1) in Birkhoff's gravitational theory based on flat space-time, the red shift is accounted for by the energy change of the photon as it travels from the emitting body, whereas the photon plays no especial role in the Einstein theory; (2) the solution of the problem of two or more bodies is feasible in the new theory because of its simpler character. Four comments of H. Weyl concerning the Birkhoff theory are discussed, and it is concluded that these are to be taken with much reserve. In regard to the third of these comments it is pointed out that the perfect used by Birkhoff as the ultimate carrier of mass and electric charge is to be characterized as the simplest fluid with disturbance velocity that of light ($c$). It is affirmed to be a glaring defect of earlier relativistic theories that the disturbance velocity in matter has been taken as arbitrary, although that of gravitation and of the electromagnetic field have been equal to $c$. The differential equations of the theory are then set up. An additional cosmological term in the gravitational potentials ${h}_{\mathrm{ij}}$ is suggested, namely, ${h}_{\mathrm{ij}}^{*}=(\frac{K}{8})({t}^{2}\ensuremath{-}{x}^{2}\ensuremath{-}{y}^{2}\ensuremath{-}{z}^{2}){g}_{\mathrm{ij}},$ where $x$, $y$, $z$, $t$ are Lorentz coordinates and $K$ is the (small) cosmological constant. The explicit formula for the rate of advance of periastron $P$ of two bodies (mass points) of masses $m$ and ${m}_{2}$ is given, as obtained from the solution of the two-body problem in the theory, and its possible application to double stars is referred to. The authors propose to give a detailed development of the theory and its applications in papers to be published shortly elsewhere.

Substance and Function and Einstein's Theory of Relativity

THE translators of Prof. Ernst Cassirer's most important contributions to mathematico-Jogical theory have done well to issue his “Substanz-begriff und Fonktionsbegriff” and his “Zur Einstein-schen Relativitatstheorie” together in one volume, although a considerable time interval separates the two works. The first appeared in 1910, the second in 1921, and the interval covers the formulation by Einstein of the new theory of gravitation. By pre-senting the two together, the philosophical significance of the principle of relativity and the intimate connexion of its mathematico-physical form with the logico-epistemological form of the philosophical problem are clearly brought out. The translation has succeeded in reproducing the clear scientific expression of the German and reads like an original English work. For an American publication there are singularly few Americanisms in the text. It is very unfortunate, however, that the word “Begriff” is not retained in the English title. The book is not about substance and function but about the concept; substance and function are meant to be adjectival, not substantival terms. Substance and Function and Einstein's Theory of Relativity. By Ernst Cassirer. Authorised translation by Dr. William Curtis Swabey and Dr. Marie Collins Swabey. Pp. xii + 465. (Chicago and London: The Open Court Publishing Co., 1923.) 3.75 dollars.