Tuesday, November 13, 2007

Dreyer's Internal Relativity

In recent years, a new school of quantum gravity research has come into view. The research programs in this group attempt to demonstrate that neither the matter fields nor the space-time geometry described by our present theories are fundamental, but instead both co-emerge from a pre-geometric quantum mechanical foundation. (Links to my prior posts on this research are at the end of this post). Olaf Dreyer is a theoretician working in this mode. He recently presented this paper, “Why Things Fall”, which nicely summarized his work to-date (hat tip: this thread maintained by marcus at Physics Forums).

What helps make the paper accessible is that Dreyer’s approach has been to work at a very stylized conceptual level. He wants to show how the path to a full theory should go, with the goal of filling in crucial details later. It is clear that this kind of theory has a long way to go, in particular to show that Einstein’s equations will specifically emerge.

In the introduction, Dreyer describes the approach where gravity is not assumed at the outset but is emergent. He breaks this down further by discussing the constraint that there is to be is no clean distinction between the emergent gravity and matter degrees of freedom (as opposed to an approach like early string theory where the graviton emerged as part of the particle family). Rather, it is only through the matter degrees of freedom that we infer the geometry. He says: “…we are taking seriously the fact that we only know geometry through matter…geometry alone is not accessible to us. (p.2)” This description of the emergence of geometry is in contrast to an approach like loop quantum gravity, where the space-time geometry of general relativity is taken as given and then quantized. What makes the theory a quantum theory of gravity is that the matter degrees of freedom and inferred geometry will emerge from a foundation which is quantum mechanical. One consequence of adopting a QM system as fundamental is that background time is assumed at this foundational level, although it will have no relationship to emergent space-time. I have no problem with this: something has to be fundamental and I think time and asymmetric causality are good candidates for this role.

The term “internal relativity” is meant to stress a key point: we ask what geometry obtains from observed degrees of freedom from a point of view within the system. Dreyer believes that if we do this, relativity naturally will emerge.

As a prepatory example, Dreyer shows (in section 3) how something like this happens in a classical theory. Specifically, if we start with an electro-magnetic field (on a Newtonian background of absolute space and time), we can see how special relativity emerges from considering how the dynamics of charged particles gives rise to contraction/dilation effects from a point of view inside the system.

Section 4 presents the main model of the paper. Dreyer begins with a simple quantum mechanical system in a ground state (level 0). Then he allows for excitations (traveling spin waves in the model). This is level 1, and the excitations are meant to be analogues of elementary particles of our world. Level 2 is given by bound states of these excitations. These bound states are meant to be analogues of the solid objects of our world. They do not leave the parameter on ground state of level 0 unchanged. Dreyer analyzes the effect of the objects on the distribution of the level 0 parameter and is able to derive Newton’s law of gravitation between the objects in a low velocity approximation. He then says the presence of Newtonian gravity means that the geometry seen by internal observers will be not flat but curved (a curved Lorentzian manifold). So while Newtonian gravity was derived, the overall framework implies something which goes beyond Newtonian gravity. He notes that the model falls short of showing that the gravitational mass implied for the bound objects is actually the same as the inertial mass.

Section 5 concludes with some discussion. Dreyer reiterates the concepts involved in having matter degrees of freedom and gravitation emerge from a fundamental level that has distinct degrees of freedom. He discusses how certain problems don’t arise in this conceptual framework, such as the “problem of time” which arises when one quantizes space-time, and the problem of incorrect predictions for the value of the cosmological constant. He also discusses some very preliminary ideas for observable consequences which may follow from this kind of theory.

Emergent Quantum Gravity Research Series (in chronological order):

What’s New in Quantum Gravity
A section of Lee Smolin’s recent book discusses new approaches.

Causality First
Rafael Sorkin’s Causal Sets and Fotini Markopoulou’s Quantum Causal Histories.

Emerging From the Noise
More on Markopoulou’s approach.

Caution: Universe under Construction
The Causal Dynamical Triangulation program.

More papers from Markopoulou and colleagues.

In the Beginning was the Qubit
Seth Lloyd’s quantum computing-inspired take on quantum gravity.

1 comment:

Steve said...

I want to distinguish the research I'm highlighting here from some other programs which also feature an "emergence" approach to spacetime geometry and matter fields. An example is in this paper, Universal Quantum Mechanics, by Steven Giddings (hat tip: Cosmic Variance).
This type of approach differs in that instead of starting with a quantum system (usually a network of interacting quantum systems) using QM as we know it, one tries to alter or generalize qm into a more general framework to handle the existence of gravity, etc. What I object to is the fact that an approach like that of Giddings removes time and measurement from QM to accomplish this. I think there is no QM without time and measurement! So this ends up being a model without conceptual appeal to me.