W. H. McCrea

Relativity Theory and the Creation of Matter

It is shown that the continuous creation of matter can be treated by the standard methods of general relativity provided that the possibility of a ‘zero-point’ stress is allowed. The matter ‘created’ is the mass-equivalent of the work done by this stress in the expansion of the universe. According to relativity theory this stress also makes a contribution to the density of gravitational mass. When these two effects are taken into account it is shown that the Newtonian analogues of relativistic models of the universe discovered by Milne and the writer can be extended to cover all relativistic models. This result makes it possible to obtain a unified physical interpretation of Hoyle’s treatment of the cosmological problem. It is suggested that the interpretation in terms of a zero-point stress may lead to a connexion with the quantum theory of fields.

Segregation of Materials in Cosmogony

Were the raw material for forming planets to have the chemical composition usually assumed, considerable segregation of light and heavy elements must have occurred to an extent that varied from one planet to another. The problem of such segregation is examined in the case of a body of the raw material acted upon by its own gravitation. If the material is entirely gaseous, segregation could not occur in any acceptable time. This shows that some other phase must have played a part, and so confirms the view that the planets were formed ‘cold Dust-grains provide the phase most likely to be required, but grains of normal interstellar dust would settle too slowly; there must have been some adhesion of such grains to form at any rate a relatively small number of somewhat larger grains. After some discussion of the resistance offered by a gas to a grain moving through it, formulae are given for characteristic times associated with various cases of such motion. These are applied to a proto-planet of the sort contemplated in one particular theory of the origin of the solar system (McCrea i 960). If some adhesion of grains results from encounters between them produced by thermal agitation, then more considerable adhesion or accretion will occur when an enlarged grain falls towards the centre of such a proto-planet. It is shown that this accounts for: (a) the existence of planetesimals having diameter of order 1 m near the centre of the proto-planet, (6) the aggregation of such planetesimals into a body of planetary mass, (c) the release of energy that could account for the dispersal of the light materials. These processes could occur in an acceptably short time interval. The formulae are also applied, more briefly, to a body of material similar to a ‘primary object’ of the sort considered by Urey (1964). They indicate that there should be even less difficulty in accounting for segregation of heavy material in this case. However, if segregation could occur as suggested in the first application, it may be difficult to see how material could reach the greater density in the second case without some segregation having already taken place. If this work is correct, a solid body like the Earth can come into being only because of the prior existence of the smallest known naturally occurring bodies in the cosmos, the interstellar grains; an Earth exists because a galaxy is slightly dusty.

Hertzian electromagnetic potentials

The general properties of the Hertzian electromagnetic potentials and their gauge transformations, recently given by Nisbet, are re-derived in tensor form appropriate to the space-time of special relativity. There appears to be a considerable gain in conciseness and comprehensibility of the general results, although it is recognized that Nisbet’s forms may be those suited to particular applications. Whittaker’s scalar potentials are briefly considered. The theory refers exclusively to flat space-time because the results require covariant differentiation to be commutative, but it is formulated in terms of any curvilinear co-ordinates in such space-time.

Vector-tetrads and the creation of matter

The possibility is examined of using a tetrad vector field to provide field relations that admit the creation of matter. Except for additive terms in certain auxiliary tensors depending on only first derivatives of the field, it is shown that a tetrad field determines two and only two linearly independent tensors corresponding in complexity to the single Ricci tensor of Riemannian geometry. It is suggested that combinations of these tensors might serve as the Einstein tensor and the ‘creation tensor’ in F. Hoyle’s proposed modification of Einstein’s field relations. Certain tetrad fields discovered by H. P. Robertson and A. G. Walker are shown to conform to the cosmological principle in a required sense. Using these in field relations of the suggested form, equations for cosmological models are obtained. One such model closely resembles that derived by Hoyle. So far as they go, the indications obtained in the paper are that tetrad fields may be appropriate for the further mathematical study of the possibility of continuous creation.

The origin of the solar system

The problem of accounting for a solar system in which about 0.1% of the mass has about 99% of the angnlar momentum and in which a mass of hydrogen greater than the remaining planet mass apparently left the planets is examined. Previous theories for the origin of the solar system are reviewed; recent relevant developments in astronomy are described; and current theories based on formation from a solar nebula, from condensation of planets, from planetesimals, and from turbulent matter are briefly presented. Origin of satellites is also mentioned. (D.C.W.)

Review Lecture. Long Time-Scale Fluctuations in the Evolution of the Earth

This lecture is an attempt to review current knowledge about certain terrestrial phenomena with the twofold purpose: (a) to discover the extent to which the behaviour of the Earth may be influenced by fluctuations in its astronomical environment, (b) to see if new knowledge of that environment may be gained from its influence on the Earth. Fluctuations in geomagnetism, climate, glaciation, biological extinctions, etc., are surveyed with special regard to datings and characteristic time-intervals; correlations between such fluctuations are discussed. Astronomical phenomena, within the Solar System and elsewhere in the Galaxy, that might cause terrestrial effects are reviewed. As regards astronomical effects on Earth: (i) There is a good case - not yet overwhelming - for the currently widely accepted view that fluctuations of glaciation within an ice-epoch result from changes of insolation accompanying fluctuations of the Earth’s motion relative to the Sun. Some evidence suggests that an ice-epoch may be triggered by variations of the astronomical environment encountered in the Sun’s motion relative to the Galaxy; but tectonic changes on Earth may be the main trigger. (ii) Impacts of planetesimals may be more important than hitherto recognized. Among astronomical results regarding the Sun, while the intensity of solar ‘activity’ is variable, terrestrial effects provide no confirmation that the Sun is a ‘variable star’. Regarding the Galaxy, impacting planetesimals may originate in interstellar clouds, and so provide on Earth samples of interstellar matter. Some unsolved problems emphasized by the review are listed; certain concepts that would call for consideration in any extended review are mentioned.

Some thoughts on Sun—weather relations

Recent measurements of variations in the total solar irradiance now offer a quantitative mechanism through which year-to-year changes in solar activity may influence surface temperature. It follows that at least a part of the global warming of the last century could be ascribed to changes in solar output, and that effects of solar radiative forcing may need to be taken into account in predictions of greenhouse warming. A number of questions still remain, however, before this thesis rests on a firm foundation.

A Class of Transformations in Special Relativity

Born & Biem have formulated a transformation from the co-ordinates used by an observer A at rest in an inertial frame, to the co-ordinates used by an observer B who has any given rectilinear motion relative to A, and who assigns co-ordinates as nearly as he can in the same way as A. The existence and properties of this transformation are discussed. Particular attention is devoted to an example proposed by Born & Biem in which Bs world-line in As co-ordinate system is part of a hyperbola meeting A’s world-line in two events. The transformation in the example is here expressed in terms of elliptic integrals. Curves are drawn for a numerical case to show how A and B each plots the motion of the other and to show the Doppler effect observed by each when the other transmits radiation of given frequency. The example usually quoted in connexion with the clock paradox is discussed as a limiting case of the preceding one and it is shown that certain features are thereby clarified. The well-known case of uniformly accelerated motion in special relativity is also a particular case of Born & Biem’s example; its properties are discussed and illustrated by diagrams. Finally, a short discussion of the clock paradox, arising out of Born & Biems treatment, is given.

Star Formation with Special Reference to Stellar Cluster

The paper deals with the processes of star formation under existing conditions in the galaxy. The raw material is that of interstellar clouds and attention is called to the inference that this material is probably mainly in the form of molecular hydrogen throughout most of the processes considered. It is found that a cloud having a mass of about 1000 solar masses may well be brought to the point of gravitational collapse by the pressure exerted by ‘hot’ interstellar material, but there is no known agency that is capable of causing a much smaller mass of the raw material to collapse. It is inferred that the material destined to form an entire galactic stellar cluster undergoes gravitational contraction as a whole. This leads to particular instances of the well-known problems in cosmogony of fragmentation and of the disposal of angular momentum . It is suggested that these problems, and others, find a natural solution if the raw material at a suitable stage may be regarded as broken up into ‘floccules’ in a state of chaotic supersonic motion. Then a condensation is formed simply from floccules that happen to be moving towards it. Thus conditions suitable for the production of any star exist only as conditions for the production of a number of stars, this being probably the fundamental reason for the cluster-origin of stars. These ideas have been found to offer what appears to be a promising theory of the origin of the solar system. Finally, reasons are briefly stated for the possible validity of the adopted representation of the state of motion of the medium by the concept of floccules.

Atomic and gravitational metrics in cosmology

Using inferences from his Large Numbers hypothesis (L. N. h.) Dirac (1979) derived a cosmological model, described by an ‘atomic’ metric, that is not in agreement with the Einstein theory of gravitation. He then showed that the same model described by a different metric appears to be the Einstein–de Sitter (E. S.) universe, and thus to agree with the Einstein theory. According to the first description, relative to electromagnetic forces, gravitation becomes weaker with advancing epoch. So long as the L. N. h. is retained, we point out how this physical feature persists no matter what metric is used. Therefore Dirac’s E. S. model is observably different from that of standard relativistic cosmology. We make this explicit by writing into the calculations a ‘Coulomb’ constant to match the gravitation constant. We show how the way we do so is internally self-consistent. In the course of the work it emerges that one of the two main inferences from the L. N. h. is automatically ensured by the E. S. model, which may call for some re-examination of the status of the hypothesis. We discuss the different cosmological redshifts predicted by Dirac’s E. S. model and by the standard model.