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Three decades ago, talk of other universes was not seen by most physicists to be part of science. Most research in theoretical physics and cosmology concerned observable FEs in our universe and most papers and seminars referred to experimental results. However, since then there has been a gradual shift, during which it first became acceptable to work on theories that described not only our universe, but other possible universes, universes with less or more dimensions, or universes with different kinds of particles and forces. In the last few years, we have moved further away from theories of our one universe, as these other worlds went from being logically possible to hypothetically actual. It is now common to hear about the multiverse – a quantum cosmology that takes for granted that the visible universe that we see around us is just one of a vast or infinite number of universes.

We study the question of whether the linearization of the Kodama state around classical deSitter spacetime is normalizable in the inner product of the theory of linearized gravitons on deSitter spacetime. We find the answer is no in the Lorentzian theory. However, in the Euclidean theory the corresponding linearized Kodama state is delta-functional normalizable. We discuss whether this result invalidates the conjecture that the full Kodama state is a good physical state for quantum gravity with positive cosmological constant., 14 pages, statement on the corresponding Yang-Mills case corrected

The 20th century has been a period of scientific revolution, unmatched in scope by anything that has come before, save perhaps the Copernican revolution in the 16th century. Ever since Newtonian physics was overthrown at the beginning of this century we have been living through a period of transition, during which the new theory that will replace Newtonian physics as a unified framework for the description of everything in nature has been steadily coming into focus. Big pieces of this theory have been discovered, such as relativity quantum theory the Standard Model of particle physics, and the standard big-bang cosmology But it is very clear that we do not yet have the full theory, because that must be based on a single theoretical framework, and such a framework is still lacking. Thus, as humanity emerges into a new century, the completion of the new theory that will finally replace Newtonian physics remains the primary goal of theoretical physics.

Using the Ashtekar formulation, it is shown that the G_{Newton} --> 0 limit of Euclidean or complexified general relativity is not a free field theory, but is a theory that describes a linearized self-dual connection propagating on an arbitrary anti-self-dual background. This theory is quantized in the loop representation and, as in the full theory, an infinite dimnensional space of exact solutions to the constraint is found. An inner product is also proposed. The path integral is constructed from the Hamiltonian theory and the measure is explicitly computed nonperturbatively, without relying on a semiclassical expansion. This theory could provide the starting point for a new approach to perturbation theory in $G_{Newton}$ that does not rely on a background field expansion and in which full diffeomorphism invariance is satisfied at each order., Comment: 14 pages

A new type of explanatory mechanism is proposed to account for the fact that many of the dimensionless numbers which characterize particle physics and cosmology take unnatural values. It is proposed that all final singularities 'bounce' or tunnel to initial singularities of new universes at which point the dimensionless parameters of the standard models of particle physics and cosmology undergo small random changes. This speculative hypothesis, plus the conventional physics of gravitational collapse, together comprise a mechanism for natural selection, in which those choices of parameters that lead to universes that produce the most black holes during their lifetime are selected for. If our Universe is a typical member of the ensemble that results from many generations of such reproducing universes then it follows that the parameters of our present Universe are near a local maximum of the number of black holes produced per universe. Thus, modifications of the parameters of particle physics and cosmology from their present values should tend to decrease the number of black holes in the universe. Three possible examples of this mechanism are described.

Physical theories are developed to describe phenomena in particular regimes, and generally are valid only within a limited range of scales. For example, general relativity provides an effective description of the Universe at large length scales, and has been tested from the cosmic scale down to distances as small as 10 meters. In contrast, quantum theory provides an effective description of physics at small length scales. Direct tests of quantum theory have been performed at the smallest probeable scales at the Large Hadron Collider, ${\sim} 10^{-20}$ meters, up to that of hundreds of kilometers. Yet, such tests fall short of the scales required to investigate potentially significant physics that arises at the intersection of quantum and relativistic regimes. We propose to push direct tests of quantum theory to larger and larger length scales, approaching that of the radius of curvature of spacetime, where we begin to probe the interaction between gravity and quantum phenomena. In particular, we review a wide variety of potential tests of fundamental physics that are conceivable with artificial satellites in Earth orbit and elsewhere in the solar system, and attempt to sketch the magnitudes of potentially observable effects. The tests have the potential to determine the applicability of quantum theory at larger length scales, eliminate various alternative physical theories, and place bounds on phenomenological models motivated by ideas about spacetime microstructure from quantum gravity. From a more pragmatic perspective, as quantum communication technologies such as quantum key distribution advance into Space towards large distances, some of the fundamental physical effects discussed here may need to be taken into account to make such schemes viable., 34 pages, 9 figures. Journal version, modified to respond to numerous suggestions

One of the most challenging problems in modern physics is the application of quantum theory to the universe as a whole. Progress in this area has been plagued by two types of problem: conceptual and technical. The conceptual problems arise from the old difficulties of interpreting quantum theory. The standard interpretations require that the measuring instruments and observers are outside the quantum system described by the wavefunction. In the late 1950s, however, Hugh Everett proposed an interpretation of quantum theory that might apply to systems that include the observers and measuring instruments, but the adequacy of such interpretations has remained controversial to this day.

Physics is the foundation of all of our knowledge of the physical world, yet relatively few people practise it professionally. As a result, most of the students that we are asked to teach are not going to become physicists. This raises two difficult questions. First, what aspects of physics should we teach to people who are not going to become professional physicists? And second, how should we teach it? While there is not much doubt about how to train a physicist, there is a lot of uncertainty about how and what to teach non-physicists. I expect that most experienced physics teachers will agree that, with some exceptions, we do not do a very good job of this.

2+1 Einstein gravity is used as a toy model for testing a program for nonperturbative canonical quantisation of the 3+1 theory. The program can be successfully implemented in the model and leads to a surprisingly rich quantum theory.

A new lattice regularization of quantum general relativity based on Ashtekar's reformulation of Hamiltonian general relativity is presented. In this form, quantum states of the gravitational field are represented within the physical Hilbert space of a Kogut-Susskind lattice gauge theory. The gauge field of the theory is a complexified SU(2) connection which is the gravitational connection for left-handed spinor fields. The physical states of the gravitational field are those which are annihilated by additional constraints which correspond to the four constraints of general relativity. Lattice versions of these constraints are constructed. Those corresponding to the three-dimensional diffeomorphism generators move states associated with Wilson loops around on the lattice. The lattice Hamiltonian constraint has a simple form, and a correspondingly simple interpretation: it is an operator which cuts and joins Wilson loops at points of intersection.

Ashtekar's new Hamiltonian formulation of general relativity is derived starting from a complex covariant four-dimensional action principle. The action is a modification of the tetrad-Palatini action that results from splitting the connection into the self-dual and anti-self-dual pieces and keeping only the former.

A new point of view towards the problem of the relationship between gravitational and quantum phenomena is proposed which is inspired by the fact that the distinction between quantum fluctuations and real statistical fluctuations in the state of a system seems not to be maintained in a variety of phenomena in which quantum and gravitational effects are both important. One solution to this dilemma is that quantum fluctuations are in fact real statistical fluctuations, due to some unknown, but universal, phenomena. At the same time quantum fluctuations have certain special properties which distinguish them from other types of fluctuation phenomena. The two most important of these are that the action of quantum fluctuations is non-dissipative for the special case of systems undergoing inertial motion in the absence of gravitational fields, and that the dispersion constant for quantum fluctuations for a particle is inversely proportional to the inertial mass of the particle. These properties are summarised in a set of principles which, it is proposed, govern the relationship between quantum phenomena, gravitation and inertia.