The Einstein equations

This chapter deals with Einstein equations. In the absence of matter there is no gravitational field, and the spacetime which represents this empty universe is Minkowski spacetime. More precisely, if the gravitational field created by the matter can be neglected, the appropriate framework for describing the matter is that of special relativity. Einstein gravitational equations relate geometry and matter: specifically, they relate the Riemann tensor, or more precisely the Einstein tensor, to the geometrical object describing ‘inertia’, the energy content of the matter—that is, the energy–momentum tensor. These equations form a set of ten nonlinear partial differential equations. The coordinate system can be chosen arbitrarily.

Can the universe be described by a wave function?

Suppose we assume that in gently curved spacetime (a) causality is not violated to leading order (b) the Birkhoff theorem holds to leading order and (c) CPT invariance holds. Then we argue that the “mostly empty” universe we observe around us cannot be described by an exact wave function [Formula: see text]. Rather, the weakly coupled particles we see are approximate quasiparticles arising as excitations of a “fuzz”. The “fuzz” does have an exact wave function [Formula: see text], but this exact wave function does not directly describe local particles. The argument proceeds by relating the cosmological setting to the black hole information paradox, and then using the small corrections theorem to show the impossibility of an exact wave function describing the visible universe.

In Search of the Postmodern Utopia: Ben Okri’s In Arcadia

This essay explores how Ben Okri’s most recent novel, In Arcadia(2002), attempts to reconstruct the possibility of utopia in the face of a fragmentation of identity and destruction of determinate certainties affecting contemporary society in the aftermath of postmodernism. By tracing the intertextual relations existing between this work and earlier works in an intellectual/literary tradition that extends from Theocritus and Virgil through Dante, More, Milton, Sannazzaro, Sidney and others, Fox shows how Okri develops the proposition that men and women confronting an ‘empty universe where the mind spins in uncertainty and repressed terror’ can recover sanity through art. Even though, in Okri’s vision, the world may be ‘a labyrinth without an exit’, presided over by Death without any hint of transcendence, men and women, he concludes, can recover paradise through the ‘painting of the mind’ which can creative complete forms that can be fed into ‘spirit’s factory for the production of reality’. This generative activity, which is at the heart of the Arcadian vision, in Okri’s view, has the power to make life a place of ‘secular miracles’, despite the limitations imposed upon it by the realities of finitude and death. The essay concludes by suggesting that Okri’s concept of utopia is very close to Kant’s idea of Aufklärung as expounded by Michel Foucault –– that is, neither a world era, nor an event whose signs are perceived, nor the dawning of an accomplishment, but rather a process of which men and women are at once elements and agents, and which occurs to the extent that they decide to be its voluntary actors. While in some respects Okri’s vision is strikingly similar to certain of its antecedents, it is thus nevertheless distinctively postmodern in the ways in which it is inflected.

Cosmology Under Milne's Shadow

Based on the magnitude–redshift diagram for the sample of supernovae Ia analyzed by Perlmutter et al. (1999), Davis & Lineweaver (2004) ruled out the special relativistic interpretation of cosmological redshifts at a confidence level of 23σ. Here, we critically reassess this result. Special relativity is known to describe the dynamics of an empty universe, by means of the Milne kinematic model. Applying only special relativistic concepts, we derive the angular diameter distance and the luminosity distance in the Milne model. In particular, in this model we do not use the underlying metric in its Robertson–Walker form, so our exposition is useful for readers without any knowledge of general relativity. We do however, explicitly use the special relativistic Doppler formula for redshift. We apply the derived luminosity distance to the magnitude–redshift diagram for supernovae Ia of Perlmutter et al. (1999) and show that special relativity fits the data much better than that claimed by Davis & Lineweaver. Specifically, using these data alone, the Milne model is ruled out only at a 2σ level. Alhough not a viable cosmological model, in the context of current research on supernovae Ia it remains a useful reference model when comparing predictions of various cosmological models.

HIGHER DIMENSIONAL COSMOLOGICAL MODEL IN LYRA GEOMETRY: REVISITED

In this paper we have revisited the research work of Rahman and Bera22on Kaluza–Klein cosmological model within the framework of Lyra Geometry. It has been shown that the empty universe model yields a power law relation without any assumption. The role of bulk viscosity on five-dimensional cosmological model is discussed. The physical behaviour of the models is examined in all cases.

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.