Hi:

Some time ago, I pointed out to a contributor at the forum that "proper" and "remote" time can get tricky in a universe with a dual geometry Ala Schwarzschild.

Essentially, (and this is why Schwarzschild HAS to be right), a GR/Quantum Mechanical universe only makes sense as it exists on 4D event horizon surfaces, and is observed from a remote frame (another 3 space) in time dilation (and space creation), which results from proximity to the universal mass.

That is only the beginning of the story! How under Gods heaven could Schwarzfield's famous two/ sphere geometry...and the first working solutions to Einsteins General Theory of Relativity manage to dovetail with quantum cosmology...and string theory?

Following is a brief excerpt from a paper by Lee Smolin, in which he discusses the work of Louis Crane. Read the excerpt first (and mull over the implications of EVERY word), and then read the section under the heading "Conceptual Advances"- carefully.

Those who wish to read more detail are invited to review HF# 38022 under special topics.

Now for Lees excerpt:

Another topic of much current interest in cosmology is the role of a cosmological constant - an energy density that can be attributed to empty space (see "Quintessence" by R R Caldwell and P J Steinhardt Physics World 2000 November pp31-37)...so one can now ask whether loop quantum gravity has anything to say about quantum cosmology in the presence of a cosmological constant.

Another important question is whether the new exact approach to quantum cosmology can predict the spectrum of fluctuations observed in the cosmic microwave radiation.

Results on both of these questions have been reported in a recent paper by Soo. He makes use of an old observation by Hideo Kodama that when the cosmological constant is non-zero, one can find an exact quantum state that solves the equations of quantum gravity.

This Kodama state has a semiclassical interpretation that predicts a spectrum of quantum fluctuations in space-time. It also has a precise Planck-scale description, which makes use of very elegant mathematics connected to the invariants of graphs and knots.

Soo also finds that this state can be used to predict fluctuations of the gravitational field, which may be observed in the microwave background and the distribution of galaxies.

CONCEPTUAL ADVANCES,

Progress on the conceptual side has been no less dramatic. It is based on a new approach to the problem of how to produce a quantum theory for a closed system, such as the universe, in which the observer must be considered part of the system.

The key idea, proposed about 10 years ago by the mathematician Louis Crane, is that the quantum state of the universe should be replaced by a whole array of states.

There should be one state for each way of dividing the universe into two regions, one containing the observer and the other containing what the observer sees. (Cf HF#38022)

This idea has given rise to what are called "relational" approaches to quantum cosmology. The conceptual structure of these approaches was further developed by Carlo Rovelli and others, while their mathematical structure has been clarified by Christopher Isham, Jeremy Butterfield, Fontini Markopoulou and collaborators.

They have given relational quantum cosmology an elegant formalism in terms of a mathematical structure called topos theory. Butterfield and Isham have also shown how an approach to quantum cosmology called "consistent histories" - originally applied to quantum cosmology by Murray Gell-Man and Hartle plus others - may be consistently reformulated as such a relational quantum theory.

Further progress was made by Markopoulou, who showed that the different regions associated with the different states can be specified in terms of the causal structure of a space-time.

Basically the outcome is that the array of different states proposed by Crane are connected by the flow of quantum information through the quantum universe.

These ideas may seem abstract, but they have been applied to several important questions. For example, Neil Turok has applied the basic idea that a quantum state is associated with an observer's past to make progress on the no-boundary proposal for quantum theory. Meanwhile, Tom Banks and Willie Fischler have argued that the same idea may be used to study string theory and M-theory in expanding universes.

There remain many open questions, but it is already clear that, on both the conceptual and technical side, quantum cosmology is waking up from a long period in which it consisted mainly of models that were proposed many years ago.

Modern techniques from quantum gravity, field theory and mathematics are already leading to new predictions concerning the very early universe, and are greatly clarifying what theorists are doing when they apply quantum theory to the universe as a whole.

Author

Lee Smolin is in the Perimeter Institute for Theoretical Physics, Waterloo, Canada